Gyula Klima Ontological Alternatives vs. Alternative Semantics Selected Essays in Logic and Metaphysics, Medieval and Modern, 1990-2000

1

Logic and Metaphysics, Medieval and Modern

1. Klima, G. (1990) "Approaching Natural Language via Medieval Logic", in: J. Bernard-J. Kelemen: Zeichen, Denken, Praxis, Institut fur Sozio-Semiotische Studien: Vienna, pp. 249-267.

2. Klima, G. (in press) "Old Directions in Free Logic: Existence and Reference in Medieval Logic", in: K. Lambert (ed.) New Directions in Free Logic, Akademia Verlag, Sankt Augustin bei Bonn

3. Klima, G. (1991) "Latin as a Formal Language: Outlines of a Buridanian Semantics", Cahiers de l'Institut du Moyen-Age Grec et Latin, Copenhagen, 61, pp. 78-106.

4. Klima, G. (in press) "Contemporary "Essentialism" vs. Aristotelian Essentialism", in: Haldane, J. (ed.) Thomistic Studies, University of Notre Dame Press

5. Klima, G. (1999) “Aquinas' Theory of the Copula”, 35th Annual Cincinnati Philosophy Colloquium: The History of Logic. University of Cincinnati, March 5-7, 1999.

Ontological Alternatives vs. Alternative Semantics in Late-Medieval Philosophy

6. Klima, G. (1991) "Ontological Alternatives vs. Alternative Semantics in Medieval Philosophy", in: J. Bernard: Logical Semiotics, S - European Journal for Semiotic Studies, Vol. 3. No. 4,Vienna, pp. 587-618.

7. Klima, G. (1993) "The Changing Role of Entia rationis in Medieval Philosophy: A Comparative Study with a Reconstruction", Synthese 96(1993) No. 1., pp. 25-59.

8. Klima, G. (1999) "Ockham's Semantics and Metaphysics of the Categories", in: Spade, P. V. (ed.): The Cambridge Companion to Ockham, Cambridge University Press, pp. 118-142.

9. Klima, G. (1999) "Buridan's Logic and the Ontology of Modes", in: Ebbesen, S. (ed.): Medieval Analyses in Language and Cognition, The Royal Danish Academy of Sciences and Letters: Copenhagen, 1999, pp. 473-495.

10. Klima, G. (1993) "'Debeo tibi equum': A Reconstruction of Buridan's Treatment of the Sophisma", in: S. Read: Sophisms in Medieval Logic and Grammar: Acts of the 9th European Symposium for Medieval Logic and Semantics, Kluwer Academic Publishers, 1993. pp. 333-347; reprinted in: K. Neumer-V. Voigt: Semiotics and Philosophy of Language in Hungary, S - European Journal for Semiotic Studies , Vol. 4. No. 1-2. Vienna, pp. 141-159.

Thomistic Semantics and Metaphysics

11. Klima, G. (1996) "The Semantic Principles Underlying Saint Thomas Aquinas's Metaphysics of Being", Medieval Philosophy and Theology, 5(1996), pp. 87-141.

12. Klima, G. (2000) "Aquinas on One and Many", Documenti e Studi sulla Tradizione Filosofica Medievale (An International Journal on the Philosophical Tradition from Late

2

Antiquity to the Late Middle Ages of the Società Internazionale per lo Studio del Medioevo Latino), 11(2000), pp. 195-215.

13. Klima, G. (1997) "Man = Body + Soul: Aquinas's Arithmetic of Human Nature", in: Philosophical Studies in Religion, Metaphysics, and Ethics. Essays in Honour of Heikki Kirjavainen, edited by Timo Koistinen and Tommi Lehtonen, Helsinki: Luther-Agricola-Society, 1997, pp. 179-197.

14. Klima, G. (2000) “Thomas of Sutton on the Nature of the Intellective Soul and the Thomistic Theory of Being”, Aertsen, J. et al. (eds.), Nach der Verurteilung von 1277. Philosophie und Theologie an der Universität von Paris im letzten Viertel des 13. Jahrhunderts, Studien und Texte (Miscellanea Mediaevalia 28), Berlin-New York: Walter de Gruyter, pp. 436-455.

15. Klima, G. (1997) “Natural Necessity and Eucharistic Theology in the Late 13th Century”, workshop study for the TransCoop-Program (Stiftung Deutsch-Amerikanisches Akademisches Konzil) Medieval Institute (Notre Dame) Thomas-Institut (Köln): “After the Condemnations of 1277: The University of Paris in the Last Quarter of the Thirteenth Century (Nach den Verurteilungen von 1277: Die Universität von Paris im letzen Viertel des 13. Jahrhunderts”; presented at the University of Notre Dame, October 10, 1997.

3

Logic and Metaphysics, Medieval and Modern

4

Approaching Natural Language via Mediaeval Logic

Anomalies of a Paradigm

"Are quantification and cross reference in English well represented by the quantifiers for ‘every’ and ‘some’, the usual propositional connectives and the equals sign? It’s my impression that many philosophers and logicians think that - on the whole - they are. In fact, I suspect that the following view of the relation between logic and quantificational and referential features of natural language is fairly widely held: No one (the view begins) can think that the propositional calculus contains all there is to logic. Because of the presence in natural language of quantificational words like ‘all’ and ‘some’ and words used extensively in cross reference, like ‘it’, ‘that’ and ‘who’, there is a vast variety of forms of inference whose validity cannot be adequately treated without the introduction of variables and quantifiers, or other devices to do the same work. Thus everyone will concede that the predicate calculus is at least a part of logic. Indispensable to cross reference, lacking distinctive content, and pervading thought and discourse, identity is without question a logical concept. Adding it to the predicate calculus significantly increases the number and variety of inferences susceptible of adequate logical treatment. And now (the view continues), once identity is added to the predicate calculus, there would not appear to be all that many valid inferences whose validity has to do with cross reference quantification and generalization which cannot be treated in a satisfactory way by means of the resulting system. It may be granted that there are certain valid inferences, involving so-called "analytic" connections, which cannot be handled in predicate calculus with identity. But the validity of these inferences has nothing to do with quantification in natural language, and it may thus be doubted whether a logic that does nothing to explain their validity is thereby deficient. In any event (the view concludes), the variety of inferences that cannot be dealt with by first-order logic (with identity) is by no means as great or as interesting as the variety that can be handled by the predicate calculus, even without identity, but not by the propositional calculus."1

I think it is significant, and generally characteristic of the change of attitudes taken by logicians and philosophers of language in the last two decades towards the relationship between quantification theory and natural languages, that George Boolos, from whom this lengthy quotation derives, gives this detailed description of what may be called the paradigmatic view of this relationship only to raise several objections to it.

This change of attitudes was mainly prompted by the recognition of a steadily growing body of anomalies in the application of quantification theory to natural languages. These anomalies may be gathered, roughly, under the following headings:

Mismatch of syntax

As is well-known, natural language sentences of evidently the same syntactic structure are represented by formulae of quantification theory of entirely different structure, while the same

1 G. Boolos: "To Be Is To Be a Value of a Variable (or To Be Some Value of Some Variable)", The Journal of Philosophy, 8(1984), pp.430-431.

5

formula may have different "readings", expressible by natural language sentences of widely different syntax.

Regarding these discrepancies, of course, one might say that there is no justifiable need of a strict correspondence between the syntactic structure of natural language sentences and the formulae representing them. After all, a logical semantics, which is to be a general semantics for all kinds of human languages, should precisely disregard accidental grammatical features of particular natural language expressions, and hence also the delusive grammatical structure of natural language sentences in general. All that is required for correspondence is that the formula should state correctly the truth conditions of the sentence which it represents, since it is only these truth conditions that determine the logical relations of sentences among each other.

Along these lines, mismatch of syntax may be made to appear entirely harmless, by making a distinction between logical form on the one hand, and grammatical form on the other, placing much confidence in the capability of quantification theory to express the former, and thereby justifiably ignoring the latter.2

Unrepresentable sentences

There is, however, a further set of anomalies, which comes as a fatal blow to this interpretation of the relationship between quantification theory and natural languages. For, as it turned out, some apparently simple quantified sentences of natural languages are demonstrably unrepresentable in first order quantification theory in the sense that no first order formula is able to give their correct truth conditions.3

As is well-known, examples of such sentences are those containing the determiners ‘most’ or ‘more than half of’, and so on. But if there are no formulae giving the correct truth conditions of such sentences, then quantification theory is simply unable to supply their logical form, and so the above-mentioned rationale for drawing the distinction between logical and grammatical form breaks down with these sentences.

Variables vs. anaphoric pronouns

But there are also other types of natural language sentences that pose a serious challenge to the claim that quantification theory has all types of quantificational and cross-referential resources that natural languages may possibly have. Recent discussions of the troubles caused by the so-called "donkey-sentences" supply ample evidence against the claim that variables of quantification theory can do everything that natural language pronouns can do.4

2 Indeed, this distinction renders mismatch of syntax the rationale of an interesting research program for linguists: if quantification theory expresses logical form, i.e., deep structure of natural language sentences, then the task of linguistic research may appear to be to reveal the intricate connections between surface and deep structures in particular languages. Cf. e.g. G. Englebretsen: "Logical Form and Natural Syntax", Indian Philosophical Quarterly, 11(1984), pp.229-254. What is more, logical form may provide means to distinguish between several senses of crucial concepts hidden by grammatical form, such as the several senses of ‘to be’. For discussions of Frege’s "ambiguity thesis" in a historical context cf. J. Hintikka-S. Knuuttila: The Logic of Being, Helsinki, 1986. 3 For proof see J. Barwise & R. Cooper: "Generalized Quantifiers and Natural Language", Linguistics and Philosophy, 4(1981), pp.159-219. 4 See e.g. G. Evans: "Pronouns, Quantifiers and Relative Clauses" and "Appendix", Canadian Journal of Philosophy

6

Intensional and intentional contexts

To be sure, the above-mentioned "anomalies" may be considered as such only because they pose problems to quantification theory that everyone feels it should handle but cannot. It was clear from the beginning that there are large portions of natural language reasonings that simply fall outside the authority of quantification theory, namely those involving intensional contexts. Nevertheless, Frege’s relegation of modal notions to the sphere of psychology notwithstanding, logicians have been working on expanding formal logic even to these contexts. Possible worlds semantics produced interesting results concerning modal notions and still seems to have some resources concerning tensed modal contexts. However, in virtue of the coarse-grained character of intensions available in possible worlds semantics, several intentional contexts, namely those created by attitude verbs, seem to defy analysis in terms of these intensions.5

Conflicts with traditional logic

The growing recognition of these and similar difficulties in the application of quantification theory to natural languages gave occasion to some historically-minded logicians to make comparisons between quantification theory and traditional logic showing traditional logic in a much more favorable light than before. The well-known differences between traditional and quantificational analyses of categorical propositions resulting in the invalidation of the Square of Opposition and several syllogistic forms by quantification theory were no longer regarded by these logicians as revelations of mistakes of an antiquated theory in the light of a better, new theory, but rather as adding to the growing evidence against the capability of quantification theory to represent natural language reasonings.6

The Splitting up of the Paradigm

Of course, all the above-mentioned troubles occasioned several new developments providing more or less conservative extensions of, or more or less radical departures from the usual construction of quantification theory.

Richard Montague’s grammar and intensional logic may be regarded as answers to the challenge posed by mismatch of syntax and intensional contexts.7 Generalized quantification theory, taking a cue from Montague, is intended to cope with the troubles caused by ‘pleonotetic’ determiners and common noun phrases of natural languages in general.8 Donkey sentences provided the main motivation for discourse representation semantics.9 Also several efforts have been made to

7(1977) pp.467-536. and pp.777-796., B. Richards: "On Interpreting Pronouns", Linguistics and Philosophy, 7(1984), pp.287-324. 5 Cf. D. Lewis: "General Semantics", in: B. Partee: Montague Grammar, New York-San Francisco-London, 1976. 6 Cf. D.P. Henry: Mediaeval Logic and Metaphysics, London, 1972; D.P. Henry: That Most Subtle Question - (Quaestio Subtilissima): The Metaphysical Bearing of Medieval and Contemporary Linguistic Disciplines, Manchester, 1984; F. Sommers: The Logic of Natural Languages, Oxford, 1982; G. Englebretsen: "The Square of Opposition", Notre Dame Journal of Formal Logic, 17(1976), pp.531-541. 7 R. Montague: "The Proper Treatment of Quantification in Ordinary English", in: J. Hintikka-J. Moravcsik-P. Suppes: Approaches to Natural Language, Dordrecht, 1973. 8 Cf. J. van Benthem-A. ter Meulen: Generalized Quantifiers in Natural Language, Foris Publications, 1985. 9 See H. Kamp: "A Theory of Truth and Semantic Representation", in: J. Groenendijk et. al. eds.: Formal Methods

7

construct systems in keeping with some basic principles of traditional logic that would match in power the resources of quantification theory.10 Game theoretical semantics tries to take an entirely fresh look at questions of natural language semantics in general.11 Situation semantics, beyond trying to provide answers to all semantic troubles of classical quantification theory and intensional logic, intends to account also for pragmatic aspects of communication within the framework of a general theory of meaning and information.12 There are even attempts at breaking with extensionalism and set theory in logic in general, by constructing intensional logics with an avowedly Platonistic ontology claimed to be the most fitting model for handling intensional and intentional contexts of natural languages.13

So what we experience nowadays in formal semantics may be described in Kuhnian terms as the splitting up of an old paradigm in consequence of the accumulation of its unsolved puzzles and a search for new unifying perspectives.

Historically, in such and similar situations scholars tend to seek for exemplars from earlier paradigms: as is well-known, the Copernican revolution was almost as much prompted by Copernicus’s sympathies with pre-Aristotelian, Platonic and Pythagorean cosmological ideas as by his calculations.

To be sure, such historical examples alone in our case would by no means justify more than mere historical interest in traditional logic.14 After all, even if quantification theory has its own problems in its application to natural language semantics, it has sufficiently proved its superiority over traditional logic in its capacity to handle inferences involving relational expressions and multiply quantified sentences like the following:

1. A man sees every horse

2. A horse of the king is a horse

———————————————

3. Thus, a man sees a horse of the king

Now I think that the mediaeval flavor of the example, familiar to many at least from Umberto Eco’s best-seller, The Name of the Rose, already intimates my intention to raise certain doubts concerning the usually unquestioned superiority of quantification theory in these matters.

in the Study of Language, Amsterdam, 1981. 10 As two main attempts in this direction, Lesniewski’s Ontology and Fred Sommers’ term logic should be mentioned here. 11 See e.g. J. Hintikka: Logic, Language-Games and Information, Oxford, 1973. 12 J.Barwise-J.Perry: Situations and Attitudes, The MIT Press, 1983. 13 G. Bealer: Quality and Concept, Oxford, 1982. 14 On the other hand, I think quite good general motivation could be taken from the "natural logic" character of mediaeval logic, in the sense of G. Lakoff: "Linguistics and Natural Logic", in: D. Davidson-G. Harmann: Semantics of Natural Language, Dordrecht, 1972. For an excellent discussion of mediaeval logic from this point of view see: A. de Libera: "La Logique du Moyen Age comme Logique Naturelle (Sprachlogik)", in: B. Mojsisch: Sprachphilosophie in Antike und Mittelalter, Amsterdam, 1986. Nevertheless, I do not wish to pursue this line here. Instead, I am going simply to try to show this character of the mediaeval approach.

8

As a matter of fact, the example derives from Jean Buridan’s Tract on Suppositions,15 where the famous 14th-century master is not at all at a loss to account for the validity of this inference in terms of the mediaeval theory of reference, the theory of supposition. Indeed, supposition theory is only one, although unquestionably the most important one, of those highly sophisticated, peculiarly mediaeval semantic theories that place mediaeval logic high above the relatively shallow standards of the so-called traditional logic of the last century, recently eliciting an ever growing appreciation of the achievements of mediaeval logicians among contemporary scholars.16 The increasing contemporary interest in supposition theory is amply testified by the proliferation of both historical and systematic studies on this theory, as well as of its reconstructions in terms of, or comparisons with modern logic.17 As far as I know, however, thus far nobody has tried to use supposition theory as what in my view it was really meant to be: namely (at least a starting point of) a unified theory of reference in natural languages.18 Now my intention is to do precisely this in the rest of this paper.

Common Personal Supposition and Suppositional Descents

Supposition theory, as it appears in mediaeval logic textbooks from the 12th century up to the 17th, usually begins with a series of definitions and divisions exhibiting sometimes considerable variations from author to author, or even explicit disagreements among the authors. So, properly speaking, there are several theories of supposition held together by a common phraseology, a common stock of background assumptions rooting mainly in Aristotelian metaphysics, psychology and epistemology, and a common intention to give a unified account of the referring function of terms in widely different contexts. For our present purposes, however, these various teachings possess a sufficient unity, so that I shall treat supposition theory rather indistinctly, even at the risk of some slight historical incorrectness to be noted when necessary. I base my treatment mainly on the accounts given by William Ockham and Jean Buridan, the two most influential authors in late mediaeval logic. Nevertheless, most of what I will say applies quite well to mediaeval authors of logic texts in general.

Supposition was commonly characterized by our authors as a property of terms in propositions, namely the taking of a term for something in a proposition, that is, as we would put it, its referring function. Generally three main types of supposition were distinguished: 1. material, when the term in a proposition stands for itself (or for some other token-term of the same type),

15 Buridanus: Tractatus de Suppositionibus (ed. Maria Elena Reina), Rivista Critica di Storia della Filosofia, 1957, pp.177-208. and pp.323-352; see pp.191-195. 16 Characteristic of this attitude is the following short evaluation of Buridan’s philosophy from Peter King’s Introduction to his translation of two logical tracts by Buridan: "Buridan’s mediaeval voice speaks directly to modern concerns: the attempt to create a genuinely nominalistic semantics; paradoxes of self-reference; the nature of inferential connections; canonical language; meaning and reference; the theory of valid argument. It is to be hoped that Buridan can reclaim his lost reputation among contemporary philosophers for his penetrating and incisive views on these and other matters." P. King: Jean Buridan’s Logic, D. Reidel Publishing Company, 1985. p.4. 17 For good bibliographies on the topic see N. Kretzmann-J. Pinborg-A. Kenny: The Cambridge History of Later Mediaeval Philosophy, Cambridge, 1982; E.J. Ashworth: The Tradition of Mediaeval Logic and Speculative Grammar, Toronto, 1978. 18 This characterization of supposition theory, which among several other attempted characterizations I find the most fitting one, comes from J. Ashworth. Cf. her "Promitto tibi equum", Vivarium, 16(1976), pp.62-78. For a similar account with good theoretical and textual support see also G. Priest-S. Read: "Merely Confused Supposition: A Theoretical Advance or a Mere Confusion?", Franciscan Studies, 40(1980), pp.265-297.

9

like the term ‘man’ in the proposition ‘man is a noun’, 2. simple, when the term stands for a universal, whatever a universal is, like ‘man’ in ‘man is a species’ and 3. personal, when the term is taken for those things upon which it is imposed, and of which, consequently, it is truly predicated.

Personal supposition was commonly divided further into discrete and common supposition. Discrete supposition is the referring function of singular terms, which, by reason of their meaning can be truly predicated only of one thing. Examples of this type are proper nouns, say ‘Socrates’, or common terms combined with demonstrative pronouns such as ‘this man’ or ‘this horse’, pointing at a particular man or a particular horse. Common personal supposition is the referring function of common terms in propositions, which, by reason of their meaning, can be truly predicated of many particular things, such as ‘man’ or ‘horse’.19

Now common personal supposition was divided further according to the different manners in which common terms may refer in different propositional contexts. These different manners, and correspondingly the different subdivisions of common personal supposition, were characterized by late mediaeval logicians by so-called suppositional descents, descensus ad inferiora; that is to say, by certain types of inferences in which the common term, of which the mode of supposition is being characterized, is replaced by singular terms falling under it, appearing in either nominal or propositional conjunctions or disjunctions. These several types of conjunctions and disjunctions of singular terms, or of propositions formed with these singular terms, served then both to characterize the mode of supposition of the original common term under which the descent was made and to give the truth conditions of quantified sentences in terms of the truth or falsity of several singular ones. The main divisions of common personal supposition may be given as follows:

1. Determinate supposition

(a) Some man is an animal, therefore this man is an animal or that man is an animal or ..., and so on for every man, and also the converse ascent holds.

(b) Some man is an animal, therefore some man is this animal or some man is that animal or ... and so on for every animal, and also conversely.

2. Confused and distributive supposition

(a) Every man is an animal, therefore this man is an animal and that man is an animal and ... and so on for every man, and also conversely.

(b) Some man is not an animal, therefore some man is not this animal and some man is not that animal ... and so on for every animal, but not conversely.20

19 The addition ‘by reason of their meaning’ in the characterization of singular vs. common terms is needed for the reason that it may well be the case that a proper noun is predicated of many, but only when used equivocally, being imposed upon different persons. It may also be the case that a common term can be predicated only of one thing because there can be only one thing of its kind. Nevertheless, this occurs not due to the meaning of the term, but because of the nature of the thing, as in the case of the term ‘God’. So this determination is added for the exclusion of such apparent exceptions. Cf. Albert of Saxony: Perutilis Logica, Hildesheim-New York, 1974. c.X.4d. 20 Concerning the development of the role of the converse ascents in supposition theory and, in general, the

10

3. Merely confused supposition

Every man is an animal, therefore every man is this animal or that animal or ... and so on for every animal, and also conversely, but not

... therefore every man is this animal or every man is that animal or ... and so on for every animal. Some later schoolmen also added a fourth mode of supposition:21

4. Suppositio copulatim

Some man is not an animal, therefore some man is not this animal and that animal and ... and so on for every animal,

and also conversely,

Some man is not this animal and that animal and ... and so on for every animal, therefore some man is not an animal.

That is to say, a term has determinate supposition in a proposition if one can descend under it to the singulars with a disjunctive proposition and conversely. A term has confused and distributive supposition, if one can descend under it by a conjunction of singular propositions, and conversely (with the exception of the controversial case of 2(b), of which, however, see n.26. below). A term has merely confused supposition, if one can descend under it with a proposition with a disjunctive term (and conversely) but one cannot do the same by a disjunctive proposition. Finally, a term has copulative supposition if one can descend under it by a proposition with a conjunct term and also, conversely, one can ascend from this proposition to the original one, but the same cannot be done with a conjunctive proposition.22

problems involved in the requirement to descend to an equivalent proposition see the excellent discussion in G. Priest-S. Read: "Merely Confused Supposition: A Theoretical Advance or a Mere Confusion?", Franciscan Studies, 40(1980), pp.265-297. For a good summary of the arguments against presenting supposition theory as a sort of quantification theory, giving the truth conditions of quantified sentences in terms of descents, precisely on account of the failure of ascents see M. McCord Adams: William Ockham, Notre Dame, 1987, pp.367-377. Adams’ alternative proposal is that "the divisions of common personal supposition are not the means to the end of giving a contextual definition of quantifiers nor for stating the truth conditions for propositions containing quantified general terms; rather the divisions of supposition generally were marshalled into service for the task of identifying fallacies". op. cit. p.382. To be sure, the development of supposition theory from its very origins was motivated by the need to detect fallacies, as it was convincingly shown by L.M. de Rijk: Logica Modernorum, I-II. Assen, 1967. Nevertheless, it may be argued that the need for fallacy detection developed also a relatively independent interest in the referring function of terms in general, which, during the development of supposition theory, evolved, among other things, the explicit requirement of analyzing quantified sentences in terms of equivalent descended forms, as we can clearly see this in such later authors as e.g. Paul of Venice. (Cf. his Logica Magna, tr.2, ed. A.R. Perreiah, St. Bonaventure, 1971.) However, without going into the debate concerning its real historical role and purpose, let me propose as a "conciliatory characterization" of supposition theory the following: supposition theory is (aimed to be) a unified theory of reference with the original intent of fallacy detection, in its most mature form having the capability of giving (as I shall argue) a complete set of truth conditions for quantified sentences in terms of equivalent descended propositions. It is this inherent capability that I wish to develop in this paper. 21 See G. Priest-S. Read, op. cit., esp. pp.289-295. 22 To be sure, this characterization of this mode as such cannot be found in the authors. (Cf. however Paul of Venice op. cit. pp. 90-92.) Nevertheless, considerations of completeness to be discussed below seem to require it. Cf. n.30.

11

I think there are two things that should strike the modern logician in these descents: the first is their suggesting the idea of restricted quantification, and the second is the problem whether in some sense they provide a complete set of truth-conditions for categorical sentences. Let me elaborate on these points.

Common Terms as Restricted Variables

I think the idea of replacing a common term by a series of demonstratives in these descents should remind a modern logician of the way variables of quantification theory pick up their values from the domain of a model. Indeed, we might even say that the several assignments of values of a variable may be conceived as several acts of pointing at several individuals, thereby associating a variable with these individuals. In this way, we may explain the function of a variable in different assignments as that of a demonstrative pronoun in different acts of pointing at a thing. So, for example, the formula representing the sentence: ‘Every man is an animal’, namely the one which reads ‘For every x, if x is a man then x is an animal’ ((x)(Mx→Ax)) may be explained as saying: this thing, if it is a man, then it is an animal and that thing, if it is a man, then it is an animal ... and so on, pointing at each and every thing in the world. And this explanation of the quantificational formula, in comparison with the suppositional descents presented above, shows us immediately the basic difference between the mediaeval and the modern approach: while the variables of quantification theory range over all the objects of the universe, the common terms of mediaeval logic range only over objects falling within their extension: that is, they function as restricted variables.

Now since common terms as restricted variables pick up their values from their extension, the question naturally arises: what is their value when their extension is empty? Well, the answer is quite simple: nothing. For a value, that is, a suppositum of a term in a proposition, according to the mediaevals, is a thing of which, when pointed at, the term is truly predicable by means of the copula of the proposition.23 For example, the term ‘centaur’ in the proposition: ‘Every centaur is running’ refers to nothing, for whatever is pointed at we cannot truly say: ‘This is a centaur’. But then even the singular terms: ‘This centaur’ or ‘That centaur’ refer to nothing, and thus, all the singular propositions formed with them, like ‘This centaur is running’ and ‘That centaur is running’ are false, in the same way as Russell’s ‘The present King of France is bald’ is false. But in this way even the universal proposition: ‘Every centaur is running’ must be false, since all the singulars to which we can descend from it and from which we can ascend to it are false. So we can easily understand why the mediaevals attributed existential import to universal affirmatives, and why they held the relations among categorical propositions to be those determined by the Square of Opposition.

Now as I have shown in some of my earlier papers, we can give formal expression to these informal ideas by a rather conservative extension of standard quantification theory. All we have to do is the following:

As for the implicational order of these modes, see again Priest-Read, op. cit. 23 Cf. e.g. Buridan: Sophismata, ed. T.K. Scott, Stuttgard-Bad Cannstatt, 1977, p.50.; Marsilius de Inghen: Treatises on the Properties of Terms, Dordrecht-London-Lancaster, 1983, p.52.

12

1. we have to add restricted variables to the language of the theory, that is, terms formed from open sentences by the following rule: if v is a variable and A is a formula in which v occurs free, then ‘v.A’ is a term,

2. we have to extend the definition of assignment to these terms so that they pick up individuals as their values of which their matrix is true, and nothing, that is, a zero-entity, if their matrix is true of nothing, by the following clause: f(v.A)=f(v) if f(A)=1, otherwise f(v.A)=0, where 0 falls outside the domain of the model, and

3. we have to adjust the clause determining the value of a quantified formula in an assignment as follows: f((Qv.A)(B))=1 iff for Q’u (u being an element of RGf(v.A)), f[v.A:u](B)=1, where Q’ is the natural language equivalent of Q, and RGf(v.A), the range of v.A with respect to f, is either identical with the extension of A with respect to v and f, if it is not empty, or is a set containing the zero-entity alone, if this extension is empty.

With these clauses added to a standard construction of quantification theory we get a powerful system, which, beyond restituting the Square of Opposition and all the syllogistic forms previously invalidated by quantification theory, is able to handle problems caused by complex noun phrases with relative clauses using any types of determiners and the problems caused by anaphoric pronouns in ‘donkey-sentences’ in perfect accordance with what the mediaevals said concerning the supposition of relative pronouns.24

If we also add terms representing common terms combined with demonstratives and interpret them relative to an index function (modeling the acts of pointing at different objects) we can provide faithful representations of the above descents. Indeed, it can be shown that these descents along with the corresponding ascents give the correct truth conditions of the corresponding quantified formulae (except for the much debated case of 2.b., but this is why we need the addition of 4.)25 And this remark leads us to the other point I mentioned above, the problem of the completeness of suppositional descents.

The Completeness of Descents

If we examine carefully the above descents, then we can see that they are basically of four kinds. Two of them lead to conjunctive and disjunctive propositions, while two of them lead to propositions with conjunctive and disjunctive terms. The conjunctive forms result from what we would call universally quantified terms, while the disjunctive forms from existentially quantified ones. The difference between the propositional and the term-descents, as can be seen, is that of scope: if the quantifier binding the term under which the descent is made has wider scope than the quantifier binding the other term, then the descent is propositional, if, however this quantifier has narrower scope than the other, then the descent is to be made to a proposition with a disjunctive or conjunctive term.26 Schematically, if x and y are variables ranging over some

24 See "General Terms in their Referring Function" in my Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1988. 25 See "The Square of Opposition, Common Personal Supposition and the Identity Theory of Predication within Quantification Theory" in the collection of my papers mentioned in the preceding footnote. 26 As a matter of fact, this understanding of the difference between nominal and propositional descents, as expressing scope relations of quantified terms, also provides a clue to resolving the notorious problem of attributing confused and distributive supposition to predicates of O-propositions, like ‘Some man is not an animal’. (Cf. 2(b)

13

countable domain, that is, from the point of view of supposition theory, variables representing terms of universal extension,27 related by a relation R and Arabic numerals are names of individuals of the domain, we have the following four cases:

(1) (∃x)(y)(R(x)(y)) ⇔ (y)(R(1)(y))∨(y)(R(2)(y))∨...

(2) (y)(∃x)(R(y)(x)) ⇔ (∃x)(R(1)(x))&(∃x)(R(2)(x))&...

(3) (y)(∃x)(R(y)(x)) ⇔ (y)(R(y)(1∨2∨...))

(4) (∃x)(y)(R(x)(y)) ⇔ (∃x)(R(x)(1&2&...))

To be sure, for a correct incorporation of these equivalences into a formal theory we should interpret the formula schemata standing on the right side of these equivalences as standing for formulae with an appropriate number of conjuncts and disjuncts that are materially equivalent to the left hand side formulae in particular models. (Of course, using restricted variables in the proper sense, this appropriate number will be the cardinality of their range in the given model.)28 But if we do give this interpretation, then these equivalences provably hold. Now given the mediaeval logical-grammatical analysis of categoricals as consisting of two terms prefixed by an explicit or implicit universal or particular determiner joined by the copula (interpreted by late mediaeval logicians as expressing identity), these equivalences provide complete truth conditions for any conceivable categorical sentence. Note here that apparent counterexamples with verbal predicates were explained away by analyzing verbs into copula and participle, and that the two terms were conceived to be of any complexity possibly involving relative clauses of any sentential complexity, so this conception involves a large class of natural language sentences indeed.

So far, so good, one might say, but, despite my sweeping claim about the possible fundamental role of supposition theory, all I have done thus far was not so much using supposition theory as a foundation of a unified theory of reference, as using it as an informal motivation for a particular sort of restricted quantification theory and using this formal theory for a (rather sketchy) reconstruction of suppositional descents. So instead of using the horse to pull the car, I fixed the car to pull the horse (admittedly, taking tips from the horse).

above.) For the real problem with the corresponding descent is that by descending propositionally we attribute wider scope to ‘an animal’ over ‘some man’ in this proposition, in which, however, clearly the converse scope relation holds. So to set things right either we have to descend by a nominal conjunction under ‘an animal’, or we have to take ‘some man’ to refer to the same man in each propositional conjunct, i.e. read ‘some man’ referentially, as if we had already descended under it propositionally to some determinate man, following a ‘priority rule of analysis’. Indeed, both of these remedies were considered in the literature. See Priest-Read, op.cit., Adams, loc. cit., King, op. cit. p.51., A. Broadie: Introduction to Mediaeval Logic, Oxford, 1987, p.24. 27 You may even think of them as x.x=x and y.y=y, respectively, I am using simple variables only to reduce the complexity of the schemata below. 28 In this case special care needs to be taken of cases when these ranges either are infinite or contain only 0. For the technical details see "The Square of Opposition, Common personal Supposition and the Identity Theory of Predication within Quantification Theory" in my Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1988.

14

Well, I accept this criticism regarding what I have said thus far, so to substantiate my claim let me show now where I think suppositional descents may, indeed should, have priority over restricted quantification, for the reason that they can serve as explanations for the behavior of certain common noun phrases much better than the idea of restricted quantification. Indeed, I wish to show how common noun phrases as restricted quantifiers can be interpreted as special cases of such descended forms, and why this interpretation is preferable particularly with regard to two special contexts: namely the context of intentional verbs and the context of numerically quantified ambiguous sentences.

Common Noun Phrases and Intentional Verbs

Consider the following sentence: ‘I owe you a horse’. According to one of its possible interpretations, this sentence is true even if no horse is such that I owe it to you - namely, when my obligation does not concern some particular horse (possibly specified by name or description in a contract), but only a horse in general, that is, any horse whatsoever.29 However, if we try to formalize this sentence in quantification theory, whether we use restricted or unrestricted quantification, we cannot give the correct truth conditions for this interpretation. (For (∃x)(Hx&O(a)(x)(b), would read as follows: ‘Something is a horse and I owe it to you’, while (∃x.Hx)(O(a)(x.Hx) (b)) as follows: ‘Some horse is such that I owe it to you’, which are clearly not equivalent to the intended interpretation. ‘x.Hx’ is a restricted variable picking up its values from the extension of ‘Hx’ in a model. Cf. my papers referred to in nn. 24. and 25.) Notice that with this example it would be highly unintuitive to try something similar to Montague’s trick with ‘John seeks a unicorn’, analyzing it essentially in terms of ‘John tries to find a unicorn’, since for this sentence there seems to be no obvious paraphrase of this kind, and, in any case, even if there were such a paraphrase, the formal analysis would apply only to the exponent sentence, leaving the semantic function of the problematic noun phrase in the original unexplained.30

Mediaeval logicians, instead of trying to avoid accounting for the semantics of this sentence by paraphrasing it away in terms of "easier" ones, faced directly the problem in terms of supposition theory. As a matter of fact, the equivalent of the above sentence receives extensive treatment by Buridan in his Sophismata, while Ockham in his Summa Logicae discusses at some length the supposition of ‘horse’ in a similar sentence: ‘I promise you a horse’.31 In his discussion Ockham writes as follows:

"... we have to say that propositions such as this: ‘a horse is promised to you’, ‘twenty pounds are owed to you’, according to their proper meaning are false, because any of the singulars is false, as is clear inductively. However, if their terms like these are placed on the part of their predicate, they can be conceded in a sense. And then we have to say that the terms following these verbs, in virtue of these verbs have merely confused supposition, and so we cannot descend to the singulars by a disjunctive proposition, but only by a disjunct predicate, enumerating not only present things, but also future ones. So this is not a valid inference: ‘I promise you a horse,

29 Cf. P. Geach: "The Perils of Pauline", in: Logic Matters, Berkeley and Los Angeles, 1972. 30 Cf. R. Montague: "The Proper Treatment of Quantification in Ordinary English", in: J. Hintikka-J. Moravcsik-P. Suppes: Approaches to Natural Language, Dordrecht, 1973; J.D. McCawley: Everything that Linguists have Always Wanted to Know about Logic - but were ashamed to ask, Oxford, 1981. pp.411-421. 31 See Buridan: Sophismata, ed. T.K. Scott, Stuttgard-Bad Cannstatt, 1977, pp.83-90; Ockham: Summa Logicae, ed. Ph. Boehner, St. Bonaventure, N.Y., 1974, P.I.c.72., pp.219-221.

15

therefore I promise you this horse or I promise you this horse and so on ... So we have to know that in such a proposition ... the common term in question does not supposit determinately, taking ‘suppositing’ in the sense in which also a part of an extreme can supposit, that is, you cannot descend under that term to the singulars by a disjunctive proposition, but only by a proposition with a disjunct extreme, or a disjunct part of an extreme.32

Now comparing Ockham’s analysis with the descent schemata above we can clearly see why we have troubles with these propositions in a quantificational approach: a term having merely confused supposition, in (restricted) quantification theory is like a quantified variable bound by a narrow scope existential quantifier; but in this case the quantifier binding (the restricted variable representing) the term ‘horse’ should have narrower scope even than the verb, indeed, the quantifier should not get out of the argument place of the verb, which is impossible already for mere syntactic reasons in any sort of quantification theory.

Indeed, the same is shown further if we consider the sentence ‘I owe you two horses’, which, in the vein of Ockham’s above analysis, is clearly not equivalent to ‘Two horses are such that I owe them to you’, which, however, is the only possible reading of the corresponding quantified formula. (‘(2x.Hx)(O(a)(x.Hx)(b))’)

On the other hand, ‘I owe you a horse’ seems to be intuitively clearly equivalent to ‘I owe you this horse or that horse and so on’ without being equivalent to ‘I owe you this horse or I owe you that horse and so on’.

Again, ‘I owe you two horses’ seems to be equivalent in the same way to ‘I owe you this horse and that horse or that one and that one and so on’ without being equivalent to ‘I owe you this horse and that horse or I owe you that one and that one and so on’.

So in this case (a generalized form of) Ockham’s account seems to be clearly preferable to a quantificational account, provided that we are able to explain why and how these verbs cause merely confused supposition in contradistinction to other, extensional verbs, and that we can supply a working semantics for the nominal disjunctions and conjunctions involved. So let me turn to these topics.

Buridan’s Appellatio Rationis

In his treatment of intentional verbs, Buridan explains the peculiarities of these verbs in the framework of his theory of appellation, which may be characterized roughly as a general theory of connotation.33 However, without going into the details of this otherwise highly interesting doctrine, let me deal here only with that part of it which concerns the context of intentional verbs. According to Buridan, the peculiarity of these verbs is that they make the terms following them connote their rationes, i.e., the concepts according to which they signify external things.34

32 Ockham: Summa Logicae, ed. cit., P.I.c.72., pp.219-221. cf. P.II.c.7. Cf. also Guillelmi de Ockham Scriptum in librum primum Sententiarum Ordinatio, St. Bonaventure N.Y., 1967-1979; d.2.q.4., pp.145-148. Cf. also the similar treatment of Albert of Saxony: Perutilis Logica, Hildesheim-New York, 1974, 14ra. 33 See King, op. cit. pp. 17-25. A. Maierú: "Signification et Connotation chez Buridan", in: J. Pinborg (ed.): The Logic of John Buridan, Copenhagen, 1976. 34 See Buridan: Sophismata, ed. cit., c.4.pp.59-90; Tractatus de Suppositionibus, ed. cit., pp.184-185, 333-335, 343-347.

16

In some of my earlier papers I made a proposal concerning how an exact reconstruction of Buridan’s concepts or rationes can be given within the framework of a general formal semantics, so that we shall have no troubles in the identification of concepts in a semantic model. But lack of space does not allow me to elaborate this proposal here.35 Nevertheless, whatever we take Buridan’s rationes really to be, it is quite clear that insofar as we are able to identify them and correctly distinguish them from one another, they may present a good explanation for the peculiar behavior of noun phrases in the context of intentional verbs.

For if we suppose that we provide an account of these rationes according to which the term ‘horse’ and the disjunctive term ‘this horse or that horse or ...’ (giving a complete enumeration of horses including even future ones, as Ockham said) have the same ratio, while all the singular terms of these disjunctions have different rationes, and we determine the truth conditions of sentences with intentional verbs so that they should depend also on these rationes, then clearly, substituting the complete disjunction for the term following such a verb will not affect the truth value of the proposition, while substituting any of the singulars will. But it is precisely substitutions of these kinds that we make in the different descents: when we descend from ‘I owe you a horse’ to ‘I owe you this horse or that horse and so on’ (giving complete enumeration), we substitute for ‘horse’ a term with the same ratio, so this substitution preserves truth value, consequently the inference is valid; however, when we descend to ‘I owe you this horse or I owe you that horse and so on’ in each member of this disjunction ‘horse’ is replaced by a term with a different ratio, so each member of the disjunction may be false while the premise is true, whence the consequence is not valid, just as Ockham claimed.36

However, to complicate matters, at one place Buridan does not allow descent even to a proposition with a disjunctive term, because he probably does not take the ratio of this term to be identical with that of the original one.37 On the other hand, contrary to Ockham, he allows the inference from ‘I owe you a horse’ to ‘A horse is such that I owe it to you’, indeed, to ‘Every horse is such that I owe it to you’ for the reason that through the general concept of ‘horse’ my obligation is related to every particular horse, which, however, does not imply that I have to give you every particular horse.38

But this difference between their particular intuitions and decisions on this matter notwithstanding, Buridan’s theory, as we could see, can be used to explain even Ockham’s rules. And even further, if we took sides with Ockham, we could explain even the apparent validity of the passage from ‘I owe you two horses’ to ‘I owe you this horse and that horse or that one and that one and so on’ (giving a complete enumeration of all pairs of horses) without committing 35 See "Understanding Matters from a Logical Angle" and "Socrates est species" in my Ars Artium. Presently I am working on a detailed and, at least according to my intentions, faithful formal reconstruction of Buridan’s theory of signification and appellation as they are set to work in his analysis of ‘Debeo tibi equum’, in a paper under this title to be presented at the 9th European Symposium of Mediaeval Logic and Semantics, in St. Andrews, Scotland. 36 For a similar analysis of Ockham’s treatment see S.L. Read: "‘I promise a penny that I do not promise’: The Realist/Nominalist Debate over Intensional Propositions in Fourteenth-Century British Logic and its Contemporary Relevance", in: The Rise of British Logic, ed. P. Osmund Lewry, O.P., Papers in Mediaeval Studies 7 (Toronto: Pontifical Institute of Mediaeval Studies, 1985), pp.335-359. 37 "... but in this kind of confusion it is not permissible to descend to the supposits either by a disjunctive sentence or by a categorical with a disjunct extreme, since such verbs make the terms following them appellate their rationes, namely those according to which they were imposed to signify." King’s translation (ed. cit. p.145.) of Buridan’s Tractatus de Suppositionibus, ed. cit. pp.333-334. 38 See Buridanus: Sophismata, ed. cit. pp.83-90.

17

ourselves to the truth of ‘Two horses are such that I owe them to you’, or ‘I owe you this horse and that horse or I owe you that horse and that horse, and so on’, provided we would work out an account of the rationes of the noun phrases involved parallel to the above case. But without going into the technical problems of assigning the appropriate rationes to these noun phrases, one thing may be interesting in these descents even regarding other contexts, namely the analysis of a numerical quantifier in terms of a disjunction of conjunctions. So let us turn now to this topic.

Ambiguous Sentences with Numerical Quantifiers

Recently several papers appeared that were addressed to the problems involved in the analysis of numerically quantified ambiguous sentences such as ‘Two examiners marked six scripts’.39 In this section I only try to indicate very briefly how I think a generalized theory of suppositional descents could provide a unified framework for handling sentences of this kind.

The basic idea can be put in one sentence as follows: we can treat all common noun phrases with numerical determiners as nominal disjunctions of nominal conjunctions having as many members as the cardinality of the numerical determiner, while we can determine scope relations by allowing further descents to disjunctive and conjunctive propositions. Semantically, we can determine the import of such a complex nominal phrase by saying that a complex predicable is true of a nominal disjunction if and only if it is true of at least one of its members, while it is true of a nominal conjunction, if and only if it is true of each of its members. But this latter holds only of the distributive reading of nominal conjunctions: further ambiguities can be accounted for by distinguishing between distributive, collective and divisive readings of nominal conjunctions, or rather of argument places of predicates in which these conjunctions occur, just as the mediaevals did.40 In this way from the general nominal descent scheme of an ambiguous numerically quantified sentence we can get specifications of its possible readings by the further possible propositional descents and these distinctions.

So e.g. the general nominal descent scheme of ‘Two examiners marked six scripts’ may be given as follows:

39 See e.g. M. Davies: ‘Two examiners marked six scripts: Interpretations of Numerically Quantified Sentences’, Linguistics and Philosophy, 12(1989) pp.293-323. Davies supplies also a number of further references. 40 Cf. e.g.: "... this sign ‘omnis’ <meaning: ‘all’ in the plural, as opposed to its distributive meaning, translatable as ‘every’, which it has in the singular>, when it is taken in the plural, may be interpreted either collectively or divisively. If it is taken divisively, it denotes that the predicate truly applies to all those things of which the subject is truly predicated, like by this: ‘All apostles of God are twelve’ is meant that this predicate: ‘twelve’ is truly predicated of all those of which the subject ‘apostles’ is truly predicated; and so, since Peter and Paul are apostles, it follows that Peter and Paul are twelve. <And in this sense the proposition is false, of course.> But if it is taken collectively, it does not denote that the predicate applies to all those to which the subject applies, but that it applies to all those things taken together of which the subject is verified; so it means that these apostles, pointing at all the apostles, are twelve." Ockham: Summa Logicae, ed. cit., p.266. Cf. further: "Introductiones Montane Minores", in: L.M. de Rijk: Logica Modernorum, ed. cit., II-2., pp.29-30.; Buridan: Tractatus de Suppositionibus, ed. cit., pp.199-200.; William of Sherwood: Syncategoremata, Mediaeval Studies, 3(1941), pp.46-93 esp. pp.84-89; Walter Burleigh: De Puritate Artis Logicae Tratctatus Longior with a revised edition of the Tractatus Brevior, St. Bonaventure, N.Y., 1955, pp.241-243, 252-253; Paul of Pergula: Logica and Tractatus de Sensu Composito et Diviso, St. Bonaventure, N.Y.-Louvain-Paderborn, 1961. pp.152-153.

18

(e1&e2 ∨ ...)M(s1&s2&s3&s4&s5&s6 ∨ ...)

or, in general, for any terms S and P, and any relation R,

(si&sj... ∨ sk&sl...)R(pm&pn... ∨ po&pq...)

where the number of conjuncts is that of the numerical determiner, the range of the numerical subscripts relative to a model is identical with the cardinality of the extensions of the original terms (in our example the terms: ‘examiner’ and ‘script’) in that model, while the number of disjuncts is to be such that the set of referents of the singular terms should be identical with the extension of the original common term in this model, if the set of singular terms occurring in the conjunctions varies from disjunct to disjunct, and arbitrary, if the same set of terms makes up the conjunctions in each disjunct. Indeed, we may take this as a degenerate case, and take here a one-member disjunction instead of one with several members, that is, one conjunction alone. As a matter of fact, this treatment of degenerate cases shows us that noun phrases with the ordinary quantifiers can be regarded as degenerate cases of the above general scheme. A universally quantified noun phrase may be regarded as a one-member disjunction of conjunctions in which all members are different and their referents together exhaust the extension of the quantified term. An existentially quantified noun phrase may be regarded as a disjunction of one-member conjunctions (that is conjunctions with the same members), but such that the referents of the disjuncts are different, and together exhaustive of the extension of the quantified term. I think it is easy to see how several other determined noun phrases of natural languages could be defined along these lines, but I do not want to linger on this point here. Instead, I would like to indicate how we can get from the above general nominal descent scheme the possible different readings of the same ambiguous sentence.

As we could see from the four types of descent schemata (1)-(4) above, descent to propositional disjunctions and conjunctions expresses the larger scope of a noun phrase in comparison with descent with nominal conjunctions and disjunctions. So descending to disjunctive propositions once under the left and once under the right side argument of M gives us two scope-differentiated readings of the restricted quantifier analysis of ‘Two examiners marked six scripts’, satisfiable either by a situation possibly involving two examiners and twelve scripts, each of them being marked by one of the examiners, or by a situation involving six scripts and twelve examiners each of the scripts being marked by two examiners and each examiner marking exactly one script.

However, we can descend by disjunctive propositions also on both sides, so that neither of the noun phrases of the original sentence gets wider scope than the other like this: ‘this and that examiner marked this and that and so on, that is, these six scripts, or that and that examiner marked those six scripts, and so on’, in which case our sentence says that we have some set of two examiners and some set of six scripts each of which was marked by each of the examiners, which is the branching quantifier reading of this sentence.

But we can get even further possible readings if we consider the collective and divisive interpretations of nominal conjunctions, or rather of argument places of predicables in which these conjunctions occur, as I have said. For, as is well-known, certain predicables can apply only to groups of individuals without applying to the members of these groups. For example,

19

even if we can truly say that six wolves surrounded two deer, it is not true of any of these wolves that it surrounded two deer, or for that matter, any number of deer. So in this case we cannot think of the predicable ‘surrounded two deer’ as applying to the conjunction enumerating six wolves if and only if it applies to each of its members, but as applying to what the conjunction as a whole applies to, namely the six wolves enumerated by it together. In general, we can say that a predicable is true of a nominal conjunction taken collectively if and only if it is true of what the conjunction as a whole applies to, namely of the collection of the individuals enumerated in the conjunction. Note here that while the first argument place of ‘surrounded’ is necessarily collective, the other may be taken either as collective or as distributive. In the latter case the sentence ‘Six wolves surrounded two deer’ may be true in a situation in which one deer is surrounded by six wolves and another by other six wolves.

But it may also be the case that six wolves so surround two deer that three of them surrounds one deer and the other three the other one. In this case neither six wolves taken one by one, nor six wolves taken together can be said to have surrounded two deer, rather we can say that some subgroups of a sum total of six wolves surrounded some one-member ‘subgroups’ of a sum total of two deer. That we should think here of one-member subgroups of deer instead of individual deer is easily seen if we take examples with higher numbers. But, of course, a predicable is true of such a one-member group if and only if it is true of its one member. Note here, that divisive reading of one argument place of a relation forces divisive reading of the other too, while distributive and collective readings could freely combine with one another. In general, we can say that if we attribute divisive readings to the two argument places of the relation R, then the truth condition of (the particular formula instantiating in a particular model) the general descent scheme of a sentence (NS)R(MP) is that there be some together exhaustive subconjunctions of the N-member and M-member conjunctions of (the formula instantiating in that model) the general scheme such that R holds of all of these subconjunctions either collectively or distributively. For example, on a divisive reading of ‘Twelve wolves surrounded three deer’ this sentence may be true in a situation in which, say, six wolves surrounded one deer and six others surrounded two other deer.

So in this way from the general nominal descent scheme of a numerically quantified ambiguous sentence by means of the further possible propositional descents and by distinguishing the three possible readings of nominal conjunctions we can generate apparently all possible readings of these sentences. We could also see how sentences with the ordinary quantifiers and possibly also with others can be regarded as special cases of these general descent schemata. We could even see how these descents might work in the thorniest intentional contexts. I think it is also quite easy to imagine how, with reference to the divisive readings of nominal conjunctions, these descent schemata could account for plurals. So I hope by now it seems not so exaggerated to claim that the theory of suppositional descents may indeed serve at least as a starting point of a unified theory of reference in natural languages. But further elaboration of this claim would exceed the limits of this paper.

Conclusion

In the first two sections I presented the state of our art as characterizable in terms of the crumbling of an old paradigm in view of the accumulation of anomalies and, at the same time, by a quest for new unifying perspectives. I took justification from this description for seeking

20

different new orientations, occasionally with a view to old exemplars. I repelled an objection to seeking our historical exemplars in traditional logic by pointing to the enormous difference between the traditional logic of last century logic textbooks and that of the mediaeval masters of logic. Making reference to the growing contemporary interest in the mediaeval theory of supposition, I set out to show how in my view this theory could be used also in modern logico-linguistic research as what it was originally meant to be, as a foundation of a unified theory of reference in natural languages. After a brief presentation of the basic definitions and divisions, I pointed out the fundamental agreement of the doctrine of suppositional descents with the idea of a particular sort of restricted quantification. I even sketched how the theory of descents can be reconstructed, and how the completeness of descents in giving the truth conditions of categorical sentences with complex noun phrases can be shown within the framework of such a restricted quantification theory. Then I tried to show that rather than using restricted quantification to explain suppositional descents, we should use descents to explain the behavior of common noun phrases both in cases in which the quantifier analysis works and in those in which it fails. I selected as test cases the contexts of intentional verbs and those of numerically quantified ambiguous sentences. In the former case I argued that the quantificational analysis should fail of necessity, already for mere syntactical reasons. Then I indicated that Ockham’s analysis of these contexts supplemented with Buridan’s theory of appellation may give satisfactory results, and may even explain the opposing intuitions of the two authors. However, instead of trying to elaborate here the technical details of appellation theory, I turned to the analysis of numerically quantified sentences in terms of suppositional descents. I tried to show how common noun phrases may be regarded as nominal disjunctions of nominal conjunctions of singular terms in general, and so how the common noun phrases with the usual quantifiers may be regarded as special (degenerate) cases of these nominal disjunctions of conjunctions. I have also made proposals as to the semantic import of these nominal disjunctions and conjunctions in determining the truth conditions of sentences in which they occur, indicating a threefold distinction of the possible readings of nominal conjunctions. Then I tried to show how the several possible readings of a numerically quantified ambiguous sentence may be generated from such a general nominal descent scheme by further possible propositional descents and by making use of the distinctions between the possible readings of nominal conjunctions. I have also remarked that the divisive readings of nominal conjunctions may be useful in the analysis of plurals.

Of course, several claims I made could not receive appropriate treatment within the confines of this paper. Most importantly, I think the following points need further elaboration:

1. an account of Buridan’s appellatio rationis, which would allow us to explain the peculiarities of the possible descents under common terms in the context of intentional verbs

2. a systematic account of the semantics of nominal conjunctions and disjunctions in general

3. an account of plurals in terms of the divisive reading of nominal conjunctions

The general semantic framework for the elaboration of these points may be, I think, also classical model theoretical semantics. But it is also a tempting idea to regard the several possible descents under common terms in several contexts as describing particular semantic games for the evaluation of a sentence in which these terms occur in a particular model. So from this point of

21

view it seems that a combination of the theory of suppositional descents with game theoretical semantics may provide even more interesting results.41

41 As a matter of fact, this paper is only a preparatory work for a joint project with Gabriel Sandu of the University of Helsinki in which we try to work out the technical details of this intuitive idea. (Appeared: Klima, G.—Sandu, G. “Numerical Quantifiers in Game-Theoretical Semantics”, Theoria, 56(1990), pp. 173-192.) Earlier drafts of this paper were presented at the Department of Linguistics and at the Department of Philosophy of the University of Helsinki during my stay in Helsinki as a member of the project ‘Ockham and the via moderna’ under the chairmanship of Simo Knuuttila, in the Fall Semester of 1989. I wish to express my gratitude to all the Finnish friends and colleagues for the inspiring discussions and all kinds of help they provided.

22

Old Directions in Free Logic: Existence and Reference in Medieval Logic

1. Introduction: Existential Assumptions In Modern vs. Medieval Logic

“The expression ‘free logic’ is an abbreviation for the phrase ‘free of existence assumptions with respect to its terms, general and singular’.”1 Classical quantification theory is not a free logic in this sense, as its standard formulations commonly assume that every singular term in every model is assigned a referent, an element of the universe of discourse. Indeed, since singular terms include not only singular constants, but also variables2, standard quantification theory may be regarded as involving even the assumption of the existence of the values of its variables, in accordance with Quine’s famous dictum: “to be is to be the value of a variable”.3

But according to some modern interpretations of Aristotelian syllogistic, Aristotle’s theory would involve an even stronger existential assumption, not shared by quantification theory, namely, the assumption of the non-emptiness of common terms.4 Indeed, the need for such an assumption seems to be supported not only by a number of syllogistic forms, which without this assumption appear to be invalid, but also by the doctrine of Aristotle’s De Interpretatione concerning the logical relationships among categorical propositions, commonly summarized in the Square of Opposition.

For example, Aristotle’s theory states that universal affirmative propositions imply particular affirmative propositions. But if we formalize such propositions in quantification theory, we get formulae between which the corresponding implication does not hold. So, evidently, there is some discrepancy between the ways Aristotle and quantification theory interprets these categoricals. One possible suggestion concerning the nature of this discrepancy could indeed be that Aristotelian logic contained the (tacit) existential assumption as to the non-emptiness of common terms. On the other hand, we know that this suggestion would definitely be rejected by the most ardent followers and expounders of Aristotle’s logic, namely, medieval logicians.5 Indeed, they would reject not only this suggestion (and for good reasons, too)6, but also the existential assumptions of standard quantification theory mentioned above.

1 Lambert, K.: Meinong and the Principle of Independence, Cambridge University Press, Cambridge, 1984, p. 104. (emphasis in the original) Cf.: Lambert, K. : “The Nature of Free Logic”, in: Lambert, K. (ed.): Philosophical Applications of Free Logic, Oxford University Press, New York-Oxford, 1991. pp. 3-13. 2 See Lambert: Meinong and the Principle of Independence, Cambridge University Press, Cambridge, 1984, p. 105. n. 9. 3 W.V.O. Quine: “On What There Is”, in: From A Logical Point of View, Harvard University Press, Cambridge MA, 1980, p.15. Concerning the real import of Quine’s dictum and its relationship to free logics see Lambert: Meinong and the Principle of Independence, Cambridge University Press, Cambridge, 1984, pp. 110-112. 4 Perhaps, the most authoritative account of this interpretation is found in: W. Kneale-M. Kneale: The Development of Logic, The Clarendon Press, Oxford, 1962, II.5., pp. 54-67. 5 To be sure, not by all of them. Cf.: S. Ebbesen: “‘The Present King of France Wears Hypothetical Shoes with Categorical Laces’: Twelfth Century Writers on Well-Formedness”, Medioevo, 7(1981), pp. 91-113. But the authors mentioned here represent the exception, rather than the rule. 6 Cf. E.J. Ashworth: “Existential Assumptions in Late Medieval Logic”, American Philosophical Quarterly, 10(1973), pp.141-147. For good arguments that we cannot afford to ignore the medievals’ treatment of empty terms see A. Broadie: Introduction to Medieval Logic, Oxford, 1987, p.120.

23

In this paper I am going to give a brief, primarily systematic (as opposed to primarily historical) account of how it was possible for medieval logicians to maintain Aristotle’s theory of the four categoricals and to dispense with these existential assumptions in the framework of their theory of reference, the theory of supposition.7 Besides the informal account I will also indicate how these informal ideas can be put to work in a formal semantic system.8 By this I hope to show how the “old directions” we can get from medieval logicians can provide us with valuable guidance even in the apparently modern field of free logic.

2. Supposition Theory and the Square of Opposition

The main reason why medieval logicians did not need any extra (tacit or otherwise) assumptions “to save” the logical relationships of the Square of Opposition is that these logical relationships are direct consequences of their semantic analysis of the four types of categorical propositions. According to this analysis, in contrast with the analysis of quantification theory, the subject terms of these propositions have a referring function: they stand for (supponunt pro) the particulars falling under them, provided there are any such particulars. If, however, these subject terms are “empty”9, then they simply refer to nothing (pro nullo supponunt). But then the affirmative categoricals are false, whence their contradictories are true, that is to say, affirmative categoricals have existential import, while negative ones do not, which “automatically” yields the relationships of the Square. Namely, if A: universal affirmative; E: universal negative; I: particular affirmative; O: particular negative, then A⇒I; E⇒O; A⇔‘~O’; E⇔‘~I’; A⇒‘~E’; ‘~I’⇒O.

Notice that from A⇒I, E⇔‘~I’ and A⇔‘~O’ the rest are derivable, that is, if A is assigned existential import and the diametrically opposed propositions are construed as contradictories, then all relationships of the Square are valid.

7 For good bibliographies on the vast recent literature on supposition theory see e.g.: E. J. Ashworth: The Tradition of Mediaeval Logic and Speculative Grammar, Toronto, 1978; N. Kretzmann-J. Pinborg-A. Kenny (eds.): The Cambridge History of Later Mediaeval Philosophy, Cambridge, 1982. For more recent references see: N. Kretzmann (ed.): Meaning and Inference in Mediaeval Philosophy, Kluwer Academic Publishers, 1989. 8 For a full-fledged formal semantics constructed along the lines presented here see the Appendix of this paper. Closely related formal semantic systems with thorough discussions of their applications in natural language semantics can be found in G. Klima: Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Institute of Philosophy of the Hungarian Academy of Sciences, Budapest, 1988. 9 ‘Empty’, in the case of natural supposition, and intensional contexts, created by tenses, modalities and what medieval logicians would call ampliative verbs and their participles, will have to be interpreted more strongly than ‘actually not true of anything’. As we shall see, A propositions with subject terms occurring in such contexts do not have ‘existential import’ properly speaking (i.e., ‘Every S is/was/will/can/could be P’ does not imply ‘Something is an S’ in these cases), still, the relation of subalternation, i.e., A⇒I, is valid even with such propositions. For more on this see section 4.2. below. Nevertheless, in sections 2, 3, and 4.1, I am considering only extensional (non-tensed, non-modal, non-ampliative, etc.) contexts, and, accordingly, throughout these sections I am going to use the phrases ‘empty’ and ‘existential import’ in their usual extensional senses, i.e., according to which the subject term of an A proposition is empty iff it is not true of anything and the proposition has existential import iff its truth implies that its subject is not empty.

24

A: Every man is mortal

I: Some man is mortal

E: No man is mortal

O: Some man is not mortal

There can be basically two types of justification for attributing this kind of existential import to affirmative categoricals (regardless of their quantity, i.e., whether they are singular, indefinite, universal or particular), on the basis of the two fundamental types of predication theories endorsed by various medieval authors.10

According to what historians of medieval logic dubbed the inherence theory of predication, an affirmative categorical proposition (in the present tense with no ampliation, cf. n. 9. above) is true only if an individualized property (form, or nature) signified by the predicate term actually inheres in the thing(s) referred to by the subject term. So, for example, the proposition ‘Socrates is wise’ is true, if and only if wisdom actually inheres in Socrates, that is, Socrates has wisdom, or, which is the same, Socrates’ wisdom actually exists. But of course Socrates’ wisdom, or for that matter any other inherent property of Socrates, can actually exist only if Socrates himself exists. So, it follows that if Socrates does not exist, then the proposition ‘Socrates is wise’ is false, and so are all affirmative categoricals the predicate term of which signifies some inherent property of Socrates.

On the other hand, according to the other basic type of medieval predication theories, the so-called identity theory, an affirmative categorical proposition is true only if its subject and predicate terms refer to the same thing or things. For example, on this analysis ‘Socrates is wise’ is true if and only if Socrates, the referent of ‘Socrates’, is one of the wise persons, the referents of the term ‘wise’. If any of the two terms of an affirmative categorical is “empty”, then the term in question refers to nothing. But then, since “nothing is identical with or diverse from a non-being”, as Buridan (the “arch-identity-theorist” of the 14th century) put it, “every affirmative proposition whose subject or predicate refers to nothing is false”.11

10 Cf. e.g. L. M. de Rijk’s Introduction to his edition of Abaelard’s Dialectica, Assen, 1956, pp. 37-38; D. P. Henry: Medieval Logic and Metaphysics, London, 1972, pp. 55-56, P. T. Geach, “Nominalism”, in his: God and the Soul, London, 1969. 11 “et tamen sequitur ‘b est aliud ab a; ergo utrumque est, scilicet b et a’, ut patet per Aristotilem decimo Metaphysicae - non enti enim nihil est idem vel diversum”, Tractatus Sophismatum Johannis Buridani, Primum Capitulum De Significatione, 4um sophisma: ‘Hoc Nomen ‘Chimaera’ Nihil Significat’. The reference to Aristotle is Met 1054b20. And somewhat later: “Unde haec est regula de qua postea magis intendimus dicere quod omnis propositio affirmativa cujus subjectum vel praedicatum pro nullo supponit est falsa.” ibid. Quinta conclusio. (John

25

In any case, as we can see, from the point of view of the doctrine of the Square it does not matter which predication theory a medieval author endorsed, as both of these theories imply that affirmative categoricals in general, including universal affirmatives, have existential import.12

3. Two Objections to the Medieval Analysis

Anyone trained in the modern Frege-Russell tradition in logic may have at least two immediate misgivings concerning attributing existential import to all affirmative categoricals, regardless of further philosophical worries concerning the above-mentioned theories of predication.13

First, if universal affirmatives have existential import, then their contradictories must be true, when their subject terms are empty. But the contradictory of, say, ‘Every winged horse is a horse’ is ‘Some winged horse is not a horse’. The latter, however, cannot be true, both because it is contradictory and because it implies the existence of winged horses, while there are no winged horses.

Second, this position seems to undermine the very idea of the affirmation of universal laws concerning hypothetical, never actualized situations. For example, Newton’s law of inertia, referring as it does to bodies not acted upon by external forces, would not be true on this analysis as a categorical statement.

Of course, our medieval colleagues were quite aware of these possible objections, and worked out their theories accordingly.

4.1. Reply #1: Reference and Negation

The first type of objection was easily dismissed by a distinction between negating (what we would call propositional or external) and infinitizing (what we would call term- or internal) negation.14 To use Russell’s famous example, the intended contrast is between

[1] The King of France is not bald [⇔ It is not true that the King of France is bald

Buridan: Sophisms on Meaning and Truth, tr. intr. by T. K. Scott, Appleton-Cenntury-Crofts, New York, 1966, p. 66. and p.72.) Cf. also: “sicut dicitur decimo Metaphysicae, ‘idem’ vel ‘diversum’ numquam dicitur nisi ens enti, licet ens non enti dicatur non idem aut non diversum.” Questiones in Analytica Priora, lb. I. q. 22.: Utrum ex puris negativis sequatur aliqua conclusio. Translations in this paper, if not otherwise indicated are mine. Quotations from Buridan are based on Prof. Hubert Hubien’s unpublished editions of Buridan’s Lectura de Summa Logicae and Questiones in Analytica Priora et Posteriora. These texts will serve as the basis for my translation of Buridan’s works in the series The Yale Library of Medieval Philosophy. (Where applicable, I will also add references to existing English translations.) The critical Latin text is being prepared by an international team with the co-ordination of Prof. Sten Ebbesen. 12 For Aristotle’s authority on this point, an important factor for the medievals’ approach, see e.g. Cat. 13a38-13b35; Periherm. 19b5-20b13; Anal. I., 51b6-52b25. (Cf. also Boethius’s comments on these texts.) 13 To help dispel such further worries let me refer the reader to my book, Ars Artium, referred to in n. 8. above, in which both predication theories receive rigorous, formal semantic treatment. For the philosophical significance of these different medieval predication theories see G. Klima: “Ontological Alternatives vs. Alternative Semantics in Medieval Philosophy”, in: J. Bernard: Logical Semiotics, S - European Journal for Semiotic Studies, 3(1991) No. 4, pp. 587-618. and G. Klima: “The Changing Role of Entia Rationis in Mediaeval Philosophy: A Comparative Study with a Reconstruction”, Synthese 96(1993) No. 1., pp. 25-59. 14 The medieval distinction goes back, of course, through the comments of Boethius, to Aristotle’s remarks in On Interpretation 16a30 and 16b13.

26

which is true, because France presently has no king, and so it is not the case that the King of France is bald [negating negation], and

[2] The King of France is non-bald

which is true when the King of France is a non-bald person, i.e., a person who is both King of France and has hair, whence the proposition is actually false, precisely because there is no such a person [infinitizing negation].

The regimented Latin syntax of medieval logic could systematically express this distinction by placing the negation [‘non’] either before [negating negation] or after [infinitizing negation] the copula, yielding

[1L] Rex Franciae non est calvus

and

[2L] Rex Franciae est non calvus,

respectively.15

Of course, anyone familiar with Russell’s treatment of this example would recognize the distinction between the scopes of the negation in [1] and [2] (or, sticking with Russell’s original terminology, the distinction between primary and secondary occurrences of the description16), but they would reject in the same breath that this scope-distinction has anything to do with the strange claim concerning the truth of

[3] Some winged horse is not a horse

implied by the medieval analysis. After all, Russell’s distinction is based on the elimination of the merely apparent reference to the King of France in both [1] and [2] by paraphrases in which there is not even an appearance of such a reference. This is immediately evident if we consider the corresponding formulae of quantification theory:

[1’] ~(∃y)(Ky&∀x(Kx⊃x=y)&By) [2’] (∃y)(Ky&∀x(Kx⊃x=y)&~By)

In these formulae (where ‘K’ represents ‘… is King of France’, and ‘B’ represents ‘… is bald’) there is not even a trace of the apparent referring phrase ‘the King of France’, and this is why there is not even an apparent reference here to a person who is presently King of France. So Russell’s distinction boils down to the difference in the position of the negation in the logical form of [1] and [2], whereas in the case of [3] no such distinction seems to make sense. Indeed, [3] can be formalized only in one way with respect to the position of negation in it, namely:

[4’] (∃x)(Wx&~Hx)

(where ‘W’ represents ‘… is a winged horse’ and ‘H’ represents ‘… is a horse’, and the reason for the apparently inconsistent numbering of this formula should become clear soon). Placing the 15 Cf.: “Again, some propositions are affirmative, some negative. An affirmative proposition is one in which its formal part is left affirmative, while a negative proposition is one in which its formal part is negated, and by the formal part of a categorical proposition I mean its verbal copula.” Albert of Saxony: Perutilis Logica, Georg Olms Verlag, Hildesheim-New York, 1974, fol. 17.vc. 16 Note that the description has what Russell calls a primary occurrence (wider scope than the negation) in [2], and what he calls a secondary occurrence in [1].

27

negation anywhere else in this formula would obviously yield a formula that is not a formalization of [3], but either of ‘No winged horse is a horse’ or of ‘Something that is not a winged horse is a horse’, which are clearly different from [3]. But then [3] evidently does not contain the kind of scope-ambiguity that sentences with definite descriptions do, which Russell’s distinction is intended to handle.

However, if we recall what I said in the second section above about the medieval analysis of the categoricals, we can easily see what connects the cases of sentences with definite descriptions and [3]. According to this analysis all categorical propositions are instances of the following scheme, regardless of their quantity:

[Cat] [neg][Q] S [neg] cop P

where bracketed parts of speech are optional, [neg] stands for negation (possibly even iterated), [Q] stands for some signum quantitatis, i.e., some determiner, cop stands for a copula (in any tense) and S and P stand for the (possibly very complex) subject and predicate term17, respectively. Accordingly, if we regard the definite article as one possible substitution in this scheme (to complicate matters, one that does not exist in Latin), we can easily see the required analogy:

[Cat]* [neg][a/the/some/every/…] S [neg] cop P

where the English determiners in the place of [Q] are going to determine that, completing the scheme with appropriate English parts of speech, the resulting categorical sentences are going to be indefinite, definite, particular and universal,18 respectively. But then, the relative scope-relations concerning negation and the definite article in this scheme will apply to the other determiners occurring in this scheme as well. Hence, [Cat]* may be completed, for example, as

[C1] [neg][a/the/some/every/…] winged horse is not a horse

or as

[C2] [neg][a/the/some/every/…] winged horse is a non-horse

where the further rule is that the initial [neg] may be replaced by the phrase: ‘It is not the case that’, yielding the contradictory of the sentence to which it is prefixed. But then it is clear that no concrete instances of [C1] and [C2] are going to be equivalent, and that, in particular, there is a clear difference between

[3] Some winged horse is not a horse and

[4] Some winged horse is a non-horse

To express the intuitive difference between [3] and [4] (matching that between [1] and [2]) in the logical forms of these sentences, we have to expand the language of standard quantification

17 It should be noted here that besides the obvious complexities obtained by genitives, relative clauses, adjectival and adverbial constructions, the “Boolean” operations (i.e., term-negation/conjunction/disjunction), and those caused by participles of transitive verbs, according to Buridan even a determiner possibly added to the predicate term is a part of that term (whereas that added to the subject is a functor operating on the whole proposition). This is why in the scheme above I did not have to add an optional occurrence of another determiner construed with the predicate term. 18 Of course, the scheme [Cat] may be completed by any other determiner besides the “classical quantifier words”. This is what is indicated by the unfinished list in the place of [Q].

28

theory with restricted variables, representing general terms in their referring function, as they occur in the subject-positions of these sentences.19 A restricted variable is a variable formed from an open sentence, which takes its values from the extension of the open sentence, if this extension is not the empty set, while it takes a zero-entity as its value otherwise. For example, let ‘x.Wx’ be the restricted variable formed from the open sentence ‘Wx’, so that, for all value assignments, it takes an element of the extension of this open sentence in a model in which this extension is not empty, while it takes 0 as its value in all those models in which this extension is empty, where the only requirement concerning 0 is that it is not an element of the universe of discourse of that model. Also, to reflect the difference between ‘is not a horse’ and ‘is a non-horse’ let me introduce a term-negation of a predicate parameter simply by bracketing a negation sign together with the predicate parameter, along with the semantic rule that the extension of the resulting negated predicate will be the complement of the original relative to the universe of discourse. So, for example, if the extension of ‘H’ in a model is some subset A of the universe of discourse U of that model, then the extension of ‘[~H]’ in that model is going to be U-A.

But then [3] may be formalized as

[3’’] (∃x.Wx)~(H(x.Wx))

while [4] will become

[4’’] (∃x.Wx) ([~H](x.Wx))

which, in view of the above-sketched semantic rules will obviously have a different import than [3’’]. Indeed, in a model in which the extension of ‘Wx’ is empty (representing the actual situation, i.e., that there are no winged horses) it is easy to see that [3’’] is true, while [4’’] is false, in perfect parallelism with [1] and [2], which, using ι as the definite descriptor, now may be re-formalized as

[1’’] (ιx.Kx)~(B(x.Kx))

and

[2’’] (ιx.Kx) ([~B](x.Kx)).

In a complete semantics for such and similar formulae (see Appendix) it is easy to see the equivalence between these and the Russellian formulae [1’] and [2’], and also between [3’’] and [4’’] and

[3’] ~(∃x)(Wx)∨(∃x)(Wx&~Hx)

and

[4’] (∃x)(Wx&~Hx)

respectively. However, the advantage of the formulations with restricted variables lies in the fact that they reveal the structural analogy between Russell’s distinction concerning only sentences with definite descriptions and the medieval distinction concerning all types of categorical propositions.

19 Of course, “identity-theorists” would regard also the predicate term as a referring expression on a par with the subject term, but I need not pursue this point here. For technical details and philosophical significance of this point see my Ars Artium.

29

But then to the original objection we can say that it fails to distinguish between [3] and [4]. For the objection draws its conclusions from ‘Some winged horse is not a horse’ using it in the sense of [4] (i.e., as having the logical form [4’’], i.e., [4’]). However, in that sense ‘Some winged horse is not a horse’ is not the contradictory of ‘Every winged horse is a horse’ (analyzed, of course, as another instance of the same scheme [Cat]). So we can hold without any absurdity that, precisely because there are no winged horses, ‘Every winged horse is a horse’ is false, and that its contradictory, [3] (having the logical form [3’’], i.e., [3’]) is true. Of course, if anyone still feels that this analysis is in conflict with their linguistic intuition in that ‘Some winged horse is not a horse’ according to that intuition has to carry existential import, they may always use this sentence in the sense of [4], but then they would have to distinguish between ‘Some winged horse is not a horse’ and the contradictory of ‘Every winged horse is a horse’, i.e., ‘It is not the case that every winged horse is a horse’. Actually, this was the course taken by Abelard in the 12th century, but later medievals rather settled on not attributing existential import to particular negatives, treating them as the genuine contradictories of universal affirmatives.20

In any case, as from the general scheme above it should be clear, the great advantage of this type of analysis is that it provides us with a uniform, systematic account of relative scope relations of negation and all sorts of determiners in categorical propositions. So the formulae with restricted variables immediately point us in the direction of formulating a generalized quantification theory, i.e., one in which for any replacement of [Q] we can easily construct the corresponding formulae giving the correct truth-conditions for the resulting sentences, some of which will demonstrably have no equivalents in classical quantification theory (those formulated with the determiner ‘most’, for example). But instead of going into the details of formulating such a generalized quantification theory, let us see how the other objection can be handled in the medieval framework.21

4.2. Reply #2: Habitual Predication, Natural Supposition and Ampliation

The second objection received two different types of answer in medieval logic, both of which introduced further distinctions concerning the possible interpretations of categorical propositions. The one distinguished between different modes of predication in a categorical proposition, while the other attributed a different type of reference to the subject terms of law-like statements.

According to the first type of answer, the predication expressed by the copula of an affirmative categorical proposition may be interpreted not only actually, or according to real existence, when it requires the existence of what it is about, but also absolutely, or habitually22, in which

20 For Abaelard’s solution see Abaelard, Dialectica, ed. L. M. de Rijk, Assen, 1956, pp. 175-177. Cf. W. and M. Kneale: The Development of Logic, Oxford, 1971, p.210-211 21 A full-fledged semantic theory constructed along these lines with a thorough discussion of its applications in natural language semantics can be found in Essay III. of my Ars Artium. The formal semantics presented in the Appendix of this paper will also show how naturally we can move in this direction within this framework. 22 Cf.: “it is in two ways that something can be said of something: in the first way absolutely, and to the truth of this the connection of the terms suffices; and in this way ‘animal’ can be said of man although of no men, just as when no rose exists ‘substance’ is said of rose [absolutely], though of no rose; and this is what Porphyry’s authority concludes to, nor Aristotle thought its contrary. But in the second way something is said of something according to real existence. And I call saying something of something according to real existence, when the predicate inheres in the subject that exists in the nature of things.” Cajetan, Thomas de Vio: Scripta Philosophica: Commentaria in Praedicamenta Aristotelis, ed. M. H. Laurent, Angelicum, 1939, Romae, pp.: 50-51. Cf. also William of Sherwood:

30

case the categorical proposition is equivalent to a hypothetical proposition, much in the way quantification theory analyzes all universal categoricals. So, accordingly, if the sentence

[5] Every winged horse is a horse

is put forth with the force of a universal truth, absolutely or habitually, concerning the analytic conceptual connection between the subject and predicate of this sentence regardless of the actual instantiation of its subject, then it may be handled as having the form:

[5’] (∀x)(Wx→Hx)

which is indeed going to be necessarily true in a formal semantics in which we stipulate that the extension of ‘W’ is a part of the extension of ‘H’ in every model, while it may well be the case that the extension of ‘W’ is empty in some models. On the other hand, as in the medieval framework this is not the only available analysis of a universal affirmative proposition, we are not stuck with the truth of such a claim when it is put forth with the force of a statement of fact, neither is the hypothetical analysis going to undermine the validity of the Square of Opposition, which concerns categorical propositions put forth with categorical force, having the form

[5’’] (∀x.Wx)(Hx.) [⇔ (∃x)(Wx)&(∀x)(Wx→Hx)

But more pertinent to our present concern with existence and reference was the second type of answer, according to which even law-like statements could be analyzed as necessarily true categoricals put forth with categorical force, despite the actual “emptiness” of their subjects, while the implication A⇒I could still be regarded as valid.23 The key to the possibility of this position is assigning the subject terms of such statements a different type of reference, commonly called natural supposition by medieval logicians.

Although natural supposition has an interesting early history24, in this brief exposition I am going to rely on the account of Jean Buridan, who explicitly defends this type of reference (against

“When I say ‘Every man is an animal’, here an habitual ‘is’ is predicated. And insofar as it is necessary, this proposition is equivalent to the following conditional ‘If it is a man, then it is an animal’.” William of Sherwood: Introductiones in Logicam, ed. M. Grabmann, Sitzungsberichte der Bayerischen Akademie der Wissenschaften, (10)1937, p. 83. (For a text to the same effect from Garland the Computist (11th century) see D. P. Henry, That Most Subtle Question, Manchester, 1984, pp. 85-86. Cf. also L. M. de Rijk (ed.), Logica Modernorum, Assen, 1967, II-2, p.730.) I think it is instructive to quote here at some length from Ockham’s criticism of this approach: “... supposing that there are no donkeys they reject this syllogism: ‘Every animal is a man; every donkey is an animal, so every donkey is a man’, saying that ‘is’ equivocates here, for in the major premise ‘is’ is taken as the operation of being, in the minor premise, however, ‘is’ is taken as the ‘is’ of habitude, or consequence, as in: ‘if it is white, then it is colored’. And this is entirely absurd, for this leads to the destruction of all syllogistic forms. For whenever I liked, I would say that ‘is’ equivocates in the propositions and reject at caprice any syllogism on account of this equivocation. Similarly, just as a syllogism is valid with any terms, so it is valid however the things may change […] So even if […] all donkeys were destroyed, this would be a valid syllogism. […] And so such distinctions as ‘is’ is either the operation of being or it is the ‘is’ of consequence are frivolous and are posited by those who are unable to distinguish between a categorical and a hypothetical proposition. So these propositions are to be distinguished: ‘A donkey is an animal’ and ‘If it is a donkey, then it is an animal’, because the one is categorical and the other is conditional or hypothetical; and they are not equivalent for the one may be true the other being false. As this is now false: ‘God not-creating is God’, but this conditional is true: ‘If this is God not-creating, then this is God’.” W. Ockham: Summa Logicae, St. Bonaventure N.Y., 1974, pp. 263-264. (See the whole chapter.) 23 Cf. n. 9. above. 24 L. M. de Rijk: “The Development of Suppositio Naturalis in Mediaeval Logic”, Vivarium, 9 (1971), pp. 71-107.

31

those of his contemporaries who did not admit it) on the basis of what he recognizes as its use in science:25

“Furthermore, fourthly, also the demonstrative sciences use this sort of supposition. For if we say in [a commentary on] the Meteorologica that every thunder is a sound made in the clouds, or that every rainbow is a reflection or refraction of light, then we do not intend to say these things only concerning the present ones; indeed, even if there were no thunder or rainbow at the present time, we would nevertheless state the same things. And if a geometer has a demonstration that every triangle has three angles equal to two right angles, we should not imagine that thereby he would have knowledge only of those triangles that actually exist, on the contrary, if this habitual knowledge of his remains for three years, and meanwhile many triangles are generated, he will have knowledge of those as well as of the others without a new demonstration. Aristotle explicitly states this in bk. 1. of the Posterior Analytics: ‘I call ‘[true] for all’ [‘de omni’] that which is not such that it holds for some and does not hold for another, nor such that sometimes it holds and sometimes it does not.’ [73a30-35] And he clarifies this by an example, saying: ‘just as ‘animal’ [is true] for all men, because if it is true to call someone a man, then it is true to call him an animal, and if the one is true now, then so is the other’. He also confirms this by a further evidence [signum], saying: ‘an evidence [signum] for this is that when we object to such a [true]-for-all-claim then we inquire whether it does not hold for some or sometimes’. Nevertheless, we can correctly say that in this case [putting forth] such a locution with this intention is not in accord with its proper meaning [de proprietate sermonis], but [it is put forth] for the sake of brevity. For when we want to speak demonstratively, and we say that every thunder is a sound made in the clouds, or that every lunar eclipse is due to the interposition of the Earth between the Sun and the Moon, these propositions would not be true in virtue of their proper meaning [de proprietate sermonis], for the verb ‘is’ in virtue of its proper meaning was imposed to signify only the present time, while there may be no thunder or lunar eclipse at the present time. And so such propositions are put forward for the sake of brevity in place of ‘Every thunder, whenever it is, was, or will be is, was, or will be a sound made in the clouds’ and ‘Every lunar eclipse, whenever it is, was, or will be, is, was, or will be due to the interposition of the Earth between the Sun and the Moon’. Such propositions therefore are not to be denied, since they are true as they are put forward, but they would be false if they were put forward and taken in their proper sense [ad sensum proprium]. And since sophists want to take propositions only in their proper sense [secundum sensus proprios], they do not use such supposition in the manner described in this case.”

In order to be able to appreciate Buridan’s point we have to know that supposition, or reference, was commonly regarded by medieval logicians as a property of terms only in the context of a proposition26 Accordingly, on this view, the same term may refer in different ways to different things in different propositional contexts, or it may even refer to some thing(s) in one proposition, while it may refer to nothing at all in another. For a medieval logician it would not make much sense to say that the name ‘Bill Clinton’ has a referent while the term ‘King of France’27 does not, without specifying a propositional context. For example, we can say that in the sentence ‘Bill Clinton is the President of the US’ the name ‘Bill Clinton’ refers to Bill Clinton, if this sentence is uttered in 1994, while the same name will refer to nothing, if the same sentence will be uttered, say, in 2194, when Clinton will not exist, and, similarly, it would have referred to nothing if the same sentence had been uttered in 1794, when Clinton did not exist.

25 Buridan: Tractatus de Suppositionibus, c. 3. 4. (Cf. P. King: Jean Buridan’s Logic: The Treatise on Supposition, The Treatise on Consequences, D. Reidel Publishing Company, Dordrecht Holland, 1985, pp. 126-127.) 26 Although Peter of Spain, e.g., regards natural supposition as the kind of supposition a term has absolutely [per se], apparently even outside of the context of a proposition. See: Peter of Spain: Tractatus, ed. L. M. de Rijk, Van Gorcum, Assen, 1972, p. 81. 27 Note the omission of the definite article here, which on this approach is just one of the possible determiners one can add to the common term ‘King of France’.

32

(To be sure, this case is not to be confused with the case when the name does have a referent, but the sentence is simply false, as the same sentence uttered, say, in 1990.) But, of course, in the sentence ‘Bill Clinton was the President of the US’, which will be true if uttered in 2194, the same name will refer to the same person, Bill Clinton, even if at the time of the utterance of this sentence the person referred to will not exist, and similarly in ‘Bill Clinton will be the President of the US’, which would have been a true sentence already in 1794, if it had been uttered then, by a soothsayer for example. Again, in ‘The King of France is bald’ the term ‘King of France’ actually refers to nothing, whence the sentence uttered now, in 1994, is false. But if the same sentence had been uttered in 844, for example, then it would have been true, as its subject would have referred to Charles the Bald, then King of France. Also, now we can truly say: ‘A King of France was bald’, precisely because France once had a bald king, who, among other past Kings of France, is referred to by the subject term of this sentence.28

As can be seen, on this approach both singular and common terms are treated as referring phrases the actual reference of which is determined (besides their meaning, the speaker’s intention, and relevant circumstances of their formation and/or interpretation) by the propositional context in which they occur. Most notably, general terms in the context of a past tense proposition can refer to things to which they applied in the past (if there were any such things), which may be things that actually do not exist but existed, and similarly, in a future tense context these terms can refer to things to which they will apply in the future (if there will be any such things), which may be things that do not exist now but will exist in the future. As medieval logicians put it, in these contexts the subject terms get ampliated (ampliantur), i.e., their range of reference extends beyond the domain of actually existing entities, and this is why affirmative categoricals about the past or the future may be true even if their subject terms are actually empty, i.e., even if in a present tense affirmation these subject terms apply to nothing. So, for example, the sentence ‘Every dinosaur was a reptile’ is true, because its subject term refers to things that either are or were dinosaurs, all of which were reptiles, even if there is nothing in the world now of which one could truly affirm that it is a dinosaur.29

But such ampliative contexts were recognized also in present tense sentences. For example, in ‘Some man is dead’ the subject term has to refer to past men, i.e., things that were men, for certainly no actually existing human being is dead (zombies do not count as humans). In the

28 Of course, we cannot truly say: ‘The King of France was bald’, but not because the common subject term ‘King of France’ (not: ‘the King of France’!) refers to nothing, but because there were many Kings of France, while a categorical determined by a definite article is true only if its subject refers only to one thing. But for the same reason it is true to say: ‘The King of France in 844 was bald’. 29 Note in this analysis the disjunctive subject term. The present tense disjunct is required to take care of cases like ‘A white thing was black’. This proposition certainly cannot be analyzed as ‘A thing that was white was black’, for in a possible situation (in casu possibili, as Buridan would put it) the one may be true and the other false; namely, if everything in the world that is now white has never been white before, but some of them were black earlier. For more on this see Buridan’s Sophismata, cc. 4-5. (John Buridan: Sophisms on Meaning and Truth, tr. intr. by T. K. Scott, Appleton-Cenntury-Crofts, New York, 1966, pp. 109-121, 144-157.) It is also worth mentioning here that medieval logicians, like Ockham, who rejected the theory of ampliation also recognized reference to non-actual, past, future, or even merely possible entities. Their rejection was not based on any qualms about this issue, but on their analysis of such propositions as being systematically ambiguous. Accordingly, they distinguished between two senses of such propositions, one in which the subject is taken to refer to what it actually applies to, and another in which it is taken to refer only to what it did/will/can apply, as the context requires. Cf.: G. Priest-S. Read: “Ockham’s Rejection of Ampliation”, Mind 90(1981), pp. 274-279. Cf. also: W. Ockham: Summa Logicae, St. Bonaventure N.Y., 1974, P. I. c. 72, pp. 215-216.

33

same way, in ‘Every dinosaur is extinct’, ‘dinosaur’ has to refer to things that were dinosaurs, despite the fact that the copula of the sentence is in the present tense. Indeed, we can say that the theory of ampliation was designed to cover all contexts which modern logicians would recognize as intensional contexts in general. So, for example, modal and intentional verbs and their participles, as well as related adjectives and adverbs were also regarded as ampliative, and so terms were also regarded as ampliated in their contexts even in present tense sentences.

But then we can see why in this analysis of the categoricals acceptance of the subalternation A⇒I does not necessarily mean attributing existential import, properly speaking, to universal affirmatives. For if their subject terms are ampliated, then neither the A nor the I propositions imply the actual existence of their referents, or supposita.

In view of these considerations, however, we can easily see why the actual emptiness of their subject terms will not falsify law-like categorical statements, whose subject terms were interpreted as having natural supposition, i.e., a type of reference ampliated to all times (or perhaps even to all [logical] possibilities), on account of the intention with which they were put forward, i.e., as concerning everything to which their subjects does or did or will [or perhaps only can or could]30 apply. And this gives us the answer to the second objection above.

Now, clearly, if we construe general terms in their referring function as restricted variables, along the lines sketched above, then accepting ampliated terms, i.e., terms referring to things that were, will be, or can be, but which actually do not exist means that here we have an analysis in which variables are allowed to range over nonexistents. So, again, this medieval analysis takes us beyond the limitations of classical quantification theory, into the realm of free logics, where we may distinguish between existent and non-existent values of our variables, if we wish to do so.31

Technically, the simplest way to construct a formal semantics of ampliated terms is to combine the well-known techniques of possible worlds or intensional semantics with the idea of using restricted variables as representing general terms in their referring function. Instead of going into the technical details here, however, let me now turn to a brief, concluding discussion of the philosophical significance of the “old directions” we could get from medieval logic.

5. Conclusion: Reference and Intentionality

The foregoing sketch of some of the main medieval ideas concerning reference and existential commitment is far from being a complete account of all the complexities of (the many varieties of) the theory of supposition. Still, I think even this sketchy account provides us with enough to reflect on the broader significance of the medieval approach. In view of the above discussion we can regard this approach as yielding a comprehensive and highly flexible system of many-sorted quantification in which the ranges of variables are determined differently in different types of propositional contexts.

Now this approach, aside from having the obvious advantage of “automatically” leading to a generalized quantification theory, also has the philosophical advantage that it is not going to

30 In medieval works natural supposition sometimes is interpreted as covering all times, sometimes as even all, perhaps absolutely unrealized, logical possibilities. Hence the need for the bracketed addition. 31 On this point see again Lambert: Meinong and the Principle of Independence, Cambridge University Press, Cambridge, 1984, pp. 110-112.

34

leave us wondering about the “weird features” of “non-actualized entities” causing so much headache to philosophers exploring, gardening or uprooting (depending on their temper) the Meinongian Jungle. For on this approach we can refer to non-existents only in contexts in which no actual properties can be attributed to them. So when we are talking about them, we are not going to get the false impression of exploring a different realm of entities, where just anything can happen, well, even things that cannot happen. For, in the first place, by contradictory terms, such as ‘round square’, we cannot possibly refer to anything even in ampliative contexts, whence not only ‘A round square is round’ will be false, but also the modal propositions with ampliated terms: ‘A round square is necessarily round’ and ‘A round square could be round’. Again, we are not going to be wondering about the mysteriously missing further properties of an “incomplete” merely possible entity, like a winged horse, for we are going to concede in the beginning that a winged horse is not winged, indeed, it is not even a horse, for it is nothing at all. Still, we might concede the truth of, say, ‘A winged horse can be pink’, in which we refer to something that can be a winged horse, which, after all, can be pink.

At this point, however, someone with a strong “taste for desert landscapes” might immediately decry this approach on the basis that despite its apparent capability of resolving many of the inconveniences of talking about entities in the Meinongian Jungle it leaves them right where they are and does nothing for eliminating them. For although now we cannot say anything truly about winged horses in a non-ampliative context, by conceding that we can refer to something that can be a winged horse we smuggle back winged horses into our universe of discourse. So the medieval universe of discourse is as overpopulated as Meinong’s, and so the medieval approach does not provide any more peace of mind to a genuine nominalist than the Meinongian Jungle does.

Well, since it is hard to imagine any “more genuine” nominalists than, say, Ockham, Buridan, or Albert of Saxony, who did not have any qualms about referring to nonexistents in the appropriate contexts (while they would certainly not tolerate the “slum” of abstract entities endorsed by their contemporary counterparts in set theory), it is perhaps not entirely unjustified here to look at the bottom of the worries of our contemporary “nominalists”.

In his comprehensive analysis of these worries, William Lycan characterizes the basis for the incapability of our “nominalists” to stomach Meinong’s Jungle in the following manner:

“In particular, what I am implicitly demanding is a model-theoretic semantics, done entirely in terms of actual objects and their properties—for what else is there really? I am allowing the Meinongian his funny operator [an “existential” quantifier ranging over possibila—G. K.] only on the condition that he explain it to me in non-Meinongian terms. To this the Meinongian may reply that he will be happy to give us a model-theoretic semantics—one whose domains include nonactual objects, true enough, but that is all right, since there are nonactual objects after all. And so it seems we have arrived at another impasse.”32

In a way, the issue is trivial. The only difference between the Meinongian and the anti-Meinongian seems to be that while the anti-Meinongian regards the notion of being, existence, reality, actuality, etc., whichever words we use, as co-extensive with the range of quantification (whence he is more than willing to call a particular—as opposed to a universal or a singular—proposition existentially quantified), the Meinongian, on the contrary, views the notion of

32 William Lycan: “The Trouble with Possible Worlds”, in: J. L. Garfield-M. Kiteley: The Essential Readings in Modern Semantics, Paragon Issues in Philosophy, Paragon House, New York, 1991, pp. 503-539. p. 511.

35

actuality, or real existence, etc., as covering only a part of the range of quantification, and hence he is prepared to make distinctions between items within that range that are actual, really existing, etc., and items that are not such, but which, still, somehow, there are. However, what seems to be the common assumption of both parties, in my view not shared by the medievals (at least the ones I am discussing here—see n. 33. below), is that for quantification and reference things somehow already have to be there, they must be somehow given in order to be referred to or to be quantified over. The only disagreement seems to be that when we come across an apparent instance of reference to or quantification over something that is agreed on all hands not to exist (really and genuinely), then the Meinongian happily admits this item in his bloated universe of discourse, i.e., within the range of his quantifiers, although outside the domain of real existents, while his opponent would try everything within his ken by which he could analyze away what he regards as an instance of a merely apparent reference to or quantification over something that does not exist, in terms of phrases in which his quantifiers will range only over admittedly existing things.

Now the medieval approach sketched here certainly has a greater superficial resemblance to the Meinongian than to the anti-Meinongian position. (And this is of course not without historical reasons. In fact, I suspect that Meinong himself was much closer to the medieval conception than contemporary American “Meinongians”, but I will not pursue this point here. My basis of comparison here are the “relentless Meinongians”, characterized as such by Lycan in his above-mentioned paper.) Nevertheless, the fundamental difference between both antagonistic modern positions and the medieval approach seems to be that from the point of view of the medieval approach discussed here it is just sheer nonsense to talk about non-actual entities somehow being out there, awaiting our reference to and quantification over them. Non-actual entities, mere possibilia, are literally nothing for this approach.33 But then how can we say we can refer to them (in the appropriate, ampliative contexts, of course)?

The answer is that ‘refer’ (‘supponit’), just as other intentional verbs, also creates an ampliative context, wherefore a term contsrued with it will also be ampliated to things that possibly do not exist, but which did, will, or can exist. For referring is not something that words, i.e., inscriptions or utterances do per se, but it is something that we humans do by means of our words. For words mean and refer to what we mean and refer to by them.34 And we mean and refer to the things we

33 Well, perhaps, Duns Scotus’ conception of possibility provides an interesting medieval counterinstance to what I say here. But of course his theological reasons for this conception were (possible as well as actual) worlds apart from the modern secular belief in the sanctity of existential quantification. Cf.: Opus Oxoniense I. d.36, n.1. As in many other matters, Henry of Ghent seems to have had some influence on Scotus’ thought also on this point. For a thorough discussion of the issue and the possible impact of the medieval discussions on Descartes’ conception of eternal truths see: Timothy J. Cronin: Objective Being in Descartes and in Suarez, Garland Publishing, Inc. New York&London, 1987. esp. Appendix II. and III. pp. 167-207. 34 Cf.: “The third opinion, with which I agree, is that an utterance does not have any proper import [virtus propria] in signifying and suppositing, except from us. So by an agreement of the disputing parties, as in obligational disputes, we can impose on it a new signification, and not use it according to its common signification, and we can also speak metaphorically and ironically, according to a different signification. But we call a locution ‘proper’, when we use it according to the signification commonly and principally given to it, and we call a locution ‘improper’, when we use it otherwise, although we can legitimately use it otherwise. So it is absurd to say that a proposition of an author is false, absolutely speaking, if he puts it forth according to an improper locution, according to which it is true. But we have to say that it is true, because it is put forth according to the sense in which it is true, in conformity with what Aristotle says in book 1. of the Ethics, namely, that locutions are to be taken and understood according to their subject matter. But we should correctly say that the proposition would not be true, if it were put forward and

36

think of. But of course we can think of whatever can be an object of our consciousness, which of course need not be an actually existing thing, as anyone who ever had dreams, memories, fantasies, wishes, expectations, let alone abstract, universal thoughts, can easily attest.

As Buridan put it in his questions-commentary on Aristotle’s De Interpretatione: “… a name signifies what is understood by it when it is put in an expression, for to signify is to give rise to some understanding of a thing [intellectum rei constituere]. But by the name ‘rose’ we understand a rose and by the name ‘roses’ we understand roses. For example, [suppose] last year we, you and I, saw many red roses together. If I ask you: ‘The roses we saw were red, weren’t they?’, then you say: ‘Indeed’. And this you know to be true. But you wouldn’t know this, unless you thought of those roses. Therefore, by the name ‘roses’, when I say ‘We saw roses’, you understand those things that we saw. But we saw red roses. So you think of roses. […] the name ‘rose’ refers to [supponit pro] roses, although nothing is a rose, for according to the above-mentioned case, namely, that last year we saw many red roses, you concede the proposition ‘There were many red roses last year’, and you know that this is true. And since this is an affirmative proposition, it would not be true, unless its subject, which is the name ‘roses’, referred to some thing or some things. But it does not refer to [any] other thing or other things, but roses. […] we should note that we can think of things without any difference of time and think of past or future things as well as present ones. And for this reason we can also impose words to signify without any difference of time. For this is the way names [as opposed to verbs—G. K.] signify. Therefore, by the specific concept of ‘man’ I conceive indifferently all men, present, past and future. And by the name ‘man’ all [men] are signified indifferently, present, past and future [ones alike]. So we truly say that every man who was was an animal, and every man who will be will be an animal. And for this reason it follows that the [verbs] ‘think/understand’ [‘intelligere’], ‘know’, ‘mean/signify’ [‘significare’] and the like, and the participles deriving from them ampliate the terms with which they are construed to refer indifferently to present, past and future and possible [things] which perhaps neither are, nor will be, nor ever were. Therefore, even if no rose exists, I think of a rose, not one that is, but one which was, or will be, or can be. And then, when it is said: the name ‘rose’ signifies something, I concede. And when you say: that [thing] is not, I concede; but it was. If, then, you conclude: therefore, something is nothing, I deny the consequence, for in the major premise the term ‘something’ was ampliated to past and future [things], and in the conclusion it is restricted to present ones.”35

But then, from this point of view, there should be nothing mysterious about objects of reference (and hence of quantification, in appropriate contexts), i.e., objects of human thought, which do not exist. At least, there are no separate ontological mysteries here, other than those involved in the nature and workings of the human mind. But, again, from the point of view of the theory of reference, all we need is the recognition of such, mysterious or not, but certainly familiar, simple taken as a proper locution.” Buridan: Tractatus de Suppositionibus, c. 3. 2. (Cf. P. King: Jean Buridan’s Logic: The Treatise on Supposition, The Treatise on Consequences, D. Reidel Publishing Company, Dordrecht Holland, 1985, pp. 121-122.) 35 Johannes Buridanus: Questiones Longe super Librum Perihermeneias, ed. Ria van der Lecq, Utrecht, 1983, pp.12-14. Cf.: “All verbs, even in the present tense, which of their very nature can concern future, past and possible things as well as present ones such as ‘think’, ‘know’, ‘mean’ and the like ampliate their terms to all times, future, past and present. And what accounts for this is that a thing can be thought of without any difference of time, namely, abstracted from any place and time. And so, when a thing is thought of in this way, then a thing which was, or will be, or can be may be thought of as well as a thing which [actually] is. Therefore, if I have the common concept from which we take this name ‘man’, then I can think indifferently of all men, past, present and future. And this is why these verbs can concern past or future things as well as present ones.” Albert of Saxony: Perutilis Logica, Georg Olms Verlag, Hildesheim-New York, 1974, Tr. 2.Tr.2. c.10. 8a regula. For an earlier example of the same explanation of ampliation see the selection from Lambert of Auxerre’s Logica in: N. Kretzmann-E. Stump (eds.): The Cambridge Translations of Medieval Philosophical Texts, Cambridge University Press, Cambridge, 1988. pp. 104-163, esp. pp. 116-118.

37

facts of human existence that we refer by our words to what we mean by them, and we mean by them things we think of when we use these words in communication, and that we certainly can think of things other than just those that are actually present in our broader or narrower physical environment. Indeed, the recognition of such simple facts about the relationship between human thought and reference will even yield such further useful conceptual tools in semantic theory as Buridan’s distinction between suppositio propria vs. impropria, rediscovered in Kripke’s distinction between linguistic reference vs. speaker’s reference,36 or Buridan’s theory of appellatio rationis for handling the problem of reference in intentional contexts, still awaiting rediscovery by contemporary semanticists.37

In any case, whether the particular answers provided by medieval philosophers to questions of the field are the right ones or not, I hope it is clear even from this sketchy overview that the greatest merit of the medieval approach to these questions in general is its placing the theory of reference in the framework of a comprehensive philosophical theory of mind, language and communication, based on a firm metaphysical view of human nature. If none else, at least this general idea of the medieval approach can certainly be regarded as pointing us in a promising direction also in our contemporary research in the field.

36 For Buridan’s distinction see Buridan: Tractatus de Suppositionibus, c. 3. 1. (Cf. P. King: Jean Buridan’s Logic: The Treatise on Supposition, The Treatise on Consequences, D. Reidel Publishing Company, Dordrecht Holland, 1985, pp. 117-118.) For Kripke’s see S. Kripke: “Speaker's Reference and Semantic Reference”, in: J. L. Garfield-M. Kiteley (eds.): Meaning and Truth: The Essential Readings in Modern Semantics, Paragon Issues in Philosophy, New York: Paragon House, 1991. 37 For a detailed discussion and formal reconstruction of Buridan’s theory see my “‘Debeo tibi equum’: A Reconstruction of Buridan’s Treatment of the Sophisma”, in: S. Read (ed.): Sophisms in Mediaeval Logic and Grammar: Acts of the Ninth European Symposium for Mediaeval Logic and Semantics held at St Andrews, June 1990, Kluwer Academic Publishers, Dordrecht-Boston-London, 1993. pp. 333-347.

38

Appendix: The Syntax and Semantics of a Theory of Ampliation

Syntax

The language AMPL* is defined as follows38:

AMPL*:=<C,P,V,T,F>,

where C:={~,&,=,Q,∃,E,ι,.,α,(,),[,]}, P is a set of parameters, V is a set of proper variables, as opposed to the set of restricted variables, Vres, a subset of T, the set of terms, and F is the set of formulae of AMPL*. P detailed: P:=Pind∪Ppred, where Pind is the set individual parameters, while Ppred is the set of predicate parameters of AMPL*. Note: Ppred∩C:={E,=}. (That is, E, the existence-predicate of AMPL*, is a distinguished predicate in the same way as identity is.) Q is a “generalized” quantifier, i.e., one that may represent various different natural language determiners depending on its actual intended interpretation. ∃ is the familiar existential quantifier with its usual interpretation. ι is the descriptor, and α is the ampliator of AMPL*, which is used here in place of the familiar tense operators as well as the possibility operator (the intended intuitive interpretation may be indicated by subscripts to α).

The sets of terms and formulae of AMPL* are defined by the following simultaneous recursive definition:

(1) If a∈Pind, then a∈T (2) If x∈V, then x∈Var, where Var:=V∪Vres (3) If x∈V and A∈F, then ‘x.A’∈Vres (4) If t1,...,tn∈T and Pn∈Ppred, then ‘Pn(t1)…(tn)’∈F, ‘[~Pn](t1)…(tn)’∈F, ‘E(ti)’∈F and

‘(ti=tj)’∈F (5) If A,B∈F and v∈Var, then ‘~(A)’∈F, ‘α(A)’∈F, ‘(Qv)(A)’∈F, ‘(∃v)(A)’∈F, ‘(ιv)(A)’∈F

and ‘(A&B)’∈F

For the sake of convenience we may apply the following abbreviations:

(Abbr1) The matrix of a restricted variable may be omitted in all of its occurrences following its first occurrence in a formula, provided different restricted variables have different operator variables.

(Abbr2) Further connectives are to be regarded as abbreviations of their usual definients. (Abbr3) When from their omission no confusion arises parentheses may be omitted.

Semantics

The definition of a model for AMPL* is the following:

M:=<W,S,as,D,R,0>,

38 The system presented here is a slightly modified version of the system AMPL, presented in Essay 4. of my Ars Artium. The proof of metatheorem (EQ) and the illustrations of its significance are taken over with slight modifications from the same essay.

39

where W and S are nonempty sets, as is a distinguished element of S, D is a function from S to the set of all subsets of W, i.e., if s∈S, then D(s)⊆W, R is a function assigning semantic values to the parameters of AMPL* and 0 is the zero-entity, the semantic value of empty terms, which falls outside W, i.e., 0∉W.

Intuitively, W is the universe of discourse of M, S is a set of situations, or states of affairs, which may be thought of as past, present or possible with respect to the actual situation as (in accordance with the intended intuitive interpretation of α), and D is the domain assignment of situations, so that D(s) is the domain of the situation s.

R is defined by the following clauses:

(R1) If a∈Pind, then R(a)(s)∈W (R2) If Pn∈Ppred, then R(Pn)(s)⊆Wn

(R3) R(E)(s)=W

Let us define further the extension of a predicate Pn in the situation s, Exts(Pn), in the following manner: Exts(Pn):=R(Pn)(s)∩D(s)n. (Whence, Exts(E)=D(s).)

An assignment in the situation s, fs (a function from T∪F to W∪{1,0})39, is defined in the following manner (for the sake of simplicity, henceforth I omit quasi-quotes):

(fs1) If x∈V, then fs(x)∈W (fs2) If a∈Pind, then fs(a)=R(a)(s) (fs3) If v.A∈Vres, then (i) fs(v.A)=fs(v), if fs(A)=1 (ii) fs(v.A)=0 otherwise (fs4) fs(Pn(t1)…(tn))=1 iff <fs(t1),…,fs(tn)>∈Exts(Pn) (fs5) fs([~Pn](t1)…(tn))=1 iff <fs(t1),…,fs(tn)>∈D(s)-Exts(Pn) (fs6) fs((t1=t2))=1 iff fs(t1)=fs(t2)∈D(s) (fs7) fs(~(A))=1 iff fs(A)=0 (fs8) fs((A&B))=1 iff fs(A)=fs(B)=1 (fs9) fs((∃v)(A))=1 iff for some u∈Rg(v)(fs), fs[v:u](A)=1; where the range of v in respect of fs,

Rg(v)(fs), is defined: Rg(v)(fs)={u∈W: for some assignment gs differing from fs at most in the value assigned to v, gs(v)=u}, if this set is not empty, otherwise Rg(v)(fs)={0}; and fs[v:u] is the same as fs except that it assigns u to v (i.e., fs[v:u](w)=fs(w), if v≠w, otherwise fs[v:u](w)=u).

(fs10) fs((ιv)(A))=1 iff for the u∈Rg(v)(fs), fs[v:u](A)=1, i.e., iff there is exactly one u∈Rg(v)(fs), and u is such that fs[v:u](A)=1

(fsQ) fs((Qv)(A))=1 iff for Q’u∈Rg(v)(fs), fs[v:u](A)=1, where Q’ holds the place of any English determiner that is intended to be represented by Q

(fs11) fs(α(A))=1 iff for some s’∈S, fs’(A)=1 (fs12) fs(A)=1 iff fs(A)≠0.

Truth in a model M is defined as follows:

(T) |A|M=T iff for some fas, fas(A)=1. 39 Notice that 0 serves as the semantic value of empty terms as well as the semantic value of false formulae. This is a mere technical device with no philosophical significance attached to it.

40

(That is to say, A is true in M, iff for some assignment in the actual situation, A is true according to, or is satisfied by, that assignment.)

As usual, a formula is satisfiable if there is a model in which it is true, valid, if its negation is not satisfiable, and an inference is valid, if the conjunction of the premises with the negation of the conclusion is not satisfiable.

In this system we can prove the following metatheorem:

(EQ) If v∈V and A∈F, then for every model M,

|(∃v)(A)|M=|E(v.A)|M iff EXT(v,M,as)(A)=∅ or EXT(v,M,as)(A)∩D(as)≠∅

where EXT(v,M,as)(A), the extension of A in respect of v in M in the actual situation, is defined as follows:

EXT(v,M,as)(A):={u∈W: for some fas, fas[v:u](A)=1}.

Proof

To simplify the proof I first prove two lemmas.

Lemma 1.

|(∃v)(A)|M=T iff EXT(v,M,as)(A)≠∅

Proof of Lemma 1.

Suppose EXT(v,M,as)(A)≠∅. Then for some fas, and for some u∈W, i.e., for some u∈Rgfas(v)—since for any v∈V and for any fs, Rg(v)(fs)=W—, fas[v:u](A)=1, and so, |(∃v)(A)|M=T; and conversely. Q.e.d.

Lemma 2.

|E(v.A)|M=T iff EXT(v,M,as)(A)∩D(as)≠∅

Proof of Lemma 2.

Suppose EXT(v,M,as)(A)∩D(as)≠∅. Then for some fas, and for some u∈Rgfas(v)∩D(as), fas[v:u](A)=1, and so, fas(v.A)=u; whence for some fas, fas(v.A)∈D(as)=R(E)(as), that is, |E(v.A)|M=T; and conversely. Q.e.d.

Proof of metatheorem (EQ)

Suppose that (1) EXT(v,M,as)(A)≠∅ and (2) EXT(v,M,as)(A)∩D(as)=∅.

Then, by (1) and Lemma 1, |(∃v)(A)|M=T, while from (2) and Lemma 2 it follows that |E(v.A)|M≠T.

On the other hand, suppose that (1) EXT(v,M,as)(A)=∅ or (2) EXT(v,M,as)(A)∩D(as)≠∅.

Then, from (1) by Lemma 1 it follows that |(∃v)(A)|M≠T. From (1) it also follows that EXT(v,M,as)(A)∩D(as)=∅; whence, by Lemma 2, it follows that |E(v.A)|M≠T. But from (2) and Lemma 2 it follows that |E(v.A)|M=T, while from (2) it also follows that EXT(v,M,as)(A)≠∅, whence also |(∃v)(A)|M=T. And this completes the proof.

41

The significance of this metatheorem is that it shows the close connection, but without blurring the distinction, between an existential statement, and an existential, or, perhaps better to say, particular quantification.

What metatheorem (EQ) states is that if the actual extension, EXT(v,M,as)(A), of the open sentence involved in the quantification and in the restricted variable of the existential statement is not ampliated to non-actual individuals, then these two forms of statement are equivalent, but if it is ampliated to non-actual individuals and does not contain actual ones, then they are not equivalent. For example, in virtue of metatheorem (EQ) the following formulae are equivalent:

[6’] (∃x)(Cx)

[7’] E(x.Cx) [⇔ (∃x.Cx)E(x.)

And this is how it should be. Clearly, the sentence

[6] Something is a centaur

is equivalent to

[7] A centaur exists [⇔ Some[thing that is a] centaur exists

This is why we are entitled to use the types of statements represented by (6’) and (7’) interchangeably.

But let us take the following two sentences:

[8] Something is destroyed40

[9] Something that is destroyed exists

These are clearly not equivalent. For if we define ‘is destroyed’ as ‘existed and does not exist’ then we get the true

[10] Something existed and does not exist

[10’] (∃x)(αP(Ex)&~(Ex))

and the false, indeed, inconsistent

[11] Something that existed and does not exist exists [⇔ A thing that existed … etc.

[11’] (∃x.αP(Ex)&~(Ex))(Ex.) [⇔ E(x.αP(Ex)&~(Ex))

And this is why we cannot use [8] and [9] interchangeably.

40 In this sentence the word ‘Something’ is to be thought of as analyzable into ‘Some thing’ only if we regard the term ‘thing’ in this analysis as ampliated to past things, and which, therefore, could be formalized as: (∃x.αP(x=x))(αP(Ex.)&~(Ex.)). In fact, it would be much more in line with the medieval conception to regard ‘something’ and ‘everything’ as always analyzable into ‘some thing’ and ‘every thing’. Formally, this could be represented by allowing only restricted variables to be bound by the quantifiers. Proper variables, on the other hand, then would have to be regarded as the formal counterparts of demonstrative pronouns, while their value-assignments might represent acts of pointing at things, at least in thought. For this point see Buridan: Tractatus de Suppositionibus, c. 1. 2. (Cf. P. King: Jean Buridan’s Logic: The Treatise on Supposition, The Treatise on Consequences, D. Reidel Publishing Company, Dordrecht Holland, 1985, p. 88.)

42

Latin as a formal language: Outlines of a Buridanian Semantics

Introduction

Originally, in this paper I wished to present a complete formal semantic system constructed for a fragment of Latin in line with the logico-semantic tenets of Jean Buridan. By the presentation of this semantic system I hoped to show that Buridan’s semantic ideas, if given the appropriate technical formulations, can provide us with a genuine alternative way of construing the relationships between language, thought and reality, worthy of our serious consideration when thinking of matters of semantics. (Which explains the intentionally provocative title.1) Though I still believe that the task is after all not impossible, work on the technical details of this project convinced me that it cannot be properly completed within the confines of a single research paper. The intuitively quite simple and transparent ideas of Buridan’s semantic theory, when one tries to convert them into strict syntactic and model theoretical formulations, turn out to “branch” into several, rather complicated formal clauses, resulting in an extremely complex, unperspicuous system.

This fact, however, in itself gives rise to a number of interesting questions. Are these complications inevitable? Are they rooted in the difference between Buridan’s mediaeval and our modern standards of what a complete semantic theory should look like? Or do they represent rather the inherent complexity of natural, as opposed to formal languages? Or do they, perhaps, have something to do with Buridan’s particularistic approach to logic in general, and his explicit admission of an infinity of first principles?2

These and similar questions will crop up inevitably even after the subsequent “rudimentary” presentation, reflection on which, I hope, may promote our understanding not only of Buridan’s semantic ideas, but perhaps also of the nature of the semantic enterprise in general.

I begin the discussion by presenting the syntactic construction of a rather restricted, but philosophically interesting fragment of Latin. In contrast with Montague’s approach, the semantic theory will be defined for this fragment, without the use of a formal language mediating between natural language sentences and their interpretation. Syntactic ambiguities will be taken care of by analyses supplied by the syntactic construction. The semantic theory, however, will not be built directly on the syntactic construction, because of Buridan’s peculiar theory of meaning in terms of a mental language. It is notably at this point that the unwieldy complexity of formulations will raise its ugly head, so, by way of a compromise, I will supply only an incomplete characterization of Buridan’s “Mentalese” in a model theoretical framework. On this incomplete basis I will be able only to indicate how further treatment of the most important properties of terms: signification, connotation, supposition, appellation and ampliation, and the definition of truth and consequence would look in a complete system. I shall close my discussion

1 The allusion in the title is to Richard Montague’s “English as a Formal Language”, in: R. Montague: Formal Philosophy, Yale University Press, New Haven-London, 1974. 2 “(1) Non autem est unicum principium primum et indemonstrabile, sed sunt plura. (2) Immo non sunt conclusiones demonstrabiles multo plures quam principia indemonstrabilia.(3) Ideo infinita sunt talia principia, quia infinitae sunt conclusiones demonstrabiles.” Johannis Buridani Lectura de Summa Logicae (henceforth: SL), unpublished edition by H. Hubien. Tracatus Octavus: De Demonstrationibus, c.5, 2. I am indebted to Professor Hubien for authorizing me to use his invaluable edition, and to Stephen Read for actually supplying me with Professor Hubien’s text.

43

with some illustrations of the workings of the system, reflecting on its philosophical and methodological implications.

Syntax

Since the primary purpose of a logical semantic theory is to define logical consequence in terms of the truth values of propositions in different interpretations, the corresponding syntactic theory is primarily concerned with the formation rules of propositions, determining the ways propositions are built up from their components.

In modern logical systems a distinction is usually drawn between atomic and molecular formulae (i.e., strings of signs representing natural language sentences expressing propositions). Atomic formulae are formulae that are not made up from other formulae, while molecular formulae are those which are made up from other formulae by means of logical connectives that take formulae in their arguments to produce further formulae.

In Buridan’s syntactic theory a somewhat similar distinction can be found between categorical and hypothetical propositions. Categorical propositions do not contain other propositions as their components, while hypothetical propositions are those formed from other propositions by means of logical connectives.3

However, despite this analogy, Buridan’s categoricals are by no means syntactically as simple as the atomic formulae of the modern theories. Categorical propositions consist of a copula, a subject and a predicate term, possibly determined by signa quantitatis, that is, determiners. Obvious counterexamples to this “canonical form”, containing verbs as their predicates, are explained away in Buridan’s theory by resolving the verb into copula and participle.4 Accordingly, atomic formulae of standard quantification theory containing a relational predicate parameter correspond to categoricals with a complex term having one or more parts in an oblique case. For example, the sentence: “Plato debet Socrati Brunellum” in its canonical form would look like: “Plato est debens Socrati Brunellum”, where the subject, ‘Plato’, is joined by the copula, ‘est’, to the complex term “debens Socrati Brunellum”.

As this example also shows, the potential complexity of a categorical proposition is due to the potential complexity of its terms, which, linguistically, can be just any noun-phrases that may occur in subject or predicate positions: singular or common nouns (with or without determiners),

3 Which, however, does not mean that a hypothetical proposition actually contains categorical propositions as its parts. As Buridan explains: “Videtur ergo mihi quod quando dicitur “propositio hypothetica est quae habet duas propositiones categoricas”, hoc, proprie loquendo, non est verum, sed ad istum sensum quod propositio hypothetica continet duo praedicata et duo subjecta et duas copulas, et quod utrumque illorum praedicatorum mediante una illarum copularum dicitur de uno illorum subjectorum; sed congregatum ex uno praedicato et uno subjecto et sua copula non est una propositio, sed est pars unius propositionis, licet talis vox, si esset separatim sumpta, esset bene una categorica.” SL, Tractatus primus: De Propositionibus, c.3, 2. 4 ... notandum est ... quod verbum non est praedicatum proprie loquendo, sed est copula praedicati cum subjecto vel implicans in se simul copulam et praedicatum. Nam hoc verbum ‘est’ tertium adjacens est copula et quod sequitur est praedicatum. Sed hoc verbum ‘est’ secundum adjacens, ut cum dico ‘homo est’, vel etiam quodlibet aliud verbum, implicat in se copulam cum praedicato vel cum parte principaliori praedicati; ideo ad explicandum subjectum, praedicatum et copulam, tale verbum debet resolvi in hoc verbum ‘est’ tertium adjacens, si propositio sit de inesse et de praesenti, et in participium illius verbi, ut ‘homo currit’ id est ‘homo est currens’, similiter ‘homo est’ id est ‘homo est ens’. SL, Tractatus primus: De Propositionibus, c.3, 2.

44

pronouns, adjectives, participles,5 common nouns determined by adjectives, by possessives (i.e., possessive pronouns or terms in the genitive case), by participles (along with their oblique complements) or by relative clauses, infinitives, accusative with infinitive constructions and complex terms obtained from the above by Boolean operations, i.e., negation, conjunction and disjunction.

In view of this enormous potential complexity, one can easily see how ill-conceived it is to think of the theory of categoricals as an insignificant, minor fragment of logical theory. Indeed, in order to obtain a tractable theory, in this paper I shall consider only a fragment of Buridan’s theory of categorical propositions.

Accordingly, I will not deal with Buridan’s propositional logic (which, as far as I can judge, would only present the historically-minded reader with just another nil-novi-sub-sole-experience anyway).6

Again, I will not deal with pronouns, the analysis of which is partly related to the logic of hypotheticals, and which form a separate issue in Buridan’s semantics under the heading: de suppositione relativorum.7 I will, however, consider some uses of relative pronouns in forming relative clauses to explain a peculiar property of terms in what modern philosophers would call intensional contexts, namely ampliation.

To fully consider intensional phenomena in Buridan’s semantics we would need tenses. However, to simplify matters, for illustrative purposes in this fragment I will deal only with the present, perfect and future forms of the copula in the third person singular, namely ‘est’, ‘fuit’ and ‘erit’ - the tenses mostly occurring in Buridan’s examples as well.

On the part of the noun phrases in this framework I am also going to leave several possible constructions aside. However, I am going to deal in more detail with complex terms containing one or more oblique terms as their parts. So in the fragment to be constructed here we shall need cases.

On the other hand, due to the special difficulties they present, I am also going to disregard plurals. Consequently, since according to Buridan “subjectum copulatum aequivalet subjecto pluralis numeri in reddendo suppositum verbo”, I shall have to omit conjunctive terms as well.8

5 Adjectives and participles can be subjects only when they are “substantivated in the neuter gender”. Cf. e.g.: “ ... quare omne subjicibile est praedicabile et non e converso. Ad quod potest responderi notando primo quod in hac tota parte nihil intendimus de subjectione vel praedicatione vocum materialiter sumptarum, sed significative. Et tunc dico primo de illis adjectivis non substantivatis in neutro genere quod secundum grammaticum non possunt reddere suppositum verbo, ideo etiam non possunt esse subjecta propositionum, propter defectum congruitatis; sed verbo jam habente suppositum, adjectiva possunt apponi ad designandum quid adjaceat subjecto vel ei pro quo subjectum supponit. Tamen verum est quod adjectivum substantivatum in neutro genere potest esse subjectum, quia resolvitur in substantivum et adjectivum, ut ‘album’ id est ‘res alba’.” SL, Tractatus Quartus: De Suppositionibus, c.2. 2. 6 For excellent presentations and evaluations of Buridan’s propositional logic from a modern point of view see e.g.: Hubien, H.: ‘Logiciens médiévaux et logique d’aujourd’hui’, Revue Philosophique de Louvain, 75, pp. 219-232, 1977 and E.A. Moody: Truth and Consequence in Medieval Logic, Amsterdam, 1957. 7 For some formal treatment of the topic see, however, my “General Terms in Their Referring Function”, in G. Klima: Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1988. 8 “Quia subjectum copulatum aequivalet subjecto pluralis numeri in reddendo suppositum verbo; ideo oportet verbum esse pluralis numeri.” SL Tarctatus Quartus: De Suppositionibus, c.2, 6. For a systematic account of the semantics of conjunctive terms and their relationships with supposition theory, however, see my “Approaching Natural Language via Mediaeval Logic”, in: J. Bernard-J. Kelemen: Zeichen, Denken, Praxis, Institut für Sozio-

45

As we are soon to see, even with so many omissions, a relatively rich, and philosophically interesting fragment of Latin can be constructed. However, since the main purpose of this construction is not to give a description of a significant part of the Latin language, but to illustrate the theoretical power of Buridan’s semantic ideas, we can afford to base this construction on a very limited vocabulary. As a matter of fact, this squares well both with Montague’s method, and with Buridan’s practice in selecting his examples and sophismata.

Vocabulary (VOC)

In the subsequent clauses: g∈{mas, fem, ne}=GENDER and c∈{nom, acc, gen, dat, abl}=CASE, indicating the appropriate gender and case of the lexical item indexed by them. PN (proper nouns):={Socratesmasc, Platomasc, Brunellusmasc, Favellusmasc} CN (common nouns):={homomasc, equusmasc, animalnec, canismasc, visusmasc, albedofec} Adj (adjectives):={caecusgc, albusgc} Prtc (participles):={mortuusgc, vidensgc,acc, debensgc,dat,acc, habensgc,acc, ensgc} Sig (signa quantitatis, determiners):={quidamgc, omnisgc} Conj (conjunctiones):={vel, non} RP (relative pronoun):={quodgc} Cop (copula):={est, fuit, erit} The whole vocabulary of our fragment, then, is the union of the above-defined sets:

VOC:=PN∪CN∪Adj∪Prtc∪Sig∪Conj∪RP∪Cop In an obvious manner, an indexed term stands for just the same term in the appropriate case and gender, e.g., “omnisnenom animalnenom quidammasgen homomasgen vidensnenom quidamfemacc albedofemacc”=“omne animal cuiusdam hominis videns quamdam albedinem”. The case indices of participles after the commas indicate the required cases of their complements, i.e., terms with which they can be construed. Indexed names of sets of expressions will serve to indicate their subsets containing just the appropriate indexed items. For example: Adjnenom={caecusnenom, albusnenom}={caecum, album}. (Correspondingly, indexed metavariables in the subsequent clauses range over terms in the appropriate genders and cases: if n ranges over common nouns, then nmasacc, e.g., ranges over only common nouns of masculine gender in the accusative case.) Brackets in the following clauses indicate that the parts of speech they enclose are optional, i.e., they may or may not be present in forming the appropriate expression. For example, in the clause: if sgc∈Sig and tgc∈CN, then “[sgc] tgc”∈TRMgc, the brackets indicate that the signum s may, but need not be concatenated with a common noun to form a term, and so, e.g. both ‘homo’ and “quidam homo” are terms. (The gender and case indices indicate that e.g. “quemdam hominem” and “quamdam albedinem” would also be terms by this clause. Double quotation marks are used as quasi-quotes, indicating the operation of concatenation. Simple expressions of our fragment are mentioned by enclosing them in single quotation marks.) Bracketed indices of metavariables ranging over participles indicate that these metavariables range both over participles that do and those that do not require complements in specified cases: pmasgen[,c1][,c2], e.g., has as its range of values: {mortui, videntis,acc, debentis,dat,acc, habentis,acc, entis}. The optional occurrence of the appropriate complements in a phrase is, of course, conditioned by the presence of the participle requiring them: such complements occur in a phrase only if the Semiotische Studien, Vienna, 1990.

46

participle requiring them occurs. Generally, bracketed occurrences of a phrase enclosed in the same pair of outer brackets with another expression below are conditioned by the occurrence of the expression with which they are bracketed together. The pairs of sub-strings enclosed by <><> may be replaced by one another (i.e. they may occur also in the reverse order).

Terms (TRM)

(0) If ngc∈PN∪CN, then ngc∈ITRMgc⊂TRMgc (1) If anec∈Adj, then anec∈ITRMnec⊂TRMnec (2) If pnec1[,c2][,c3]∈Prtc, t2c2, t3c3∈TRM and snec1∈Sig, then “<pnec1[,c2][,c3]><[t2c2] [t3c3]>“∈ITRMnec1⊂TRMnec1 and “<snec1 pnec1[,c2][,c3]><[t2c2] [t3c3]>“∈DTRMnec1⊂TRMnec1 (3) If ngc∈PN∪CN, sgc∈Sig and agc∈Adj, then “[non] ngc [non] agc”∈NAgc⊂ITRMgc⊂TRMgc and “sgc [non] ngc [non] agc”∈NAgc⊂DTRMgc⊂TRMgc (4) If ngc∈PN∪CN∪NA.c..c..c..c..c..c.⊂ITRM, tgen∈elemTRMgen and sgc∈Sig, then “<ngc><tgen>“∈NAGgc⊂ITRMgc “<sgc ngc><tgen>“∈DTRMgc (5) If ngc1∈PN∪CN∪NA∪NAG, pgc1[,c2][,c3]∈Prtc, sgc1∈Sig, and t2c2, t3c3∈TRM, then “<ngc1 [non] pgc1[,c2][,c3]><[t2c2] [t3c3]>“∈ITRMgc1⊂TRMgc1 “<sgc1 ngc1 [non] pgc1[,c2][,c3]><[t2c2] [t3c3]>“∈DTRMgc1⊂TRMgc1 (6) If t∈TRM, then “non t”∈TRM, where if t∈ITRM, then also “non t”∈ITRM (7) If tgc∈ITRM and sgc∈Sig, then “sgc tgc”∈TRMgc (8) If t1gnom∈TRM, t2nom∈TRM, cop∈Cop and qgnom∈RP, then “t1gnom qgnom cop t2nom”∈TRMgnom (9) If qnenom∈RP, cop∈Cop and tnom∈TRM, then “qnenom cop tnom”∈ITRMnenom (10) If t1gc, t2gc∈ITRM, then “t1gc vel t2gc”∈ITRMgc

For semantic purposes we shall have to distinguish between categorematic (CAT) and syncategorematic terms (SYNC):

SYNC:=Sig∪Cop∪Conj; CAT:=TRM∪RP∪Adj∪Prtc Again, we shall have to distinguish abstract (ABTR), from concrete (CONCR) terms:

ABTR:={visusmasc, albedofec}; CONCR:=CAT-ABTR

Propositions (PROP)

(11) If t1, t2∈TRMnom and cop∈Cop, then “t1 [non] cop t2”∈PROP

47

(12) If p∈PROP, then “non p”∈PROP

Examples and Discussion

Since the clauses above are rather complicated, I think it is worth providing some examples to illustrate how they are supposed to work. Through these examples we can also assess the adequacy of these rules and the extent of the fragment of Latin they cover.

Clauses (1) and (2) take care of simple as well as complex terms formed with adjectives and participles substantivated in the neuter gender, i.e., in their capacity of forming standalone terms without attaching to nouns as their adjuncts (sicut determinatio ad determinabile). So, e.g., ‘album’ in itself is a term, indeed, an indefinite term (ITRM), i.e., a term not determined to some definite quantity by some signum, by clause (1). Similarly, “videns hominem”, “habentis omnem equum”, or “debentem cuidam homini quemdam equum” are all indefinite terms by clause (2), while they would become definite terms by prefixing them with a signum of the appropriate case and gender as is prescribed by clause (7).

Note here that, for semantic reasons, Buridan himself does not regard signa quantitatis as parts of terms (in particular, of subject terms) of propositions.9 It is quite harmless, however, to treat them in this way in the syntactic theory, and renders much easier the formulation of recursive clauses.

Another feature of these clauses worth noticing is their making complex terms inherit the case and gender of their core-terms. This is important again from the point of view of the recursive applicability of these clauses. This feature of these rules makes their application possible also to 9 Cf.: “Sed de signis affirmativis, ut ‘omnis’, ‘quilibet’, quare non possunt ita bene esse partes subjectorum sicut praedicatorum? Potest dici quod signum distributivum positum a parte praedicati nihil operatur super copulam vel super subjectum, ideo totaliter dicitur pertinere ad praedicatum. Sed positum a parte subjecti operatur super copulam et super praedicatum, confundendo ipsum, licet non distributive, ideo nec ponitur esse pars subjecti nec pars praedicati, sed ponitur tamquam condicio totalis propositionis. Sed tunc videtur difficilius de signo particulari: quia nihil operatur super copulam vel super praedicatum si ponatur a parte subjecti, propter quod videtur quod ita bene deberet poni pars subjecti, sicut esset pars praedicati si poneretur a parte praedicati. Ad hoc possunt dari multae responsiones. Prima est quod signum particulare omnino frustra ponitur in propositione, sive a parte subjecti sive a parte praedicati, prout ista regula concederetur, scilicet quod indefinita et particularis aequipollent gratia formae, quia sic omnino nihil mutatur de summa propter additionem vel subtractionem signi; ideo nec debet reputari pars subjecti nec pars praedicati, nec aliqua condicio propositionis nisi frustratorie apposita. Et ego ostendo quod illud signum particulare, etiam positum a parte praedicati, non sit pars praedicati. Quia istae duae gratia formae aequipollent ‘B est A’ et ‘B est aliquod A’; ideo quaecumque contradicit uni contradicit alteri; modo constat quod ista ‘nullum B est A’ contradicit primae; ergo similiter contradicit secundae, et tamen non contradiceret ei si iste terminus ‘aliquod’ esset pars praedicati, quia jam non essent de eodem subjecto et eodem praedicato, quod tamen requiritur ad contradictionem formalem. Ideo videtur mihi quod talis dictio posita sive in subjecto sive in praedicato non debet dici pars subjecti nec pars praedicati; vel si ponatur esse pars praedicati, ita debet poni pars subjecti, sed tamen pars frustratorie apposita, quia ea ablata nihil mutaretur de summa. Sed alio modo signum particulare ponitur aliquando in propositione, vel etiam signum universale, ad determinandum indefinitam, scilicet signum universale ad designandum quod praedicatum verificatur de subjecto pro omni ejus supposito et particulare ad designandum quod veritas sit pro aliquo et non pro omni, vel saltem quod veritas sit nota pro aliquo et non sit nota pro omni; et propositio indefinita se habet ad hoc indifferenter. Unde sic proprie sumendo signum particulare leges bene ponunt differentiam inter propositionem particularem et indefinitam, et saepius per indefinitam intelligunt universalem, et non particularem. Et isto modo signum universale et particulare non deserviunt ad subjiciendum, sed ad designandum quantitatem propositionis quando ponuntur a parte subjecti.” SL, Tractatus Quartus: De Suppositionibus, c.2, 2.

48

the result of their previous applications. For example, by clauses (1) and (7) “omne album” is a term not only in the nominative, but also in the accusative case. So this term can occur as the complement in the accusative case required by ‘videns’, whence, by clause (2) , “videns omne album” will also be a term.

Indeed, “videns omne album” may itself also be in the accusative case (provided ‘videns’ is in the accusative), whence it may be the complement of ‘videns’ again, and so “videns videns omne album” will also be a term. The same kind of construction can be repeated an unlimited number of times.10

On the other hand, since the case of a complex term depends on the case of its core, if this core is, say, in the dative, as in “videnti videns album”, then this cannot be the complement of ‘videns’ again. It can, however, be the complement of ‘debens’, as in “debens videnti videns album omne videns album” (possibly referring to something that owes everything that sees a white thing to something that sees something that sees a white thing, which may be complicated but after all not impossible).

Clause (2) also allows for different word order, which has semantic significance in Buridan’s theory. As we shall see, for example, “debens Socrati equum” and “equum Socrati debens” need not have the same semantic value.

Note here that by clause (7) we would not be able to obtain e.g. “quemdam equum omne videns” from “quemdam equum videns” obtained by clause (2). So it is the second half of clause (2) that takes care of this possibility, stating that the participle itself may also be determined by a signum even when occurring after its adjunct(s), in which case, however, the resulting term will be determinate (DTRM) to which clause (7) is not applicable.

The subsequent clauses provide for the construction of complex terms with a noun as their core along with several types of possible adjuncts.

In virtue of clause (3) “homo albus”, “equus non caecus”, and the like constructions are indefinite terms, obtained by the concatenation of a noun and an adjective (NA) with the optional interposition of a negation.

Note that in clause (4) the term that, concatenated with the genitive of another term yields a new indefinite term can also be obtained by clause (3). So “equus non caecus cuiusdam hominis” is also a possible result of the application of clause (4).

Again, the clause takes care of semantically relevant variations of word order. As we shall see, “equus omnis hominis” and “omnis hominis equus” may have different semantic values. (The former can refer to a horse only if it is possessed by all men, while in the latter, on one of its possible readings, for every given person some or other of his horses is being referred to, without implying that any horse would belong to all persons.)

Note also that the second part of the clause makes it possible that the core of such a complex term be determinate (DTRM), which is especially relevant when the genitive precedes it, as in: “cuiusdam hominis omnis equus”, which is again semantically different from “omnis equus 10 To be sure, in real Latin, as in any human language, there should probably be some limit on the repeatability of this construction. But this may concern the limited short-term memory capacity of human language users, which may have to do rather with pragmatics than syntax. Anyway, in this paper I shall not consider the theoretical implications of this potential of the syntactic theory presented here.

49

cuiusdam hominis”. (The former concerns all of some man’s horses, while in the latter reference is made to all horses possessed by someone or other.)

By clause (5) we can build further the term obtained above to get, e.g., “equus non caecus cuiusdam hominis videns omnem hominem”. In view of the possibility changing word order, by this clause also “omnem hominem cuiusdam hominis equus non caecus videns” is a term.

In virtue of clause (6) any of the above-mentioned indefinite terms prefixed with a negation are also indefinite terms, while a definite term prefixed with a negation is a definite term.

By clause (7) any indefinite term prefixed with a signum (which itself may also be prefixed with a negation) is a definite term.11

Clauses (8) and (9) take care of complex terms formed with relative clauses. Clause (8) treats relative clauses as adjuncts to other terms, as in “omnis equus Socratis qui est album”, while clause (9) treats them as independent terms in their own right, as in “quod est equus Socratis”. Of course, these clauses are also applicable recursively, as in the case of “quod est quod est equus Socratis”, which may be redundant, but is otherwise acceptable.

Note here that these clauses do not provide for constructions like “homo qui est albus”, but do allow constructions like “homo qui est album”. This apparent oddity is introduced only to simplify these clauses, and is after all in good accord with Buridan’s theory of predication, in which a predicate term is supposed to be a referring expression in the same way as a subject term in order to be convertible with it.12

As can be seen, these clauses do not generate relative clauses in oblique cases, like the one in: “homo quem equus est videns”. But since the incorporation of such clauses would be just further complication without much theoretical import, we can disregard them in this fragment. (On the basis of the existing clauses, I think it is quite easy to imagine how they could be handled anyway.)

11 Note here that proper nouns are also included here as possible core-terms, and so the rule allows them to be determined not only by adjuncts, but also by signa, that is, determiners. This would probably not be endorsed by Buridan. Nevertheless, from a semantic point of view their inclusion here is rather harmless (they just provide cases of “vacuous quantification”), and in any case simplifies the formulation of these clauses. 12 Cf.: “Et tunc distinguitur triplex passio, una substantiva, alia adjectiva adjective sumpta et tertia adjectiva in neutro genere substantivata. De primo modo dicimus ‘tempus’ esse passionem ‘motus’ et ‘simitatem’ ‘cavitatis’: nam ultra significationem ‘cavitatis’ ‘simitas’ appellat nasum; est ergo praedicatio passionis de subjecto ‘motus est tempus’ vel ‘cavitas est simitas’. De secundo autem modo, ‘simum’ est passio ‘nasi’ et ‘album’ ‘hominis’, vel ‘lapidis’, vel ‘entis’; et est praedicatio passionis de subjecto dicere ‘nasus est simus’, ‘homo est albus’, vel ‘res est alba’, et cetera. De tertio modo, est praedicatio passionis de subjecto dicere ‘nasus est simum’, ‘homo est album’. In primo autem modo et in tertio convertitur praedicatio passionis de subjecto in praedicationem subjecti de passione, ut ‘cavitas est simitas; ergo simitas est cavitas’, similiter ‘homo est album; ergo album est homo’. Sed in secundo modo non sic fit conversio; dicimus enim ‘nasus est simus’, sed non dicimus ‘simus est nasus’, quia oratio esset incongrua, vel imperfecta, sicut dictum est prius, sed convertendo oportet adjectivum substantivare ut ‘homo est albus; ergo album est homo’. Et ex his statim manifestum est quod passiones de secundo dictorum modorum non sunt per se acceptae diffinibiles diffinitione praedicabili de diffinito significative sumpto, quia non possunt per se subjici in propositione categorica, ut dictum est.” SL, Tractatus Octavus: De Divisionibus, c. 2, 4. In view of this it is probable that Buridan would also have accepted the construction: ‘homo qui est album’, that is, ‘homo qui est quoddam album’.

50

Clause (10) generates disjunctive terms in all cases and genders, the only restriction in this respect being that the disjuncts be of the same case and gender. Its recursive applicability also allows these terms to contain an unlimited number of disjuncts.

Clause (11) takes care of both affirmative and negative propositions including constructions like “homo est album”, or “homo est omne album”, where concerning gender agreement the same considerations apply as in the case of relative clauses above.

Finally clause (12) allows negation to appear also as a prefix to a proposition as a whole, as in “Non non omnis homo est albus”.

A notable general feature of these clauses is that they allow the construction of syntactically ambiguous complex expressions, i.e., expressions that can be obtained from the vocabulary by applying different sets of these rules in different order. Of course, in the semantic theory we shall have to be able to distinguish between these different possible constructions, which shall correspond to different “readings” or senses of these expressions. To distinguish these different constructions, we can assign the syntactic clauses given above characteristic functions, i.e., functions that correspond to the applications of these clauses, taking the input expressions of the clauses as their arguments, and yielding the output expressions as their values:

(F1) F1(pnec1,c2[,c3])(t2c2)[(t3c3)]=“pnec1,c2[,c3] t2c2 [t3c3]” (F2) F2(pnec1,c2[,c3])(t2c2)(t3c3)=“t2c2 [t3c3] pnec1,c2[,c3]” (F3) F3([non] agc)([sgc] [non] ngc)=“[sgc] [non] ngc [non] agc” (F4) F4(tgen)([sgc] ngc)=“[sgc] ngc tgen” (F5) F5(tgen)([sgc] ngc)=“tgen [sgc] ngc” (F6) F6([non] pgc1,c2[,c3])([sgc1] ngc1 )(t2c2)[(t3c3)]=“[sgc1] ngc1 [non] pgc1,c2[,c3] t2c2 [t3c3]” (F7) F7([non] pgc1,c2[,c3])([sgc1] ngc1 )(t2c2)[(t3c3)]=“t2c2 [t3c3] [sgc1] ngc1 [non] pgc1,c2[,c3]” (F8) F8(non)(t)=“non t” (F9) F9(sgc)(tgc)=“sgc tgc” (F10) F10(qgnom)(t1gnom)(cop)(t2nom)=“t1gnom qgnom cop t2nom” (F11) F11(qnenom)(cop)(t2nom)=“qnenom cop t2nom” (F12) F12(vel)(t1gc)(t2gc)=“t1gc vel t2gc” (F13) F13([non] cop)(t1)(t2nom)=“t1 [non] cop t2” (F14) F14(non)(p)=“non p”

Where the metavariables in (F1)-(F2), (F3), (F4)-(F5), (F6)-(F7), (F8)-(F14) are the same as in (2), (3), (4), (5), (6)-(12), respectively.

With the help of these characteristic functions we can supply disambiguated analyses of ambiguous complex expressions of our fragment, in such a manner that these analyses can serve in the semantic theory to distinguish between the different senses of these expressions. Just by way of illustration consider the following two simple examples: “omnis hominis equus”, “non homo vel equus est albus”.

The first of these can be analysed in two different ways: it may be regarded either as a complex term which is formed from a noun and a genitive, determined by a signum, or as a complex term formed from a noun as its core, and a genitive determined by a signum in the genitive case.

/A/ F9(omnis)(hominis equus)

51

/B/ F5(omnis hominis)(equus) Of course both of these can be analysed further as follows:

/A’/ F9(omnis)(F5(hominis)(equus))) /B’/ F5(F9(omnis)(hominis))(equus)) For the second example I give here only the fully expanded analyses, showing how they generate the same ambiguous sentence:

/1/ F14(non)(F13(est)(F12(vel)(homo)(equus))(albus))=“non homo vel equus est albus” /2/ F13(est)(F12(vel)(F8(non)(homo))(equus)))(albus)=“non homo vel equus est albus” /3/ F13(est)(F8(non)(F12(vel)(homo)(equus)))(albus)=“non homo vel equus est albus”

Semantics

Preliminary Remarks

A Buridanian semantics cannot be one that construes meaning as a relation between words and extramental things alone. To be sure, for Buridan many words of our languages are imposed to signify extramental things. However, several expressions of our languages, namely some syncategorematic expressions, signify nothing at all in external reality, but only concepts of the mind (which, though, are real entities, ontologically on a par with other qualities); and even those that signify extramental things do so only by signifying concepts of the mind immediately, and signify extramental things only by the mediation of these, namely signifying the things that are conceived by the concepts signified by them immediately. This mediation also means that an expression signifying something ad extra owes its external signification exclusively to the concept that it signifies apud mentem, i.e. to which it is subordinated: should the same expression be subordinated to another concept, it would thereby signify those things which are conceived by this other concept, that is, it would have a different meaning.

This two-tier structure of meaning, which, to be sure, was not a peculiarity of Buridan’s semantics in the Middle Ages, was developed to its utmost consequences by Buridan. Most importantly, he went as far as supposing the existence of a fully articulated mental language immediately signified by, and thereby conferring meaning on (vocal and written forms of) any kind of human idioms (including even sign-languages).

This “mentalese”, however, is by no means an in principle inaccessible “private language” of individual language users. It is precisely its systematic bit-by-bit relationship with spoken and written languages that makes it accessible in ordinary communication, whereby individual language users are able to think the same thoughts, despite the fact that this is realized through their having numerically distinct, individual mental acts. For example, even if the concept immediately signified by the term ‘homo’ in my mind is a numerically distinct entity from the concept signified immediately by the same term in your mind, provided we conceive the same things by these concepts, namely human beings, we assign the same meaning to the same term and we are able to form the same thoughts with these concepts. Indeed, the same concept in my mind (as well as in yours) can be immediately signified also by the English word ‘man’, which explains why we are able to think of the same things by using either of these words, i.e., why we understand both the Latin and the English word as meaning the same.

52

To be sure, since subordinating words to concepts by imposing them to mean something is conventional and is entirely in our power, it may happen that the same word is assigned different meanings by different persons on different occasions. So the immediate signification of a term is always dependent on its actual imposition. But given this imposition the term is subordinated to some particular concept of a human mind, and provided users of the same term agree on imposing the same word to signify one of their concepts by which they conceive the same things in the same way, they mean the same by the same term.

The restriction: “conceive the same things in the same way” is significant here. For our concepts representing extramental things may relate to the things they represent in different ways according to Buridan. Our absolute concepts signify directly and in the same way all the things they represent. Our connotative concepts, however, signify some of the things they represent directly, but some of them obliquely, as adjacent or non-adjacent to what they signify directly, which means that whatever they signify directly they signify only in relation to what they connote either positively or negatively.

For example, the English terms ‘sighted’ and ‘blind’ and, correspondingly (and indeed primarily), the concepts associated to them, according to this analysis both signify directly animals. Indeed, both of these terms signify animals connoting their sight. But while ‘sighted’ connotes the sight of a particular animal positively, as adjacent to that animal, ‘blind’, on the contrary, connotes its sight negatively, as non-adjacent to it. Consequently, the term ‘sighted’ will refer to this animal in a present tense affirmative proposition only if it actually does have sight, while ‘blind’ would do the same only if the animal does not have sight. In fact, both of these terms have reference not only to what they stand for in a proposition but also an oblique reference to what they connote even outside a proposition. Buridan calls this oblique reference appellation. As can be seen, positive or negative appellation of their connotata is of primary importance in determining the reference of connotative or, as Buridan more frequently calls them, appellative terms.

Since according to Buridan the import of the affirmative copula is the identity of the supposita of the terms flanking it, reference, or using the mediaeval technical term, supposition of a categorematic term in a proposition is crucial in determining the truth conditions of categorical propositions. But supposition (and appellation) of terms in the context of a proposition is dependent on their signification (and connotation in the case of connotative terms) even outside a proposition, which in turn is dependent on the signification of the concepts to which they are subordinated.

Accordingly, in constructing the semantics for the fragment defined above, first we have to establish the relation of subordination, or immediate signification between items of our fragment and concepts of human minds. As a second step, we have to define their ultimate signification in terms of their immediate signification. Finally we have to define the supposition of terms in several propositional contexts, by which we shall be able to provide a definition of truth and consequence for this fragment.

The definition of these semantic relations in a model theoretical framework can be given in basically the standard way, namely defining them as mappings from syntactic items to a domain containing their possible semantic values, a so-called universe of discourse, usually an arbitrary set. However, to provide a construction true to the spirit of Buridan’s ideas several further qualifications are in order.

53

First of all, as the above-sketched analysis of the semantics of the term ‘blind’ should already suggest, we have to distinguish between actual and non-actual elements of our universe of discourse. But of course, since actuality is time-bound - what is actual now was not necessarily so in the past and need not be so in the future -, we have to think of actual entities as forming some subset of the universe of discourse relative to some given time t. So if the universe of discourse is some set W, then the set of actual things at time t, A(t), is to be a subset of W. (A(t)⊂W)

In this way we can easily account for the fact that in some contexts we can successfully refer to something that actually does not exist. For example, if it is winter and there are actually no roses in my garden, I can successfully refer to the roses we saw last summer in my garden with the true sentence “I had beautiful roses here last summer”. On the other hand, the sentence “I have beautiful roses in my garden”, uttered at the same time is false, precisely because there are actually no roses in my garden at the time of its utterance.13

The difference, as Buridan explains, is that in the first sentence the past tense of the verb makes the range of reference of the term ‘rose’ extend beyond the domain of actual entities, permitting it to refer to what was a rose, even if now it is perished, and so does not exist. But in the present-tense sentence the same term cannot refer to anything, there being nothing to which it would actually apply. In the model theory we can represent this situation by assigning a zero-entity, say 0, which falls outside the universe of discourse (0üW), as its value to the function assigning terms their supposita at some given present time t. (Say, SUP(‘rose’)(t)=0) On the other hand, in the past tense context, in which its range is extended, or ampliated, to use Buridan’s term, to past roses, a suppositum of this term is an element of a domain of entities which were actual at some earlier time: SUPP(‘rose’)(t)∈A(t’)∪A(t), where t’<t.

13 “... hoc significatur per nomen quod per ipsum positum in oratione intelligitur, cum significare est intellectum rei constituere. Sed per hoc nomen ‘rosa’ intelligitur rosa, et per hoc nomen ‘rose’ intelliguntur rose. Verbi gratia tu et ego simul anno preterito vidimus multas rosas rubras. Si ergo ego peto a te: “nonne rose quas vidimus erant rubre?”, tu dicis quod “ymmo”. Quod scis esse verum. Quod tamen tu non scires si non intelligeres istas rosas. Tu ergo per illud nomen ‘rosas’ cum dico “vidimus rosas” intelligis ea que vidimus. Sed vidimus rosas rubras. Igitur intelligis rosas. Quarta conclusio est quod hoc nomen ‘rosa’ supponit pro rosas et hoc nomen ‘rose’ supponit pro rosis, licet nulla sit rosa, quia secundum casu predictum, scilicet quod anno preterito vidimus multas rosas rubras, tu concedis illam ‘multe rose rubre fuerunt anno preterito’; et eam scis esse veram. Et cum sit affirmativa, non esset vera nisi subiectum, quod est hoc nomen ‘rose’, pro aliquo supponeret, vel pro aliquibus. Sed tamen non supponit pro alio vel pro aliis quam pro rosis. ... notandum est quod possumus intelligere res sine differentia temporis et intelligere preteritas vel futuras sicud presentes. Propter hoc etiam possumus inponere vocem ad significandum sine differentia temporis. Sic enim nomina significant. Unde specifico conceptu ‘hominis’ ego indifferenter omnes homines concipio presentes preteritos et futuros. Et per hoc nomen ‘homo’ omnes indifferenter significantur presentes, preteriti et futuri. Ideo vere dicimus quod omnis homo qui fuit, fuit animal, et omnis homo qui erit, erit animal. Et propter hoc consequitur quod ista ‘intelligere’, ‘scire’, ‘significare’, et huiusmodi, et participia inde descendentia ampliant terminos cum quibus construuntur, ad supponendum indifferenter pro presentibus, preteritis et futuris et possibilibus que forte nec sunt nec erunt nec unquam fuerunt. Quamvis igitur nulla sit rosa, ego intelligo rosam non que est sed que fuit vel erit vel que potest esse. Et tunc quando dicitur: hoc nomen ‘rosa’ significat aliquid, concedo. Et cum dicis: illud non est, concedo. Sed fuit. Si tunc concludis: igitur aliquid est nichil, nego consequentiam, quia in maiore iste terminus ‘aliquid’ erat ampliatus ad preterita et futura, et in conclusione est restrictus ad presentia. Et dictum fuit quod quod a termino ampliori et non distributo ad seipsum minus amplum non valet consequentia.” Johannes Buridanus: Questiones Longe super Librum Perihermeneias, ed. Ria van der Lecq, Utrecht, 1983, pp.12-14.

54

The second point to be considered here is the representation of the signification of connotative, or appellative terms. As we have seen, such terms signify whatever they signify only in relation to other things, for example, the term ‘album’ signifies white things (including past, future and possible ones, since ‘signify’ ampliates also to these domains) only by connoting their whitenesses, whether these whitenesses are actual or not. Of course, it will, nevertheless, supposit only for things which are actually white in a sentence like ‘Animal est album’. But to supposit for them this term first has to signify them, and it signifies them only in relation to their whitenesses. Similarly, it will supposit for past white things in a sentence like “Animal fuit album”, but it can supposit for them also in this sentence only because it signifies them connoting their past whitenesses, which need not be actual at the time of the utterance of this sentence.

On the other hand, the term ‘albedo’ signifies individual whitenesses of individual substances absolutely, without connoting anything, in the same way as the term ‘homo’ signifies individual men, or the term ‘rosa’ signifies individual roses. So if we denote a significate of the term ‘albedo’ like this: SGT(‘albedo’), we can say that it is just an element of a subset of the universe of discourse, namely an element of the signification of ‘albedo’, the set of things naturally and directly represented by the concept to which the term ‘albedo’ is subordinated. (SGT(‘albedo’)∈SG(‘albedo’), where SG(‘albedo’)⊂W.) A suppositum of the same term in a present tense proposition uttered at some time t is identical with one of its significata that are actual at that time, provided there are any, otherwise it supposits for nothing, that is to say, it takes 0 as its value:

SUP(‘albedo’)(t)=SGT(‘albedo’), if SGT(‘albedo’)∈A(t), otherwise SUP(‘albedo’)(t)=0. In a very interesting passage Buridan analyses the semantics of adjectives in comparison with the way possessives determine the supposition of their head-nouns.14 According to this analysis ‘album’ in “animal album” bears a similar relationship to ‘albedo’ as ‘hominis’ in “animal hominis” to ‘homo’.

Now ‘hominis’ is certainly a phrase that does not signify ad extra anything different from what the term ‘homo’ signifies, namely individual men. However, it signifies them differently, namely as adjacent to what the term with which ‘hominis’ is constructed signifies. But in view of the above considerations this should mean that the complex term “animal hominis” is a connotative term, signifying animals in relation to men. So ‘hominis’ in itself is a connotative term as well, connoting men, and the things to which these men are signified as adjacent.

14 Sed cum dico ‘homo albus currit’, ego credo quod ‘albus’ nullam substantiam significat, sed albedinem tantum. Et ita nihil plus vel aliud, nisi quantum ad modos significandi grammaticales, significat iste terminus ‘albus’ quam iste terminus ‘albedo’, sed idem diversimode significant, scilicet albedinem; nam ‘albedo’ significat ipsam per modum subsistentis et ‘albus’ per modum alteri adjacentis. Et sic puto debere intelligi quod bene dicit Aristotiles in Praedicamentis, scilicet quod ‘album’ nihil aliud significat quam qualitatem, quod credo esse verum accipiendo ‘album’ adjective, ut dicendo ‘lignum album’. Puto ergo quod ‘album’ in neutro genere substantivatum et supponit et appellat; ‘albus’ autem non supponit, sed solum appellat, et illud appellat quod significat. Ita etiam ego credo quod nomen substantivum obliquum non supponit, sed solum, et appellat illud quod significat, et appellando bene determinat suppositionem substantivi cui adjungitur. Et idem, et non aliud, significat rectus et ejus obliquus, sed diversis modis quantum ad diversos modos significandi grammaticales; quia rectus significat secundum modum subsistentis et obliquus per modum adjacentis, seu habentis se aliquo modo ad rem quem rectus cum quo construitur significat vel pro qua supponit. SL, Tractatus Octavus: De Divisionibus, c. 2, 4.

55

Consequently, we should treat the genitive case as an “unsaturator”, indicating that the genitive form of a noun signifies apud mentem a connotative concept connoting what is signified directly by the absolute concept to which the nominative form is subordinated and what is signified by the head-noun with which the genitive form is constructed. And this, by the way, explains why such a genitive cannot be a subject or a predicate of a proposition in itself. For in itself it is incomplete, to be completed by a nominative supplying one of its connotata. So along these lines we can construct a significate of “animal hominis” as follows:

SGT(“animal hominis”)=SGT(‘hominis’)(SGT(‘animal’))(SGT(‘homo’)), where SGT(‘hominis’)(u)(SGT(‘homo’))=u∈W. But then, in a similar manner, a significate of ‘animal album’ should be constructed as follows:

SGT(“animal album”)=SGT(‘album’)(SGT(‘animal’))(SGT(‘albedo’)), where SGT(‘album’)(u)(SGT(‘albedo’))=u∈W. Technically, SGT here is a function which for the term ‘album’ as its argument yields another function as its value, which can take another thing as its argument, namely the thing having whiteness (whether actually or not), yielding another function as its value that can take a further thing as its argument, a significate of the term ‘albedo’, that is, an individual whiteness connoted by ‘album’ as adjacent to this thing, yielding this thing as its value. Of course, a suppositum of this term in the context of a present tense proposition uttered at some time t can be only a thing that actually has whiteness at t, that is to say, if the term ‘albedo’ can successfully refer to (supposit for) this whiteness at that time as an appellatum of the term ‘album’:15

SUP(“animal album”)(t)=SGT(‘album’)(SUP(‘animal’)(t))(SUP(‘albedo’)(t)) if SUP(‘animal’)(t)∈A(t) and SUP(‘albedo’)(t)∈A(t), otherwise SUP(“animal album”)(t)=0. The main advantage of this treatment of connotative terms is that the arity of the term which it interprets does not determine the arity of SGT, still we do not have to take, e.g., ordered n-tuples as its arguments. For otherwise we could take SGT to be, e.g., a two-place function having a term in its first, and the term’s connotatum in its second argument place, but then the same function could not interpret terms of different arities. Alternatively, we could define it as a two-place function taking a term in its first, and ordered n-tuples in its second argument place. But in this case, still, the same function could not interpret absolute terms (unless we would introduce some artificial null-tuple) and we would have to regard a connotative term’s connotata to be entities which do not occur in Buridan’s nominalist ontology.

Furthermore, the treatment proposed above renders technically easy and quite natural the representation of a peculiar feature of the Buridanian semantics of connotative terms, namely that their semantic arity is not determined by the number of their syntactic complements. What matters in this regard is only that at the end of the iterated application of functional composition we get a saturated entity, an element of the universe of discourse, but the number of intermediary functions is dependent solely on whether at any given step a given function for a given argument will yield a further function again or a saturated entity, thereby ending the process.

15 Cf.: “Et primo dico quod terminus substantivus obliquus appellat illud pro quo rectus suus supponeret per modum adjacentis ei pro quo rectus regens ipsum supponit.” SL, Tractatus Quartus: De Suppositionibus, c.5, 4.

56

Indeed, this kind of construction makes it possible that the same expression has different arities, as it should be the case e.g. with adjectives or participles occurring either as standalone terms substantivated in the neuter gender, or as adjuncts to nouns.

A further point worth preliminary consideration is Buridan’s theory of appellatio rationis used by him to explain the peculiarities of reference in intentional contexts.

Although several recent commentators think differently, I think we can treat this theory as a consistent part of Buridan’s general theory of appellation.16 The only difference between appellation of an appellative term in general and a case of appellatio rationis is that in the latter case oblique reference is made not to the connotata of an appellative term, but to the ratio signified by any term, whether appellative or not, in the context of an intentional verb or, rather, the participle derived from it.

For example, according to Buridan, the participle ‘debens’ makes the accusative constructed with it appellate its own ratio, which explains why it cannot be replaced by a term in a proposition like “Plato est debens Socrati equum”, unless this term is strictly synonymous with it. For in this sentence a significate of the term “debens Socrati equum”, in accordance with our previous considerations, is to be constructed as follows:

SGT(‘debens’)(SGT(‘Socrates’))(RAT(‘equus’))(SGT(‘equus’))(t), where RAT(‘equus’) is the ratio of the term ‘equus’. Accordingly, a suppositum of the same term in the above proposition is:

SUP(‘debens tibi equum’)(t)= =SGT(‘debens’)(SUP(‘Socrates’)(t))(RAT(‘equus’))(SUP(‘equus’)(t’))(t), if this is an element of A(t), otherwise SUP(“debens tibi equum”)(t)=0. (Where t’ is equal to or greater than t, because of the ampliative force of ‘debens’.) But so, since the sentence is true iff the supposita of its terms are the same, and whether this or that individual is supposited for by its predicate term depends on the ratio of its accusative, clearly, replacing the accusative may change the truth value of this sentence, even if the replacing term would refer to the same thing(s).17

For this idea to work in general, however, we clearly should be able to identify rationes of terms. But to this end first we have to be clear about what rationes are.

In many places, Buridan uses the term ‘ratio’ interchangeably with the term ‘conceptus’, or ‘intentio’. But, as we have seen, concepts are individual mental acts of individual human minds, which, when by an act of imposition get associated with vocal or written expressions, are responsible for the meaning of these expressions.

This understanding of concepts (as individual mental acts) and their relation to the meaning of linguistic items, renders meaning doubly relative. On the one hand, you and I may associate different concepts with the same expression, and hence attribute to it different meanings, while on different occasions even I may use the same expression in a different sense, associating it with some different concept, and thereby imposing it to mean something different, on the other.

16 For references see my “‘Debeo tibi equum’: A Reconstruction of the Theoretical Framework of Buridan’s Treatment of the Sophisma”, in: S.L. Read (ed.): Sophisms in Mediaeval Logic and Grammar: Acts of the Ninth European Symposium of Mediaeval Logic and Semantics, to appear. 17 For more detailed discussion see again my paper referred to in the previous note.

57

Whether on these different occasions you will be able to understand what I mean depends on whether you will be able to associate with the expression in question the same (type of) concept, i.e. a mental act by which you conceive the same things and in the same way as I do. If so, and this usage catches on, i.e., also other users of our language are able and willing to use this expression in the same way in the future (at least, perhaps, in virtue of some temporary agreement, for a limited period of time, as in obligational disputes frequently referred to by Buridan in this context), then my act of imposition will constitute a new meaning for the expression, observed by everybody who understands this expression in this sense. Otherwise my usage of the expression is an idiosyncrasy, having to do perhaps with my linguistic incompetence, my joking mood, momentary insanity, or grave conceptual differences (which may be but a euphemism for permanent insanity), etc. We can say, however, that if there is a valid convention of its usage, the ratio of an expression is but a concept associated with this expression by an act of imposition, no matter whose concept, mine or yours, insofar as we use this expression subordinated to the same type of concept. But, as I have said above, our individual concepts can be said to be of the same type, if we conceive by them the same things in the same way, i.e., if they have the same meaning.

With this, however, we seem to have entered a vicious circle: our expressions mean the same, if they are subordinated to the same concepts, while these concepts are said to be the same, if they signify the same; that is to say, concept identity is just synonymy and vice versa, but neither of these is clearer than the other, and Quineans may rejoice.

Despite appearances, however, this is no more vicious than it is a circle. For the signification of a concept is a natural relation, determined by the nature of the concept alone, not dependent on any further semantic medium. So we can say that simple absolute concepts are identical if and only if they signify the same, i.e., the set of their significata is the same, and simple connotative concepts are the same if and only if they signify the same, i.e., the sets of their significata and connotata are the same. But in a model theory sets are well-behaved entities with respect to identity. So in such a theory the identification of simple concepts should present no extra difficulty, provided we assign them in a model their significata (and connotata) in a systematic manner, which renders the identification of these sets possible.

Now in view of these considerations we can say that our model theory will have to contain a function assigning concepts of individual minds (m) to linguistic expressions (X) relative to individual acts of imposition (i), like this: CON(m)(i)(X)∈W.

These individual concepts, provided they are simple, will be identified on the basis of their significations:

CON(m)(i)(X)=CON(m)(i)(X’) iff SG(CON(m)(i)(X))=SG(CON(m)(i)(X’)) The rationes of these expressions, on the other hand, will be identified with these concepts, provided these concepts are of the same type, i.e., if they signify the same:

RAT(i)(X)=CON(m)(i)(X) /that is to say, RAT=CON(m)/ if SG(CON(m)(i)(X))=SG(CON(m’)(i)(X)), for any m’, otherwise RAT(i)(X)=0. To be sure, rationes in this way will be just the same individual mental acts as concepts, nevertheless, these concepts will be identified as rationes only if their individual differences, depending on to which individual mind they belong, are irrelevant from the point of view of their significative function. (Otherwise, as the second half of the clause above states, we cannot assign a definite ratio to a given expression, but we can, of course, assign it several idiosyncratic

58

concepts of individual users of it, which, however, may be interesting more from a pragmatic, than from a semantic point of view.18) This significative function, however, is affected by different impositions: if a term, like e.g. ‘seal’ in English, is correlated with two different types of concepts by different acts of imposition, then also the rationes corresponding to this term are different depending on according to which imposition we interpret it. On the other hand, if the expression in question is unequivocal, this means that the meaning of this expression is not a function of different impositions. (Which is equivalent to saying that it is never imposed to mean something different: it signifies the same for any imposition i, that is, it is a constant function of these different impositions.) So to simplify matters, in the case of such an expression we can omit reference to different impositions and give its ratio directly, like this:

RAT(X)=CON(m)(i)(X) if SG(CON(m)(i)(X))=SG(CON(m’)(i’)(X)) for any m’ and any i’, otherwise RAT(X)=0. In the case of complex concepts, on the other hand, the guide for their identification should be their structure, i.e., the way they are built up from their already well-identifiable components. The reason for this is that complex concepts may signify exactly the same thing or things, but be distinct from one another due to their different structure. Buridan’s most frequently used example is the pair of mental propositions expressed by the sentences “Deus est Deus” and “Deus non est Deus”.19 The vocal or written sentences both signify one and the same thing ad extra, namely God. The two sentences, nevertheless, are not synonymous, because they signify different mental propositions apud mentem. For the negative sentence beyond the concepts signified by the affirmative one also signifies the concept of negation, which makes it signify the same thing in a different manner, namely negatively, which renders these two sentences contradictory, i.e., the one true if and only if the other is false. But sentences are true or false only in virtue of the truth or falsity of the mental propositions they express; but no mental proposition can be true and false at the same time. Therefore, the mental propositions corresponding to these sentences are different, having different internal structures.

18 For a discussion of these topics, though in a different formal framework, see my “Understanding Matters from a Logical Angle: Logical Aspects of Understanding” in: G. Klima: Ars Artium: Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1988. 19 Cf.: “Sed statim tu quaeres “si in re significata vel in rebus significatis non sit aliqua complexio, quid ergo significat oratio mentalis qua intellectus dicit deum esse deum vel deum non esse deum?”. Respondeo quod nihil plus vel aliud significat ad extra una dictarum orationum quam alia. Neutra enim significat ad extra nisi deum; sed alio modo significat affirmativa et alio modo negativa, et illi modi sunt in anima illi conceptus complexivi quos secunda operatio intellectus addit supra simplices conceptus, qui designantur per istas copulas vocales ‘est’ et ‘non est’.” SL, Tractatus Primus: De Propositione, c.3, 1. “... istae propositiones ‘deus est deus’ et ‘deus non est deus’ nihil omnino aliud, plus aut minus significant ad extra quam iste terminus ‘deus’, dum tamen haec dictio ‘est’ sumatur praecise ut copula, sicut post dicetur. Nec ista oratio ‘omnis homo est animal’ plus vel minus vel aliud significat praeter conceptus animae quam ista ‘nullus homo est animal’. Unde signa solum significant quo modo termini vocales et mentales eis correspondentes supponunt, nihil ultra significando. Et istae copulae ‘est’ et ‘non est’ significant diversos modos complectendi terminos mentales in formando propositiones mentales, et illi modi complectendi sunt conceptus complexivi pertinentes ad secundam operationem intellectus, prout ipsa addit super primam operationem. Et ita etiam istae dictiones ‘et’, ‘vel’, ‘si’, ‘ergo’ et hujus modi designant conceptus complexivos plurium propositionum simul, vel terminorum, in mente, et nihil ulterius ad extra. Et tales voces vocantur ‘pure syncategorematicae’ quia non sunt significativae ad extra nisi cum aliis, ad istum sensum quod totum aggregatum ex dictionibus categorematicis et syncategorematicis significat bene res extra conceptas, sed hoc est ratione dictionum categorematicarum. SL, Tractatus Quartus: De Suppositionibus, c.2, 3.

59

But what is it that accounts for these different structures? For it is certainly not the temporal or spatial order of their parts as is the case with the spoken or written counterparts of these mental sentences. The answer lies in the operation of the “glue” of these mental propositions, the syncategorematic, or as Buridan also most aptly calls them, complexive concepts. The role of these concepts is to form complex concepts out of other concepts, thereby modifying the ways these other concepts relate to the things conceived by them. So these complexive concepts can be represented by functions taking concepts into complex concepts, the semantic relations of which will be determined how they are constructed by way of these complexive concepts.

For example, the copula, ‘est’, is a complexive concept, taking other, simple or already complex, categorematic concepts as its arguments (and connoting some time t), yielding a mental proposition, like this:20

RAT(‘est’)(c1)(c2)(RAT(t))∈W. (Where RAT(t) is the concept of the present time connoted by the copula of the proposition. So RAT is defined not only for linguistic expressions, but also for time-points, or intervals.)

Accordingly, the mental proposition corresponding to “Deus est Deus” may be constructed as follows:

RAT(“Deus est Deus”)(RAT(t))=RAT(‘est’)(RAT(‘Deus’))(RAT(‘Deus’))(RAT(t)) On the other hand, the concept of propositional negation, RAT(‘non’), is a one-place functor taking a mental proposition as its argument, yielding a complex concept, another mental proposition, the truth value of which is the opposite of that of its argument. So the mental proposition signified apud mentem by “Deus non est Deus” is to be constructed as follows:

RAT(“Deus non est Deus”)(RAT(t))= RAT(‘non’)(RAT(‘est’))(RAT(‘Deus’))(RAT(‘Deus’))(RAT(t)) Since according to Buridan spoken or written sentences are true only in virtue of being subordinated to true mental propositions,21 indeed, truths and falsities are nothing but true or false mental propositions, in our model theory we can define truth as the set of all true mental propositions, and the truth-conditions of these propositions as the conditions of membership in this set.

For example, if V is the set of all truths:

RAT(“Deus est Deus”)(RAT(t))∈V iff SUP(RAT(‘Deus’))(t)=SUP(RAT(‘Deus’))(t) But of course, in the actual construction of the model theory we shall have to build such and similar particular conditions into general recursive rules defined for whole classes of expressions and concepts associated with them. However, as I indicated in the introduction, for want of space I cannot present here a complete model theory for the fragment of Latin constructed above. So I

20 Cf.: “Credo enim quod illi conceptus a quibus sumuntur istae dictiones syncategorematicae ‘et’, ‘vel’, ‘si’, quamvis sint conceptus complexivi plurium propositionum vel terminorum, tamen non sunt complexi ex pluribus, sed simplices. Et ita etiam est de conceptu hujus verbi ‘est’ prout praecise sumitur tamquam copula. Unde sic est dictio pure syncategorematica; tamen forte prout connotaret certum tempus, jam exiret a simplicitate, nec esset purum syncategorema, prout alias dicetur.” SL, Tractatus Quartus: De Suppositionibus, c.2, 4. 21 “Et ideo non dicitur oratio vel propositio vocalis nisi quia designat orationem vel propositionem mentalem, nec dicitur propositio vocalis vera vel falsa nisi quia designat mentalem veram vel falsam, sicut nec urina dicitur sana vel aegra nisi quia designat animal esse sanum vel aegrum.” SL, Tractatus Primus: De Propositione, c.1, 6.

60

am going to provide only some of the most essential clauses along with some illustrations of how they are supposed to work, and base my concluding discussion on these.

Semantic Categories

As from the foregoing it should be clear, for the formulation of the semantic definitions we shall have to introduce some further classifications of the expressions of our fragment beyond those provided by the syntactic construction.

First of all, univocity or equivocity are semantic properties of terms that are not reflected by their syntactic categories. In our fragment the only equivocal term is ‘canis’, which, in mediaeval examples, in one sense was taken to signify man’s best friend, in another, the corresponding constellation. Accordingly, in the definitions above and hereafter all specifications concerning equivocity or univocity concern the term ‘canis’ on the one hand, and the rest of categorematic terms, on the other. So, if by EQU, we denote the set of equivocal terms, then this set in our fragment is defined simply as follows:

EQU:={canisgc}. Correspondingly, the set of univocal terms (UNI) is defined in the following manner:

UNI:=TRM∪VOC-EQU Secondly, for semantic purposes we have to distinguish between absolute (ABS) and appellative terms (APP):

ABS:=PNgnom∪CNgnom∪RPnenom; APP:=TRM-ABS. It will greatly simplify the formulation of semantic definitions if we distinguish between functorial and non-functorial expressions, and also between functorial expressions of different arities. Functorial expressions are appellative terms of our vocabulary subordinated to simple concepts, plus the syncategorematic terms:

FUNC:=(VOC∩APP)∪SYNC. Indeed, we may treat non-functorial expressions, i.e., absolute terms, as 0-ary functorial terms, which will also simplify later formulations. The sets of n-ary functorial terms, FUNCn are defined by the following clauses:

FUNC0:=ABS

FUNC1:={non, quodgc}∪Sig∪PNgen∪CNgen

FUNC2:={vel, albusgc, vidensnenom, habensnenom, mortuusnenom}

FUNC3:={est, vidensgc, habensgc, mortuusgc}

FUNC4:={fuit, erit, debensnenom}

FUNC5:={debensgc}

Note here that adjectives, participles and relative pronouns in the neuter gender and nominative case, which can form standalone terms without a head-noun, appear also in a lesser functorial category. Let us denote the set of these functorial terms by Fn-1.

As from the above definitions can be seen, all complex terms are appellative, but not all appellative terms are complex. As Buridan insists, semantic simplicity or complexity is not determined by syntactic simplicity or complexity. This is determined on the level of concepts, to

61

which the several, either simple or complex syntactic items are subordinated. Since, however, he admits the possibility of there being simple appellative concepts,22 in this fragment I shall treat all syntactically simple appellative terms as being subordinated to some simple appellative concept, except for ‘caecum’, which, for illustrative purposes, I shall regard as synonymous with the phrase “animal non habens visum”. Accordingly, I will treat ‘caecum’ as semantically complex, being subordinated to the same complex ratio as its nominal definition: “animal non habens visum”.

The sets of simple (SIM), and of complex (COMP) terms are, therefore, defined as follows:

SIM:=VOC-{caecumgc}; COMP:=TRM-SIM. Furthermore, we need to distinguish between apmliative (AMPL) and non-ampliative terms. Also, among ampliative terms we have to distinguish those that ampliate to the past (AMPLP), from those that ampliate to the future (AMPLF) and from those that ampliate to the possible (AMPLM) and from the further possible combinations of these specifications, such as from those ampliating to the future and the possible (AMPLFM), etc. In our fragment:

AMPLP:={mortuusgc} AMPLFM:={debensgc,dat,acc*}, where the asterisk indicates that it is the accusative complement that is ampliated to the future and possible. Again, we have to distinguish intentional participles (INT), i.e., participles that signify mental acts, and which, therefore, make (some of) their complements appellate their rationes. In our fragment:

INT:={debensgc,dat,acc*}, where the asterisk indicates that it is the accusative complement that is forced to appellate its own ratio.

The Model

A model for the above-defined fragment is the following set-theoretical structure:

M:=<W,T,I,C,S,A,P,CON,RAT,SG,0>,

where W, T, I, C and S are nonempty sets, such that T,I,C,S⊂W, A(t)⊂P(t)⊂W, where t∈T; CON(m)(X)∈C, provided X is some univocal expression of our fragment (X∈UNI), otherwise CON(m)(i)(X)∈C, where m∈S, i∈I and X is an equivocal expression of our fragment (X∈EQU);

RAT(X)=CON(m)(X) if SG(CON(m)(X))=SG(CON(m’)(X)), for any m’, otherwise RAT(X)=0, where X∈UNI, and RAT(i)(X)=CON(m)(i)(X) if SG(CON(m)(X)(i))=SG(CON(m’)(X)(i)), for any m’, otherwise RAT(X)(i)=0, where X∈EQU; 0üW, and SG is a function defined recursively below. Intuitively, W is the universe of discourse, the set of all items signifiable by expressions of our fragment, T is a set of time-points, or time-intervals, I is a set of acts of imposition, C is a set of concepts, S is a set of human souls or minds, A(t) and P(t) are the sets of signifiable things that are actual, and of those that are potential at time t, respectively; CON is a function assigning 22 See especially in this connection A. Maierú: ‘Significatio et Connotatio chez Buridan’, in: J. Pinborg (ed.): The Logic of John Buridan, Copenhagen, 1976. pp.110-111.

62

individual acts of individual human minds, m, with respect to some act of imposition, i, to expressions, X, of our fragment; RAT is a function assigning concepts to expressions in some mind m, provided that the concepts associated with the same expressions signify the same in any other mind, either directly, if the expression in question is unequivocal, or depending on some act of imposition otherwise; SG is the function representing the relation of signification, defined both for concepts of human minds and for linguistic expressions subordinated to these.

In the same model categorematic concepts and expressions will have further semantic values, namely significata and supposita (also connotata and appellata in the case of appellative terms) to be assigned to them by functions in a similar manner as in standard quantification theory value-assignments defined for variables assign several values to variables in the same model.

“Mentalese” and Signification

In the subsequent clauses RAT=CON(m), and the metavariables t, s, ti, ci and ui range over elements of T, Sig, TRM, C and of W, respectively.

The rationes of (syntactically as well as semantically) simple terms are given by the following seven clauses:

(RATun) If X∈UNI, then RAT(X)∈C (RATeq) If X∈EQU and i∈I, then RAT(X)(i)∈C (RATfn) If X∈FUNCn, then RAT(X)(c1)...(cn)∈C (Of course, if n=0, then RAT(X)∈C.) (RATfn-1) If X∈FUNCn-1, and c1...cn are as above, then RAT(X)(c2)...(cn)∈C. (This should be

understood so that if X∈FUNC1-1=0, then RAT(X)∈C.) (RATnon) If c=RAT(X), where X∈FUNCn, then RAT(non)(c)(c1)...(cn)∈C (RATadj) If anec∈Adj, then RAT(“[non] agc”)= RAT(“[non] agc”)(RAT(agcabs))= [RAT(non)](RAT(agc))(RAT(agcabs))= RAT(agc)(RAT([non] agcabs))∈C, where aabs is the abstract form of an adjective

signifying quality (in our fragment: ‘albumgc’abs=‘albedo’). (RATmort) If pnec∈Prtc∪AMPLP) , then RAT(pnec)(RAT(t’))(RAT(t))∈C, where t’<t The rationes of semantically complex expressions are given as follows:

(RATamb) If Fi(x1)(x2)...(xm)=X=Fj(y1)(y2)...(yn), then RAT(i)(X)=RAT(x1)(RAT(x2))...(RAT(xm))[(RAT(wo))], RAT(j)(X)=RAT(y1)(RAT(y2))...(RAT(yn))[(RAT(wo))], where wo is some further, syntactically unanalysed concept needed to complement RAT(x1) or RAT(y1), say the concept of some past, present or future time required by the concept of a participle, marked syntactically by the tense of the participle alone.

(RAT1a) If pnec1[,c2][,c3]∈Prtc-(INT∪AMPL) and t2c2, t3c3∈TRM, then RAT(“pnec1,c2[,c3] t2c2 [t3c3]”)=RAT(pnec1,c2[,c3])(RAT(t2c2))[(RAT(t3c3))](RAT(t))

(RAT1b) If pnec1,c2[,c3]∈Prtc-(INT∪AMPL) and t2c2, t3c3∈ITRM, then RAT(“[s2c2] t2c2 [[s3c3] t3c3] pnec1,c2[,c3]”)= [RAT(s2c2)]([RAT(s3c3)](RAT(pnec1,c2[,c3])(RAT(t2c2)) [(RAT(t3c3))](RAT(t)))) (RAT1c) If pnec1[,c2][,c3]∈Prtc∪AMPLFM∩INT) and t2c2, t3c3∈TRM, then

63

RAT(“pnec1,c2,c3* t2c2 t3c3”)= RAT(pnec1,c2,c3*)(RAT(t2c2))(RAT(t3c3))(RAT(t3c3))(RAT(t’))(RAT(t)), where t’>t (RAT1d) If pnec1[,c2][,c3]∈Prtc∪AMPLFM∩INT) and t2c2, t3c3∈TRM, then RAT(“t2c2 t3c3 pnec1,c2,c3*”)= RAT(pnec1,c2,c3*)(RAT(t2c2))(RAT(t3c3))(RAT(xc3))(RAT(t’))(RAT(t)), where t’>t

and xc3 is some term coextensive with t3c3. (RAT2) If ngc∈PN∪CN, agc∈Adj, then RAT(“ngc [non] agc”)= RAT([non] agc)(RAT(ngc))(RAT(agcabs))= [RAT(non)](RAT(agc))(RAT(ngc))(RAT(agcabs))= RAT(agc)(RAT(ngc))(RAT([non] agcabs)), where aabs is the same as above. (RAT3) If ngc∈PN∪CN∪NA, t1gen∈TRMgen, t1nom is t1gen’s nominative form and nt1gen is

t1gen’s head-noun, then RAT(“<ngc><t1gen>“)=RAT(nt1gen)<(RAT(ngc))><(RAT(t1nom))> Here should follow four clauses running parallel with (RAT1a-d) above (indeed, we would need also a fifth one corresponding to (RATmort)), inserting the ratio of the head-noun with which a participle is construed, but for brevity, I omit them.

(RAT5) If X∈TRM∪PROP∪Cop∪Prtc∪Adj, then RAT(“non X”)=RAT(non)(RAT(X)) (RAT6) If tgc∈ITRM and sgc∈SIG, then RAT(“sgc tgc”)=RAT(sgc)(RAT(tgc)) (RAT7) If t2nom∈TRM and qnenom∈RP, then RAT(“qgnenom est t2nom”)= RAT(est)(RAT(qnenom))(RAT(t2gnom))(RAT(t)) (RAT7a) If t1gnom∈TRM, t2nom∈TRM and qgnom∈RP, then RAT(“t1gnom qgnom est t2nom”)= RAT(est)(RAT(qgnom)(RAT(t1gnom)))(RAT(t2gnom))(RAT(t)) Here further clauses should follow taking care of relative clauses in different tenses, but for the sake of brevity I omit them. See, however, the analoguous clauses for propositions below.

(RAT8) If t1gc, t2gc∈TRM, then RAT(“t1gc vel t2gc”)= RAT(vel)(RAT(t1gc))(RAT(t2gc)) (RAT9) If t1∈TRMgnom and t2nom∈TRM∪Adjgnom∪Prtcgnom then RAT(“t1 [non] est t2”)(RAT(t))= RAT([non] est)(RAT(t1))(RAT(t2))(RAT(t)) (RAT10) If t1∈TRMgnom and t2nom∈TRM∪Adjgnom∪Prtcgnom then RAT(“t1 [non] fuit t2”)(RAT(t’))(RAT(t))= RAT([non] fuit)(RAT(t1))(RAT(t2))(RAT(t’))(RAT(t)), where t’<t. (RAT11) If t1∈TRMgnom and t2nom∈TRM∪Adjgnom∪Prtcgnom then RAT(“t1 [non] erit t2”)(RAT(t’))(RAT(t))= RAT([non] erit)(RAT(t1))(RAT(t2))(RAT(t’))(RAT(t)), where t’>t. (RAT12a) RAT(caecumgc)=RAT(“animalgc non habensgc visum”)= RAT(“non habensgc”)(RAT(animalgc))(RAT(visus))(RAT(t))= RAT(non)(RAT(habensgc))RAT((animalgc))(RAT(visus))(RAT(t)) (RAT12b) RAT(“ngc [non] caecumgc)=RAT(“ngc [non] non habensgc visum”)= RAT(“[non] non habensgc”)(ngc)(RAT(visus))(RAT(t))= RAT([non] non)(RAT(habensgc))(ngc)(RAT(visus))(RAT(t))= [RAT(non)](RAT(non)(RAT(habensgc)))(RAT(ngc)) (RAT(visus))(RAT(t))

64

The purpose of these clauses is to assign a ratio to all expressions of our fragment, i.e. a concept common to all those who understand these expressions in the same way. Since understanding of the complex expressions should depend on the understanding of the simple ones that build them up, the rationes of complex expressions are to be determined in a compositional manner, on the basis of the rationes of their simple constituents.

Simple univocal terms are assigned a single ratio, by the first clause, while simple equivocal terms are assigned different rationes relative to different impositions. For example RAT(i)(canis) is a concept representing man’s best friend, while RAT(j)(canis) is another concept, representing the constellation.

Simple functional n-ary terms are assigned concepts, which are themselves functions that take further concepts in their arguments, yielding further concepts, etc., n times. For example, RAT(videns)∈C is a concept, which is such that it can be complemented with further concepts, to yield a further concept, like this: RAT(videns)(c1)(c2)∈C, where c1 is a concept signified immediately by an accusative that can be constructed with the term ‘videns’, while c2 is a concept of a time-point (or interval) connoted by the present tense form of this participle, though not marked by a distinct part of speech. If the ratio of ‘videns’ is complemented with both of these kinds of concepts, then it yields a concept that cannot be complemented any further, being in itself “saturated”, making some perfect, determinate sense, like the concept corresponding to “videns hominem”. Indeed, we get the concept corresponding to this complex phrase, if we complement the concept of ‘videns’ first with the concept corresponding to ‘hominem’, and then with the concept of the time of the actual application of this phrase, just as it is prescribed by clause (RAT1a), like this:

RAT(“videns hominem”)=RAT(videns)(RAT(hominem))(RAT(t)). Simple functional n-ary terms may also appear in constructions in which they need less complements to make perfect sense. Indeed, in the above example, ‘videns’ appeared like this, in its capacity to form a standalone term, without being an adjunct to a noun. However, when it is such an adjunct, as in “homo videns hominem”, then its ratio is complemented first with the ratio of the noun which is in the same case as itself, and only afterwards with the other complements, like this:

RAT(“homo videns hominem”)= RAT(videns)(RAT(homo))(RAT(hominem))(RAT(t)), as it would be prescribed by the rule corresponding to (RAT1a) omitted here for brevity. Notice that what makes the difference of this construction from that above is that the first complement concept here is a concept corresponding to the noun which is in the same case as the participle. If this head-noun is in the accusative itself, then so is the participle, yielding:

RAT(“hominem videntem hominem”)= RAT(videntem)(RAT(hominem))(RAT(hominem))(RAT(t)). Clause (RATnon) stipulates that if the concept complementing the argument-place of the ratio of negation is an n-ary concept (i.e. a concept corresponding to an n-ary simple term), then the resulting concept is n-ary too, that is to say, it may, and indeed, should be complemented by n further concepts to yield a saturated concept. For example, if the concept to which the concept of negation is applied is the concept signified by the term ‘videns’, then the resulting concept is still to be complemented, as it is so complemented in the complex concept corresponding to the phrase “homo non videns hominem”, like this:

65

RAT(“homo non videns hominem”)= RAT(non)(RAT(videns))(RAT(homo))(RAT(hominem))(RAT(t)). Notice here that we are compelled to introduce this narrow-scope concept of negation, i.e., a negation that negates only a part of a term, as opposed to a negation negating a whole complex term yielding an infinite term, in order to distinguish the concept corresponding to “homo non videns hominem” from that corresponding to “non homo videns hominem”. For the latter, at least on one of the possible readings of this phrase can be constructed as follows:

RAT(1)(“non homo videns hominem”)= RAT(non)(RAT(videns)(RAT(homo))(RAT(hominem))(RAT(t))), where the concept of negation is applied to the whole concept corresponding to the complex term: “homo videns hominem”. Evidently, this distinction needs to be made, because while the latter concept may apply to anything that is not a man seeing a man, like a stone, the former can apply only to a man not seeing a man.

But the above, as I said, is only one of the possible readings of “non homo videns hominem”. We can also understand this phrase so that the negation is applied only to the concept corresponding to the term ‘man’ in it, like this:

RAT(2)(“non homo videns hominem”)= RAT(videns)(RAT(non)(RAT(homo)))(RAT(hominem))(RAT(t)), Notice that in accordance with clause (RATamb), these two constructions are based on the two different analyses of the same syntactically ambiguous phrase, i.e., on the two different ways this complex phrase may be built up from its components according to the syntactic rules of our fragment. Using the characteristic functions defined above, we can distinguish these two analyses in the following manner:

(1) F8(non)(homo videns hominem)= F8(non)(F6(videns)(homo)(hominem)) (2) F6(videns)(non homo)(hominem)= F6(videns)(F8(non)(homo))(hominem) The first of the remaining two clauses assigning a ratio to simple terms is (RATadj), which specifies that the concept of an adjective in the neuter gender in its capacity to form a standalone term is such that it gets saturated with the concept of the quality connoted by this adjective, like the concept of whiteness connoted by ‘album’, i.e., the concept signified immediately by the term ‘albedo’.

In a similar manner, the last of this group of clauses specifies that the ratio of an ampliative participle of the neuter gender having no complements and ampliating to the past, like ‘mortuum’, gets saturated by the concepts of some past and the present time. Actually, this clause is very ad hoc, and is added only for the sake of the term ‘mortuum’ in our fragment. But since I think the more general formulations could quite easily be given on the basis of the formulations I provide here, I am ready to sacrifice generality on the altar of simplicity in this case.

Because of their semantic diversity, we have four different clauses for complex terms formed by participles in the neuter gender with their complements. For the first of these we have already seen an example above, with ‘videns’. The second clause serves to make the semantic distinction between, e.g., “videns omnem hominem” and “omnem hominem videns”. Clearly, to these

66

complex terms there should correspond different concepts. For consider the following sentences: “Videns omnem hominem est equus” and “Omnem hominem videns est equus”. The first can be true only if there is some horse that sees every man, while the latter can be true, if every man is seen by some horse or other. But so to these sentences there should correspond different mental propositions, which, however can only differ in their subjects, which are precisely the concepts signified by our two complex terms differing only in word order.

Now according to the first clause (RAT1a), the ratio of “videns omnem hominem” is to be constructed as follows:

RAT(“videns omnem hominem”)= RAT(videns)(RAT(omnem hominem))(RAT(t))= RAT(videns)(RAT(omnem)(RAT(hominem)))(RAT(t)) On the other hand, in accordance with the second clause (RAT1b), the ratio of “omnem hominem videns” can be obtained thus:

RAT(“omnem hominem videns”)= RAT(omnem)(RAT(videns)(RAT(hominem))(RAT(t))) As I think already these simple illustrations sufficiently show how the construction of complex rationes could be achieved in this system, instead of going into further details let me try to round out the picture by some simple schematic indications of how the remaining semantic properties of expressions of our fragment could be defined and base my concluding remarks on these.

I hope it is already clear from the foregoing that if all simple rationes building up a complex one were syntactically marked and the syntactic construction faithfully mirrored the conceptual construction, one simple and elegant clause could do the whole job of assigning rationes to complex expressions in the following manner:

If X=Fn(x0)(x1)...(xn), then RAT(X)=RAT(x0)RAT(x1)...RAT(xn). Indeed, all the clauses above seem to agree with this general pattern, the only reason for their complexity apparently lying in the diversity of the ways different expressions in the various syntactic categories of our fragment indicate (or fail to indicate) the arity of the concept corresponding to them, and the type of concepts this concept requires as its complements.

On the basis of such a simple clause, also the further semantic values of the expressions of our language would be easy to assign, along the lines indicated in the preliminary semiformal discussion. Significata of simple terms should be first assigned by free-choice functions of appropriate arity, which could then determine the significata of complex expressions parallel with the construction of the corresponding complex ratio. Significations could then be defined as appropriate sets of significata and connotata, these sets providing suitable identity conditions for the rationes of simple categorematic terms. On this basis supposita of simple as well as complex terms could be defined as those significata of the terms of a proposition which are (or were or will be) actual at the time connoted by the copula (or by the ampliative terms, if there are any) of the proposition. Of course, to this end separate clauses would be needed to determine the effect of syncategorematic, and ampliative terms on the supposition of a complex term in which they occur. Finally, on this basis a definition of truth could be provided, based on the idea that the truth of an affirmative proposition requires the identity of the supposita of its terms. Here again, a whole series of separate clauses would be needed to define truth for categorical propositions of different quantity, quality and tense. Also, since the quantity of oblique terms, depending on word-order influences supposition and truth conditions in different ways (identifying different

67

mental propositions as corresponding to the sentences in which these oblique terms occur, as we could see), separate clauses should take care of these different cases as well.23

But now, instead of going into these details, let us turn to the methodological questions raised in the introduction, to reflect on this complexity of the semantic theory, arising so unexpectedly for such a simple fragment as we have been considering.

CONCLUSION: SOME METHODOLOGICAL LESSONS

As I remarked in the previous section, if all simple rationes building up a complex one were syntactically marked and the syntactic construction faithfully mirrored the conceptual construction, one simple clause could do the job of assigning rationes to complex expressions, since in this case, the way complex concepts are built up from simple ones could be directly read off from the syntactic construction. Indeed, it is precisely this easy identifiability of conceptual structure on the basis of perceptible syntactic structure that seems to motivate the construction of artificial languages, to develop some direct “conceptual notation”, Begriffsschrift, to help the mind’s eye in discerning the thoughts not so revealed by the syntactic structures of natural languages.

On the other hand, the very idea of the constructibility of a single conceptual notation presupposes that there is some uniform conceptual structure, identifiable as such lurking behind the various, accidentally developed façades of natural languages. Now despite the apparently Aristotelian origin of this idea, and despite Buridan’s own avowal of Aristotelianism even in this respect, I think the Buridanian approach to semantics presented above suggests a much more intricate and intimate relationship between language and thought, determining further the relationship of language to reality.

As the very complexity of the above clauses shows, a natural language, indeed, even such a simple fragment of it as presented above, uses various different syntactic clues to identify concepts in different semantic and syntactic categories. But these different clues seem to do even more than just showing various ways to hit upon this or that concept, which would be there anyway, whether we have this clue to identify it or another. Some concepts owe their very existence to these syntactic clues, whence according to this semantic approach, different people using different languages must have different conceptual structures operative in their minds, owing to the differences in the structure of their languages. For example the idea of definiteness (unicity in a certain context) carried uniformly in English by the definite article is certainly not so carried in Latin, which lacks articles. So while in a Buridanian semantics for English we probably should have a simple syncategorematic concept corresponding to the definite article, the same concept could not occur in the Buridanian semantics of Latin.

As even these simple considerations show, on the Buridanian approach there is no uniform semantics for all natural languages: there are as many different semantics, as there are different languages. Indeed, since even users of the same idiom may widely differ in their usage, different socio-linguistic communities may have further strong claims to autonomous semantics, on account of their specific usage, associated with specific concepts. Buridan himself is perfectly 23 For a thorough discussion of the problems arising for Buridan’s semantics in this regard, see: É. Karger: “Un débat médiéval sur le concept de sujet d’énoncé catégorique: étude d’un texte de Jean Buridan”, in: z. Kaluza-P. Vignaux: Preuve et raisons à l’Université de Paris: logique, ontologie et théologie au XIVe siècle, Paris, 1984.

68

aware of these implications of his approach: his references to jargon and obligational disputes clearly indicate this.24

On the other hand, all this semantic and conceptual diversity need not necessarily impede communication and understanding between people brought up using different idioms. As the concepts of others are not in principle inaccessible, as argued above, despite the fact that they are not directly observable, it is possible to acquire the concepts of others and develop common concepts between users of different languages. In such a case, however, we do not have even those relatively safe syntactic clues to the meaning of others as we have with persons speaking our own idiom. It is only through cooperation and coexistence, sharing the same form of life that our concepts can get so harmonized that we shall be able eventually to speak the same language.

But if this is so, then we may indeed not expect anything so simple and perspicuous from a natural language semantics as we are used to in our formal semantic studies. However unwieldy and cumbersome the Buridanian approach may seem in comparison to, say, a Fregean approach, it probably more faithfully reflects the real semantic situation, with all its intricacies, uncertainties and contingencies.25

24 For a discussion of this aspect of Buridan’s semantics see J. Pinborg: “The Summulae, Tractatus I De Introductionibus”, in: J. Pinborg (ed.): The Logic of John Buridan, Copenhagen, 1976. 25 Research for this paper was done during my visit in the Copenhagen Institute for Greek and Latin Mediaeval Philology, in 1991, January-March. My thanks are due to Sten Ebbesen, director of the Institute, for his kind invitation and his personal and scholarly help, to the staff of the Institute, for their kind hospitality, and to the Augustinus Foundation, for their generous financial assistance which made this visit possible.

69

Contemporary “Essentialism” vs. Aristotelian Essentialism

1. The principal theses of contemporary “essentialism” vs. Aristotelian essentialism

Contemporary “essentialism”, if we want to provide a succinct, yet sufficiently rigorous characterization, may be summarized in the thesis that some common terms are rigid designators.26 By the quotation marks I intend to indicate that I regard this as a somewhat improper (though, of course, permitted) usage of the term (after all, nomina significant ad placitum27). In contrast to this, essentialism, properly so-called, is the Aristotelian doctrine summarizable in the thesis—as we shall see, no less rigorous in its own theoretical context—that things have essences.

The two theses, although related, are by no means identical. In this paper I wish to show exactly how these theses differ in virtue of the radically different conceptual frameworks in which they acquire their proper meaning, yet without these conceptual differences rendering them logically “incommensurable”. By this comparative analysis I hope to provide reasons to reconsider our contemporary philosophical problems in a historical perspective, realizing how their intrinsic difficulties stem from a contingently evolved conceptual heritage. In these considerations, being primarily concerned with the distinction between them, I am going to treat both contemporary “essentialism” and Aristotelian essentialism very broadly and rather indistinctly in themselves, in the sense that I am not going to delve into otherwise importantly different versions of either of the two. For reasons of clarity and influence I have selected Kripke and Aquinas as paradigmatic representatives of their respective conceptual frameworks. Nevertheless, I will try to treat these frameworks in such general terms as to be able to cover the thought of a great number of similarly important thinkers.

2. The problems of contemporary “essentialism”

The most widely recognized framework of contemporary “essentialism” is possible worlds semantics. That a common term is taken to be a rigid designator might be reflected in the formal system by stipulating that if an individual is an element of the extension of the corresponding

26 To be sure, this characterization by no means covers all versions of what goes by the name of “essentialism” in contemporary philosophy. Still, this is arguably the most widespread notion of “essentialism” nowadays, and it certainly does serve as “the least common denominator” in discussions concerning “essentialism”. Indeed it could also be argued that most of the more stringent versions of “essentialism” are just further refinements of the same notion in basically the same logical semantic framework. Therefore, since in the present discussion my main concern will be to contrast the underlying logic of (the Thomist version of) medieval Aristotelianism with that of contemporary “essentialism”, I think in this comparison this “simplification” is justified. 27 This phrase (or some other of its variants) was used by medieval logicians time and again to stress the fact, established by Aristotle at the beginning of his On Interpretation, that linguistic items, considered as mere utterances or inscriptions, signify by convention, that is, on the basis of some (mostly tacit) agreement among users of the same language, or among members of some smaller linguistic community (cf. slang, which Jean Buridan explicitly considered in this context) concerning what they are supposed to have in mind when they use any of these items with proper understanding.

70

predicate parameter in one possible world, then it is an element of the extension of the same predicate parameter in all other possible worlds in which that individual exists, i.e., the domain of which contains that individual as its element. Such a stipulation basically amounts to saying that rigid designators “stick with their individuals” (“their individuals” being the individuals that fall within their extension in a possible world) across all possible worlds in which those individuals exist.

Now clearly, rigidity is an independent, additional stipulation on the possible worlds framework. For all the logical machinery of possible worlds semantics requires is that the semantic values of the expressions of a modal language be assigned in models involving possible worlds. But this much is obviously taken care of without stipulating that some predicate terms are such that whatever falls within their extension in one possible world falls within their extension in any other possible world in which it exists. Thus, this stipulation is in no way part of the logical machinery of possible worlds semantics itself, but something that may or may not be added to this machinery for independent reasons. This is how it comes about, then, that while various intuitions of several philosophers clash over admitting or omitting this additional essentialist stipulation, none of them can have decisive logical grounds for definitively proving their own position and/or definitively refuting the positions of others.

To be sure, there is nothing wrong per se in having recourse to extra-logical intuitions in philosophical debates. However, what renders using these extra-logical intuitions in the particular debates concerning “essentialism” highly dubious is that these intuitions are formulated and understood within the conceptual framework of a historically quite recent philosophical tradition, which for the most part evolved on the basis of a radically anti-essentialist, indeed, generally anti-metaphysical mentality. Perhaps, a general characterization of what I take to be two main families of arguments in these debates—significantly, comprising arguments both from “essentialists” and anti-“essentialists”—will make clear what I have in mind.

2.1 “Opacity/transparency” arguments

The cluster of arguments I would gather under this heading range from Quine’s cyclist mathematician and number-of-planets arguments, to Kripke’s pain-argument, to Yablo’s statue-argument, and many others.28 All these arguments are based on the perceived inconsistency of three propositions of the following form:

d1 is essentially P

d2 is not essentially P

d1=d2

In the various arguments, either these three propositions are used as premises to establish an inconsistent conclusion (e.g., Quine’s cyclist mathematician argument follows this pattern), or

28 All these are conveniently brought together by Michael della Rocca in his: “Recent Work on Essentialism”, Philosophical Books, 37(1996), pp. 1-13, and 81-89. For a particularly vivid documentation of the earlier debates on essentialism and modal logic, which already contained virtually everything that came to the fore in the later discussions, see R. B. Marcus: Modalities: Philosophical Essays, Oxford University Press: New York-Oxford, 1993, especially essays 1, 3 and 4.

71

two of them are used to conclude to the negation of the third (e.g., Quine’s number-of-planets argument uses propositions exemplifying 1 and 2 to establish the allegedly absurd denial of 3;29 while Kripke’s and Yablo’s above-mentioned arguments use propositions exemplifying 1 and 2 to establish the denial of 3, which in Kripke’s case is hailed as a significant philosophical conclusion concerning the non-physical nature of pain, while in Yablo’s case it is deemed to be an unacceptable conclusion, causing much philosophical pain).

The different uses to which these arguments are put by their “essentialist” or anti-“essentialist” proponents depend on the intuitions these philosophers have concerning the particular formulations of their premises and/or conclusions. Yet, what remains common in all these different arguments, despite their conflicting intents and various formulations, is the realization that 1-3 can be regarded as inconsistent only if 1 and 2 provide referentially transparent contexts for d1 and d2—or, what amounts to the same, if both d1 and d2 are treated as rigid designators of what they designate. Accordingly, whenever philosophers intend to neutralize the force of any of these arguments (whether for or against some essentialist conclusion), they point out that the proposition corresponding to either 1 or 2 has an equally (or even more) intuitive opaque (or de dicto) reading or reformulation which invalidates the argument in question, or correlatively, if they want to preserve the validity of such an argument, they try to show why such a reading or reformulation is unacceptable.

For example, consider Kripke’s argument concerning heat and molecular motion.

(H1) Molecular motion is essentially molecular motion

(H2) Heat is not essentially molecular motion

therefore,

(H3) Heat is not molecular motion

Provided that ‘molecular motion’ and ‘heat’ are “rigid designators”, the argument is valid, but the conclusion is scientifically false, hence a problem for “essentialism”.30 A “Kripkean reconstrual”31 accounting for the alleged “strong intuition” for (H2), but invalidating the argument, points out that ‘heat’ can be taken in two ways. It can be taken either as referring to the physical phenomenon which actually causes in us the sensation of heat, which is nothing but molecular motion, and which, therefore, is essentially molecular motion. On this reading ‘heat’ rigidly refers to molecular motion, but then (H2) is false. The other reading, however, takes ‘heat’ as referring non-rigidly to anything whatsoever that may possibly cause in us the sensation of heat, which may back up the intuition behind (H2), but then, since it renders ‘heat’ non-rigid, it invalidates the argument.

Now, whatever one’s reactions to particular formulations of this type of argument may be, it should be clear that such moves merely transform questions of intuitions about the essentiality of 29 Quite characteristically, “essentially” and “necessarily” are often used interchangeably in these arguments, so I am just following this practice here. Cf., however, R. B. Marcus: “Essential Attribution” in: Modalities: Philosophical Essays, Oxford University Press: New York-Oxford, 1993, p. 60. 30 A good example of a contrary use of the same type of argument, to establish an essentialist conclusion, is Kripke’s argument against body-mind identity. Although in this case Kripke argues that a reformulation is unavailable, his critics’ arguments are intended to show precisely this, thereby showing that one of the premises has to receive an opaque reading, which invalidates the argument. 31 To adopt Michael della Rocca’s somewhat odd, but fitting expression.

72

certain terms into questions of intuitions about the essentiality of other terms. (In this case, the question whether ‘molecular motion’ is an essential predicate of heat is transformed into the question whether ‘heat’ is a rigid designator, that is, an essential predicate, of the phenomenon that it actually designates.) This, again, would not be harmful in itself, if questions concerning terms about which our intuitions are uncertain could in this way be transformed into questions about terms about which we can be certain. However, given that the underlying logical framework in these discussions not only fails to sort out which particular terms should be deemed essential,32 but it also fails to give any reason whatsoever why there should be any essential terms at all, arguments of this sort within this framework are doomed to inconclusiveness.

Indeed, as the previous example shows, since nomina significant ad placitum, to ask whether, for example, ‘heat’ is a rigid designator, is not a very illuminating question. For the answer is that it depends. If we use it as such, making it stick with the phenomenon it actually designates, come what may, then of course it is rigid. But if we use it in another way, making it stick with its actual conditions of applicability (perhaps, expressed in a nominal definition), whether in a possible situation these conditions are satisfied by the same phenomenon that satisfies them in the actual situation or not, then of course it is not rigid.33 But then it seems that the whole issue about essential vs. non-essential predicates boils down to determining the proper usage of certain terms, concerning which philosophers may have different intuitions, but certainly no principled metaphysical reasons for preferring one usage over the other.

As a matter of fact, this last remark shows one of the most basic problems with Kripke-style “essentialism”, namely, that the modal approach to essence apparently puts the cart before the horse. Since it seeks to explain essence in terms of essential properties, rather than the other way around, it certainly cannot invoke essences in trying to cope with its primary task presented by anti-essentialist criticisms: to offer some reason why some common terms have to be regarded as essential to the things they are actually true of. So while the issues in this framework could not be settled on logical grounds, in the same framework they cannot be settled on principled metaphysical grounds either.

2.2 Insufficiency arguments

This realization seems to be the main motivation for recent criticism of the modal approach by Kit Fine. As he puts it, his objections to the modal account “will be to the sufficiency of the proposed criterion, not to its necessity”.34 These objections show that it is easy to find properties deemed essential by the modal criterion; that is, properties that in the Kripkean parlance would be rigid designators of an object, which, however, nobody would take to be essential in the stronger sense of somehow characterizing or expressing the nature of the thing.

32 To be sure, this is good; after all, if essential, or even “essential”, terms should have to do something with the nature of things, such sorting out should not be simply a matter of logic. 33 After all, it did not take Locke more to turn the traditional stock-example of an essential predicate, ‘man’, into an accidental predicate: all he had to do was to insist that the meaning of this term is determined by its nominal definition. For more on this issue see the last section of this paper. 34 Kit Fine: “Essence and modality”, in: J. E. Tomberlin: Philosophical Perspectives, 8, Logic and Language, Ridgeview Publishing Company Atascadero, California, 1994, pp. 1-15. p. 4.

73

Take for instance Socrates and the singleton whose only member is Socrates. On the Kripkean account it would be essential both for the singleton to contain Socrates and for Socrates to belong to the singleton. However, it is hard to see what it has to do with the nature of Socrates whether he belongs or not to any set whatsoever. Socrates would certainly be both the same thing and the same kind of thing, even if there were no sets at all.

But there is no need to appeal to such abstract objects. Consider two distinct physical objects, such as Socrates and the Eiffel Tower. On the Kripkean account each would necessarily have the property of being distinct from the other; yet, why should his being distinct from the Eiffel Tower belong to the nature of Socrates?

In general, the Kripkean account renders any necessary property “essential” to anything, however extrinsic such a property to the thing in question may be. For example, the property λx[Px∨~Px], or the property λx[Px→Px] should be essential to any individual whatsoever. Consequently, it should be essential to you that you are either reading or not reading this paper, or that if you are reading it, then you are reading it, which on a stronger reading of ‘essential’ would mean that these properties, and along with them this paper, somehow belong to, and therefore constitute your nature, which is absurd.

Well, of course, these arguments can “work” only if someone is willing and able to recognize a sense of “nature” or “essence” that is somehow stronger than what can be reached on the basis of the modal account. As Fine himself cautions: “I am aware, though, that there may be readers who are so in the grip of the modal account of essence that they are incapable of understanding the concept in any other way. One cannot, of course, argue a conceptually blind person into recognizing a conceptual distinction, any more than one can argue a colorblind person into recognizing a color distinction. But it may help such a reader to reflect on the difference between saying that singleton Socrates essentially contains Socrates and saying that Socrates essentially belongs to singleton Socrates. For can we not recognize a sense of nature, or of "what an object is", according to which it lies in the nature of the singleton to have Socrates as a member even though it does not lie in the nature of Socrates to belong to the singleton? Once we recognize the asymmetry between these two cases, we have the means to present the objection. For no corresponding modal asymmetry can be made out. If the singleton essentially contains Socrates, then it is necessary that Socrates belongs to the singleton if the singleton exists. Granted that it is necessary that the singleton exists if Socrates does, it follows that it is necessary that Socrates belongs to the singleton if Socrates exists. But then Socrates essentially belongs to the singleton, which is the conclusion we wished to avoid.”35

But then, again, it seems that we are left here with an appeal to intuition which does not have much to do with the nature of things, but rather with a “feeling”36 as to linguistic usage, this time concerning the usage of ‘nature’. However, especially nowadays, when every single philosopher seems to have their own “theory of meaning and/or reference”37 such an appeal cannot be 35 Ibid. 36 In fact, in another argument Fine explicitly appeals to such “feelings”: “We have no "feeling" when we say that Socrates is essentially a man but not essentially existent that there has been a shift in the use of the term. If the term had these two senses, then there should be a sense in which Socrates was not essentially a man (in addition to the sense in which he is essentially a man). But there appears to be no such sense.”. 37 Cf. “the double indexical definition of meaning” provided by William Lycan: “meaning=df.whatever aspect of linguistic activity happens to interest me now”, quoted by Devitt, M.: "The Methodology of Naturalistic Semantics", The Journal of Philosophy, 91(1994), p. 545-572, p. 548.

74

expected to have a universally compelling force; and again, after all—nomina significant ad placitum.

However, despite these and similar concerns, I assume that many philosophers are both willing and able to recognize a stronger sense of “essence” or “nature”. Indeed, I think that many philosophers will also recognize the need for such a stronger sense, given the intuitive troubles with the modal approach. But the question then is what we should take as the standard for the proper expression of such a stronger sense.

Again, when it comes to stipulating a certain usage, anyone has the right to introduce any sorts of “strengthening” of the sense of this term ad placitum. But when it comes to the question of the proper usage of a technical term of a philosophical or scientific theory (as the term ‘essence’ and its equivalents, such as ‘nature’, ‘quiddity’, etc. clearly did function as such in the Aristotelian philosophical tradition), then we have to turn to the usage of those who used the term within the context of that theory within which it originally acquired its proper, intended meaning.38 Kit Fine, proposing in his alternative approach to recover the lost connection between the notions of essence and real, as opposed to nominal, definition, clearly moves in this direction. However, because of failing to reconstruct the traditional theoretical context of this distinction—which in fact is a comprehensive semantic theory connecting the notions of meaning, reference, predication and being in a particular manner to the notion of essence—his approach, as we shall see, is still significantly different from this tradition. In any case, in the next section I will reconstruct precisely this proper theoretical context, thereby providing not only some ad hoc strengthening of the sense of the term ‘essence’, but also reconstructing the sense in which it was properly used in the medieval Aristotelian tradition.

3. The conceptual framework of medieval Aristotelian essentialism

In what follows I present a brief, summary reconstruction of the most basic, formal semantic principles that served as the theoretical background for the traditional Aristotelian concept of essence. For want of space, in this reconstruction I will proceed rather “dogmatically”, without discussing the textual evidence backing the reconstruction. In a historical study such a procedure would be totally unjustifiable. However, what justifies it here is that in the present comparison it is only the reconstructed theory itself that will be relevant, not the historical verification of the reconstruction; and, in any case, I have already done the job of the historical verification in other papers.39 So, instead of a piecemeal reconstruction based on the texts, I present here only some formal clauses describing (part of) the semantic theory in question, along with some brief explanatory comments on each. 38 For a brief description of the proper usage of these terms see the first chapter of St. Thomas’s On Being and Essence. 39 Klima, G. (1996) “The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being”, Medieval Philosophy and Theology, (5)1996, pp. 87-141; Klima, G. (1993) “The Changing Role of Entia Rationis in Medieval Philosophy: A Comparative Study with a Reconstruction”, Synthese 96 No. 1., pp. 25-59; Klima, G. (1993) “‘Socrates est species’: Logic, Metaphysics and Psychology in St. Thomas Aquinas’ Treatment of a Paralogism”, in: K. Jacobi (ed.): Argumentationstheorie: Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns, Brill: Leiden, the Netherlands, pp. 489-504; Klima, G. “On Being and Essence in St. Thomas Aquinas’s Metaphysics and Philosophy of Science”, S. Knuuttila - R. Työrinoja - S. Ebbesen (eds.): Knowledge And The Sciences In Medieval Philosophy: Proceedings of the Eighth International Congress of Medieval Philosophy (S.I.E.P.M.), Helsinki 24-29 August 1987, Vol. II, Publications of Luther-Agricola Society Series B 19, Helsinki, 1990, pp. 210-221.

75

3.1 Semantics

Concrete common terms signify individualized forms of individual things.

Formally: SGT(P)(u)(t)∈W∪{0}, in a model <W,T,A,SGT,0>, where W≠∅, T≠∅, t∈T, A(t)⊆W, u∈W∪{0}, 0∉W, and SGT(P)(0)(t)=0; where W is the domain of discourse, comprising both actual and non-actual individuals, A(t) is the set of actual individuals at time t, SGT is the signification function to be defined (in part) below,40 and 0 is a zero-entity, a technical device used to indicate the case when a semantic function for a certain argument lacks a value from W.

Comments:

Concrete common terms, such as ‘man’, ‘stone’, ‘tall’, ‘runs’, etc., which are predicable of several individuals, signify individualized forms of these individuals, that is, those individual features of these things in virtue of which these terms apply or may apply to these things, if they can apply to them at all. As this remark intends to make it clear, the term ‘form’ in this rule need not—indeed, must not—be interpreted with all the metaphysical weight it had in Aristotelian metaphysics.41 Since this is a rule describing the semantic function of common terms, it only serves to specify how their significata, as I will call them, are assigned, regardless of what the ontological status of these semantic values may be. For to show which semantic values of which expressions fall into which ontological categories can be only the subsequent task of a metaphysical inquiry, to be carried out in the language whose semantics has been so specified. As can be seen, these significata, or “individualized forms”, are assigned to concrete common terms in relation to two individualizing factors, namely, their subject and time, regardless of whether these “forms” are actual or not in these individuals at a given time. For example, the term ‘sighted’ in this framework is interpreted as signifying the individual sights of individual animals (that is, whatever it is in their constitution that enables them to see), at any given time; therefore, if in the formal clause above in an interpretation we let u range over the domain of the things and let t range over the dates of our actual universe, then we may get, say, the following instance of this clause:

40 A description of the complete technical apparatus can be found in Essay 5. of Klima, G.: ARS ARTIUM: Essays in Philosophical Semantics, Medieval and Modern, Budapest: Institute of Philosophy of the Hungarian Academy of Sciences, 1988, or, for a simpler language, in my “On Being and Essence in St. Thomas Aquinas’s Metaphysics and Philosophy of Science”, S. Knuuttila - R. Työrinoja - S. Ebbesen (eds.): Knowledge And The Sciences In Medieval Philosophy: Proceedings of the Eighth International Congress of Medieval Philosophy (S.I.E.P.M.), Helsinki 24-29 August 1987, Vol. II, Publications of Luther-Agricola Society Series B 19, Helsinki, 1990, pp. 210-221. Here I only supply some of the relevant clauses of the definition of an interpretation for a language similar to the one described in this paper. I think that even without going into further technical details, these clauses will sufficiently indicate how the construction of the whole theory should proceed. In any case, they should be sufficient to serve the purpose of the present comparison. 41 As St. Thomas wrote: "...dicendum est quod illud a quo aliquid denominatur non oportet quod sit semper forma secundum rei naturam, sed sufficit quod significetur per modum formae, grammatice loquendo. Denominatur enim homo ab actione et ab indumento, et ab aliis huiusmodi, quae realiter non sunt formae." QDP, q. 7, a. 10, ad 8. Cf. also e.g. Cajetan: "Verum ne fallaris cum audis denominativum a forma denominante oriri, et credas propter formae vocabulum quod res denominans debet esse forma eius quod denominatur, scito quod formae nomine in hac materia intelligimus omne illud a quo aliquid dicitur tale, sive illud sit secundum rem accidens, sive substantia, sive materia, sive forma." Cajetan, Thomas de Vio: Scripta Philosophica: Commentaria in Praedicamenta Aristotelis, ed. M. H. Laurent, Angelicum: Romae, 1939, p. 18.

76

SGT(‘sighted’)(Socrates)(400 B.C.)∈A(400 B.C.),

which merely states that Socrates’s sight was one of the actual things in this universe in 400 B.C. Of course, since u ranges over all things in the universe, it can take up values for which this term is not interpreted. It is such cases that are represented by assigning the term the zero-entity as its value. Thus, for example,

SGT(‘sighted’)(the Statue of Liberty)(1996 A.D.)=0

As can be seen, in general, by picking up various individuals in the place of u, and various times (dates, time-points, or any other time-intervals, depending on the scale of the actual interpretation), we get the significata of a common term belonging to these individuals at these different times, whatever these semantic values are, regardless of whether they are actual or potential, or even whether the term can apply to the thing in question at all (for if not, then it simply gets 0 as its value).42

A concrete common term, as the subject of a proposition, has the function to supposit for (refer to) the individuals in which its significata are actual at the time connoted by the copula of the proposition.

Formally: SUP(S)(t)∈{u: SGT(S)(u)(t)∈A(t)}, provided this set is not empty, otherwise SUP(S)(t)=0.

Comments: If we say: ‘A dinosaur is running’, the term ‘dinosaur’ should refer to, or using the transliteration of the medieval technical term, supposit for,43 individual, actually existing dinosaurs at the present time of the actual use of the proposition. But of course only those things are actual dinosaurs in which the significate of the term ‘dinosaur’ is actual (i.e. those individual u’s, for which it holds that SGT(‘dinosaur’)(u)(1996 A.D.)∈A(1996 A.D.)). However, since at this time there is no such a thing in our actual universe, this term refers to nothing, that is, since {u: SGT(‘dinosaur’)(u)(1996 A.D.)∈A(1996 A.D.)} = ∅, given that for any u, SGT(‘dinosaur’)(u)(1996 A.D.)∉A(1996 A.D.), since nothing is a dinosaur at this time, SUP(‘dinosaur’)(1996 A.D.) = 0. On the other hand, if we say: ‘A dinosaur was running’, the term ‘dinosaur’ should, and actually does, refer to whatever was a dinosaur, that is, whatever had the significata of the term ‘dinosaur’ in actuality in the past relative to our present. That is to say, since {u: SGT(‘dinosaur’)(u)(t<1996 A.D.)∈A(t<1996 A.D.)}≠∅ in our actual universe, this term will successfully refer to, or supposit for things that were dinosaurs at some time in our

42 We may also suggest that “in between” these two cases, that is, getting an actual form or 0 as it value, a predicate may get non-actual forms as its values, ‘non-actual’ covering several possible sorts of natural potentiality (or the lack thereof), which is a very rich field of further metaphysical inquiry, but which is irrelevant in our present analysis. For further technical details the reader should consult Essay 5. of Klima, G.: ARS ARTIUM: Essays in Philosophical Semantics, Medieval and Modern, Budapest: Institute of Philosophy of the Hungarian Academy of Sciences, 1988. 43 Medieval supposition theory, as even the enormous recent secondary literature proves, is a topic deserving a book in itself. Here I reconstruct only one particular aspect of a tiny fragment of this theory. For further references, both to primary and secondary literature, and for further details of my reconstruction of the “core theory” see Klima, G.: ARS ARTIUM: Essays in Philosophical Semantics, Medieval and Modern, Budapest: Institute of Philosophy of the Hungarian Academy of Sciences, 1988. To see how this theory of reference can be developed into a formal theory equivalent to generalized quantification theory see especially Essay 3, “General Terms in their Referring Function” in the same book, and Klima, G.-Sandu, G. (1990) “Numerical Quantifiers in Game-Theoretical Semantics”, Theoria, 56, pp. 173-192.

77

past: SUP(‘dinosaur’)(t<1996 A.D.)∈{u: SGT(‘dinosaur’)(u)(t<1996 A.D.)∈A(t<1996 A.D.)}. Aside from this contextual character of this theory of reference, another important thing to notice here is that as far as the semantic theory is concerned, there is no stipulation as to the identity or distinctness of the significata and supposita of the same term. So, anyone who is taken aback by the apparently “obscure” character of these significata is free to identify these semantic values in their metaphysics. Then, for example, a “dinosaurhood” will be no more “obscure” than a dinosaur is, but obviously such a position will have its own further metaphysical consequences. In fact, the possibility of identifying a concrete term’s significata with its supposita is one of the most important conceptual tools in Aquinas’ arsenal to express divine simplicity. For, expressed in terms of this reconstruction, Aquinas has proofs to the effect that SGT(‘God’)(God)(t) = SUP(‘God’)(t), that is, that God’s deity is God; or that SGT(‘good’)(God)(t) = SUP(‘God’)(t), that is, that God’s goodness is God, etc. But note that these formulations are not semantic stipulations concerning the usage of the term ‘God’, but only metalinguistic expressions of what has to hold in the actual interpretation of the language in which Aquinas’s conclusions are true. As can be seen, however, in these remarks I was already compelled to use the abstract counterparts of the concrete terms in order to be able to refer to the significata of these concrete terms. In fact, according to this theory, this is precisely the function of abstract terms, as stated in the next rule.

The abstract counterpart of a concrete common term both signifies and supposits for the significata of the concrete common term.

Formally: SGT([P])(u)(t)=SGT(P)(u)(t), and SUP([P])(t)=SGT(P)(SUP(P)(t))(t), where [P] is the abstract counterpart of P.

Comments: As has been remarked above, the semantic rules concerning concrete terms do not stipulate anything concerning the identity or non-identity of the supposita and significata of concrete terms. This semantic rule, however, does stipulate this identity concerning abstract terms, and it also stipulates that these semantic values of the abstract terms have to be identified with the significata of their concrete counterparts.

The predication of a common term of an individual supposited for by the subject of the predication is true if and only if the significate of the common term in the individual thus supposited for is actual at the time connoted by the copula of the predication.

Formally: SGT(S—P)(SUP)(t)=1 iff SGT(P)(SUP(S)(t))(t)∈A(t)44

Comments: Take, for instance, the proposition: ‘Socrates is sighted’. According to this theory, the predication expressed by this proposition is true if and only if what is signified by ‘sighted’ in the suppositum of ‘Socrates’ at the time of the actual use of this proposition is actual at that time. That is, assuming that we are using (i.e. forming, asserting, or reading and actually understanding) this proposition at the date 1996,45 then

44 Since it is only the significata of predicates that are relevant in the present analysis, here I omit the reconstruction of Aquinas’s theory of the copula altogether. The reconstruction of that theory can be found in the papers referred to in n. 39. 45 Of course the scale might be different, say, decades, centuries, or months, days, hours, etc.

78

SGT(‘Socrates is sighted’)(SUP)(1996)=1 iff SGT(‘sighted’)(SUP(‘Socrates’)(1996))(1996)∈A(1996),46

which, in our actual case would evaluate this proposition as false, because Socrates’s sight is certainly not among the actually existing things at this date, given the fact that now Socrates is dead, and only an actually living animal can have sight.47

As can be seen, this formulation is just one possible way of putting what historians of medieval logic usually refer to as the inherence theory of predication.48 Even without going into its further technical details, I think it is clear that it is this theory which establishes the crucial conceptual connection between what may be called the via antiqua semantics of medieval Aristotelianism, and the essentialist metaphysics of the pre-Ockhamist tradition.49 For this is the theory that, by providing the truth conditions of simple predications in terms of the actuality of the significata of the predicates in the supposita of the subjects, connects the notion of the signification of forms of individual things to the central notion of this metaphysical tradition, the notion of being.

3.2 Metaphysics

Of course, there are many technical issues that would need to be clarified regarding exactly how this theory works. However, even this skeletal presentation of this semantics will be sufficient to deal with our central concern at the moment: the metaphysical payoff of this theory in handling the contemporary issues. To be sure, this payoff cannot be gained simply by deriving certain essentialist metaphysical principles from these semantic principles. On the contrary, as we could see, this semantics does not dictate to metaphysics any more than the contemporary framework does. However, by providing the above-described systematic connection between the semantic notions of the signification and supposition of both concrete and abstract terms and the central metaphysical notion of actual being, it provides a natural framework for formulating such plausible metaphysical principles from which the essentialist conclusions at issue are easily derivable.

To see this in detail, let us consider first how the semantics of the verb ‘exists’ and its abstract counterpart, the noun ‘existence’, as determined by the above semantic principles provides grounds for formulating some metaphysical principles. Let us take the proposition: ‘Socrates

46 Here we assume that for any t and any SUP, SUP(‘Socrates’)(t)=Socrates, if Socrates∈A(t) and SUP(‘Socrates’)(t)=0 otherwise. 47 Indeed, given the rule in the previous note, we get that since Socrates∉A(1996), for any SUP, SUP(‘Socrates’)(1996)=0. Then, since by rule 1 above SGT(‘sighted’)(0)(1996)=0, for any SUP, SGT(‘sighted’)(SUP(‘Socrates’)(1996))(1996)=0, and of course 0∉A(1996). Therefore, for any SUP, SGT(‘Socrates—sighted’)(SUP)(1996)≠1, that is, the predication is false. As can bee seen, if we had a common term as the subject of the predication, the truth value of the predication might be different for different supposition functions, so such a predication would behave exactly like a propositional matrix with a free (restricted) variable. This is the feature of this conception that can be exploited in dealing with quantification, but I need not pursue this line here. I have already dealt with these issues in my technical essays referred to in the earlier notes. 48 Cf. e.g. L. M. de Rijk's Introduction to his edition of Abaelard, P.: Dialectica, Assen, 1956, pp. 37-38; Henry, D. P.: Medieval Logic and Metaphysics, London, 1972, pp.55-56, Geach, P.T.: "Nominalism", in Geach, P. T.: God and the Soul, London, 1969. 49 For more on these qualifications see Klima, G.: “Ontological Alternatives vs. Alternative Semantics in Medieval Philosophy”, in: J. Bernard: Logical Semiotics, S - European Journal for Semiotic Studies, 3(1991), No.4,Vienna, pp. 587-618.

79

exists’. In accordance with rule 4 above, this proposition is true if and only if the significate of its predicate in the suppositum of its subject is actual. But given that ‘existence’ is the abstract counterpart of ‘exists’, we can use the term ‘existence’ to refer to this significate, and so we can say that this proposition is true if and only if Socrates’s existence50 is actual. Now, of course, as far as the above-described semantics is concerned, it would be possible to have models in which, say, Socrates is an element of the domain of actual things, while, his existence is not, or vice versa, but such models would verify the metaphysical absurdity that Socrates would be actual while he would not exist, or that his existence would be actual while he himself would not be one of the actual things. Therefore, on the basis of these considerations it is reasonable to add the further rule concerning the metaphysically relevant notion of existence that

(E) SGT(‘exists’)(u)(t)∈A(t) if and only if u∈A(t).

But this will immediately establish the predicate ‘exists’ as an essential predicate of anything in the contemporary sense, for, of course, on the basis of this rule the predicate ‘exists’ will necessarily51 be true of anything as long as it exists, that is, as long as it is actual.

In fact, Kit Fine has already drawn this conclusion concerning the modern theory, namely, that the predicate ‘exists’, interpreted as true on the basis of elementhood in the actual domain, will be one of the “trivial” essential predicates of things. However, he found this conclusion to be unacceptable, because on his reading this would mean that a contingent being, such as Socrates, essentially exists.52

But in this framework we need not regard this conclusion unacceptable at all. On the contrary, St. Thomas explicitly holds that existence in this sense has to be an essential predicate of all beings53, which, nevertheless, does not mean that he would identify the essence of any creature with its existence. In fact, this is precisely the point of St. Thomas’s famous metaphysical thesis of the real distinction between essence and existence in the creatures, which, for want of the required expressive resources, could not even be formulated in the contemporary framework, let alone be argued for or against.

To see this in more detail, having seen what the semantic values of ‘existence’ are, now we have to see what the semantic values of ‘essence’ are. To put it briefly, in accordance with what Aquinas says, the term ‘essence’ primarily stands for the significata of substantial predicates of substances,54 while these substantial predicates are those terms the existence of the significata of

50 Of course, strictly speaking, to express this in the formal system, we would have to introduce such complex singular terms that refer to some singular significate of a concrete term, but I think it is quite obvious how this can be done. In general, if s is a singular term, P is a common concrete term, and ‘s[P]’ is the complex singular term in question, then SUP(‘s[P]’)(t)=SGT(‘s[P]’)(t)=SGT(P)(SUP(s)(t))(t), that is to say, for example, the term ‘Socrates’s whiteness’ supposits for what the term ‘white’ signifies in the suppositum of the term ‘Socrates’. For the rule concerning SUP(s)(t) see n. 46. 51 Interpreting necessity as alethic necessity, that is, truth in all models. 52 “In addition to the difficulties which are common to the two forms of the modal account, there is a difficulty which is peculiar to the conditional form. Consider Socrates again: it is necessarily the case that he exists if he exists. But we do not want to say that he essentially exists.” ibid. p. 6. 53 Cf.: “Esse vero quod in sui natura unaquaeque res habet, est substantiale. Et ideo, cum dicitur, Socrates est, si ille Est primo modo accipiatur, est de praedicato substantiali. Nam ens est superius ad unumquodque entium, sicut animal ad hominem.” in Meta 5, 9. n. 896. 54 Secondarily, that is, in a secondary, analogical sense, it stands for the significata of the essential predicates of accidents; as St. Thomas explains in the last chapter of his De Ente et Essentia and in his comments on bk. 7 of the

80

which is identical with the existence of the things that have these significata. This criterion of the substantiality of a predicate (other than ‘exists’), therefore, can be formulated in the semantics as follows:

(SP) P is a substantial predicate if and only if SGT(‘exists’)(SGT(P)(u)(t))(t)=SGT(‘exists’)(u)(t)

and thus, if P is a substantial predicate, and in line with Aquinas’s metaphysical theory we also assume that all substantial predicates have the same significata in the same individuals, then the semantic values of ‘essence’ can be assigned by the following rules:

(ES1) SGT(‘essence’)(u)(t)=SGT(P)(u)(t) and

(ES2) SUP(‘essence’)(t)=SGT(P)(SUP(P)(t))(t)

So, for example, to say that Socrates is essentially a man means that what ‘man’ signifies in him, his humanity, is such a form that the actual existence of this form is nothing but the actual existence of Socrates, or, to put the same in perhaps more familiar terms, for Socrates to be is for him to be a man.55

Now, of course, upon this understanding of ‘essence’, ‘exists’ and ‘existence’, it is clearly possible to hold that ‘exists’ is an essential predicate of everything in the modern sense, and yet, it is not an essential predicate in the stronger sense that it would signify every thing’s essence. For although in virtue of (E) above, it will be necessary for the predicate ‘exists’ to be true of everything if it exists, still, the significate of the predicate ‘exists’ in a thing need not be identical with the significate of any of the thing’s substantial predicates. However, of course, this identity is not excluded by the semantic theory either; so, again, it takes separate metaphysical arguments to establish what the actual truth is, indeed arguments of the sort Aquinas used to establish the real distinction of these semantic values in the case of creatures, and their real identity in the case of God. But rather than going into these traditional metaphysical issues, it is time for us to see what we can gain from this approach in handling the contemporary issues outlined above.

4. Traditional essentialism, and the problems of contemporary “essentialism”

First of all, even if the semantic apparatus sketched above does not in itself determine that there are any essential predicates, it allows us to formulate plausible metaphysical reasons for showing that there have to be some, since such predicates are those that signify the essences of things, and we have to concede that things have essences.56

Metaphysics. However, here I cannot go into this issue. 55 To be sure, the same goes for his other substantial predicates, say, ‘animal’, ‘body’, etc. 56 In case anyone has doubts about the “logical order” here, the procedure is this: first we start out with a metaphysically neutral, noncommittal formal semantics, which stakes out the “playground” for a number of possible metaphysics. Then, using this semantics, we find that a number of propositions that in this noncommittal semantics would come out as possible, are in fact unacceptable. On the basis of this realization, then, we restrict the available models in the semantics, thereby producing a metaphysically somewhat more “loaded” version, which, however, may still leave a number of open alternatives, which can be the subject matter of further, even more specific metaphysical considerations. Well, of course, basically the same procedure would be, and in fact is, available in the modern framework. However, due to the inherent non-metaphysical origins of this framework, lacking the required expressive devices systematically connecting the semantics of concrete and abstract terms to the semantics and metaphysics of being, it is just not the “natural playground” for such sort of metaphysical inquiry.

81

For suppose there is a substance that has no substantial predicates. This would mean that the existence of the significata of all predicates of this substance other than ‘exists’ would be distinct from the existence of the thing itself. This substance, therefore, would have existence, but no essence. So it would be possible for this substance to exist, but not to have any true predicates besides ‘exists’ at all. But then it should be possible that there is a substance which is neither material nor immaterial, that is to say, which is neither a body nor a non-body, and which is neither a man nor any kind of thing other than a man, etc., but this is impossible.

As the Philosopher says: vivere viventibus est esse—for a living thing to be is for it to live. Therefore, for a living thing to begin to live and to cease to live is for it to come to exist and to cease to exist; indeed, everybody would agree that the birth and the death of living things is their coming to be and passing away. However, if there were no essences, then, since it is the essence of a thing that constitutes it in its specific kind, determining what (kind of thing) it is, a living and a non-living thing would not differ as to what (kind of thing) the one and what (kind of thing) the other is. Consequently, a living thing could turn into a non-living thing without ceasing to be what it is. However, whenever a thing changes, but without ceasing to be what it is, it can continue to exist.57 So, if things had no essences, a living thing could pass away without ceasing to exist, which contradicts what we have just conceded above.

Again, existence is nothing but the actuality of essence, since an essence is nothing but the determination of a certain kind of existence.58 But then, whenever a thing exists in its determinate kind of existence, say, as this kind of thing rather than that, there also has to be an essence, namely, this thing’s essence in actual existence. So, if there exists anything at all, its essence also exists. But we know that there exist certain things in our actual reality (at least, nobody can reasonably doubt his or her own existence), and that these things exist in some determinate way, as this kind of thing rather than that; therefore, we should also know that things actually have essences in our actual reality.

Furthermore, the essence of a thing, which determines what kind of a thing it is, determines what species of entities the thing in question belongs to. Therefore, whoever denies that things have essences has to deny that there is any specific difference between him or her and, say, an ass or a cabbage. But then such a person is no more worth talking to than an ass or a cabbage.59

So, on the basis of these and similar metaphysical reasons, and on the basis of the overwhelming evidence in our experience that things come in different kinds, it is safe to conclude that things in our actual reality do have essences. But then, since the essences of things are the significata of substantial predicates, it follows that there indeed are such predicates in our actual language(s)

57 For an extremely clear, brief description of the distinction between substantial and accidental (acts of) being, and the corresponding distinctions between substantial and accidental forms and change, see the first chapter of Aquinas’s De Principiis Naturae (On the Principles of Nature). 58 What exactly a “determination of a certain kind of existence” means, and how this can be expounded with reference to the medieval Aristotelian theory of qualified vs. absolute (secundum quid vs. simpliciter) predication, is an issue I cannot go into here. I am only hoping the notion is intuitively clear enough for the purposes of this argument. (The point, after all, simply is that whatever exists, exists as this or that kind of thing.) I did, however, deal with the issue at length in Klima, G.: “The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being”, Medieval Philosophy and Theology, (5)1996, pp. 87-141. 59 Anyone who feels shocked by the apparently rude ad hominem character of this argument should consult Aquinas’s discussion of Aristotle’s instructions concerning the necessity to use ad hominem arguments contra principia negantes, that is, against those who deny some first principles, in bk. 4 of the Metaphysics.

82

interpreted in our actual reality. Furthermore, since, as we have seen, such predicates are necessarily true of the things whose essences they signify, provided these things exist, these predicates will also be essential predicates of these things in the modern sense. Therefore, the Aristotelian position that things have essences implies the modern claim that things have essential predicates in the modern sense, thereby providing the required metaphysical underpinning for the modern claim. But the converse claim does not hold. Of course, all the “trivial” properties listed in the objections of Kit Fine are also necessary properties of anything in this semantics, yet in this semantics they need not signify the essences of anything; indeed, they are probably best handled as signifying some entia rationis, which do not have essences, given that essence is the determination of the act of existing of a real being.60

However, even if we could in this way come up with principled metaphysical reasons to support the modern “essentialist” claim, neither these metaphysical reasons, nor the semantic rules that make their formulations intelligible are sufficient to sort out which predicates of our language(s) should be regarded as substantial. Yet this is how it should be. For, in the first place, nomina significant ad placitum, so just any term of any language can be used by anyone in any way, of course, under pain of occasionally making a fool of themselves. (Such occasions occur when their usage is blatantly divergent from the received usage without any acceptable justification for such a divergence.) But the really interesting cases are the subtle, hardly detectable deviations, or indeed cases where the established usage is underdetermined, allowing individual users leeway in stipulating usage as they please.

In any case, it is sometimes possible that users of the same language might disagree as to what should count as the correct specification of the proper usage of some term. While some users may insist that a certain term should stick with the things it normally designates, under whatever “abnormal” circumstances, others may insist that “the proper meaning” of the same term is correctly specified by some sort of nominal definition specifying the actual conditions of applicability of the term, no matter what may satisfy these conditions under various possible circumstances.

For example, take the term ‘water’ in English. On the former user’s account the rule governing its use would be:

(U1) SGTU1(‘water’)(SUP(‘water’)(t))(t)=SGTU1(‘essence’)(SUP(‘water’)(t))(t)

On the other user’s account, however,

(U2) SGTU2(‘water’)(SUP(‘water’)(t))(t)=SGTU2(‘TCDL’)(SUP(‘TCDL’)(t))(t),

where ‘TCDL’ is short for ‘tasteless, colorless, drinkable liquid’, or anything of that kind of nominal definition, the actual values of which should of course be determined compositionally on the basis of the values of its constituents, but we need not go into such technical details here. We may simply assume that this has already been done in the framework of a fully articulated semantics. Since, however, the thing which under the present “normal” circumstances both users would identify as water could stay in existence without satisfying this definition under different circumstances, under those different circumstances ‘water’ would still signify the actually 60 A similar solution is available for Fine’s problem concerning Socrates and singleton Socrates. Since singleton Socrates is just a degenerate one-member collection, and collections are entia rationis, singleton Socrates does not have an essence at all, since it exists only in the mind with some fundamentum in re. For a detailed analysis of what this means see again the papers referred to in n. 39.

83

existing essence of water according to the first user’s usage, while according to the second user’s it would signify some non-actual (potential, or even no longer potential) feature of the same thing.61 Hence, clearly, SGTU1(‘water’)≠SGTU2(‘water’).

So, they are obviously using the same term with different significations, that is, equivocally, so their disagreement is merely verbal, and can easily be settled by making this difference clear. In any case, the philosophically important point is that it is only after this issue of usage is settled that we can start the metaphysical inquiry into the natures of the things that are picked out by means of their essential terms.62 For in merely specifying the meaning (signification) of a term by means of a nominal definition, we simply cannot go wrong as to the nature of the thing actually referred to by the term, since the nominal definition has nothing to do with the nature of the thing, it merely specifies the proper usage of the term (although, of course, we may have disagreements over what the proper usage is). However, when it comes to trying to characterize the nature of the thing referred to by the term by means of a real, essential, or quidditative definition, we definitely can, and very often do, go wrong.

In fact, among other things, it was precisely this type of error that discredited most of Aristotelian science in the late medieval and early modern period. But later on, it was not only particular Aristotelian claims concerning the natures of specific kinds of things that were called into doubt, but the whole Aristotelian conceptual apparatus with the entire metaphysical enterprise it defined. By now, however, we have come full circle. The originally anti-metaphysical trends of modern philosophy gave rise to analytic philosophical techniques which not only allowed, but more recently even demanded metaphysical reflection. Furthermore, the development of modern science recently put us into a position from which we can quite safely provide the real definitions of several natural kinds. For example, the essence of water is by all probability correctly described by saying that water is a body of H2O molecules. If this is indeed the correct essential definition of water, then (taking ‘H2O’ short for ‘body of H2O molecules’) what this means is the following:

61 Obviously, it is the first user’s usage that follows actual English, for of course ‘water’ in English is used as a substantial term, so no wonder it cannot apply to Putnam’s XYZ. In fact, the only reason why this otherwise trivial observation could be hailed as the harbinger of a “new theory of reference” was the tremendous influence of empiricism, which for its own epistemological reasons (in fact, going back to the original British empiricist program of trying to analyze all our mental contents ultimately in terms of simple sensible ideas), tied the meaning of all terms to their nominal definitions, ideally, ultimately analyzable in terms of simple sensible qualities. But since all such qualities are accidents, no wonder that in this (mostly programmatic) analysis all terms came out as accidental, non-essential, non-rigid designators of their individuals. However, if we abandon the rather narrow-minded empiricist platform and the consequent philosophy of language (as most analytic philosophers by now have done), it is no longer a sacrilege to insist that some terms do designate “rigidly” their individuals, regardless of their accidental features, which of course under “normal” circumstances may be useful indicators of what kind of thing we are actually dealing with, but which, under “abnormal” circumstances may be deceptive, in that they may not belong to the kind of thing they normally belong to, and/or they may belong to some other kind of thing that normally they do not belong to. 62 As Saint Thomas says, the question of what a thing is [quid est?] is preceded by the question of whether the thing is [an est?], but even this question presupposes that we know what is meant by the name of the thing in question [quid significatur per nomen]. Cf.: "... antequam sciatur de aliquo an sit, non potest sciri proprie de eo quid est: non entium enim non sunt definitiones. Unde quaestio, an est, praecedit quaestionem, quid est. Sed non potest ostendi de aliquo an sit, nisi prius intelligatur quid significatur per nomen. Propter quod etiam Philosophus in iv Metaphysicae, in disputatione contra negantes principia docet incipere a significatione nominum." in PA lb. 1, lc. 2, n. 5.

84

(H2O) SGT(‘water’)(SUP(‘water’)(t))(t)=SGT(‘essence’)(SUP(‘water’)(t))(t)= SGT(‘H2O’)(SUP(‘water’)(t))(t)

Of course, this move will make ‘water’ and ‘H2O’ have the same signification, that is, synonymous. Yet, this need not imply that whoever knows the signification of ‘water’ would thereby know that water is H2O. For one of course can have perfect possession of the concept of water without having any idea of chemistry whatsoever. What this person does not know is only that the chemical concept, which he or she does not have, picks out the same essence that his or her concept of water does. So to acquire this knowledge is to acquire this concept and to establish this quidditative definition. But the original acquisition of this concept was precisely what happened in the recent history of chemistry, in the course of scientific research. So it should be clear that, contrary to the apparent practice of “essentialists”, to find out what is essential to a given kind of thing is not a matter of personal intuitions, but rather a matter of experience, indeed, of scientific experiments, putting the thing in “abnormal” circumstances, making it interact with other things (after all, as St. Thomas says, the nature of the thing is the principle of its proper operation), precisely the way modern science investigates the nature of things.63 So modern science in no way needs to undermine Aristotelian essentialism. On the contrary, if we manage to recover the adequate conceptual framework of traditional essentialism in the broadest, formal semantical terms, modern science can in principle just as well be integrated into the project of the traditional metaphysical enterprise, studying the first principles of being qua being, as Aristotelian science could. All in all, it seems that the time is ripe for a radical recovery of our lost metaphysical tradition, yet this is possible only through recovering the language in which it is properly conveyed, uniting the formal rigor of contemporary logical techniques with the metaphysical vigor of the pre-modern tradition.

Fordham University

63 In fact, this has also been the way we acquired our pre-scientific substantial concepts, but in a slow, uncontrolled, unsystematic accumulation of experience, getting encoded in, and passed down to generations by, language. This is precisely the point Aristotle makes at the end of his Posterior Analytics, and, not by pure chance, also at the beginning of his Metaphysics.

85

Aquinas’ Theory of the Copula

Introduction

The modest aim of this paper is to reconcile several, apparently conflicting claims Aquinas makes in various contexts concerning the semantic function of the copula. But this paper also targets an immodest aim. That immodest aim is to present Aquinas’ theory of the copula as a coherent part of his overall theory of the analogy of being. Given the all-encompassing character of Aquinas’s theory of the analogy of being, fully accomplishing that immodest aim cannot be the task of a brief paper. Nevertheless, as we shall see, the modest aim cannot properly be achieved without at least indicating how the immodest aim can be achieved. But first of all, let us see what causes the problem.

The problem

St. Thomas speaks most often about the semantic function of the copula in the context of making a distinction between two senses in which something can be said to be a being. The most comprehensive account of this distinction is given by St. Thomas in the following passage:

… ‘being’ is used in many senses. For in one sense ‘being’ is used as it is divided by the ten genera. And in this sense ‘being’ signifies something existing in the nature of things, whether it is a substance, such as a man, or an accident, such as a color. In another sense ‘being’ signifies the truth of a proposition; as when it is said that an affirmation is true when it signifies to be what is, and a negation is true when it signifies not to be what is not; and this ‘being’ signifies a composition produced by the judgment-forming intellect. So whatever is said to be a being in the first sense is a being also in the second sense: for whatever has natural existence in the nature of things can be signified to be by an affirmative proposition, e.g. when we say that a color is, or a man is. But not everything which is a being in the second sense is a being also in the first sense: for of a privation, such as blindness, we can form an affirmative proposition, by saying: ‘Blindness is’; but blindness is not something in the nature of things, but it is rather a removal of a being: and so even privations and negations are said to be beings in the second sense, but not in the first. And being is predicated in different manners according to these two senses: for taken in the first sense it is a substantial predicate and pertains to the question ‘What is it?’, but taken in the second sense it is an accidental predicate, ... and pertains to the question ‘Is there (such and such a thing)?’.1

St. Thomas derives this distinction from Aristotle’s discussion of ‘being’ in the fifth book of the Metaphysics. Commenting on Aristotle’s text, St. Thomas has the following to say about the second member of this distinction:

We have to know that this second mode is related to the first as effect to cause. For it is from the fact that something exists in the nature of things that the truth or falsity of a proposition follows, which the intellect signifies by the verb ‘is’, as it is the verbal copula. But, since some things which in themselves are not beings the intellect considers as some sort of beings, such as negations and the like, sometimes ‘is’ is said of something in this second sense, but not in the first. For it is said that blindness is in the second sense because the proposition is true by which something is

1 2SN 34.1.1. Cf. 1SN 19.5.1.ad1., 33.1.1.ad1.; 2SN 37.1.2.ad1. & ad3.; De Ente 1.; De Pot 7.2.ad1.; De Malo 1.1.ad19.; Quodl 9.2.2.; In Meta 4.1., 5.9., 6.2., 6.4., 9.11., 11.8.; ST1 3.4.ad2., 16.3.ad2.; 48.2.ad2.; ST1-2 36.1.; ScG 1.12., 1.58., 3.9. Cf. also Cajetan (1964, 1590) c.1.; C. Alamannus (1888) Tom.1. sect. II. 5. 1.; Schmidt (1966) Part II. ch. 4. and Part III. ch. 8.

86

said to be blind, but this is not said to be true in the first sense. For blindness does not have real being, but is rather a privation of some being.2

Now, let us suppose that we understand that the copula of a categorical proposition indicates the composition of the subject with the predicate, and thus it somehow expresses truth or falsity – after all, it is by means of this copula that we express that something is or is not the case.3

But then how should we understand, for example, (1) that it is by means of the sense of the copula of an affirmative categorical proposition that we can express the way blindness, as opposed to sight, exists, (2) that it is the sense of such a copula that answers the question whether there is such and such a thing, and (3) that it is in the sense of such a copula that ‘being’ is an accidental predicate of things? Even if we accept that existence may in some sense be treated as a (first-order) predicate, it still appears to be nonsensical to claim that the copula, which merely joins the predicate to the subject, expresses the existence of anything.

The inherence theory of predication

Despite appearances to the contrary, I think we can make good sense of St. Thomas’ claims, provided we are ready to understand them in their proper theoretical context, namely, in the context of the so-called inherence theory of predication.4

This theory can easily be formulated in one sentence: a predicate is true of a thing if and only if what the predicate signifies in respect of the thing actually exists, or, in other words, the thing is actual in respect of what the predicate signifies in it.5

Understood in this theoretical context, then, the copula of an affirmative categorical proposition can clearly be said to express somehow the existence of something, namely, the existence of what is signified by the predicate in the suppositum or supposita of the subject, as required by the quantity of the proposition. (Nevertheless, to simplify matters, in the subsequent discussion I will consider only singular propositions; quantified propositions would only add technical complications that are irrelevant from our present theoretical point of view.)6

Consider, for example, the proposition ‘Socrates is wise’. The copula of this proposition somehow expresses the existence of Socrates’s wisdom, since the proposition is true if and only if Socrates’s wisdom exists. Likewise, the proposition ‘Homer is blind’ is true if and only if Homer’s blindness exists, and the proposition ‘Socrates is a man’ is true if and only if Socrates’s humanity exists, and so on for all similar cases.

2 In Meta lb. 5, lc. 9, n. 896. 3 Cf. “Cum enim dicimus aliquid esse, significamus propositionem esse veram. Et cum dicimus non esse, significamus non esse veram; et hoc, sive in affirmando sive in negando. In affirmando quidem, sicut dicimus quod Socrates est albus, quia hoc verum est. In negando vero, ut Socrates non est albus, quia hoc est verum, scilicet ipsum non esse album.” In Meta lb. 5, lc. 9, n. 895. 4 Concerning the inherence theory in general, as opposed to the identity theory see L. M. de Rijk’s Introduction to Abelard (1956, pp. 37-38) and Henry (1972, pp. 55-56). Concerning St. Thomas’s inherence theory in particular see H. Weidemann (1986) and Schmidt (1966). 5 For a detailed account of the relevant notion of signification see Klima (1996). 6 For the relevant reconstruction medieval supposition theory, in relation to the semantics of modern quantification theory, see Klima, 1988, Essays 2 and 3.

87

Now, even if in this way we may say that the copula somehow expresses or indicates the existence of what is signified by the predicate in the suppositum of the subject, there is still an apparent difficulty. In view of what Thomas said about the difference between the way privations exist and the way positive qualities exist, the copula of the corresponding propositions cannot directly signify the existence of the significata of their predicates. For according to Thomas, the copula always signifies existence in the same sense, namely, in the sense in which for example Homer’s blindness can be said to exist.

So our problem now becomes the following: how can Aquinas state, on the one hand, that the copula somehow indicates the being of the significata of predicates in several senses, and, on the other hand, that the copula always signifies being in one and the same sense?

Predications as predications of being simpliciter or secundum quid

First of all, let us see why Thomas would claim that the significata of various predicates can be said to be in several senses. In his commentary on the Metaphysics, he writes:

…. being cannot be narrowed down to something definite in the way in which a genus is nar-rowed down to a species by means of differences. For since a difference does not participate in a genus, it lies outside the essence of a genus. But there could be nothing outside the essence of being which could constitute a particular species of being by adding to being; for what is outside of being is nothing, and this cannot be a difference. Hence in book III of this work (see n. 433) the Philosopher proved that being cannot be a genus. Being must then be narrowed down to diverse genera on the basis of a different mode of predication, which flows from a different mode of being; for “being [esse] is signified,” i.e., something is signified to be, “in just as many ways as something is said to be a being [ens dicitur]”, that is, in as many ways as something is predicated. And for this reason the first divisions of being are called predicaments [i.e., categories], because they are distinguished on the basis of different ways of predicating. Therefore, since some predicates signify what, i.e., substance; others of what kind [i.e., quality]; and yet others how much [i.e., quantity]; and so on; it is necessary that for each mode of predication, being should signify the same [mode of being]. For example, when it is said that a man is an animal, ‘is’ signifies [the mode of being of] substance; and when it is said that a man is white, is signifies [the mode of being of] quality; and so on. (in Meta, 5, 9)7

The main point of this passage is that the division of being into the categories is not like the division of a genus into its species by means of specific differences. This contrast is made clear also in the following passage:

... there are two ways in which something common can be divided into those that are under it, just as there are two ways in which something is common. For there is the division of a univocal [term] into its species by differences by which the nature of the genus is equally participated in

7 “… ens non potest hoc modo contrahi ad aliquid determinatum, sicut genus contrahitur ad species per differentias. Nam differentia, cum non participet genus, est extra essentiam generis. Nihil autem posset esse extra essentiam entis, quod per additionem ad ens aliquam speciem entis constituat: nam quod est extra ens, nihil est, et differentia esse non potest. Unde in tertio huius probavit philosophus, quod ens, genus esse non potest. Unde oportet, quod ens contrahatur ad diversa genera secundum diversum modum praedicandi, qui consequitur diversum modum essendi; quia quoties ens dicitur, idest quot modis aliquid praedicatur, toties esse significatur, idest tot modis significatur aliquid esse. Et propter hoc ea in quae dividitur ens primo, dicuntur esse praedicamenta, quia distinguuntur secundum diversum modum praedicandi. Quia igitur eorum quae praedicantur, quaedam significant quid, idest substantiam, quaedam quale, quaedam quantum, et sic de aliis; oportet quod unicuique modo praedicandi, esse significet idem; ut cum dicitur homo est animal, esse significat substantiam. Cum autem dicitur, homo est albus, significat qualitatem, et sic de aliis.” In Meta, lb. 5, lc. 9, n. 5

88

the species, as animal is divided into man and horse, and the like. Another division is that of something common by analogy, which is predicated according to its perfect concept [ratio] of one of those that divide it, and of the other[s] imperfectly and with qualification [secundum quid], as being is divided into substance and accident, and into being in actuality and in potentiality, and this sort of division is as it were midway between [the division of something] equivocal and [something] univocal.8

So, Aquinas’s idea seems to be the following. Every predication we make is a predication of being, but, depending on the predicate we use, it is a predication of being with some qualification. This qualification is expressed by the predicate, which determines the relevant sense of being in which the significate of the predicate in the suppositum of the subject can be said to be. But what is this supposed to mean?

Let us take, for example, the following two propositions:

(1) Socrates is sighted

(2) Socrates is blind

According to the inherence theory of predication, these propositions are true if and only if the following are also true:

(1’) Socrates’ sight is (exists)

(2’) Socrates’ blindness is (exists)

According to Aquinas, however, sight is a real being in the category of quality, whereas its lack is only a privation, a being of reason. Thus, the senses of being expressed by the predicate of these propositions must be different, insofar as they are true. But what does this have to do with the idea that the former propositions express somehow differently qualified predications of being? The answer can quite clearly be indicated if we consider also the following two propositions:

(1’’) Socrates is with respect to his sight

(2’’) Socrates is with respect to his blindness

In these two propositions the sense of the predicate ‘is’ is explicitly qualified by the addition of the significata of the predicates of (1) and (2) in the supositum of their subject, namely, Socrates’s sight, and his blindness, respectively. But then we are certainly entitled to claim that the senses of being thus qualified are exactly the senses in which ‘is’ (or ‘exists’) can be predicated of these significata in (1’) and (2’). So in this way it is clear that regarding (1) and (2) as expressing the qualified predications of being explicated by (1’’) and (2’’), also allows us to regard (1’) and (2’) as predicating being precisely in the sense thus qualified of their subjects, which are nothing but the significata of the predicates of (1) and (2). In general, on this basis we can claim that any ordinary predication of a common term is but a qualified predication of being, 8 “… est duplex modus dividendi commune in ea quae sub ipso sunt, sicut est duplex communitatis modus. Est enim quaedam divisio univoci in species per differentias quibus aequaliter natura generis in speciebus participatur, sicut animal dividitur in hominem et equum, et hujusmodi; alia vero divisio est ejus quod est commune per analogiam, quod quidem secundum perfectam rationem praedicatur de uno dividentium, et de altero imperfecte et secundum quid, sicut ens dividitur in substantiam et accidens, et in ens actu et in ens potentia: et haec divisio est quasi media inter aequivocum et univocum.” 2SN d. 42, q. 1, a. 3, in corp. Cf.: “Unum enim eodem modo dicitur aliquid sicut et ens; unde sicut ipsum non ens, non quidem simpliciter, sed secundum quid, idest secundum rationem, ut patet in 4o Metaphysicae, ita etiam negatio est unum secundum quid, scilicet secundum rationem.” in Peri lb. 2, lc. 2, n. 3.

89

in which the significate of the common term in the suppositum of the subject specifies the sense in which that significate can be said to exist.9

Indeed, this claim seems to be in perfect agreement with what Thomas says in his commentary on Aristotle’s On Interpretation, where he explicitly deals with the semantic function of the copula:

The reason why [Aristotle] says that the verb ‘is’ consignifies composition is that it does not principally signify composition, but secondarily; for it primarily signifies what occurs to the mind in the way of actuality absolutely: for ‘is’, uttered absolutely, signifies being in act, and hence it signifies as a verb. But since actuality, which the verb ‘is’ principally signifies, is in general the actuality of every form, whether it is a substantial or an accidental actuality, this is why when we want to signify any form or act to actually inhere [inesse] in a subject, we signify this by means of the verb ‘is’, either absolutely, or with some qualification: absolutely, in the present tense, and with qualification in the other tenses. And thus the verb ‘is’ secondarily signifies composition.10

Now even if in this passage Thomas is mainly concerned with the qualifications that the various tenses can add to the primary meaning of the verb ‘is’, in other contexts he clearly distinguishes the qualifications imposed upon the absolute sense of this verb by the accidental forms signified by predicates from the categories of accidents:

… there are two kinds of being [esse], namely the essential, or substantial being of the thing, as for a man to be [hominem esse], and this is just to be, without any qualification. The other kind of being is accidental being, such as for a man to be white [hominem esse album], and this is [not just to be, but] to be something [esse aliquid].11

So, it seems that according to Aquinas’s view, the copula is not just a merely syncategorematic particle, with the sole function of joining the predicate to the subject, but it retains the primary signification of the verb ‘is’, which predicated in itself signifies the actual existence of the thing of which it is predicated. Indeed, according to the previous passage from the On Interpretation-commentary, this is precisely the reason why we use the verb ‘is’, rather than any other verb, also in the function of the copula, to assert in general the actuality of the suppositum of the subject in respect of what is signified in it by the predicate. But then, when it has the function of joining another predicate to the subject, the existence the verb ‘is’ signifies is not the absolute existence of the suppositum of the subject, but the qualified existence of the form signified by the predicate, namely, the inherence of this form in the suppositum of subject, which renders the suppositum actual in respect of this form. And so, since the forms signified by the predicate may be of various sorts, namely, substantial or accidental, or even not really existing forms but beings

9 Schematically, the claim is the following: SGT(1’)(P) = SGT(1’’)(P), and SGT(2’)(P) = SGT(2’’)(P); but then, since SGT(1’’)(P) ≠ SGT(2’’)(P); therefore, SGT(1’)(P) ≠ SGT(2’)(P); where SGT(n)(P) is the signification of the predicate of sentence n. 10 “Ideo autem dicit quod hoc verbum est consignificat compositionem, quia non eam principaliter significat, sed ex consequenti; significat enim primo illud quod cadit in intellectu per modum actualitatis absolute: nam est, simpliciter dictum, significat in actu esse; et ideo significat per modum verbi. Quia vero actualitas, quam principaliter significat hoc verbum est, est communiter actualitas omnis formae, vel actus substantialis vel accidentalis, inde est quod cum volumus significare quamcumque formam vel actum actualiter inesse alicui subiecto, significamus illud per hoc verbum est, vel simpliciter vel secundum quid: simpliciter quidem secundum praesens tempus; secundum quid autem secundum alia tempora. Et ideo ex consequenti hoc verbum est significat compositionem.” In Peri lb.1, lc. 5, n.22 11 “Sed duplex est esse: scilicet esse essentiale rei, sive substantiale ut hominem esse, et hoc est esse simpliciter. est autem aliud esse accidentale, ut hominem esse album, et hoc est esse aliquid.” De Principiis Naturae, c. 1. Cf. In Boethii De Hebdomadibus, lc. 2, nn. 26-28, Marietti, 1954.

90

of reason, such as privations, the existence thus signified will be existence in various senses demanded by the nature of the forms signified.

But then, again, the claim that the copula signifies the existence of these significata in the various senses demanded by the nature of these significata seems to be entirely incompatible with the other claim that the ‘is’ occurring in these predications is but the ordinary copula, which uniformly has the same sense which is expressed for instance by the predicate of (2’), i.e., the sense in which beings of reason can be said to exist.

At this point, however, we should consider just what it is that the copula joins to the subject when it occurs in a proposition. As St. Thomas remarks in his De Ente et Essentia, what is predicated in a proposition is the nature signified by the predicate considered absolutely, in abstraction from its individuating conditions.12 So although we may say that the copula insofar as it signifies existence, expresses the inherence of the individualized forms ultimately signified by the predicate in the supposita of the subject, and hence it signifies existence in various senses depending on the nature of the form signified, nevertheless, it does so by joining the nature immediately signified by the predicate, in abstraction from its individuating conditions.13 Therefore, on this basis, the copula expresses not only the actuality of the suppositum of the subject in respect of the individualized form signified by the predicate in that suppositum, but also with respect to the nature signified by the predicate absolutely. So the qualified existence expressed by the copula is not only the actuality of the suppositum in respect of an individualized form signified in it by the predicate, as was indicated by the examples of (1’’) and (2’’) above, but also in respect of the form or nature signified by the predicate in general, as can be expressed by the following propositions:

(1’’’) Socrates is with respect to sight

(2’’’) Socrates is with respect to blindness

Now it is crucial here to notice the difference between the qualifications imposed upon the sense of the verb ‘is’ in these predications and those expressed by (1’’) and (2’’), respectively. Whereas in (1’’) and (2’’) the qualifier phrases referred to the ultimate significata of the predicates ‘sighted’ and ‘blind’, here the qualifier phrases refer to the immediate significata of the same. Therefore, since the natures of those ultimate significata are different, the first being a positive quality and the second being a privation of that quality (i.e., a being of reason), no wonder that they qualify the primary sense of being expressed by the verb ‘is’ differently, yielding different secondary senses for this verb. The first qualifies the sense of ‘is’ so as to yield the secondary sense in which it signifies the act of being of a really inherent accident, while the second yields the sense in which the same verb signifies the being of a being of reason. On the other hand, since it is not only privations, but also all natures according to their absolute

12 De Ente, c. 4, cf. Cajetan, 1590, 1964, q. 6. 13 Cf. the following passage from Aquinas’s commentary on Aristotle’s On Interpretation: “Therefore 'passions of the soul' must be understood here as conceptions of the intellect, and names, verbs, and speech signify these conceptions of the intellect immediately according to the teaching of Aristotle. They cannot immediately signify things, as is clear from the mode of signifying, for the name 'man' signifies human nature in abstraction from singulars; hence it is impossible that it immediately signify a singular man. The Platonists for this reason held that it signified the separated idea of man. But because in Aristotle's teaching man in the abstract does not really subsist, but is only in the mind, it was necessary for Aristotle to say that vocal sounds signify the conceptions of the intellect immediately and things by means of them.” Aristotle: 1962, p. 25.

91

consideration have the same ontological condition, namely, that their actuality depends on the activity of the human mind along with some foundation in reality, it is equally not surprising that the immediate significata of all predicates impose the same sort of qualification on the primary sense of being. Therefore, the sense of ‘is’ as qualified by ‘with respect to sight’ is the same as the sense of ‘is’ as qualified by ‘with respect to this blindness’, and by ‘with respect to blindness’, but different from the sense of ‘is’ as qualified by ‘with respect to this sight’.14

However, if this is true, then it is not an absurd claim after all that the copula expresses existence in the same sense in which a privation, a being of reason can be said to be. But then, what is it that it expresses the existence of? Well, the obvious answer is that it is the complex being of reason it constitutes by joining the semantic values of the subject and the predicate, which 12th and 13th century logicians often referred to as the enuntiabile, signified by a proposition as a whole.15 Although Aquinas nowhere discusses the issue of the total significate of propositions explicitly, his remarks on the relationship between propositional composition and beings of reason in his commentary on the sixth book of the Metaphysics quite clearly indicate that he may well have had something like this in his mind, when he lumped all sorts of beings of reason together with what he speaks of as ens ut verum, which is signified by the copula.16

In any case, if we adopt this interpretation, we are able to make coherent sense of all the scattered remarks Thomas makes in various contexts concerning the copula. So, it is this interpretation that I am going to provide in the subsequent summary reconstruction of what I take to be a coherent account of St. Thomas’s theory of the copula.

Summary reconstruction

All in all, Aquinas’s theory of the copula, as a coherent part of his overall theory of the analogy of being, can be summarized in the following points:

The verb ‘is’ in its primary sense signifies the existence (esse) of primary beings, that is, primary substances. Thus, a primary substance is if and only if the act of being signified in it by the verb ‘is’ in this sense is actual. Of any other type of entity, this verb is false in this sense.

However, the same verb is truly applicable to other types of entities in several secondary, derivative senses. Most importantly, it is applicable in a secondary sense to accidents, that is, to individualized significata of predicates in the nine accidental categories distinguished by Aristotle. Everything that can be said to be either in the primary sense or in this secondary sense is called a real being, to be distinguished from mere beings of reason.

14 That is to say, using the notation of n. 9, SGT(1’’’)(P) = SGT(2’’’)(P) = SGT(2’’)(P) ≠ SGT(1’’)(P). 15 I would tentatively identify the significate of a proposition as the enuntiabile expressed by the proposition, expressly called by St. Thomas an ens rationis in 1SN 41.1.5. I say “tentatively”, because of St. Thomas’s tendency to use the term enuntiabile as a synonym for enuntiatio (although “emphasizing the objective meaning of enuncia-tion”, as remarks Schmidt, 1966, p. 223, n. 84). For St. Thomas’s use of the term see 3SN 24.1.1b.; 1SN 38.1.3.; De Ver 2.13.ad7., 1.6., 14.8., 2.7., 1.5., 14.12.; Quodl 4.9.2.; ST1 14.14., 14.15.ad3., 16.7., ST3 1.2.ad2. For a clear 13th-century expression of the view that an enuntiabile is the significate of a proposition see e.g. Peter of Spain, 1972, pp. 205-207. 16 In Meta, lb. 6, lc. 4. For more on this interpretational issue see Klima, G.: 1993. Cf. also G. Nuchelmans, 1973, pp. 165-194; de Rijk 1967, pp. 357-359.

92

The same verb is also applicable in another secondary sense to beings of reason. The difference between real beings and mere beings of reason is that real beings exist apart from any activity of the human mind, whereas beings of reason exist only as objects of some activity of the human mind with some foundation in reality. (Having a foundation in reality, i.e., the real existence or non-existence of something else, is what distinguishes beings of reason from mere figments, i.e., such objects of mental activities that do not have any foundation in reality.)17

The several secondary senses of being can be obtained from the primary sense by adding appropriate qualifications to ‘is’ in its primary sense. Indeed this is the point of Aquinas’s drawing the distinction between substantial being and accidental being (as well as other secondary senses of being, such as being of reason, being in potency) in terms of esse simpliciter vs. esse secundum quid.18

The secondary sense in which a really inherent accident is can be obtained by adding to the verb ‘is’ predicated of a substance a qualification referring to the significate of an accidental predicate in that substance. The reason for this is that for an accident to be is for the substance to be [actual] in respect of that accident.

Likewise, the secondary sense in which a being of reason is can be obtained by adding a qualification referring to the being of reason in question.

The copula has two semantic functions: (a) to signify the existence of the significate of the predicate in the suppositum of the subject, in the sense determined by the nature of this significate, which is “the foundation in reality” of the existence of the enuntiabile signified by the proposition as a whole; (b) to consignify composition and truth by signifying the existence of the enuntiabile.

The existence of the enuntiabile is signified by the copula in the sense of the existence of a being of reason. Since this sense can also be obtained by adding a qualification to the verb ‘is’ that refers to the nature signified absolutely by the predicate of the corresponding categorical proposition, we can assign a unique signification to ‘is’ in the sense in which it asserts the existence of any being of reason as its absolute predicate, and in the sense in which it asserts the existence of an enuntiabile as the copula of the proposition that signifies this enuntiabile.

17 For detailed discussion see Klima, G.: 1993. 18 Cf. n. 11 above. For a detailed analysis of the idea that all predications can be regarded as predications of being with some qualification see Klima, G.: 1996. For discussions of the metaphysical implications of this idea see Velde, R.A. te: 1995, Wippel, J. F.: 1987, and Klima, G. (in press).

93

Appendix: The logic of being in Aquinas

In this Appendix I provide a brief sketch of how the foregoing points can be given precise meaning in a model theoretical semantics for unquantified categorical sentences. The generalization of the theory on the basis of this illustration should be pretty obvious.19

Primitive symbols

If P is a common term, then SGT(P)(u)(t) ∈ W!, in a model M = <W, T, A, SB, SGT, 0>, where W ≠ ∅, T ≠ ∅, t ∈ T, A(t) ⊆ W, SB ⊆ W, u ∈ SB!, 0 ∉ W, SB! := SB∪{0}, W! := W∪{0}, and SGT(P)(0)(t) = 0; where W is the domain of discourse, comprising both actual and non-actual individuals, A(t) is the set of actual individuals at time t, SB is the set of primary substances, SGT is the signification function, and 0 is a zero-entity, a technical device used to indicate the case when a semantic function for a certain argument lacks a value from W.

If S is a common term occurring as the subject of a proposition, then SUP(S)(t) = u if SGT(S)(u)(t) ∈ A(t), otherwise SUP(S)(t) = 0, where SUP(S)(t) is a suppositum of S at the time t (which is the time connoted by the copula in which S occurs). Note that SUP functions in a model just as ordinary value-assignments of variables of standard quantification theory do, with the only difference that SUP assigns those individuals to a common term of which it is true (i.e., in which the significate of the common term is actual) at a given time t.

SGT(‘is1’) (u) (t) ∈ W!

This clause defines the signification of ‘is’ being used in the primary sense, as that of an ordinary predicate. I inserted spaces between the main arguments for ease of reading. This will come in handy below, where we’ll have more complex arguments.

SGT(‘is1’) (u) (t)∈ A(t) iff u ∈ A(t), where u ∈ SB

This clause adds a stipulation that renders ‘is1’ a distinguished logical predicate, one that is true of every primary substance that is actual at a time t. In fact, we may also stipulate that for anything that is not a primary substance (i.e., if u ∉ SB), SGT(‘is1’) (u) (t) = 0.

SGT(<) (SGT(‘is1’)) ((SGT(Px)(u)(t)) (u) (t) ∈ W!

This clause defines the significate of the “qualifier” (the phrase ‘with respect to’) qualifying the primary signification of ‘is’ in respect of the significate of a qualifying predicate in respect of u and t, and in respect of u, and in respect of t.

19 A description of the general technical apparatus used here can be found in Essay 5 of Klima, G.: ARS ARTIUM: Essays in Philosophical Semantics, Medieval and Modern, Budapest: Institute of Philosophy of the Hungarian Academy of Sciences, 1988. The theory provided there, however, did not deal with details concerning the copula. A more specific system taking into account of Aquinas’s theory of the copula can be found in Klima, 1990; but the system presented there does not reconstruct the sense of the copula as obtained by means of the appropriate qualification of the primary sense of ‘is’.

94

SGT(<) (SGT(‘is1’)) ((SGT(Px)) (u) (t) ∈ W!

This clause defines the significate of the “qualifier” qualifying the primary signification of ‘is’, in respect of the signification of a qualifying predicate (i.e., the function that assigns the significata of this predicate in respect of u and t), and in respect of u, and in respect of t. The important difference between (5) and (6) is that the same qualifying predicate may have different effects depending on whether it figures in a construction with the former or with the latter semantic value. The intuitive difference between the two will be illustrated later. The superscript x on the qualifying predicate, its “category index”, indicates the sense in which its significata, if they are actual, exist, namely, whether these significata are real inherent substantial or accidental forms (in which case the index is [1] and 1.5, respectively), or just mere beings of reason (in which case the index is 2, in accordance with the notation of Klima, 1996, changing the awkward ½ to 1.5, which also has technical advantages besides getting rid of the awkwardness).

SGT(<) (SGT(‘is1’)) ((SGT(Px)(u)(t)) (u) (t) ∈ A(t) iff SGT(Px)(u)(t) ∈ A(t)

SGT(<) (SGT(‘is1’)) ((SGT(Px)) (u) (t) ∈ A(t) iff SGT(Px)(u)(t) ∈ A(t)

These two clauses only add the further stipulation that the actuality of the significata of the qualifier in respect of its relevant arguments will depend on the actuality of the significata of the qualifying predicate in respect of its relevant arguments.

Derivative symbols

SGT(‘isx’) ((SGT(Px)(u)(t)) (t) = SGT(<) (SGT(‘is1’)) ((SGT(Px)(u)(t)) (u) (t)

Note that here the signification of ‘is’, as used in a derivative sense in which it is applicable to the significate of a predicate P, is defined in terms of the signification of the qualifier. An example illustrating the point of this clause is the following: consider ‘Plato’s wisdom isx’ and ‘Plato is1 with respect to his wisdomx’. (The importance of adding ‘his’ here will be explained later.) In these two sentences ‘isx’ in respect of Plato’s wisdom (that is, the significate of ‘wise’ in Plato at t) and ‘is1 with respect to his wisdomx’ in respect of Plato signify the same thing at the same time. We can refer to this significate as the being of Plato’s wisdom. Indeed, since ‘wise’ is a term signifying a real accident, its “category index” would be 1.5, that is, we should rather have ‘Plato’s wisdom is1.5’ and ‘Plato is1 with respect to his wisdom1.5’, which shows that qualifying ‘is1’ with ‘his wisdom1.5’ yields that sense of ‘is’ in which it is truly predicable of really inherent accidents. On the other hand, with ‘blind’ (or rather the corresponding ‘blindness’) we would have a different index, and thus a different sense of ‘is’ (namely, the ens rationis sense), but the same formal structure. Furthermore, we would have the same structure, but again a different sense with ‘man’ (or any other substantial predicate, or rather their corresponding abstract forms, in which case the index would be [1], according to the notation of Klima, 1996). The particular case of the ens rationis sense is spelled out in (10) and the corresponding (15) below. Note that the difference between (9) and (10) consists merely in replacing the variable “category index” with the particular

95

value 2, indicating the secondary sense of ‘is’ and the type of qualifying predicate which determines that sense:

SGT(‘is2’) (SGT(Px)(u)(t)) (t) = SGT(<) (SGT(‘is1’)) ((SGT(Px)(u)(t)) (u) (t)

The next clause shows how the signification of the copula can be derived from the signification of ‘is1’ (that is, ‘is’ as used in the primary sense) by means of adding the appropriate qualification, and how this can be regarded as the same as that of ‘is2’. (10) above already defined the secondary sense of ‘is’ (that is the signification of ‘is2’) for the significata of such predicates that signify beings of reason. In the next step the same sense is shown to cover also the copulative usage of ‘is’ by simply defining the signification of ‘is2’ for the significations (or, in another terminology, immediate significata) of all sorts of predicates. The technical trick here is that the first argument of this function is not the significate of P in respect of u at t (namely, SGT(P)(u)(t)), but the signification function of P (namely, SGT(P)), and then the second argument is u, and the third is t. This is what allows us to define for this argument a value that may be different from, but may also be the same as what it would yield for SGT(P)(u)(t) on the basis of (7) and (9). The philosophical significance of this move is that the signification of P (namely, SGT(P), the immediate significate of P), as opposed to the significate of P in respect of u at t (namely, SGT(P)(u)(t), or the ultimate significate of P in u at t), is something that abstracts from both subject and time, that is, the individuating conditions of what is signified by P. Hence what we have here is something that is signified by P in its absolute consideration, precisely what Thomas says is the appropriate semantic value of the predicate of a categorical proposition. Therefore, no wonder that the relevant sense of ‘is’ according to which we can attribute being to this in a judgment is the ens rationis sense.

SGT(‘is2’) (SGT(Px)) (u) (t) = SGT(<) (SGT(‘is1’)) ((SGT(Px)) (u) (t)

An example illustrating how this clause is supposed to work is the following. Take ‘Plato is2 wise’ and ‘Plato is1 with respect to wisdom’. Note the important difference from the previous example! Here we are not considering ‘Plato is1 with respect to his wisdom’, but in abstraction from the subject: ‘Plato is1 with respect to wisdom’. What (11) states is that in ‘Plato is wise’ and in ‘Plato is with respect to wisdom’ the significate of ‘is’ with respect to the signification of ‘wise’ (considered absolutely) in Plato at t is the same as the significate of the qualifier in the signification of ‘is1’ with respect to the signification of ‘wise’ in Plato at t. But this latter, in turn, will be identified below in (13) as the significate of the qualified predicate ‘is1 with respect to wisdom’ (NB not: ‘with respect to his wisdom) in Plato at the same time. Thus, the effect of (10) and (11) together is that we have a unique signification of ‘is2’, which is defined both for the significata of predicates that signify entia rationis, such as privations, in respect of their subject, and for the significations of any predicates, considered in abstraction from their subjects. But it is precisely as defined for these significations that ‘is2’ functions as the copula of propositions, in which these predicates figure with their significations considered in abstraction from their subjects, and are applied to the supposita of the subject term of the proposition in the act of composition (cf. (16) below).

96

Complex expressions

SGT(‘S isx’)(SUP)(t) = SGT(‘isx’)(SUP(S)(t))(t)

This clause provides the significata of the predication of ‘is’ as an absolute predicate, in any sense of any subject, with respect to the supposita of the subject (according to the given assignment of supposita) and at a given time t. Note that this is the significate of the whole proposition ‘S isx’, which is here being identified with the significate of the predicate in the suppositum of the subject (according to the given assignment of supposita by the SUP function). Perhaps Aquinas would not agree with this identification, but rather he would say that the proposition as a whole signifies an enuntiabile, which is always a being in the secondary sense, regardless of what sort of being the significate of the predicate is. I can easily accommodate this point, however, by saying that Aquinas’s putative claim should be interpreted as concerning fully expounded subject-predicate propositions, in this case ‘S is2 a beingx’, and then I’d have the significate of this proposition as a being in the secondary sense in accordance with (14) below, and yet the predicate can signify being in the supposita of the subject in any of the analogical senses of ‘being’. But I will not pursue this matter here. The only semantically important thing in this regard is that if we assign significata to whole propositions, then we can have a unique clause assigning the truth conditions of any proposition whatsoever in the following form: p is true iff SGT(p)(SUP)(t) ∈ A(t). But then again, we are not concerned here with the truth conditions of propositions in general, but with deriving the various analogical senses of being from the primary sense by means of the appropriate qualifications, so that among these derivative senses we shall also find the sense of the copula expressing the ens rationis sense of being.

SGT(‘S is1<[Px]’)(SUP)(t) = SGT(<) (SGT(‘is1’)) ((SGT(Px)) (SUP(S)(t)) (t)

This clause determines the significata of the predication of ‘is1’ is explicitly qualified with the addition of the abstract form of any sort of qualifying predicate. Since this qualification concerns what is signified by the predicate in its absolute consideration, these significata are determined in accordance with (6) above. But this, along with (11) entails that SGT(‘S is1<[Px]’)(SUP)(t) = SGT(‘is2’) (SGT(Px)) (SUP(S)(t)) (t), and this along with (16) below entails that this qualification is precisely what yields the ens rationis sense, which is also expressed by the copula of ‘S is2 P’. (So ‘is’ in ‘Plato is wise’ and ‘is with respect to wisdom’ in ‘Plato is with respect to wisdom’ signify the same.)

SGT(‘S[Px] isx’)(SUP)(t) = SGT(<) (SGT(‘is1’)) (SGT(Px) (SUP(S)(t)) (t)) (SUP(S)(t)) (t)

This clause assigns the significata of ‘is’ in any of its analogical senses as an absolute predicate of the significate of a predicate P in a suppositum of the term S (and this significate is what is supposited for by the term ‘S[Px]’, if this significate is actual, otherwise SUP(‘S[Px]’) = 0). As can be seen, this significate is determined in accordance with (5) above. Thus, any such predications are analyzed as containing ‘is’ in the same sense as is expressed by the predication of ‘is1’ qualified by the significate of the

97

qualifying predicate in the suppositum of the subject. Now, let us express such a qualified predication of ‘is1’ as follows: ‘S is1<S[Px]’. (Note the difference here in the qualifying term: it is not only [Px], say ‘wisdom’, but S[Px], say, ‘Plato’s wisdom’, provided S = ‘Plato’, that is to say, if our sentence is: ‘Plato is wise with respect to Plato’s wisdom’.) Then we can say that SGT(‘S is1<S[Px]’)(SUP)(t) = SGT(<) (SGT(‘is1’)) (SGT(Px) (SUP(S)(t)) (t)) (SUP(S)(t)) (t); whence it follows that SGT(‘S[Px] isx’)(SUP)(t) = SGT(‘S is1<S[Px]’)(SUP)(t). Furthermore, in accordance with (9), it also follows that SGT(‘S is1<S[Px]’)(SUP)(t) = SGT(‘isx’) (SGT(Px) (SUP(S)(t)) (t)) (t) which is precisely what we want to say, namely, that for example in ‘Plato is1 with respect to Plato’s wisdom’ the complex qualified predicate signifies the same in respect of Plato as ‘is1.5’ signifies in respect of Plato’s wisdom in ‘Plato’s wisdom is1.5’. (Note that along with (14) I also assume here the following: SGT(‘is1<S[Px]’) (SUP(S)(t)) (t) = SGT(<) (SGT(‘is1’)) (SGT(Px) (SUP(S)(t)) (t)) (SUP(S)(t)) (t).)

SGT(‘S is1<S[P2]’)(SUP)(t) = SGT(‘is2’) (SGT(P2)(SUP(S)(t))(t)) (t)

This clause identifies the significate of ‘is1’ qualified by a predicate which signifies some ens rationis with what is signified by the secondary sense of ‘is’ in the significate of this predicate in what is supposited for by the subject at time t, at time t. Example: ‘Socrates is1 with respect to Socrates’s blindness’ and ‘Socrates’s blindness is2’.

SGT(‘S is2 P’)(SUP)(t) = SGT(‘is2’) (SGT(P)) (SUP(S)(t)) (t)

Finally, this clause determines the significate of a categorical proposition as the significate of the secondary sense of ‘is’, which is its copula, in respect of the signification of the predicate, and in respect of a suppositum of the subject at a certain time, in perfect accordance with Aquinas’s claim that the predicate terms of categoricals signify whatever they signify in their “absolute consideration”, provided we are allowed to identify this as the signification function, which abstracts from its arguments, the individuals and times which individuate its values, namely, the significata of this predicate in the individuals at given times.

REFERENCES

Aristotle: 1962, On Interpretation: Commentary by St. Thomas and Cajetan, tr. J. T. Oesterle, Marquette University Press, Milwaukeee, Wisconsin

Abaelard, P.: 1956, Dialectica, ed. L.M. de Rijk, Van Gorcum, Assen

Alamannus, C.: Summa Philosophiae, P. Lethielleux, Paris, 1888

Aquinas, T.: 1980, Opera Omnia, Frommann-Holzboog, Stuttgart-Bad Cannstatt

Cajetan, T. de Vio: 1590, “Super Librum De Ente et Essentia Sancti Thomae Aquinatis”, in: Opuscula Omnia, Typis Comini Venturae, Bergomi

98

Cajetan, T. de Vio: 1964, Commentary on Being and Essence, transl. L.J. Kendzierski, F.C. Wade, Marquette Univ. Press., Milwaukee, Wis.

Cajetan, Thomas de Vio: 1939, Scripta Philosophica: Commentaria in Praedicamenta Aristotelis, ed. M. H. Laurent, Angelicum, Romae

Henry, D.P.: 1972, Medieval Logic and Metaphysics, Hutchinson, London

Klima, G.: 1988, Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Institute of Philosophy, Budapest

Klima, G.: 1990, “On Being and Essence in St. Thomas Aquinas’s Metaphysics and Philosophy of Science” in: Knuuttila et al. (1990) pp. 210-221, and in Klima 1988 pp. 150-164.

Klima, G.: 1993, “The Changing Role of Entia Rationis in Mediaeval Semantics and Ontology”, Synthese 96(1993), No. 1, pp. 25-59

Klima, G.: 1996 “The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being”, Medieval Philosophy and Theology, 5(1996), pp. 87-141.

Klima, G.: in press “Aquinas on One and Many”, Documenti e Studi sulla Tradizione Filosofica Medievale (Società Internazionale per lo Studio del Medioevo Latino)

Knuuttila, S. and Hintikka, J. (eds.): 1986, The Logic of Being, D. Reidel, Dordrecht

Knuuttila, S. and Työrinoja, R. and Ebbesen, S. (eds.): 1990, Knowledge and the Sciences in Medieval Philosophy: Proceedings of the Eighth International Congress of Mediaeval Philosophy, (S.I.E.P.M.), Publications of Luther-Agricola Society Series B 19, Helsinki 24-29 August 1987, vol. II. Helsinki

Nuchelmans, G.: 1973, Theories of the Proposition - Ancient and Medieval Conceptions of the Bearers of Truth and Falsity, North Holland Publishing Company, Amsterdam-London

Nuchelmans, G.: 1980, Late-Scholastic and Humanist Theories of the Proposition, North Holland Publishing Company, Amsterdam-Oxford-New York

Peter of Spain: 1972, Tractatus, ed. L. M. de Rijk, Van Gorcum, Assen

Rijk, L. M. de (ed.): 1967, Logica Modernorum, Vol. II, Part II, Van Gorcum, Assen

Schmidt, R.W.: 1966, The Domain of Logic according to Saint Thomas Aquinas, Martinus Nijhoff, The Hague

Velde, R.A. te: 1995 Participation and Substantiality in Thomas Aquinas, Brill: Leiden-New York-Köln

Weidemann, H.: 1986 “The Logic of Being in Thomas Aquinas”, in: Knuuttila et al. 1986, pp. 181-200.

Wippel, J. F.: 1987 “Thomas Aquinas and Participation”, in: Wippel, J. F. (ed.): Studies in Medieval Philosophy, The Catholic University of America Press: Washington D.C.,

99

Ontological Alternatives vs. Alternative Semantics in Medieval Philosophy

100

Ontological Alternatives vs Alternative Semantics In Mediaeval Philosophy1

Introduction: The False Alternatives of ‘Realism’, ‘Conceptualism’ and ‘Nominalism’ in Mediaeval Philosophy

‘Realism’, ‘conceptualism’ and ‘nominalism’ are terms that one is most likely to come across in history of philosophy textbooks, presented as ones labeling three major ontological alternatives provided by mediaeval philosophy. The general inadequacy of these labels is perhaps best shown by the desperate efforts to provide further, modified labels, the well-known ‘moderate’ and ‘extreme’ or ‘exaggerated’ versions of the above, in hopes of implying at least a lesser amount of falsehood in hanging these on views of particular mediaeval philosophers.2

In what follows, however, it is not my intention to undermine the methodological foundations of ‘labeling’ philosophers or philosophies in general, which are shaky enough in themselves anyway, nor to question the use of these labels in particular. Indeed, by the end of this paper I hope to come to certain conclusions which may justify a certain careful usage of these terms, in which I think they do express something fundamental about the overall philosophical attitudes of several, though, as we shall see, mainly non-mediaeval philosophers. On the other hand, I also think that the main borderlines separating major trends in mediaeval philosophical thought lie miles away from the lines suggested by the current, however confused and indeterminate use of these terms. But since nomina sunt ad placitum, and just anyone may have one’s own favorite conception of the proper meaning of these terms, a discussion targeting their current usage might easily lapse into verbal quibbles over misunderstood conceptions, a phenomenon so painfully familiar in philosophical or scientific polemics.

So what I do wish to do in this paper is rather the following:

1. I present how different ontological alternatives were treated by mediaeval authors within basically the same semantic framework before the advent of Ockham’s semantic innovations.

2. I give a short reconstruction of Ockham’s semantic innovations.

1 Reprinted from S-European Journal for Semiotic Studies Vol. 3 (4) 1991, pp. 587-618, with minor corrections by the author. 2 It is not unusual in the secondary literature to characterise these alleged ontological alternatives in terms of distinguishing between universale ante rem, in re and post rem. For the original use of this distinction consider the following: "Patet, secundo, doctorum sententia dicentium quod triplex est universale, scilicet ante rem individuam, ut idea, in re, ut forma multis rebus communicata, et post rem, ut species vel signum priorum." John Wyclif: Tractatus de Universalibus, (ed. I.J. Mueller), Clarendon Press, Oxford, 1985. c.2. p.69. Cf. also: "Isti autem duplici modo universalis <Platonis et Aristotelis> superadditur modus tertius; videlicet quod species quae est in intellectu abstracta a rebus dicitur universale, eo quod habet respectum ad plura, non quia de pluribus praedicatur, sed quia pluribus est similis. ... Et hinc forte habuit ortum illa distinctio quod tripliciter est universale, ante rem, in re, et post rem. Nam universale primo modo dictum est ante rem, quia causat res. Secundo modo dictum est in re, quia est idem essentia cum rebus. Tertio vero modo est post rem, cum sit species a rebus abstracta et ab ipsis causata." Aegidius Romanus, 1SN, d.19. pars 2., q.1. Utrum in divinis sit totum universale?, Venetiis, 1521, Minerva, Frankfurt/Main, 1968. Concerning alleged "ontological extremities" in mediaeval philosophy see J. A. Trentman's Introduction to his edition of Vincent Ferrer's Tractatus de Suppositionibus, Stuttgart-Bad Cannstatt, 1977. esp. pp.20-30.

101

3. In the light of this reconstruction I wish to point to the logical independence of widely different ontological alternatives from the alternative semantic frameworks thus reconstructed.

4. I discuss how, despite its logical independence, the new semantics changed the research program for ontology and, through this, the paradigm of mental representation in the so-called via moderna trend of late-mediaeval philosophy, which, I conjecture, directly paved the way for modern treatments of ontological and epistemological questions in post-scholastic philosophy.

5. In conclusion I propose an interpretation of the above-mentioned terms, which may render them more useful in characterizing certain general philosophical attitudes. I will also remark on the value of these considerations for contemporary research in the philosophy of language and cognitive science.

Ontological Alternatives within the General Semantic Framework of Pre-Ockhamist Scholasticism

All semantics in mediaeval philosophy begins with Aristotle’s famous remark in the beginning of his Perihermeneias to the effect that words signify “passions”, i.e., concepts of the soul immediately and it is only through the mediation of these that they signify things. Commenting on Aristotle’s remark, St. Thomas Aquinas writes as follows:

... ‘passions of the soul’ must be understood here as conceptions of the intellect, and names, verbs, and speech signify these conceptions of the intellect immediately according to the teaching of Aristotle. They cannot immediately signify things, as is clear from the mode of signifying, for the name ‘man’ signifies human nature in abstraction from singulars; hence it is impossible that it immediately signify a singular man. The Platonists for this reason held that it signified the separated idea of man. But because in Aristotle’s teaching man in the abstract does not really subsist, but is only in the mind, it was necessary for Aristotle to say that vocal sounds signify the conceptions of the intellect immediately and things by means of them.3

So according to St. Thomas the mode of signification of general terms shows that these signify the natures of individual things in abstraction from the singulars. But these natures cannot exist in abstraction from the singulars. So these abstractions, the universals, are products of the activity of the intellect representing the individual natures of the singulars in an abstract, universal manner. As in his Summa Theologiae St. Thomas remarks:

When we speak about an abstract universal, we imply two things, namely the nature of the thing itself, and abstraction or universality. So the nature itself to which it is accidental that it is thought of or is abstracted or that the concept of universality applies to it exists only in the singulars, but the nature’s being abstracted or its being thought of or the concept of universality is in the intellect ... <For example,> humanity that is thought of exists only in this or that man; but that humanity is apprehended without its individuating conditions, which is nothing but for it to be being abstracted, which confers on it the attribute of universality, is an accidental feature of humanity in virtue of its being perceived by the intellect, in which there is a similitude of the nature of the species but not of the individuating principles.4

3 in Peri lc.2.n.5. Aristotle: On Interpretation: Commentary by St. Thomas and Cajetan, tr. J.T. Oesterle, Marquette University Press, Milwaukeee, Wisconsin, 1962, p.25. 4 "Cum dicitur universale abstractum, duo intelliguntur, scilicet ipsa natura rei et abstractio seu universalitas. Ipsa igitur natura cui accidit vel intelligi vel abstrahi vel intentio universalitatis non est nisi in singularibus; sed hoc ipsum quod est intelligi vel abstrahi vel intentio universalitatis est in intellectu ... Humanitas quae intelligitur non est nisi in hoc vel in illo homine; sed quod humanitas apprehendatur sine individualibus conditionibus, quod est ipsam

102

So for St. Thomas the immediate significata of our general terms, like ‘man’, are abstract natures, existing in the intellect. But their ultimate significata are the individual natures of singulars from which the intellect forms its universal concept by abstraction, that is, by thinking of these natures without the individuating conditions that cause them to be the nature of this or that singular.5

That the word ‘man’ signifies human nature, however, does not mean that it does not refer to, or, to apply a modern re-coinage of the mediaeval technical jargon, supposit for individual men in a proposition like ‘Some men are white’. For, as St. Thomas says:

In respect of any name we have to consider two things, namely that from which the name is imposed, what is called the quality of the name, and that to which the name is imposed, what is called the substance of the name. And the name, properly speaking, is said to signify the form, or quality from which the name is imposed, and is said to supposit for the thing to which it is imposed.6

So the term ‘man’ signifies human nature in abstraction from the singulars immediately (in the mind), and signifies individual human natures ultimately (in the things), but normally supposits for the things bearing the nature it signifies, namely individual men. It is only in virtue of some special adjunct that a term is made to refer to what it normally signifies. As St. Thomas says: “this term ‘man’ does not supposit for the common nature unless for the reason of something added, as when it is said ‘man is a species’.”7

As is well-known, in systematic treatises on the theory of supposition, the mediaeval theory of reference, this kind of supposition was distinguished as simple supposition, as contrasted with material supposition, when a term refers to itself, as in ‘‘man’ is a noun’, and with personal supposition, when the term refers to what falls under it, as in ‘a man runs’.8 So we can say that for Aquinas a term has simple supposition when it refers to what it (immediately) signifies,9 while it has personal supposition when it refers to what falls under its immediate significate.

abstrahi, ad quod sequitur intentio universalitatis, accidit humanitati secundum quod percipitur ab intellectu, in quo est similitudo naturae speciei et non individualium principiorum." ST1 q.85.a.2.ad2. Unless otherwise indicated, as in the note above, translations in this paper are mine. 5 "Non enim oportet si hoc est homo, et illud homo, quod eadem sit numero humanitas utriusque, sicut in duobus albis non est eadem albedo numero; sed quod hoc similetur illi in hoc quod habet humanitatem sicut illud: unde intellectus, accipiens humanitatem non secundum quod est huius, sed ut est humanitas, format intentionem communem omnibus." 2SN d.17.q.1.a.1. 6 "... in quolibet nomine est duo considerare: scilicet id a quo imponitur nomen, quod dicitur qualitas nominis, et id cui imponitur, quod dicitur substantia nominis. Et nomen, proprie loquendo, dicitur significare formam sive qualitatem a qua imponitur nomen; dicitur vero supponere pro eo cui imponitur." 3SN d.6.q.1.a.3. 7 "Unitas autem sive communitas humanae naturae non est secundum rem, sed solum secundum considerationem; unde iste terminus ‘homo' non supponit pro natura communi, nisi propter exigentiam alicuius additi, ut cum dicitur, ‘homo est species'." ST I. q.39.a.4., cf. ST III. q.16.a.7. 8 For good bibliographies on the vast recent literature on supposition theory see e.g.: E.J. Ashworth: The Tradition of Mediaeval Logic and Speculative Grammar, Toronto, 1978; N. Kretzmann-J. Pinborg-A. Kenny: The Cambridge History of Later Mediaeval Philosophy, Cambridge, 1982. For more recent references see: N. Kretzmann (ed.): Meaning and Inference in Mediaeval Philosophy, Kluwer Academic Publishers, 1989. 9 For a detailed discussion of Aquinas' treatment of the problems connected with the supposition of ‘man' in ‘man is a species' see my "‘Socrates est species': Logic, Metaphysics and Psychology in St. Thomas Aquinas' Treatment of a Paralogism", in: G. Klima: Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1988, also to appear in K. Jacobi (ed.): Acts of the 8th European Symposium of Mediaeval Logic and Semantics, Munich, Philosophia Verlag, 1990. Cf.: Walter Burleigh: De Puritate Artis Logicae Tractatus Longior with a revised edition

103

Now the semantic ideas touched upon in these brief quotations from St. Thomas, along with some further considerations concerning predication and the concept of existence, add up to a rather consistent general semantic theory, which was fairly common to the whole pre-Ockhamist scholastic tradition.10

According to the concept of signification involved in this theory, a general term ultimately signifies numerically distinct, inherent natures, forms or properties of individuals, distinguishable from one another by which individuals they belong to. Such a general term signifies these individualized properties because it signifies immediately the universal concept that represents them in an abstract manner in the intellect. Accordingly, a term signifying immediately such a concept is true of a thing just when the individualized property ultimately signified by it in the thing actually inheres in this thing, i.e., if this property actually exists. So when such a term occurs as the predicate of an affirmative categorical sentence, the truth of this sentence ultimately depends on whether the property signified by this term in the thing or things supposited for, that is, referred to, by its subject term actually exists. On the other hand, the subject term of such a sentence supposits for those things which actually bear the property signified by this term. For example, in the sentence ‘Some men are white’ the subject term refers to those things that have human nature, that is, individual human beings. The predicate term, on the other hand, signifies individual whitenesses inhering in white things. The sentence is true if and only if some of the supposita of its subject actually have the property signified by its predicate, that is, if the individual whitenesses of some human beings actually exist.11

Now even without going into the finer details of this semantic conception, it clearly seems to imply an enormous amount of ontological commitment. For seemingly, beyond the generally acceptable, “ordinary” ontology of individual substances, it commits itself to huge domains of quite extraordinary entities, indeed, also of several kinds of non-entities. For this semantic conception demands that for every true predicate of a thing there should be a property of the thing actually inhering in it, and also that for every false predicate of the thing there should be a non-actual property signified in it by the predicate in question. Indeed, beyond these individualized properties signified by our general terms in the singulars, this conception also admits universal properties, which, although admittedly are abstracted from the former by the mind, still, exist in a sense, to mediate between the universal terms and their individual instances.

of the Tractatus Brevior, (ed. Ph. Boehner) St. Bonaventure, N.Y., 1955, c.3. p.7. 10 For a complete technical description of a model theoretical semantics constructed along the lines described here see the Appendix of my "Understanding Matters from a Logical Angle", in Gyula Klima: Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1988. Further formal approximations of the finer details of St. Thomas' semantic theory can be found in the last two essays of the same volume. By an attempt to characterise what I think to be a common semantic framework in pre-Ockhamist scholasticism, I do not mean to imply that there existed no substantial differences between particular semantic views of pre-Ockhamist mediaeval thinkers. My concern in this paper, however, is to contrast the paradigmatically different ways of constructing semantic theory before and after the advent of Ockhamist semantics, so for the most part I will disregard individual differences that are accidental from this point of view. 11 Concerning this theory of predication in general, the inherence theory, as opposed to the identity theory see L.M. de Rijk's Introduction to his edition of Abaelard's Dialectica, Assen, 1956, pp.37-38; also D.P. Henry, Medieval Logic and Metaphysics, London, 1972, pp.55-56. Concerning St. Thomas's inherence theory in particular see H.Weidemann, "The Logic of Being in Thomas Aquinas", in: S. Knuuttila-J. Hintikka (eds.), The Logic of Being, Dordrecht, Holland, 1986; R.W. Schmidt S.J., The Domain of Logic according to Saint Thomas Aquinas, The Hague, Martinus Nijhoff, 1966. See also the interesting note in Trentman, op. cit., p.97. For formal reconstructions of these predication theories see again my Ars Artium.

104

But this specification of the sense of existence in which these universals may be said to be immediately leads us to one of the basic tactics used by mediaeval philosophers working in this semantic framework to reduce the apparent ontological commitments of this conception. The works of these philosophers abound with distinctions of different senses of existence. Consequently, the sense in which ordinary individuals are said to exist was only one among these, although generally enjoying the rank of real existence, as opposed to other, diminished kinds of existence.

St. Thomas, e.g., distinguished between esse reale and esse rationis, the latter being possessed by negative and privative properties, certain relations, universals and propositional complexes.12 His followers sometimes extended this notion of ens rationis to cover also possibilia indeed, even impossibilia, that is, anything that can be thought of.13 Scotus and his followers admitted even a third type of existence, supposed to be half-way between esse reale and esse rationis, the so-called esse intentionale, which things were supposed to have when conceived by cognitive powers other than the intellect.14 If we add to this the distinction between esse essentiae and esse actualis existentiae, the former of which was thought to be possessed by essences even when they did not possess the latter, there being no supposita actually bearing them,15 we can see how the apparent proliferation of entities or pseudo-entities required by this semantic framework prompted also a proliferation of several types and notions of existence in this tradition. 12 For a detailed discussion of St. Thomas's distinction see my paper: "The Changing Role of Entia rationis in Mediaeval Semantics and Ontology: A Comparative Study with a Reconstruction", to appear in Synthese, 1991. 13 Cf.: "Nam multa cogitantur ab intellectu nostro quae in se non habent reale esse, etsi cogitentur ad modum entium, ut patet in exemplis adductis de caecitate, relatione rationis, etc. Item multa cogitantur quae sunt impossibilia et modo possibilium entium finguntutr, ut chymaera, quae non habent aliud esse quam cogitari." Francisco Suarez: Disputaciones Metafisicas, disp.LIV. sect.1. n.7. Editorial Gredos, Madrid, 1966. p. 394. Cajetan also included chimeras among entia rationis in his commentary on St. Thomas' De Ente et Essentia. Cf. also: John Poinsot (Iohannes a Sancto Thoma): Tractatus de Signis (part of his Cursus Philosophicus, ed. by R.A. Powell), University of California Press, 1985. pp.49-52. (Quid sit ens rationis in communi et quotuplex) 14 "... triplex est esse in universo: scilicet esse reale, esse intentionale et esse rationis. Esse reale est illud quod convenit rei ut existit formaliter et in natura propria et tale esse non convenit nisi singulari vel ei quod habet esse in singulari, quia solum singulare existit in natura propria per se et primo; universalia autem non existunt nisi ut habent esse in singularibus de quo esse intelligitur illud Philosophi in Praedicamentis: ‘destructis primis impossibile est aliquod aliorum remanere'. Esse vero intentionale est illud quod convenit rei ut habet esse representative sive esse representatum in aliquo alio ente reali, et quia representari in aliquo alio obiective indifferenter convenit tam universali quam singulari, ideo esse intentionale convenit tam universali quam singulari, ideo esse intelligibile non magis appropriat sibi esse universale quam singulare nec econverso, et tale esse intentionale est debilius esse reali et ideo semper fundatur in ipso licet obiective. Esse vero rationis convenit rei ut habet esse conceptus in sola consideratione intellectus operantis et tale, cum sit esse diminutum, semper praesupponit alterum duorum praecedentium." Fr. Guillelmus Alnwick O.F.M.: Quaestiones Disputatae de Esse Intelligibili, (ed. P. Athanasius Ledoux, O.F.M.) Ad Claras Aquas, Florentiae, 1937. p.6. Cf. J. Duns Scotus: Opus Oxoniense, I. d.36.q.unica. St. Thomas also uses the term esse intentionale, see e.g. ST1 q.56.a.6.; ST1 q.67.a.3.; De Ver q.22.a.3.; 4SN d.44.q.2.a.1.; in De Anima lb.2.lc.14, lc.24. etc. 15 Cf. e.g. "... non sequitur ‘homo est ens ergo homo est', quia sicut ista est vera ‘homo est animal' propter convenientiam intellectuum, similiter dico quod ista est vera ‘homo est ens' propter convenientiam intellectuum entis et hominis. Unde dico quod ibi ‘ens' non sumitur pro significato entis actu, sed pro intellectu ipsius. Et ideo non sequitur ‘homo est ens, ergo homo est'." Quoted by D.P. Henry: "Some Thirteenth-Century Existential Disputes: Their Identification and Its Status", in: P. Osmund Lewry O.P. (ed.) The Rise of British Logic, Toronto, 1985, pp.226-227. Cf. further Aegidius Romanus: Theoremata de Esse et Essentia, (ed. E. Hocedez), Louvain, 1930. XIII. pp.78-84.; Henricus de Gandavo: Quodlibet I, Opera Omina, vol. V, (ed. R. Macken), Leuven University Press-E.J. Brill, Leiden, 1979. q.9. See also S. Ebbesen: "The Chimaera's Diary", in: S. Knuuttila-J. Hintikka: The Logic of Being, Helsinki, 1987.

105

Ontological commitment with such an abundance of existence-types is certainly not an unequivocal matter. We can indeed say that there are as many types of ontological commitment implied by this framework as many types or notions of existence are distinguished.

Of course, if we apply Quine’s standard for ontological commitment, then these distinctions are of not much help in reducing the ontological commitment of this conception. For even despite the difference in the way they handled reference, in terms of their theory of supposition, the mediaevals certainly admitted propositions which we would regard as involving quantification over nonexistents.16 On the other hand, this very formulation, speaking about “quantification over nonexistents”, shows that it is possible to apply a notion of existence that has a narrower extension than the range of quantification. In other words this is to say that Quine’s notion of existence, whose extension coincides with the range of (unrestricted) quantification, corresponds to the weakest of the senses of existence endorsed by the mediaevals, namely the sense in which whatever can be thought of or referred to by any means is said to exist, in an abstract, atemporal manner.17 This, however, was by no means the primary sense of the several senses of existence distinguished by the mediaevals, and certainly not one that carried the ontological burden of real existence. The extension of the notion of real existence, as it was understood by the mediaevals, constitutes only a proper subset of the universe of discourse of this semantic framework. This sense of existence is always temporal, expressing actuality. So this kind of existence was held to be possessed only by actually existing real things, such as individual substances and their real properties, that is, their forms, whether substantial or accidental, actually informing their matter. The items in the other domains of the universe of discourse of this semantic conception were accordingly held to have the other, diminished types of existence touched upon above, or indeed no existence at all.18

Now whether one is ready to subscribe to such distinctions of different types of existence or not, one thing about these distinctions should be clear: they did not reduce the ontological commitment of this semantic framework by reducing the number of the semantic values of expressions, but by assigning different, reduced ontological statuses to several classes of them. What did the job of reducing the number of these semantic items, was their identification sometimes across different grammatical categories. Indeed, we may say that most of the

16 For example: "Nota quod qoddam potest esse licet non sit, quoddam vero est." St. Thomas Aquinas: De principiis naturae, c.1. 17 It is this sense of being that Burley called "maximally transcendent" (ens maxime transcendens). Walter Burley's De Ente, (ed. H. Shapiro), Manuscripta, 7(1963), pp.107-108. Cf.: "Nearly everyone who mentioned Gregory of Rimini at all pointed out that he had introduced a distinction between three senses of such terms as aliquid and ens. In the first and broadest sense, everything which was signified complexly or incomplexly was something, whether it was true or false or even impossible. In the second sense, every true thing which was signified complexly or incomplexly was something. In the third and strictest sense, only things existing in nature, whether substance or accident, creator or creature, could count as something." E.J. Ashworth: "Theories of the Proposition: Some Early Sixteenth Century Discussions", Franciscan Studies, 38(1978), pp.88-89. Of course, this does not mean that Quine commits himself to all kinds of intelligibilia. His tactic to reduce ontological commitment is to eliminate "apparently" referring expressions by means of quantified formulae in which the variables may be interpreted as ranging only over "legitimate" entities (in the vein of Russell's analysis of definite descriptions). This is the tactic comparable to Ockham's which I call elimination by definition (see below). 18 For an interesting example of this latter opinion see R. Lambertini: ‘Resurgant Entia rationis: Matthaeus de Augubio on the object of Logic', Cahiers de l'Institut du Moyen-Age Grec et Latin, 59(1989), pp.3-60, esp. p.29. Lambertini's paper supplies also a wealth of further references.

106

substantial metaphysical issues formulated in this framework concerned precisely the identity or difference of such semantic items, the significata or supposita of different expressions.

This is immediately clear for example in the case of the debate concerning the plurality of substantial forms. According to the famous claim of St. Thomas Aquinas, condemned among others by Robert Kilwardby in Oxford in 1277, individual substances do not have different substantial forms corresponding to their different substantial predicates. For St. Thomas, it is the same substantial form that accounts for a man’s being a substance, a body, a living, a sensitive, and a rational being, namely his soul. But this, in terms of the above-discussed semantic framework, is to say that the substantial predicates of individual substances have the same ultimate significatum in the same individual. For example, although Socrates is both a body and a man, i.e., a rational animal, his true predicates, ‘body’ and ‘man’, do not signify in him distinct forms: both of these predicates signify in him the same form, his soul, only according to different concepts, which represent this form more or less specifically. Indeed, the other two predicates occurring in the definition of man, ‘rational’ and ‘animal’, and the definition itself as a whole, also signify the same form in Socrates, but again according to different concepts, representing the same individualized form from different aspects, possibly common also to beings other than humans.19

But at this point, I think, it is time to give these informal semantic considerations a somewhat more rigorous formulation.

As I said above, the individualized forms, or properties ultimately signified by the same general term are numerically distinct in different individuals. Therefore we can say that such a term signifies these individualized properties in respect of the individuals in which they inhere, i.e., it signifies such a property for this individual, and another for that one, etc. But so we may represent the signification of a general term as a function assigning inherent properties to individuals. In a model theoretical reconstruction of this conception, therefore, a significate of a one-place general term can be denoted as the value of the signification function of this general term for a substance from the domain of our model like this: SGT(T1)(u). (Read: a significate of T1 in u.)20 Notice here that SGT is not a two-place function, with a term in its first, and a thing in its second argument-place, but a one-place function, which for a one-place term in its argument-place yields another one-place function, which for a thing in its argument-place yields an individualized property (the property signified by this term in this thing). In this way, applying the same trick, we can give a uniform treatment of the signification of general terms of any arity, and so, generally speaking, we can denote a significate of an n-place general term like this: SGT(Tn)(u1)...(un). (Read: a significate of Tn in u1 and ... and un.)

With this notation at hand we can express the Thomist claim concerning the unity of substantial forms in the following manner:

if S and G are (true) substantial predicates (Species and Genus) of the same substance u, then SGT(S)(u)=SGT(G)(u).

19 Cf. De Ente c.3. 20 SGT(T1)(u)∈WU{0}, where W is the universe of discourse and 0 is a zero-entity falling outside the universe of discourse. The case SGT(T1)(u)=0 (read: a significate of T1 in respect of u is 0) represents the situation when the term in question signifies nothing in u. This may be the case when a predicate simply does not apply to certain things, like e.g. colour predicates to numbers.

107

Accordingly, the opposite claim of the plurality of substantial forms will, of course, take the form of the denial of such identities.

But the above treatment of many-place terms also allows us the reconstruction of another widely disputed question: that of the identity of relations with their fundaments. The claim of those who held that relational properties are identical with the absolute properties founding the former, in the way the whitenesses of Socrates and Plato found their similarity, may be expressed as follows:

if R is a relational term which is true of two substances u and v, founded by the absolute property of u signified by the absolute predicate F, then SGT(R)(u)(v)=SGT(F)(u).

Also a great deal of ontological debates centered around questions regarding the distinctness of the significate of the predicate ‘est’, in the sense of actuality, from the significates of other, especially substantial predicates of a thing, that is, the distinction of existence from essence. The famous Thomist claim of the real distinction between essence and existence in creatures can be represented in this reconstruction by saying that, since for Aquinas substantial predicates of a thing signify the nature of this thing, if S is a substantial predicate of a creature u, then SGT(S)(u) is distinct from SGT(‘est’)(u)(t).21 On the other hand, since the name ‘God’ signifies the divine essence according to St. Thomas, his claim that in God, nevertheless, essence and existence are not distinct from one another can be expressed by the following identity: SGT(‘God’)(God) = SGT(‘est’)(God)(t).

Many others held, however, the view that essence and existence are not distinct even in the creatures, that is to say, that the significates of substantial predicates of individual creatures are identical with what the verb ‘est’, in its primary sense, expressing actual, real existence, signifies in them.

Now I think already these few examples are sufficient to show how several metaphysical problems of the pre-Ockhamist mediaeval tradition presupposed the same general semantic framework, and how the identification of the semantic values of different expressions contributed to reducing the ontological commitments of this framework. So in view of these considerations we can see actually how unjust it was on Ockham’s part to charge his predecessors with what he identified as “the root (principium) of many errors in philosophy: to want that to a distinct word there always correspond a distinct significate, so that there is as much distinction between the things signified as between the nouns or words that signify”.22 Nevertheless, it was in this spirit that he discarded the semantic framework that for him seemed to be committed to this “root of many errors”, in favor of a total reinterpretation of the relationships between language, mind and reality. 21 Here t is a time-point connoted by the present tense of the verb. For more on technical details, and complete description of formal semantic systems constructed along these lines see again G. Klima: Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1988. Since in this paper I am mainly concerned with the philosophical implications of the paradigmatically different ways mediaeval thinkers constructed their semantic theories, formalizations in this paper serve only to indicate how fundamental semantic ideas of the mediaevals may be reconstructed in a model theoretical framework. These simple formal devices are, therefore, only meant to facilitate the identification of conceptual differences of crucial importance. 22 "Et hoc est principium multorum errorum in philosophia: velle quod semper distincto vocabulo correspondeat distinctum significatum, it quod tanta sit distinctio rerum significatarum quanta est nominum vel vocabulorum significantium ..." Guillelmi de Ockham Summula Philosophiae Naturalis, ed. S. Brown, Opera Philosophica, vol. VI., St. Bonaventure N.Y., 1984, p.270.

108

A Brief Reconstruction of Ockham’s Semantic Innovations

A presentation of Ockham’s semantic innovations has to start with an account of his distinction between absolute and connotative terms. An absolute term signifies equally and in the same way all its significata. A connotative term, on the other hand, has both primary and secondary significata, and signifies its primary significata only in relation to its secondary significata or connotata. As we could see, in the older framework the significations of one-place general terms could be characterized as semantic functions assigning individualized forms or properties to individual substances. For Ockham, however, the significations of absolute terms are just sets of their significata. So absolute terms are general names of their significata, these being, according to Ockham, either substances, like men, trees or stones, or inherent, individual qualities, like this whiteness, that blue color or this concept of, say, horses, inhering in Socrates’s mind. So if T is an absolute term, then a significate of T is just an element of a subset of the universe of discourse.23

The signification of a connotative term is more like the signification of terms in general in the older framework, for Ockham’s connotative terms also signify certain things in respect of others. The difference, however, is that while in the older framework general terms signified inherent forms in respect of individual substances, Ockham’s connotative terms, conversely, signify individual substances in respect of their inherent qualities or other individual substances.24 For example, while on the older view the term ‘white’ signified individual whitenesses of individual substances, for Ockham the same term signifies individual substances, connoting their individual whitenesses.25 So we can bring out the contrast between Ockham’s and the older view by the following equations:

23 SGT(T)∈U, where U=SG(T), the signification of T, is a part of W. "Hoc enim nomen ‘homo' non significat primo unam naturam communem omnis hominibus, sicut multi errantes imaginantur, sed significat primo omnes homines particulares ... Ille enim qui primo instituit hanc vocem ‘homo', videns aliquem hominem particularem, instituit hanc vocem ad significandum illum hominem et quamlibet talem substantiam qualis est ille homo. Unde de natura communi non oportuit eum cogitare, cum non sit aliqua talis natura communis." Ockham: Summa Logicae, ed. Ph. Boehner, Opera Philosophica, vol. I. (henceforth: SL), St. Bonaventure, N.Y., 1974. p.124. Cf.: "Et si dicas: nomina communia, puta talia ‘homo', ‘animal' et huiusmodi, significant aliquas res substantiales et non significant substantias singulares, quia tunc ‘homo' significaret omnes homines, quod videtur falsum, igitur talia nomina significant aliquas substantias praeter substantias signulares: dicendum est quod talia nomina significant praecise res singulares. Unde hoc nomen ‘homo' nullam rem significat nisi illam quae est homo singularis, et ideo nunquam supponit pro substantia nisi quando supponit pro homine particulari. Et ideo concedendum est quod hoc nomen ‘homo' aeque primo significat omnes homines particulares ... " SL p.60. Cf. also: "Hic primo notandum est quod non intendit Philosophus quod voces omnes proprie et primo significant passiones animae, quasi sint impositae ad significandum principaliter passiones animae. Sed multae voces et nomina primae intentionis sunt impositae ad significandum primo res, sicut haec vox ‘homo' imponitur primo ad significandum omnes homines ..." Ockham: Expositio in Librum Perihermeneias Aristotelis, eds. A. Gambatese-S. Brown, Opera Philosophica, vol. II., St. Bonaventure N.Y., 1978., p.347. 24 "Whether or not Ockham's criteria of primary and secondary signification are adequate, his predecessors and contemporaries thought that Ockham had the priorities exactly reversed." M. McCord Adams: William Ockham, Notre Dame, 1987, Vol.I. p.325. For a detailed discussion of the niceties connected to earlier views see Sten Ebbesen: "Concrete Accidental Terms: Late Thirteen-Century Debates About Problems Relating to Such Terms as ‘Album'", in: N. Kretzmann (ed.): Meaning and Inference in Mediaeval Philosophy, Kluwer Academic Publishers, 1989. See also the related papers by R. Andrews and R. Huelsen in the same volume. 25 Whether these whitenesses are actual or not. The term ‘white' will supposit, however, in a proposition with a present tense copula only for those of its significata whose whitenesses are actual. See e.g. SL p. 95. Cf. Walter

109

Older view: SGTa(‘white’)(Socrates)= Socrates’s whiteness

Ockham’s view: SGTo(‘white’)(Socrates’s whiteness)=Socrates

But Ockham’s innovations, of course, concerned not only denominative terms, a subclass of the class of connotative terms, but connotative terms in general, i.e., terms which have both primary and secondary significata, indeed, in Ockham’s view all terms belonging in categories other than substance and quality.26

For example, the relative term ‘father’ signifies those men who have sons in relation to their sons:27

SGTo(‘father’)(son)=father

In contrast to this, on the older view, heavily criticized by Ockham,28 the term ‘father’ was taken to signify a relation, “fatherhood”, holding between two persons, the son and his father:

SGTa(‘father’)(father)(son)=fatherhood of father

Indeed, this formulation immediately shows why the question whether the same person’s having several sons multiplies his fatherhoods so naturally arises in this context.29 On the other hand, it also shows why Ockham did not have to worry about such questions: for him what such a term signifies are just the things which it can stand for in propositions, namely its possible supposita, signified in relation to other things, the term’s connotata. The only thing Ockham had to worry about concerning his ontological program was the elimination of any apparent reference to things seemingly belonging in categories other than substance and quality. To this end he used basically two tactics, one of which can be called 1. elimination by identification, and the other 2. elimination by definition.

1. The first tactic served for Ockham and his followers to handle the reference of abstract terms. In the case of absolute terms in the category of substance, they simply identified the supposita and significata of abstract terms with those of the corresponding concrete ones. So ‘humanitas’, e.g., was no longer conceived as signifying or referring to some abstract entity different from individual men, but to the individuals themselves.30 In the case of connotative terms the significata and supposita of abstract terms were identified either with the significata, or, according to Buridan at least in some cases more properly, with the connotata of the corresponding concrete terms.31 In fact, Ockham also entertained the idea of identifying the supposita of abstract relative terms with the sets of the relata of the corresponding concrete terms, construing them as collective names. According to this conception the term ‘similitude’, for example, refers to individual things that are similar collectively (coniunctim), that is, to a

Burleigh: De Puritate Artis Logicae Tractatus Longior with a revised edition of the Tractatus Brevior, (ed. Ph. Boehner) St. Bonaventure, N.Y., 1955, c.3. p.9. ll.6-16. 26 See e.g. SL, pp.37-38. 27 Cf. e.g. Guillelmi de Ockham: Quodlibeta Septem (henceforth Quodl.), ed. J.C.Wey, Opera Theologica, vol.IX., St. Bonaventure N.Y., 1980. V.25, VI.20-25. 28 Cf. e.g. SL, cc.50-54. 29 A theologically more intriguing question of this kind was whether Christ's being the son of both the Holy Mother and the Heavenly Father multiplies his filiations. See e.g. St. Thomas Aquinas, ST III, q.35.a.5. 30 See SL Pars I. cc.5-9. pp.16-34; Quodl. V. qq.9-11. 31 See Buridanus: Kommentar zur Aristotelischen Metaphysik, Minerva G.M.B.H. Frankfurt a.M., 1964, lb.5.q.9. Utrum sit aliqua relatio preter animam distincta a suo fundamento.

110

number of individuals at once, but without referring to any of them, just like the terms ‘people’, ‘army’, ‘crowd’ or ‘company’.32

2. The second tactic was used to eliminate apparent signification or connotation of, or reference to, entities that could not plausibly be identified as either substances or qualities. Consider for example the term ‘blind’. It evidently does not signify animals absolutely, but only by connoting a certain property, namely lack of sight. However, this property cannot be identified as a positive quality of a substance, being by its very concept rather a lack of a positive quality, namely sight. This is precisely what is spelt out by the nominal definition of this term, an expression which is synonymous with it, but showing in detail the complex conceptual structure hidden by the syntactic simplicity of the term. Indeed, several of his formulations suggest that according to Ockham all connotative terms are subordinated to complex concepts, because all connotative terms have such nominal definitions, namely complex expressions subordinated to the same complex concept and hence having the same meaning, but at the same time by their syntactic structure revealing the structure of this complex concept.33 For example, for the sake of simplicity let’s assume that ‘blind’ has as its nominal definition ‘not sighted’. Then ‘blind’ is no longer to be regarded as semantically primitive, but its significata are to be constructed as a function of the significata of the constituents of its nominal definition. But providing this construction means that there is no need to suppose that there is a curious kind of property of things, blindness, which cannot be identified with either a substance or a quality: what the term ‘blind’ signifies are substances, connoting particular qualities, namely individual sights that are not actual in their subjects, and the concept of negation, a certain syncategorematic mental act of individual human minds modifying the way other concepts are related to things, in this particular case, signifying precisely the absence of the connoted sight.34

32 Cf. Quodl. VI.q.25.pp.681-682: "abstracta relationum non supponunt nisi pro pluribus rebus absolutis coniunctim, sicut nomen collectivum, puta ‘populus', ‘exercitus', ‘turba', ‘societas'. ... sicut conceditur quod Ioannes est socialis et ista negatur ‘Ioannes est societas', ita est concedendum quod Sortes est similis, Sortes est aequalis, sed ista negatur ‘Sortes est similitudo', ‘Sortes est aequalitas', ista tamen conceditur ‘Sortes et Plato sunt aequalitas', ‘duo alba sunt similitudo'. Et ita in omnibus esset dicendum quod talia nomina abstracta relationum sunt nomina collectiva." 33 Here I follow what can be regarded as the received view on Ockham's connotative concepts. This view, however, was recently severely criticised by Claude Panaccio in his "Connotative Terms in Ockham's Mental Language", Cahiers d'épistémologie, Université du Québec à Montréal, Cahier no 9016, 1990, pp. 1-22. In this paper Panaccio argues that Ockham could consistently endorse the existence of simple connotative concepts, not admitting, though, that a simple connotative term is synonymous with its nominal definition. It is an open question, however, whether Ockham can consistently maintain this latter position. It may well be the case that on the basis of his general semantic principles Ockham is after all committed to holding that nominal definitions are synonymous with their definita, being subordinated to the same concepts. But this would need further inquiry. In any case, from the point of view of its import on the attitude towards ontological questions, it is enough if Ockham's treatment of connotative terms merely gave the impression (whether falsely or not) of what the received interpretation suggests. We may also add that Buridan, while endorsing the existence of simple connotative concepts, treated nominal definitions in the above-described way, not claiming, however, that all connotative terms have nominal definitions. Cf. n.34. below. 34 For Ockham's treatment of the term ‘caecus' in this spirit see SL pp.101-103. The presentation of the actual construction would unfortunately involve technicalities that would be quite out of place in this paper. The job will be done in my paper under preparation: Latin as a Formal Language: A Buridanian Semantics, attempting a full reconstruction of Buridan's basic semantic ideas in the framework of a complete formal semantic system. For suggestions in this direction see my "The Changing Role of Entia rationis in Mediaeval Semantics and Ontology: A Comparative Study with a Reconstruction", to appear in Synthese, 1991. and "‘Debeo tibi equum': A Reconstruction of the Theoretical Framework of Buridan's Treatment of the Sophisma", to appear in: S. Read (ed.): Acts of the

111

Generally speaking, by this method Ockham might hope eventually to eliminate (at least in principle - an important qualification of all kinds of reductionist programs) all apparent reference to entities other than substances and qualities, by supplying in the last analysis nominal definitions containing only syncategoremata, signifying qualities of the mind, and absolute terms, signifying substances or their qualities. To be sure, in the above example, ‘sighted’ is still a connotative term, so it demands further analysis. In fact, since nothing guarantees that in any nominal definition we may supply for a connotative term another connotative term will not crop up again, by this move Ockham stakes his semantics on his ontological program.

It is Buridan who could safely get out of this difficulty, by admitting the existence of simple connotative concepts.35 Indeed, he could do so without any ontological compromise. For his simple connotative concepts may signify the same absolute things ad extra as Ockham’s complex connotative concepts. The only difference is that these are not constructed out of simple absolute concepts plus syncategoremata as Ockham’s putative connotative concepts, but they simply signify absolute things connoting others as adjacent or non-adjacent to what they signify. So the appearance of connotative terms subordinated to these concepts in nominal definitions does not force further analysis. On the other hand, one may also point out that Buridan’s option helps only to the extent it enhances the vocabulary available for analysis, which alone may hardly guarantee universal success.

But whatever are the merits and demerits of Ockham’s ontological program, it surely gave a new direction to later ontological research.

The Independence of Ontological Reductionism From Semantics

From the above presentation it may seem that the basic import of Ockham’s semantic innovations was a genuine reduction of the ontological commitment of semantic theory. Indeed Ockham himself seems to discredit the older semantics precisely for its apparently enormous ontological commitments. However, as I remarked above, the tactic of identifying the semantic values of different expressions was open also in the older framework. Also it is a simple fact that by our very awareness of time and unrealized possibilities we can think of, refer to, or signify items that are not actually realized. So it seems to be a mere verbal difference whether we are ready to apply the verb ‘exists’ and its equivalents in a thinner, reduced sense to items in our

Ninth European Symposium for Mediaeval Logic and Semantics. 35 Cf.: "Comme on le sait, Occam pense qu'il est toujours possible de donner une definitio quid nominis des termes connotatifs (SL III-2, 28. p.556. III-3, 26. pp.689-691.) La position de Buridan est différente. ... Buridan réserve explicitement la definitio exprimens quid nominis aux termes vocaux simples auxquels corresponde un terme mental complexe. (Soph. I. concl.11.; Summulae VIII, 2, f. 100ra.) Le problème de savoir si ‘res alba' et ‘nasus cavus' sont les orationes dicentes quid nominis respectivement de ‘album' et de ‘simum' s'étant posé, Buridan répond conditionaliter: si à ‘album' correspond dans la pensée un concept complexe, ‘res alba' sera sa definitio dicens quid nominis (il en est de même pour ‘simum' et ‘nasus cavus'); si au contraire, à ‘album' et à ‘simum' ‘correspondent in mente conceptus incomplexi quibus confuse et indistincte substantiam et albedinem, vel nasum et simitatem concipimus, et non substantiam uno conceptu et albedinem alio, nec nasum uno conceptu et simitatem alio, tunc istae definitiones non sunt dicentes quid nominis sed quid rei'. (Summulae VIII.2. 102va; cf. Meta VII, 5.)" A. Maierù: "Significatio et Connotatio chez Buridan", in: J. Pinborg (ed.): The Logic of John Buridan, Copenhagen, 1976. pp.110-111. For the niceties of the differences between Ockham's and Buridan's ontological views see C. Normore: "Buridan's Ontology", in: J. Bogen-J.E. McGuire: How Things Are, D. Reidel Publishing Company, Dordrecht, Holland, 1985.

112

universe of discourse beyond the actually existing ones or not.36 In any case, Ockham himself, although he insists that there is not “another tiny world” reserved for non-real things and what is not real is nothing at all,37 finds no faults with referring to things that do not actually exist, although he refuses to allow a thinner sense of existence to be applied to these. So despite his apparent concern with ontological reduction, it seems that Ockham’s program is rather contingently connected to reducing ontological commitment, for in principle the same amount of reduction could be achieved also in the older framework, by using the tactic of identification and allowing only one, restricted sense of existence, to be denied to items in our universe of discourse that fall beyond the sphere of actually existing things.38

But if not in the ontological reductions, then in what does the real import of Ockham’s innovations consist? I suggest that in transforming the very idea of the task of ontological research and through this in transforming the paradigm of the theory of mental representation in a manner that even nowadays influences our thinking about the subject.

The Real Import of Ockham’s Innovations

As we could see, the reductionist tactic used by Ockham that was not so used in the older framework was what I called elimination by definition. We could also see that in the ideal, “finished” case, this tactic would eliminate all kinds of fortuitous terms, hiding by their syntactic simplicity a complex conceptual structure, consisting only of absolute concepts (and possibly some simple connotative concepts) and their “glue”, our syncategorematic concepts.

Now regarding this tactic we can say that the real value of such an analysis for the ontologist is not so much the sheer possibility of reducing the number of kinds of entities his theory is committed to, as the possibility of showing what there really is in external reality. For by this analysis, it seems, we may be able to identify those of our concepts that anchor our thoughts immediately and directly to the building blocks of the external world, thereby uncovering its real, independent structure, which without such a revelation is ordinarily hidden by the web of conceptual structures woven by our minds for mere convenience of expression, and for similar, merely accidental, pragmatic and historical reasons.39 These “anchors of thought”, for Ockham,

36 Cf.: "... Non enim sequitur: ‘Signum in actu est, ergo res significata est' quia non entia possunt significari per voces sicut et entia, nisi velimus dicere quod esse quod necessario requiruitur ad significatum non est nisi apud intellectum vel imaginationem." Roger Bacon: De Signis, (ed. K.M. Fredborg-L. Nielsen-J. Pinborg), Traditio, 34(1978), pp.75-136. p.82. 37 Cf.: "dico quod non sunt talia esse obiectiva, quae non sunt nec possunt esse entia realia; nec est unus parvus mundus alius entium obiectivorum; sed illud quod nulla res est, omnino nihil est ..." Quodl. III.q.4. pp.218-219. Cf. also the discussion of the problem by E. Karger: "Would Ockham Have Shaved Wyman's Beard?", in: H.A.G. Braakhuis-C.H. Kneepkens-L.M. de Rijk (eds.): English Logic and Semantics, Nijmegen, Ingenium Publishers, 1981. 38 For a formal treatment of quantification over and reference to nonexistents applying the mediaeval idea of ampliation, see "Existence, Quantification and the Mediaeval Theory of Ampliation" in my Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1988. In the system presented there existence is simply denied to any objects of reference that do not actually exist. 39 Cf.: "Here is a recipe for ontology. First divide the expressions of one's language into those which purport to pick things out and those which don't. Then see whether some of those which purport to pick things out can be defined in terms of others. Finally admit in your ontology whatever an undefinable term purports to pick out. This scheme expresses (though vaguely and incompletely) one of the central intuitions behind many ontological programmes. What is admitted by an ontologist operating within this framework will depend, of course, upon how he or she

113

are our absolute concepts. These are the ones that we acquire by direct acquaintance with things in our natural environment, the ones that are naturally caused in us by external things and which are therefore the immediate natural signs of these things.40

And it is at this point that the real import of Ockham’s innovations comes in. For the causal story Ockham has to tell us about the acquisition of our absolute concepts, there being no place for universal natures in his universe, not even in their tokens in individuals, is based on the notion of efficient causality. In contrast to this, the older framework had a story to tell us about concept acquisition in terms of formal causality. In what follows I wish to argue that this seemingly slight shift in the paradigm of the account of mental representation had a tremendous significance with far-reaching consequences.41 (Just remember what Aquinas says quoting the Philosopher: parvus error in principio magnus est in fine.)

The efficient causality model fixes the relation of natural signification on the basis of natural laws systematically connecting causes with their effects. But all that these natural laws guarantee is the systematic correspondence between causes and their effects, supposing the normal course of nature. The effects, however, may be essentially different from their causes, and may, therefore, be produced also by other essentially different causes too, which means that it is clearly possible that an absolute concept be caused in our intellects by a cause which is totally alien from what this concept is supposed to represent.

On the other hand, the formal causality model inherent in the older semantic framework is based on the idea that the natures informing the things of external reality, and making them to be what they are, are the very same natures that inform our minds when we have the concepts of these things. To be sure, this sameness of nature is not a numerical identity: the concept of man I have in my mind is a distinct entity from the nature of Socrates making him a man. However, what necessarily connects these two distinct entities is that they are tokens of the same nature, indeed, they are the same nature, in the same way as different tokens of the same word are the same word, despite the fact that they are numerically distinct entities.42 (Just recall Aquinas speaking about the same nature whether in the thing or in the intellect.)

To see the difference between these two models in somewhat more exact terms let’s take a look again at the ways the significations of substance-terms were construed in the two semantic frameworks discussed above.

divides expressions, on what resources of definition are available, and, perhaps, on pressures from other theories." C. Normore: "Buridan's Ontology", in: J. Bogen-J.E. McGuire: How Things Are, D. Reidel Publishing Company, Dordrecht, Holland, 1985. p.189. 40 For detailed account and ample references see Adams, op. cit. vol. I. part 3, cc.13-14. 41 I was pleased to learn that John Haldane identified the same kind of paradigm-shift in Ockham's epistemology in his: "Mind/World Identity and the Anti-realist Challenge", forthcoming in: J. Haldane-C. Wright: Realism, Reason and Projection, Oxford University Press, 1991. 42 For a suggestion concerning the semantics of relative identity, see n.5. of "On Being and Essence in Saint Thomas Aquinas's Metaphysics and Philosophy of Science", in my Ars Artium, also in S. Knuuttila (et. al. eds.): Knowledge and the Sciences in Mediaeval Philosophy: Proceedings of the Eighth International Congress of Mediaeval Philosophy Vol. II., Helsinki, 1990. The idea is that if we adopt the inherence theory of predication and the corresponding theory of signification, then we may say that ‘a is the same F as b' is true iff SGT(F)(a)=SGT(F)(b), which certainly may hold good even if a and b are numerically distinct entities. (Where on the right-hand side of the equivalence a and b are items of the universe of discourse that the object-language names ‘a' and ‘b' refer to.)

114

In what I called the older framework, the signification of such a term could be reconstructed as a function assigning individualized instances, or tokens of the nature signified by this term in the individuals having this nature, to the individuals. Now since the concepts of individual human minds representing this nature are again but tokens of the same nature, we can say that these concepts should be construed as values of the same function for individual human minds as its arguments.

On the other hand, although these concepts are individual tokens of the same nature in that they inhere in this or that particular mind, since they are obtained by the mind’s activity through a process of abstraction, in relation to the individual tokens of the same nature informing the individuals they are universal. Indeed, as I said in the beginning, the universal term subordinated to such a concept was held to be universal precisely on account of this universal relation of the concept to the other tokens of the same nature. For the word was held to signify precisely those individualized natures which the corresponding concept represented in a universal manner. So the concept itself also should be regarded as a function, assigning individualized natures to individuals, those natures which the word subordinated to it ultimately signifies. So if CON(m)(T) is a concept subordinated to the term T in a mind m, and u is some extramental individual, then we can say that:

SGTa(T)(m)=CON(m)(T) and SGTa(T)(u)=CON(m)(T)(u)

Now what is important about these concepts from our present point of view is that they are individuated both by their subjects and their objects. For from the above characterization of concepts it follows that, for any u and m:

CON(m)(T1)=CON(m)(T2) iff CON(m)(T1)(u)=CON(m)(T2)(u)43

That is to say, two concepts may differ either because they inhere in different minds, or, more importantly, because they are concepts of different objects. I say, “more importantly”, because the sheer numerical difference between concepts belonging to different minds is a rather trivial matter and is usually disregarded when conceptual differences are under discussion. For example, it is a trivial matter that Euclid and Aristotle had numerically different concepts of a triangle, only because they were distinct individuals. The more interesting difference between concepts is the difference e.g. between Euclid’s and Bolyai’s concept of a triangle, on account of the difference between the thought-objects they had in their minds. It is precisely the lack of this kind of difference that entitles us to say that Aristotle after all had the same concept of a triangle as Euclid did, despite the numerical distinction of the mental acts by which they conceived triangles.

So if we disregard the trivial numerical difference between concepts on account of their subjects, then we can say that what accounts for the distinction or identity of concepts is whether they concern the same thought-objects or not. And note here that this criterion of identity for concepts

43 Note here that it also follows that CON(m)(T1)(u)=CON(m)(T2)(u) iff SGT(T1)(u)=SGT(T2)(u), for any u, that is two terms signify the same things, i.e., they are synonymous, iff they are subordinated to the same concept. The point is that these follow from our characterisation of concepts by means of model-theoretical functions, and hence from the standard identity conditions for functions. For a detailed formal account see again the Appendix of my "Understanding Matters from a Logical Angle" and "‘Socrates est species': Logic, Metaphysics and Psychology in St. Thomas Aquinas' Treatment of a Paralogism", in: G. Klima: Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1988, also to appear in K. Jacobi (ed.): Acts of the 8th European Symposium of Mediaeval Logic and Semantics, Munich, Philosophia Verlag, 1990.

115

is not something that we have to stipulate: this is a plain corollary of the way we described concepts, as being tokens of the same nature as their objects.

In contrast to this, on Ockham’s account of the matter, the identity or difference of their objects need not necessarily enter the identity-conditions of concepts. Of course we may, as Ockham and his followers in fact did, stipulate that two concepts are distinct if and only if they concern different objects, but this is an extra stipulation that does not follow from the characterization of concepts in this framework. A concept for Ockham is but a quality of mind distinct by place and subject from its objects, connected to them by the logically contingent relation between effect and cause. But since, generally speaking, the same effects in principle may be produced by different causes, the identity or difference of their objects is not necessarily involved in the identity-criteria of concepts on this characterization.44

The skeptical implications of this conception of mental representation were soon recognized by the Avignon commission examining Ockham’s doctrines and were developed into a fully-fledged skeptic doctrine by the “mediaeval Hume”, as he is sometimes called, Nicholas of Autrecourt. For, concluded the Avignon commission, if the object and its concept are connected by the relation of efficient causality alone, it may well be the case that the effect, the concept of the object, is produced by a superior agent, God, without the presence of the object.45 But if this may happen in this or that particular case, then nothing prevents the possibility of this being always the case, Nicholas argued further.46

I think it is quite obvious how small, logically, is the further step to be taken to get from here to Descartes’ Demon, or its modern, suitably secularized and technicized version, the Evil Scientist with his envatted brains. Also it is the presuppositions of the same model of mental representation that later on called for desperate efforts to explain the mysterious match between mental and external structures, if there was supposed to be any, in terms of direct causality, occasionalism, or pre-established harmony; or to explain it away as naturally surpassing our cognitive capacities altogether.

44 Indeed, the conclusion of this view of concepts, that qualities of the mind that are concepts are only contingently concepts, i.e. qualities that represent external objects to a mind, is explicitly stated by Pierre d'Ailly: "illa qualitas que est conceptus, licet naturaliter sit conceptus, non tamen necessario est conceptus, quare conceptus potest non esse conceptus". See Pierre d'Ailly: Conceptus, text edited in: L. Kaczmarek: Modi Significandi und Ihre Destruktionen, Munster, 1980, (contaning editions of Pierre d'Ailly: Destructiones Modorum Significandi and Conceptus), p.92. Cf. also pp.82. and 91-92. 45 "... Omnis res absoluta distincta loco et subiecto ab alia re absoluta potest per divinam potentiam existere alia re absoluta destructa. Sed visio intuitiva tam sensitiva quam intellectiva est res absoluta distincta loco et subiecto ab obiecto viso, sicut si videam intuitive stellam existentem in celo, ista visio intuitiva, sive sit sensitiva sive intuitiva, distinguitur loco et subiecto ab obiecto viso. Ergo ista visio potest manere stella destructa." A. Pelzer: "Les 51 articles de Guillaume Occam censurés, en Avignon, en 1326", Revue d'histoire ecclésiastique, 1922, pp.240-70. Quoted by E.A. Moody: "Ockham, Buridan, and Nicholas of Autrecourt", in: Studies in Medieval Philosophy, Science and Logic, UC Press, Berkeley-LA-London, 1975. p.134. 46 "Sed forsan dicetis, prout mihi videtur, volebatis innuere in quadam disputatione apud Predicatores, quod, licet ex visione non possit inferri obiectum visum esse, quando visio ponitur in esse a causa supernaturali vel conservatur ab ipsa, tamen quando posita est in esse a causis naturalibus precise, concurrente influentia generali primi agentis, tunc potest inferri. Contra. Quando ex aliquo antecedente, si esset positum ab aliquo agente, non poterit inferri consequentia formali et evidenti aliquod consequens: nec ex illo antecedente poterit inferri illud consequens, a quocunque fuerit positum in esse." ibid. p.135.

116

Note that in the earlier, formal causality model of mental representation no similar cognitive predicaments can occur: if I have a donkey-concept, than it cannot be but of donkeys. I think this is precisely the point of Aquinas’s seemingly cryptic, but repeatedly made remark that “the intellect is not deceived about its proper object” (intellectus non decipitur circa obiectum proprium), namely the quiddity of material things. By my donkey-concept being what it is, a token of the same nature that informs donkeys, I can conceive but donkeys.

To be sure, it may well be the case that I mistakenly judge this particular individual to be a donkey, when it is not a donkey, but say, a pony. This is what Aquinas speaks about when he says that the intellect may be deceived per accidens about its proper object, namely when it mistakenly subsumes an individual under another concept, forming a judgment about it. What is excluded by this model, however, is that I have a donkey-concept which is not of donkeys, but of, say, electronic impulses from the Evil Scientist’s computer.

On the other hand, in the framework of the efficient causality model, since the identity of their objects does not enter the identity conditions of mental acts, it may very well be the case that a poor envatted brain has a mental act, which is exactly like my donkey-concept, with the only deplorable difference that the brain does not conceive by it donkeys but only electronic impulses. And so, again, since mental acts have identity-conditions of their own, irrespective of their objects, it may very well be the case that my concept is indistinguishable from that of the envatted brain, so there is no way of telling whether I myself, who is thinking about this problem, am not an envatted brain.

In the formal causality model, however, the objects of concepts cannot be swapped without affecting their identity. So it simply cannot be the case that I have a genuine donkey concept, by which I conceive donkeys, which is indistinguishable from the fake donkey concept of an envatted brain conceiving by it only electronic impulses. Also, since if I have a genuine donkey concept, then my concept is an instance of the same nature that informs donkeys, it cannot be the case that I have a genuine donkey concept and I don’t conceive by it donkeys, but only electronic impulses. Indeed, it cannot be the case either that I have a genuine concept of brains-in-a-vat, conceiving by it only electronic impulses instead of real brains in a vat. But I can conceive a real situation only by genuine concepts. So I conceive a real situation as described in the brains-in-a-vat story only if I have a genuine concept of brains-in-a-vat. But then I am not a brain in a vat.

So as understood in the formal causality model, the very description of the situation guarantees that whatever mental acts an envatted brain has, since by them it conceives only electronic impulses which I don’t, while I have to conceive things, which it doesn’t (at the very least some real envatted brains), its mental acts are different specie from mine. So the description of the situation entails that I am not in its situation, that is, I am not an envatted brain. So Descartes’ Demon, or the brains-in-a-vat story and their kin can present difficulties only for the efficient causality model of mental representation, and so may, perhaps, be utilized not so much as arguments for skepticism, but rather as arguments against this model.

Conclusion: Realism, Conceptualism and Nominalism

In conclusion of this discussion let me return for a while to the “philosophical labels” mentioned in the introduction, and propose for them a certain interpretation which, in the light of the above reflections, may be useful in characterizing certain general philosophical views on mental representation.

117

In the history of philosophy textbooks referred to above, Ockham is usually presented as a nominalist or a conceptualist and sometimes also as a skeptic, although the latter label has been vigorously challenged by many recent historians.47 I think the arguments and the textual evidence for the claim of these historians are conclusive: Ockham himself was by no means a skeptic, for he did believe that human cognitive powers are capable of adequately capturing the essential features of external reality. Nevertheless, what even so justifies to a certain extent the charge of skepticism is that in his zeal for ontological reductions, by changing the concept of signification, Ockham shifted the burden of natural signification from formal causality to efficient causality, thereby making it dependent on a contingent natural order of creation, suspendable at any time, if by no-one else, at least by its Maker.

To be sure, creation and natural order are contingent and subject to God’s almighty power in the older framework too. The difference is that on the older view God’s universal design pervades the whole of creation including conceptual structures of the human mind as well.48 So even if it is quite possible that God could have had a different plan with a different design and different creatures having different cognitive capacities, what is excluded by this conception is that in this creation with the conceptual capacities we actually have at our disposal we should be systematically deceived by a Great Deceiver in a way that his plot could never in principle be disclosed by us.

It is this kind of homogeneity of real and mental structures that was severed by Ockham’s paradigm-shift, which opened up the logical possibility of a systematic, essential and in principle undetectable mismatch between these structures. Nevertheless, Ockham did believe that as long as we can suppose the normal workings of nature our cognitive powers are in fact capable of grasping the essential features of independently existing external reality.49 So we can say that far from being a skeptic, Ockham was, in one sense of the term, the first modern realist. The sense of the term I have in mind is characterized by Crispin Wright in the following words:

The view of the world which Putnam calls metaphysical realism is nothing very precise. It involves thinking of the world as set over against thought in such a way that it is only by courtesy of a deeply contingent harmony, or felicity, that we succeed, if we do, in forming an overall picture of the world which, at least in its basics, is correct. This is what commits the metaphysical realist to the possibility that even an ideal theory might be false or seriously incomplete. And the same kind of thinking surfaces in the idea that the world comes prejointed, as it were, into real kinds, quite independently of any classificatory activity of ours. For once one thinks of the world in that way, one is presumably committed to the bare possibility of creatures naturally so constituted as not to be prone to form concepts which reflect the real kinds that there are. The real character of the

47 Two outstanding examples are Moody and Adams in their opp. cit. 48 "Et patet quod impossibile est rem communem pluribus rebus extra habere illud esse secundum, nisi tantum dum fuerit in anima secundum esse spirituale vel intentionale in suo signo. Et sic intelliguntur quotquot dicta Commentatoris et philosophorum loquentium de ista materia. Metaphysici tamen sciunt quod natura communis prius naturaliter intelligitur a Deo ut communicata multis suppositis quam in effectu communicatur eisdem. Et sic universalitas vel veritas metaphysica non dependet ab intellectu creato, cum praecedit ipsum, sed dependet ab intellectu increato. Quae - ex aeterna notitia intellectuali - producit omnia in effectu! Et ignorantia huius sensus fecit Ockham et multos alios doctores signorum ex infirmitate intellectus declinare ab universali reali." John Wyclif: Tractatus de Universalibus, (ed. I.J. Mueller), Clarendon Press, Oxford, 1985. c.2. p.65. 49 No wonder Buridan, the great systematiser and developer of Ockham's doctrine of concepts, in his refutations of Nicholas of Autrecourt's scepticism, resorted to the notion of ex suppositione necessity and to a probabilistic interpretation of certainty in natural science. Cf. Moody, op. cit.

118

world and its constituents would thus elude both the cognition and the comprehension of such creatures.50

I think this description excellently fits both the actual picture suggested by Ockham’s model and its implications, developed mainly by others, influenced in one way or another, after some centuries’ while largely unknowingly, by Ockham’s new paradigm. One type of reaction to this picture was certainly skepticism. But those who still believed in some match between thought and reality devised several ways to account for it. Earlier I mentioned causality, occasionalism and the idea of pre-established harmony. I think that all these may find their place under the concept of realism in that they think of the external world as absolutely unaffected by our thinking, and its intact structure as to be discovered and mirrored by our minds either through the things’ action on our cognitive faculties, or through the graceful activity of a superior agent.

A radically different reaction to the same picture is one that reverses the direction of explanation and says that what accounts for the match between our conceptual structures and the essential categories of reality is that it is our very concepts that structure this reality for us, so no wonder we find what our minds posited there. To be sure, the reality thus constituted may be just a mere phenomenal reality, the world as it appears to us, human beings, endowed with just the kind of cognitive powers we happen to have. So even if the Ding an Sich may or may not have some structure of its own, that structure is necessarily beyond our reach. But at least in the phenomenal reality, constituted by our own concepts, we may feel safely at home. I think it is this type of attitude that, with its reliance on the priority of our conceptual structures, may justly be called conceptualism.

Finally, we have many modern examples of the kind of reaction to the same picture that says that we simply should not be bothered by any kind of mysterious match between the categorial structure of thought and reality, but should rather choose and stipulate those forms of expression of our generalizations that promise the best predictive success and fit in the simplest and easiest way into the present, well-established forms. This kind of attitude, with its disregard for either real or conceptual structures and its obsession with stipulating certain convenient uses of expressions, I think may duly be termed nominalism.

As can be seen, what I called the “older”, or “formal causality” model of mental representation could hardly find its place under any of these characterizations. In fact, in this paper I have tried to argue that it was Ockham’s paradigm-shift that set the stage for these alternatives, and for the demise of the older model together with its own, rather different ontological alternatives.51 But it is precisely for this reason that a reconstruction of the alternative semantics involved in this older model may shed some fresh light also on our modern problems, presupposing so much in their formulations from a historically rather contingent conceptual heritage.52

50 C. Wright: "On Putnam's Proof That We Are Not Brains-In-A-Vat", for the Gifford Conference on the philosophy of Hilary Putnam, held at St. Andrews Nov.23-26, 1990. draft, p.21. I owe thanks to Crispin Wright for his kindly supplying me with a copy of this particularly inspiring paper even before its final completion. 51 Note here that by calling this the "older model" I by no means wish to imply that the other model, what I called "the efficient causality model", was entirely Ockham's invention. In fact, I suspect that what partly motivated Plato's introduction of what I called "the formal causality model" was the scepticism of Protagoras and other sophists, formulated in an efficient causality framework. But the details of this ancient story are beyond the scope of this paper. 52 This paper was written during my stay in St. Andrews, Scotland, as Gifford Visiting Fellow of the Department of Logic and Metaphysics of the University of St. Andrews in the second half of 1990. An earlier version was

119

presented and discussed there at a meeting of the Philosophy Club, followed by further inspiring discussions with John Haldane and Stephen Read. I would like to thank the University of St. Andrews for the wonderful time we spent there with my family, for the kindness and hospitality we received from everyone we met during our whole visit. I owe special thanks, however, to Stephen Read, chairman of the Department, for having arranged this visit in the first place, for the fruitful scholarly discussions and for kindly correcting whatever I committed in my paper against the English language.

120

The Changing Role of Entia rationis in Mediaeval Semantics and Ontology: A Comparative Study with a Reconstruction

Introduction: Two Theses about Entia rationis

In this paper I wish to argue for two theses concerning entia rationis. My first thesis is that entia rationis, in what I would call the via antiqua1 sense, are objects of thought and signification, required by a certain kind of semantics, but undesirable as objects simpliciter in ontology. My second thesis is that this systematic role of entia rationis in the via antiqua tradition of mediaeval thought was simply eliminated by the advent of Ockhamist semantics, which opened up the way towards a radical reinterpretation of the concept of entia rationis and towards a new research program for ontology.

In the next section of the paper, therefore, I start my discussion with a case study of the systematic role played by entia rationis in the philosophy of St. Thomas Aquinas, a typical representative of the via antiqua tradition, occasionally drawing parallels with and taking illustrations from the works of other mediaeval thinkers too.2 In the third section I give a systematic account of all kinds of entia rationis against the background of a comprehensive semantic theory constructed in the spirit of the via antiqua tradition. In the fourth section I describe the ways Ockham's approach changed this semantic background, and examine how these changes influenced the concept of entia rationis. In the concluding section of the paper I present a simple formal reconstruction of what I take to be Ockham's basic innovations in semantics and discuss briefly the new ontological program it initiated.

The Need for Entia rationis: Aquinas on the Two Senses of esse

St. Thomas' conception of entia rationis is based on his account of the Aristotelian distinction between two senses of being. The most comprehensive account of this distinction is given by St. Thomas in his Sentences-commentary in relation to the question whether evil is something:

By way of answer we have to say that the Philosopher shows that `being' is said in many ways.3 For in one way `being' is said as it is divided by the ten genera. And in this way `being' signifies

1 One of course has to be very cautious when applying such an expression, so much involved in scholarly debate. In the rest of this paper I wish to use it in a very restricted, technical sense, referring to a particular way of constructing semantic theory, sharply distinguishable from Ockham's and his followers' way (both to be described later). What I think may justify such a usage is the clear connection of these ways of doing semantics with the ways broader philosophical, theological and methodological issues were treated in the two great trends getting separated later in mediaeval thought. Indeed, this paper may perhaps serve as a modest contribution to the characterisation of the two viae from the point of view of the connections between semantics and ontology. As to the debates concerning the proper characterisation of via antiqua vs. via moderna see e.g. Moore (1989). 2 To be sure, by presenting Aquinas' views as representative of what I call "via antiqua semantics" I do not wish to deny the immense variety of semantic views in mediaeval philosophy even before Ockham. I take Aquinas' views typical, however, as contrasted with Ockham's, precisely in those of their features which rendered the via antiqua framework unacceptable for Ockham. 3 The notorious lack of the use/mention distinction in St. Thomas' texts renders their translation sometimes extremely difficult, and at some places faithfulness inevitably results at least in clumsiness of style, if not in confusion. With due apologies for clumsiness I only hope that the subsequent discussion will at least help dispel confusion. Translations in this paper if not otherwise indicated are mine. Texts from St. Thomas translated here are from Aquinas (1980). References to Aquinas's single works are by their standard abbreviations and divisions.

121

something existing in the nature of things, whether it is a substance, like a man, or an accident, like a color. In another way `being' signifies the truth of a proposition; as when it is said that an affirmation is true, when it signifies to be what is, and a negation is true, when it signifies not to be what is not; and this `being' signifies composition produced by the judgment-forming intellect. So whatever is said to be a being according to the first way, is a being also in the second way: for whatever has natural existence in the nature of things can be signified to be by an affirmative proposition, e.g. when it is said: a color is, or a man is. But not everything which is a being in the second way is a being also in the first way: for of a privation, like blindness, we can form an affirmative proposition, saying `blindness is'; but blindness is not something in the nature of things, but it is rather a removal of a being: and so even privations and negations are said to be beings in the second way, but not in the first. And being is predicated in different manners according to these two ways: for taken in the first way it is a substantial predicate and pertains to the question `What is it?', but taken in the second way it is an accidental predicate, ... and pertains to the question `Is there (such and such a thing)?'.4

This distinction derives from Aristotle's discussion of the concept of being in the fifth book of his Metaphysics, where concerning the second member of this distinction in St. Thomas' commentary we find the following:

We have to know that this second mode is related to the first one as effect to cause. For it is from the fact that something exists in the nature of things that the truth or falsity of a proposition follows, which the intellect signifies by this verb `is', as it is verbal copula. But, since some things which in themselves are not beings, the intellect considers as some sort of beings, like negations and the like, sometimes `is' is said of something in this second way, but not in the first. For it is said that blindness is in the second way, for the reason that the proposition is true in which something is said to be blind, but this is not said to be true in the first way. For blindness does not have real being, but is rather a privation of some being.5

Now from these passages at least the following points seem to be clear:

(1) a being in the first sense belongs in one of the ten Aristotelian categories, while one in the second sense, by opposition, does not belong to any of these, but owes its existence somehow to the activity of the mind

(2) `being' in the second sense signifies truth and composition, and this sense of being is expressed by the copula of categorical propositions

(3) beings in the first sense form a proper subclass of beings in the second sense

(4) `being' in the first sense is a substantial predicate of things, while in the second sense it is an accidental predicate

(5) `being' in the first sense answers the question `what is it?', while in the second sense it answers the question: `is there (such a thing)?'

But with these points clarity seems to come to an unhappy end. For it seems to be difficult, if not impossible, to make any consistent sense of these points. Indeed, even if we set aside modern worries as to the concept of existence as a first-order predicate in the Fregean sense,6 what St.

4 2SN 34.1.1. Cf. 1SN 19.5.1.ad1., 33.1.1.ad1.; 2SN 37.1.2.ad1. & ad3.; De Ente 1.; De Pot 7.2.ad1.; De Malo 1.1.ad19.; Quodl 9.2.2.; In Meta 4.1., 5.9., 6.2., 6.4., 9.11., 11.8.; ST1 3.4.ad2., 16.3.ad2.; 48.2.ad2.; ST1-2 36.1.; ScG 1.12., 1.58., 3.9. Cf. also Cajetan (1964, 1590) c.1.; C. Alamannus (1888) Tom.1. sect. II. 5. 1.; Schmidt (1966) Part II. ch. 4. and Part III. ch. 8. 5 In Meta 5.9.n.896. 6 To help settle these worries let me refer the reader to Klima (1988b). For more on Frege's "ambiguity thesis" in a historical perspective see Knuuttila et al. (1986).

122

Thomas says here about the second member of his distinction simply does not seem to make any good sense. For let us suppose that we understand that the copula of a categorical somehow expresses truth or falsity - after all, it is by this copula that we express that something is or is not the case.7 But then how should we understand for example that it is by the copula of an affirmative categorical that we can express the way blindness, as opposed to sight, exists, that such a copula answers the question whether there is such and such a thing and, to cap it all, that such a copula is an accidental predicate of things? Even if we accept that existence in some sense may be treated as a (first-order) predicate, it should clearly be nonsense to claim that a copula can be a predicate of anything, whether accidental or not.

Well, I think that despite appearances to the contrary we can make good sense of St. Thomas' distinction, provided we are ready to understand it in its proper theoretical context, namely in the context of the theory of predication upheld, among others, also by St. Thomas, and what is justly called by historians of mediaeval logic the inherence theory of predication.8

This theory can easily be formulated in one sentence: a predicate is true of a thing if and only if the form signified by the predicate in the thing actually inheres in the thing, i.e., if this form, or property of the thing actually exists.

But this simple, one-sentence theory has far-reaching implications as to the ways language and thought are conceived to be related to reality. (Perhaps, this is why nobody ever held it in this simplistic form.) For if it is conceived as a general theory of predication, applying to any predicate whatsoever, then in this simple form the theory clearly implies a very close and homogeneous correspondence between linguistic items and items of reality. For in this simple form the theory says that for any true predicate of a thing there is a corresponding form, or property actually inhering in the thing, regardless of what kind of a property it is. But such a close and homogeneous correspondence cannot be maintained for a variety of reasons.

First, since this would mean that e.g. if Socrates is white, he would not only possess the property of whiteness, but, of necessity, also all negations of the corresponding contrary properties, e.g., the properties of being non-red, non-green, non-blue, etc. But these "negative colors" seem not to be properties of Socrates of the same kind as his whiteness, for clearly his color, the property whose existence verifies the predicate `colored' of him, is his whiteness, but not any of these "negative colors".

Second, this one-one correspondence would imply that whenever something else changed in the world Socrates would gain and lose an infinite multitude of properties as his relations to other things changed with this change. Indeed, he would not only gain and lose properties while he himself exists, but also before and after his lifetime, as even nowadays, whenever a new student of philosophy comes to admire him, he should acquire the actually existing property of being admired by the student in question, that is, he would undergo change, even if he himself does not exist, which seems to be absurd.

7 Cf. "Cum enim dicimus aliquid esse, significamus propositionem esse veram. Et cum dicimus non esse, significamus non esse veram; et hoc, sive in affirmando sive in negando. In affirmando quidem, sicut dicimus quod Socrates est albus, quia hoc verum est. In negando vero, ut Socrates non est albus, quia hoc est verum, scilicet ipsum non esse album." In Meta 5.9.n.895. 8 Concerning the inherence theory in general, as opposed to the identity theory see L. M. de Rijk's Introduction to Abaelard (1956, pp. 37-38) and Henry (1972, pp. 55-56). Concerning St. Thomas's inherence theory in particular see H. Weidemann (1986) and Schmidt (1966).

123

Third, since to have a privative or negative property is nothing but not to have the corresponding positive property, like to be blind is nothing but not to have sight, the existence of the privative or negative property should be nothing but the nonexistence of the corresponding positive property. But since nothing can be both existence and nonexistence in the same sense, if we want to maintain that such negative and privative predicates are true of the thing in virtue of the existence of the corresponding negative and privative properties, we have to conclude that these properties have a different kind of existence from the one enjoyed by the corresponding positive properties.

So, for such and similar reasons it seems that if we accept the inherence theory as our general theory of predication, we cannot maintain a completely homogeneous ontology, with a single domain of entities containing equally all the properties signified by our predicates, but we have to distinguish between at least two kinds of entities, namely between those that really exist, either as complete substances or the properties really informing them, and those that exist only in a derivative sense, as consequent upon the actual state of the former, and somehow superimposed on this actual state by the mind conceiving this state in some manner.

Indeed, it is precisely this feature of St. Thomas' distinction that is brought out very clearly by his famous commentator Cajetan, in his commentary on St. Thomas' De Ente et Essentia:

... although Socrates may be blind without any intellect considering this, and does not become more or less blind because an intellect does consider it, yet blindness has no being (esse) in Socrates when an intellect does not consider it; for both of these propositions are true at the same time. This is explained thus. For Socrates to be blind as such is not for Socrates to have any substantial being (esse), as is clear, nor accidental, because Socrates is blind by the sole absence of visual power, and this adds nothing to Socrates; whence blindness adds no being (esse) whatever to Socrates. Thus, because the power of vision is lacking in Socrates without the consideration of any intellect, Socrates must be blind without any intellect considering it. A question arises here because one does not correctly see that to be blind is not to be something, but to lack the power of vision. For example, a ship is without a pilot, and no intellect considers this. The absence of the pilot does not give the ship any substantial or accidental being (esse), whence for the ship to be without a pilot is not to be something outside the soul, but not to be piloted. For privations and negations acquire being (esse) and become beings <in the second sense - G.K.> because the intellect, conceiving (intelligens) privations through positive properties (habitus) and negations through affirmations, in some way forms in itself some sort of image of the thing lacking. For example, when the intellect forms in itself a kind of image of a ship without a pilot, which is this mental proposition, the ship is without a pilot, the non- presence of the pilot, which is nothing outside the soul, becomes a being in the soul because the intellect makes it the term of a proposition; and since this being (esse) is in the soul and it has no other being (esse), the result is that negations and privations of this kind are not beings except in the soul objectively. Thus their being (esse) is nothing else than to be thought of (intelligi), the only manner in which all beings of reason have being (esse).9

From this lengthy quotation I think at least this much is clear, that the derivative existence of a being of reason is such that beyond the actual state of affairs' being in reality as it is, for the existence - to wit, existence in the second sense - of such a being something more is required, namely the activity of a mind, which is able to conceive this state of affairs in such a way as to project, as it were, into it this being of reason, as a kind of summation of this state of affairs.

9 Translation is from Cajetan (1964, pp. 64-65), which I slightly modified at some points on the basis of Cajetan (1590, pp. 299-300).

124

To see this in more detail, let us consider again the example of blindness. According to the inherence theory, someone is blind if and only if there is blindness in his eyes. But, as we could see, this blindness cannot be said to exist in the blind eye in the same sense as sight exists in the seeing eye. Sight exists in the first, while blindness only in the second of the senses of being distinguished above. This second sense is expressed by the copula of categorical propositions. In the case of this particular blindness, its existence in the second sense is expressed by the copula of the proposition by which this eye is said to be blind. But the same situation may be expressed also by saying that this blindness is, or exists, in which case the verb `is' or `exists' is not a copula, but an absolute predicate of this blindness. However, of course, also in this case this verb can express the existence of this blindness only in the second sense, for as we said, blindness can exist only in this second, derivative sense. For this blindness has no existence in the first sense at all, since for it to be (in the second sense) is precisely for something, namely for the sight of this eye, not to be (in the first sense). It is only because the intellect forms the concept of blindness so that it includes the lack of sight from an eye that the eye lacking sight can be said to have blindness, and so blindness can be said to be in this eye.

We can also illustrate the dependence of blindness on the activity of mind, as opposed to the independence of a real being from the same, by saying that if there were no minds at all forming the concept of blindness, then there would be no blindness either, even if there were eyes lacking sight. By opposition, however, even if there were no minds forming the concept of whiteness, still, there would be whitenesses in reality, provided there would be white things. The difference between the two cases is that since the concept of blindness includes some mental act, namely negation, for there to be anything characterizable as blindness, it is not enough that such and such real things should exist in such and such a way, but it is also required that there be a human mind capable of exercising this mental act.

But now I think we are already in a position to see a consistent interpretation of the points of St. Thomas' distinction listed above. The background theory of this interpretation is the inherence theory of predication: for every true predicate of a thing there is some property inhering in the thing. It is precisely the existence, or actual inherence of such a property that verifies the predicate of the thing. But since it cannot be the case that every true predicate of a thing should pick out some really existing property, a distinction had to be made between two senses of being, one of them predicable of the truly existing things, substances as well as their properties, while the other predicable of those significates of true predicates of things which cannot be regarded as their real properties. The mode of existence of the latter is said to be expressed by the copula of categorical propositions, which, however, is claimed to be expressed also by `is' as an absolute predicate, for it is the same sense of esse that is applied both in `Aliquid est caecum' and in `Caecitas est'. (See again the passage quoted from St. Thomas' Metaphysics-commentary above.) I think this is how we can account for St. Thomas' seemingly confused remarks concerning the copulative `esse' as a predicate.10

Nevertheless, it would be rash to conclude from this that the copula of a proposition attributes existence directly to a significate of its predicate. As Cajetan warns us in his commentary on the Categories:

And pay attention carefully to the fact that Aristotle's maxim put forward here: `it is on account of whether the thing is or not that a proposition is said to be true or false' is not to be understood as

10 For a formal reconstruction and more detailed discussion of St. Thomas's distinction see Klima (1990).

125

concerning the thing which is <signified by> the subject or the predicate <term> of the proposition, but of the thing that is signified by the proposition itself. For example, when it is said that a man is white, this is not true because a man or a white thing is, but because a man being white is; for this is signified by this proposition.11

This is why, regardless of whether the predicate term of the proposition signifies real or rationate properties, its copula expresses always existence in the second sense, namely the existence of the propositional complex signified by the proposition.

Unfortunately, St. Thomas himself is not very explicit about the significate of propositions,12 but what the anonymous author of the 12th-century tract Ars Burana says about enuntiabilia would fit in very nicely with Aquinas' conception of entia rationis:

Note that whether we speak about the dictum of a proposition or of the significate of a proposition or of an enuntiabile it is the same. For an enuntiabile is what is signified by a proposition. For example: `a man is an animal', this proposition is true, because what it signifies is true; and that true thing that you in this way understand is the enuntiabile, whatever it is. Similarly, when I say: `Socrates is an ass', this proposition is false, because what it signifies is false, and the false thing that you conceive in this way is the enuntiabile. And this cannot be seen, nor heard or sensed, but it is only perceivable by the intellect. If you ask in which category of things it belongs, whether it is a substance or an accident, of the enuntiabile we have to say that it is neither a substance nor an accident nor does it belong to any of the categories. For it has its own peculiar type of existence. And it is said to be extrapredicamental, not because it does not belong to any category, but because it does not belong to any of the categories distinguished by Aristotle. Therefore it belongs to some category that can be called the category of enuntiabilia. And in this category the most general item will be that consignified by the term `enuntiabile'. And this can be divided further as follows. Some enuntiabilia are of the present, some are of the past and some are of the future. Furthermore, some enuntiabilia are true and some are false. And further: of the true ones some are necessary and some are not necessary, and of the false ones some are possible and some are impossible. So it is to be understood what an enuntiabile is. (Rijk 1967, pp. 357-359)

So enuntiabilia so understood would form just another type of entia rationis beyond the ones already discussed. Those discussed explicitly by St. Thomas and Cajetan in the above- quoted passages may be characterized as significates of certain predicates in their subjects, namely of those predicates which in their concept involve some operation of the mind, like negation, and

11 "Et adverte hic diligenter quod illa maxima Aristotelis hic posita: `ab eo quod res est vel non est oratio dicitur vera vel falsa', non intelligit de re quae est subiectum aut praedicatum orationis, sed de re significata per ipsam orationem, verbi gratia: cum dicitur homo est albus, non ideo est vera ista quia homo vel album sit, sed ideo, quia hominem esse album est: hoc enim est significatum per illam orationem." Caietan (1939, p. 87). Cf. St. Thomas: in Peri I.9. Of course, by `res quae est subiectum or praedicatum orationis' Cajetan understands the things signified by the corresponding terms of the proposition, hence my additions in the translation. For an excellent modern discussion of Aristotle's relevant texts see Matthen (1983). 12 I would tentatively identify the significate of a proposition as the enuntiabile expressed by the proposition, expressly called by St. Thomas an ens rationis in 1SN 41.1.5. I say "tentatively", because of St. Thomas's tendency to use the term enuntiabile as a synonym for enuntiatio (although "emphasizing the objective meaning of enuncia-tion", as remarks Schmidt (1966, p. 223, n. 84)). For St. Thomas's use of the term see 3SN 24.1.1b.; 1SN 38.1.3.; De Ver 2.13.ad7., 1.6., 14.8., 2.7., 1.5., 14.12.; Quodl 4.9.2.; ST1 14.14., 14.15.ad3., 16.7., ST3 1.2.ad2. For a clear 13th-century expression of the view that an enuntiabile is the significate of a proposition see e.g. Peter of Spain (1972, pp. 205-207). Cf. also G. Nuchelmans (1973, pp. 165-194).

126

which, consequently, cannot be regarded as constituents of "intact reality". Rather, these are to be construed as objects of thought, formed by the operation of the intellect, although having a foundation in reality, the actual way real beings are. In the same way, enuntiabilia are objects of thought formed by the operation of the intellect, though having a foundation in reality. The difference is that they are not significates of predicates, but of whole propositions including somehow both what is signified by the predicate and the subject and the other, syncategorematic elements of the proposition, most notably, the copula.

In view of these considerations we may say that in this semantic construction there is a three-layer structure underlying a simple categorical proposition with a predicate term signifying some non-real property, like the property of blindness. What immediately accounts for the truth of, say, `Homer is blind' is the existence of the enuntiabile signified by this proposition, namely the state of affairs that Homer is blind. But this state of affairs can exist, in the sense signified by the copula of the proposition, only if Homer actually has the property signified by the predicate, that is, if his blindness actually exists, but again, only in the sense of existence expressed by the copula. However, in virtue of the concept of blindness involving the negation of the corresponding positive property, this privative term applies to the subject, namely Homer, only if he lacks sight, i.e., if his sight, the significate of the corresponding positive term, does not exist, this time in the sense of real existence expressed by `est' used as an absolute, substantial predicate of real beings.

But even this three-layer structure has some further, inner complexity, namely that expressed by the syntactic structure of the proposition. For to this syntactic structure, according to St. Thomas, there corresponds a conceptual structure, existing in the mind, which reflects the composition of the things conceived by this conceptual structure.13

Indeed, this conceptual structure existing in the mind also has two aspects to it. For, as Cajetan explains, we can speak about "being in the mind" in two senses:

"To be in the intellect can occur in two ways, namely subjectively and objectively. To be in the intellect subjectively is to inhere in it, like an accident inheres in its subject, as whiteness inheres in a surface. To be in the intellect objectively is to terminate the act of the intellect." (Cajetan 1590, p. 327)

What are subjectively in the mind are its real qualities, existing in the first sense of the two senses of `esse' distinguished by St. Thomas. These are the mental acts, or thoughts by which individual minds conceive external things, forming their specific and proper thought objects, the universal concepts, existing merely objectively in the mind.

Our concepts, as we are taught by St. Thomas,14 are the result of an operation of our mind, which uses as its principle of activity a species intelligibilis abstracted by the active intellect, intellectus agens, from the sensual representations of particulars, from phantasms. In the process of abstraction the active intellect separates the universal nature intuited within the phantasms from its individuating conditions, though without the exclusion of these, and creates in the receptive intellect, intellectus possibilis, a universal similitude of the individuated natures of individual 13 "Cum autem intellectus compositionem format ..., oportet quod in compositis substantiis ipsa compositio formae ad materiam ... vel etiam compositio accidentis ad subiectum respondeat, quasi fundamentum et causa veritatis, compositioni quam intellectus interius format et exprimit voce." In Meta 9.11.n.749. 14 For a detailed analysis of and a wealth of references to this doctrine of St. Thomas see Schmidt (1966, pp. 94-122).

127

things, a so-called species intelligibilis. This species intelligibilis serves as the principle of the operation of the receptive intellect called formatio, the term, or result of which is the concept, intention, or mental verb signified immediately by the external, vocal verb.15 By forming this universal concept the mind is directed to things sharing the nature represented by this concept, and this is why the external word signifying immediately this concept, through the mediation of the concept, signifies ultimately all things falling under it.

But the intellect forms not only concepts, but by their composition or division it also forms judgments about how things are. These judgments, again, can be regarded from two perspectives. As they are subjectively in the mind, they are its individual qualities, individual acts of human thought occurring in this or that human mind. But as they are the objects of the mind, they exist in it merely objectively, as some complex entia rationis, formed by the activity of the mind. I suggest that we identify these complex entia rationis as the enuntiabilia signified by propositions as described by our anonymous 12th century author in the passage quoted above. It is, then, the actual existence or nonexistence (in the second sense of `esse') of such an enuntiabile that verifies immediately the proposition signifying it, but this, as we have seen, depends ultimately on the way real things are. This would be then the `thing' referred to by Aristotle's above-quoted maxim - `it is on account of whether the thing is or not that a proposition is said to be true or false' - the existence of which is expressed by the copula of the proposition that signifies it.

A Sketch of a "Via Antiqua Semantics"

As from this account of St. Thomas' distinction there emerged the outlines of a rather complicated semantic and ontological picture, at this point it may be worthwhile to give at least a sketch of a systematic reconstruction of it.

At the heart of this picture, as we have seen, lay the inherence theory of predication. This theory, however, presupposes a more basic theory, a peculiar theory of signification. According to this theory a categorematic term signifies individualized properties of particulars, either inherent forms, really informing the matter of material substances, or entia rationis, i.e., properties of things that do not really inhere in them, but belong to them in virtue of some more complex pattern of reality conceived by the intellect in this property.

But these properties, as we have seen, were not the only kind of entia rationis required by this theory. For the terms signifying any properties of things do so only in virtue of signifying immediately the universal concepts formed by the intellect, by which it conceives the things sharing these properties. These universal concepts, as they are formed by the intellect to direct its thinking towards the objects having the nature or property represented by these concepts, are also entia rationis, which do not exist in reality according to their proper nature, i.e., in their universality, though they have a foundation in real beings, namely the individual natures or individualized properties, represented in an abstract, universal manner by these concepts. On the other hand, these objective concepts, as in late-scholasticism they became to be called, owe their existence to the formal concepts inhering in individual minds, i.e., to individual thought-acts by which the human intellect forms to itself its peculiar, immediate thought objects, the universals.16

15 See e.g. ST1.85.2.ad3; ScG 1.53. and 4.11. 16 "Supponenda imprimis est vulgaris distinctio conceptus formalis et obiectivi; conceptus formalis dicitur actus ipse, seu (quod idem est) verbum quo intellectus rem aliquam seu communem rationem concipit; qui dicitur

128

It is only through this twofold conceptual structure that our simple words are related to what they ultimately signify, the natures, forms, or properties of things existing in reality. But then, proportionally, our propositions are related through a similar twofold structure to the way things are, which ultimately accounts for the truth and falsity of our judgments. For judgments are formed by the human intellect through its second operation, by which it combines the concepts formed by its first operation. But so just as our concepts have a twofold structure, so should have our judgments: just as the conceptus formales inhere in particular minds as their real qualities, so do the judgments formed from them; while just as the conceptus objectales exist merely objectively in the mind so do the propositional complexes formed from them.17 These propositional complexes, the objective contents of our judgments form then a further class of entia rationis, which we identified as the enuntiabilia signified by our propositions.18 It is the actuality of such a propositional significate that verifies immediately the proposition signifying it, though, of course, depending on the complexity of the structure of the proposition and the meaning of its terms, this may require a rather complex situation to obtain in reality. For example, what immediately verifies the proposition: `Some men are not white' is the actual state of affairs signified by this proposition, namely that some men are not white. However, what is required a parte rei for this state of affairs to be actual is that the individualized properties signified by the predicate of this proposition in some individuals referred to by the subject term should be non-actual. As this example shows, in this framework the syntactic structure of a proposition serves not only to identify the state of affairs signified by the proposition as a whole, but indicates also what conditions should hold in reality so that this state of affairs obtains. This is why the Aristotelian definition of truth can be put in one sentence referring to the existence of conceptus, quia est veluti proles mentis; formalis autem appellatur, vel quia est ultima forma mentis, vel quia formaliter representat menti rem cognitam, vel quia revera est intrinsecus et formalis terminus conceptionis mentalis, in quo differt a conceptu obiectivo, ut ita dicam. Conceptus obiectivus dicitur res illa, vel ratio, quae proprie et immediate per conceptum formalem cognoscitur seu representatur; ut, verbi gratia, cum hominem concipimus, ille actus, quem in mente efficimus ad concipiendum hominem, vocatur conceptus formalis; homo autem cognitus et representatus illo actu dicitur conceptus obiectivus, conceptus quidem per denominationem extrinsecam a conceptu formali, per quem obiectum eius concipi dicitur, et ideo recte dicitur obiectivus, quia non est conceptus ut forma intrinsece terminans conceptionem, sed ut obiectum et materia, circa quam versatur formalis conceptio, et ad quam mentis acies directe tendit, propter quod ab aliquibus, ex Averroe, intentio intellecta appellatur; et ab aliis dicitur ratio obiectiva. Unde colligitur differentia inter conceptum formalem et obiectivum, quod formalis semper est vera ac positiva res et in creaturis qualitas menti inhaerens, obiectivus vero non semper est vera res positiva; concipimus enim interdum privationes et alia, quae vocantur entia rationis, quia solum habent esse obiective intellectu. Item conceptus formalis semper est res singularis et individua, quia est res producta per intellectum eique inhaerens; conceptus autem obiectivus interdum quidem esse potest res singularis et individua, quatenus menti obiici potest, et per actum formalem concipi, saepe vero res est universalis vel confusa et communis, ut est homo, substantia, et similia." Suarez (1960, pp. 360-361). For a somewhat different interpretation of the same distinction, however, cf. also Cajetan (1590, pp. 301, 316-317). For translation see Cajetan (1964, pp. 67-71, 121-124). 17 Cf. Nuchelmans (1980, pp. 50-52). Although here, instead of referring to the conceptus formalis vs. obiectalis distinction, Nuchelmans refers to the distinction between species intelligibilis impressa vs. expressa. Nevertheless, from the point of view of the contrast between subjectively vs. objectively existing concepts of the mind the former seems to be more to the point than the latter. Cf. Suarez (1966, pp. 451-452). On the other hand, in Cajetan's terminology it is indeed the species intelligibilis impressa vs. expressa distinction that applies here. Cf. previous note and Cajetan (1590, p. 327). 18 Note here that that this classification of beings of reason, according to what linguistic items signify them and in which ways, does not contradict the traditional division of entia rationis into negations, privations and relations. (cf. e.g. Suarez (1960, pp. 92-93); R. McInerny (1961, p.44). I simply use this division because this discussion centres around the semantic function of entia rationis, as semantic values of different expressions.

129

what is signified by the proposition as a whole, instead of the recursive satisfaction-clauses of a Tarskian truth-definition. On the other hand, in a fully-fledged semantic theory constructed in this style one would have to give the recursive clauses for identifying the significata of propositions in terms of the semantic values of their components and specifying the conditions for their actuality on the basis of the syntactic structure of the propositions signifying them. By providing these clauses one may give a unique assignment of significata to propositions and a literal formal equivalent of the above-quoted Aristotelian definition of truth. If, on the other hand, one also gives the relevant clauses for identifying the mental acts giving rise to these entia rationis, namely the formal concepts and the judgments formed from them, one may also give precise meaning to St. Thomas' concept of truth as consisting in what he called adaequatio intellectus et rei.19

As can be seen, these ideas together form a comprehensive theory as to the ways words are related to thoughts and their objects, the things of extramental reality. In this sense this is a comprehensive semantic theory with an apparently enormous ontological commitment to all sorts of weird entities, in fact, to anything that can be thought of or signified by any means. But the "hard" ontological commitments of this theory are (supposed to be) drastically reduced by making a distinction between what is merely signified, referred to or thought of, i.e., what is merely an object of thought, what exists in a diminished sense only if some mind conceives it, on the one hand, and what is an object simpliciter, regardless of whether there are any minds conceiving it, on the other. "Hard" ontological commitment therefore attaches only to objects which are claimed to exist in the first of the senses of St. Thomas' above-discussed distinction. On the other hand, the theory has an enormous amount of "soft" ontological commitment to several kinds of entities existing in the second sense of the distinction, as objects of thought. As we have seen, these objects were required by the peculiar construction of this semantic theory built on the concept of signification implied in the inherence theory of predication. So anyone who wishes to get rid even of this "soft" ontological commitment has to construct his semantic theory in a different way, built on a different concept of signification. This was precisely the course taken by William Ockham.

Ockham's Semantic Innovations and Their Influence on the Concept of Entia rationis

That the basic source of the unwelcome ontological commitments of his predecessors' theories was the concept of signification implied in the inherence theory of predication was clearly realized by Ockham. For it is this concept of signification that requires that any true predicate of a thing should be verified by the property signified by the predicate actually inhering in the thing. But then, this implies that "the column is to the right by to-the- rightness, God is creating by creation, is good by goodness, just by justice, mighty by might, an accident inheres by inherence, a subject is subjected by subjection, the apt is apt by aptitude, a chimaera is nothing by nothingness, a blind person is blind by blindness, a body is mobile by mobility, and so on for other, innumerable cases". (Ockham 1974, p. 169) And this is nothing, but "to multiply beings according to the multiplicity of terms ..., which, however, is abusive and leading far away from 19 For a complete technical description of a model theoretical semantics constructed along the lines described here see the Appendix of Klima (1988c). Further formal approximations of the finer details of St. Thomas' semantic theory can be found in Klima (1988d, 1990).

130

truth" - says Ockham (Ockham 1974, p. 171). Indeed, he identifies this as "the root (principium) of many errors in philosophy: to want that to a distinct word there always correspond a distinct significate, so that there is as much distinction between the things signified as between the nouns or words that signify". (Ockham 1984, p. 270).

How then could Ockham free philosophy from such abuses and errors? By discarding the concept of signification that led to them, of course.

According to this conception, as we have seen, general terms ultimately signify those individualized properties of things that the concept immediately signified by the term represents in a universal, abstract manner in the mind. Indeed, St. Thomas Aquinas, commenting on Aristotle's famous claim, in the beginning of his Perihermeneias, that words signify things not immediately but by the mediation of concepts, justifies this claim in the following way:

Therefore `passions of the soul' must be understood here as conceptions of the intellect, and names, verbs, and speech signify these conceptions of the intellect immediately according to the teaching of Aristotle. They cannot immediately signify things, as is clear from the mode of signifying, for the name `man' signifies human nature in abstraction from singulars; hence it is impossible that it immediately signify a singular man. The Platonists for this reason held that it signified the separated idea of man. But because in Aristotle's teaching man in the abstract does not really subsist, but is only in the mind, it was necessary for Aristotle to say that vocal sounds signify the conceptions of the intellect immediately and things by means of them. (Aristotle, 1962, p. 25)

That the word `man' signifies human nature does not mean, however, that it does not refer to, or, to apply a modern re-coinage of the mediaeval technical jargon, supposit for individual men in a proposition like `Some men are white'. For, as St. Thomas says:

In respect of any name we have to consider two things, namely that from which the name is imposed, what is called the quality of the name, and that to which the name is imposed, what is called the substance of the name. And the name, properly speaking, is said to signify the form, or quality from which the name is imposed, and is said to supposit for the thing to which it is imposed.20

So the term `man' signifies human nature in abstraction from the singulars immediately, and signifies individual human natures ultimately, but normally supposits for the things bearing the nature it signifies, namely individual men. It is only in virtue of some special adjunct that a term is made to refer to what it normally signifies: "this term `man' does not supposit for the common nature unless for the reason of something added, as when it is said `man is a species'."21 As is well-known, in systematic treatises on the theory of supposition, this kind of supposition was distinguished as simple supposition, as contrasted with material supposition, when a term refers to itself, as in ``man' is a noun', and with personal supposition, when the term refers to what falls under it, as in `a man runs'.22 So we can say that for Aquinas a term has simple supposition when it refers to what it (immediately) signifies,23 while it has personal supposition when it refers to what falls under its significate. But it is precisely at this point where Ockham introduced a small,

20 3SN d.6.q.1.a.3. 21 ST I. q.39.a.4., cf. ST III. q.16.a.7. 22 For good bibliographies on the vast recent literature on supposition theory see e.g. Ashworth (1978); Kretzmann et al. (1982). For more recent references see Kretzmann (1989). 23 For a detailed discussion of Aquinas' treatment of the problems connected with the supposition of `man' in `man is a species' see Klima (1988d)

131

but as we shall see, very significant innovation in semantic theory. As Walter Burleigh, a staunch defender of what I call via antiqua semantics, describes it:

Some people, however, reprove what is said, namely that a term has simple supposition when it supposits for its significate, for they say reprehending the antiquiores that that saying is false and impossible. They say on the contrary that it is personal supposition when the term supposits for its significate or significates; and it is simple supposition when the term supposits for the intention or intentions of the soul. And so they say that in this proposition `Man is a species' the term `man' has simple supposition but does not supposit for its significate, for the significates of this term are this man and that man. But in this: `Man is a species', the term man supposits for an intention in the soul, which is really a species of Socrates and Plato. (Burleigh 1955, p.7)

I think it is also significant that Burleigh, among several other arguments in defense of the view of the antiquiores, provides also the same kind of justification for this view that was alluded to by St. Thomas in the above-quoted passage from his commentary on the Perihermeneias:

But beyond doubt this is very unreasonably said, for in this: `Man is a species' this term `man' supposits for its significate. For ... this name: `man' signifies something primarily, and does not signify primarily Socrates, nor Plato, for so someone hearing this word and knowing what it signifies would determinately and distinctly think of Socrates, which is false; therefore this name `man' does not signify primarily some singular; so it signifies primarily something common, and that common thing is a species, whence that which is primarily signified by the name `man' is a species. (Burleigh 1955, pp. 7-8)

Ockham does not accept this kind of justification: For this noun `man' does not signify primarily some nature common to all men, as is fancied erroneously by many, but signifies primarily all particular men ... For the one who first instituted this noun `man', seeing some particular man, instituted it to signify that man and whatever substance of the same sort as him. So he did not have to think about a common nature, for there is nothing like such a common nature.24

So Ockham insists that what common terms primarily signify are not some universal natures that can be found individualized in the singulars and exist in their universality, abstracted from all individuating conditions in the mind, but are the singulars themselves. As a consequence, for him, in contrast with the view of Burleigh's antiquiores,25 the significata of common terms are their personal supposita, and not their simple supposita, the universal natures abstracted by the mind from their instances inhering in the personal supposita as their individualized natures. (Ockham 1974, pp.95, 195-196) Indeed, Ockham deploys several arguments to show that there are no such natures inhering in, but distinct from the individuals having them.26 On the other hand, in this framework there is still need of some sort of universals to account for the difference between the significative function of general and of singular terms. However, these universals 24 Ockham (1974, p.124). Cf.: "Et si dicas: nomina communia, puta talia `homo', `animal' et huiusmodi, significant aliquas res substantiales et non significant substantias singulares, quia tunc `homo' significaret omnes homines, quod videtur falsum, igitur talia nomina significant aliquas substantias praeter substantias signulares: dicendum est quod talia nomina significant praecise res singulares. Unde hoc nomen `homo' nullam rem significat nisi illam quae est homo singularis, et ideo nunquam supponit pro substantia nisi quando supponit pro homine particulari. Et ideo concedendum est quod hoc nomen `homo' aeque primo significat omnes homines particulares ... " Ockham (1974, p.60). Cf. also: "Hic primo notandum est quod non intendit Philosophus quod voces omnes proprie et primo significant passiones animae, quasi sint impositae ad significandum principaliter passiones animae. Sed multae voces et nomina primae intentionis sunt impositae ad significandum primo res, sicut haec vox `homo' imponitur primo ad significandum omnes homines ..." Ockham (1978, p. 347). 25 Whom, however, Ockham himself frequently refers to as moderni. Cf.: Adams (1987, vol.I, p. 144) 26 See e.g. Ockham (1974, pp. 23-34) and Ockham (1980, pp. 518-528)

132

need not be abstract likenesses of the individualized natures of particulars existing merely objectively in the mind, but simply natural signs signifying many things and suppositing for the same:

But what is it in the soul that is such a sign? We have to say that concerning this question there are several opinions. Some people say that it is nothing but some sort of fictum of the soul. Others say that it is some quality existing subjectively in the mind, distinct from the act of understanding. Others say that it is the act of understanding. And in their favor is the principle that `it is futile to do with more what can be done with fewer'. But anything that is explained by positing something distinct from the act of understanding can be explained without it, for the act of understanding can supposit and signify in the same way as any other sign. So there is no need to posit something beyond the act of understanding.27

So by this move, i.e., by identifying the ultimate significata of general terms with their personal supposita, Ockham was able to get rid at once both of universal natures and of their instances, what were traditionally conceived as the immediate and the ultimate significata of general terms. But this move, of course, affected not only those terms which traditionally were held to signify the individualized, distinct natures of individuals, i.e. substance-terms, but also those that were held to signify other properties, whether they be real accidents belonging in any of the nine accidental categories, or entia rationis, privations, negations or relations of reason.

As is well-known, Ockham divided terms into absolute and connotative ones. Absolute terms are those that signify equally all their significata primarily, while connotative terms are those that signify some of their significata primarily, and some of them secondarily.28 The primary signficata of the latter are those which they supposit for in propositions, i.e. their personal supposita, while their secondary significata are those in relation to which they supposit for their primary significata. But given this conception of the signification of connotative terms, there would in principle be no need to posit any inherent properties at all: an absolute term signifies equally all and only those things which it can supposit for in propositions in no relation to other things, while a connotative term primarily signifies all and only those things that it can supposit for in propositions in relation to those things which it secondarily signifies. But these things, whether signified primarily, or secondarily by a term, in principle, as far as the semantic theory is concerned, could belong to any of the categories, indeed, they might all belong to the category of substance alone. As is also well-known, however, for independent reasons, Ockham retained distinct entities also in the category of quality.29 But from a semantic point of view terms connoting such real qualities do not differ essentially from those that would connote only substances: these terms signify what they can supposit for in propositions, namely the subjects of these qualities, in relation to the qualities of which they are the subjects.

In any case, this new conception of signification gave Ockham the chance to get rid not only of universals and distinct individualized natures answering them a parte rei, but also of privations and relations, in brief, any sort of inherent properties that were required by the above- discussed semantic framework. Indeed, as in this new framework predicate terms of propositions no longer signify inherent forms, but directly the individuals falling under them, the affirmative copula is

27 Ockham (1974, p. 43). For a compendious description of the development of Ockham's view on the matter see Adams (1987, vol. I, p. 74, n. 10). For a detailed analysis of Ockham's earlier theory of universals in terms of esse obiectivum, and a presentation of the ideas of his immediate predecessors see Read (1977). 28 For detailed analysis of this distinction and ample references see Adams (1987, pp. 319-327). 29 For a discussion of Ockham's reasons see Adams (1987, pp. 277-285).

133

no longer taken to express the existence of inherent forms through attributing existence to a propositional complex, but the identity of the supposita of the terms of the proposition in which it occurs. So the resulting theory of truth need not commit itself to the (merely objective) existence of dicta, enuntiabilia, or their 14th-century counterparts, complexe significabilia, i.e., to adequate significates of whole propositions either.30 As a matter of fact, Ockham himself never addresses explicitly the question of the ontological status of the adequate significate of the whole proposition.31 But what may be regarded as a consistent extension of Ockham's account in this respect is Buridan's, wherein he explicitly refuses to admit complexe significabilia in his ontology and provides an account of truth much closer to contemporary truth-definitions, by determining the truth-values of propositions of different syntactical complexity separately in terms of the semantic values of their components.32

So, as a result of Ockham's new semantic approach, in principle all entia rationis became dispensable.33 But is there, then, any room for the mere concept of entia rationis in this new conceptual framework? Ockham's answer is affirmative. However, he gives a radically new interpretation to this concept:

something is not said to be a being of reason because it is not some real thing existing in the nature of things, but because it is only in reason, as something that the mind uses for something or for the sake of something. And in this way all propositions and all consequences and all mental terms are beings of reason, nevertheless, they are really existing in the nature of things, and are, indeed, more perfect and more real beings, than any corporeal qualities. (Ockham 1974, p. 113)

So for Ockham entia rationis are not a special sort of entities enjoying a peculiar sort of existence, totally different from the one had by ordinary beings; on the contrary, they are ordinary beings, having a totally ordinary kind of existence, differing from the rest only in that they have this ordinary existence in the mind. But it is not only qualities of the mind that Ockham regards as entia rationis. Although apparently considering it as a kind of concession, he is prepared to regard also some relations as entia rationis:

although `relation of reason' is not a philosophical expression, for I believe that this expression does not occur in Aristotle's philosophy, nevertheless, for the sake of what is commonly said, namely that a relation of reason is something, I say that real relations and relations of reason are to be distinguished. And this is clear from the following. For whenever without the operation of the intellect a thing is not such as it is denoted to be by the relation or by its concrete form, then it is a relation of reason. For example, ... since a coin is not the price of something, unless by voluntary institution, which is preceded by an act of the intellect, price can be called a relation of reason. ... But whenever a thing is such as it is denoted to be by the relation or by its concrete form without the operation of the intellect, so that the operation of the intellect does nothing to this effect, then it can be said to be a real relation. (Ockham 1980, p. 699)

But, as we can see, these relations of reason, again, are not some inherent properties, distinct from the things having them, but just the ordinary things themselves, as conceived or signified 30 For an excellent, comprehensive account of the later developments of the problem see Nuchelmans (1980). See also relevant chapters of Ashworth (1974). 31 Cf. Adams (1987, pp. 310-313) and Adams (1985). 32 For Buridan's refusal of complexe significabilia and for his own positive theory of the signification of propositions, according to which, roughly, propositions signify whatever their parts signify, see Buridan (1977, pp. 23-24, 32-34); Buridan (1964a, lb. 4, q. 10, f. 20); for his theory of truth see Buridan (1977, c.2) and Buridan (1976, lb. 1, cc. 1-2). 33 Cf.: "dico quod non sunt talia esse obiectiva, quae non sunt nec possunt esse entia realia; nec est unus parvus mundus alius entium obiectivorum; sed illud quod nulla res est, omnino nihil est ..." Ockham (1980, pp. 218-219).

134

by some relative concept or term, like a coin, when it is considered to be the price of something.34 Indeed, since relations in general are not some "tiny things" (res parvae) inhering in and distinct from other, absolute things, a claim argued for at several places by Ockham, neither can relations of reason be such "tiny things".35

However, one may feel somewhat uneasy about Ockham's characterization of these relations of reason. For the mind- dependence of beings of reason in the via antiqua sense was clear enough: such a being of reason can exist, in the sense of mere objective existence, only as long as some intellect thinks it, because its esse is nothing but intelligi: for it to be is to be thought of. But Ockham's relations of reason being identical with real beings conceived in some way, they surely can continue to exist whether a human intellect thinks of them or not. On the other hand, what Ockham says here is not that something is a relation of reason if it would cease to be without the operation of the intellect, but that if it would cease to be such as it is denoted to be by a relative concept. But this again can be understood in two ways. First: it would cease to be such as it is denoted to be by this concept, i.e., it would undergo change if the operation of any human intellect would cease to be, which is certainly not meant here, since no thing can be said to undergo change by ceasing to be thought of by any human intellect. Second: it would cease to be such as it is denoted to be by the concept, i.e., it would be signified no longer by the concept, if the operations of any human intellect would cease to be. But this again cannot be meant here, since by removing all operations of all human intellects we remove all concepts, and so after this removal nothing would be signified by any concept whatsoever.

But there is still another way of understanding the mind- dependence of Ockham's entia rationis. In this way a relation of reason would be something that would cease to be such as it is denoted to be by a relative concept, provided all acts of any human intellect would cease to be except for the concept in question signifying it. So understood, an ens rationis would cease to be signified by the concept signifying it, provided all other mental acts were removed, although the concept itself would not cease to be. This can precisely be the case when a concept signifies something connoting, i.e., only in relation to, some mental act. For example, a banknote is signified to be the price of something only in relation to the mental acts of those people who acknowledge it as a suitable means of payment for goods: were these acts removed, the banknote would still exist, but would be just a worthless scrap of paper, no longer properly signified by the term `price' or, for that matter, even by the term `banknote'. Similarly, a once meaningful inscription remaining carved in rock after the extinction of the community to whose idiom it belonged ceases to be meaningful by the demise of the mental acts connoted by the term `meaningful' that once conferred meaning on it. In view of these considerations, we can simply say in general that for Ockham a being of reason is something that is signified by a term or concept that signifies or connotes an act of mind.36

34 At least according to the opinion held by Ockham, but which, in his view, was not Aristotle's, according to which `relatio' is a noun of first, and not of second intention. Cf. Ockham (1980, p.700) and Ockham (1974, p. 155). Although Buridan calls this improper usage: "prout improprie vocamus relationem illam rem pro qua terminus relativus supponit". Buridan (1964a, l.5, q.9, f.33). 35 For discussion and references see Adams, pp.215-276. 36 In any case it is precisely this concept that seems to be operative in Buridan's discussion of the question whether there would be time, if there were no intellect to count it. See Buridan (1964b, lb.4, q.16, ff. 84-85).

135

With this new interpretation of what an ens rationis is Ockham was able to save, at least verbally, an old distinction, but in a radically different conceptual framework, which opened up the way towards a new research program for ontology.

Conclusion: A Reconstruction of Ockham's Semantic Innovations

In conclusion let me present a simple reconstruction of what I take to be Ockham's basic semantic innovation. I wish to suggest that Ockham's crucial move in semantics can be very simply described as a certain sort of type-lowering of the signification of categorematic terms. But to make sense of this claim, of course, I have to explain what I mean by this type-lowering, which will also involve some further suggestions as to how we could reconstruct the different semantic and ontological frameworks discussed above.

According to the concept of signification that I take to be characteristic of the via antiqua tradition a general term ultimately signifies numerically distinct inherent natures, forms or properties of individuals, distinguishable from one another by which individuals they belong to. Therefore we can say that such a term signifies these individualized properties in respect of the individuals in which they inhere, i.e., it signifies such a property for this individual, and another for that one, etc. But so we may represent the signification of a general term as a function assigning inherent properties to individuals. This means that in a semantic model we need to distinguish between two types of individuals, namely individual substances, and their inherent properties (including really distinct natures, inherent forms, and merely objectively existing properties). So the domain of our model W, will contain two subclasses, S, the class of substances, and P, the class of properties. A significate of a one-place general term, therefore, can be denoted as the value of the signification function of this general term for a substance from S like this: SGT(T1)(u)∈P, where u∈S. Notice here that SGT is not a two-place function, with a term in its first and a thing in its second argument- place, but a one-place function, which for a one-place term in its argument-place yields another one-place function, which for a thing in its argument-place yields an individualized property (the property signified by this term in this thing). In this way, applying the same trick, we can give a uniform treatment of the signification of general terms of any arity,37 and so, generally speaking, we can denote a significate of an n-place general term like this: SGT(Tn)(u1)...(un)∈P. Now we can classify these functions and the entities they operate on in different types as follows: let elements of S and P be of type s and p, respectively; and let a mapping from entities of type t1 to entities of type t2 be of type <t1,t2>.

In this way, if we designate the type of an entity e as TYPE(e), then e.g.,

TYPE(SGT(T2)(u1)(u2))=p

TYPE(SGT(T2)(u1)) = <s,p>

TYPE(SGT(T2)) = <s,<s,p>>, etc.

37 To be sure, determining a term's arity even in the highly formal Latin of the mediaevals is far from being unproblematic. Nevertheless, since discussion of this problem would exceed the limits of this paper, with this reservation in mind, for the sake of this discussion let me simply call a term n-ary, if it were represented in standard quantification theory by an n-ary predicate parameter. For a more detailed discussion of this problem within the framework of Buridanian semantics see Klima (1991b).

136

We can define the level of each of these types as follows: let the level of type s and of p be 1 and 2, respectively; and let the level of type <t1,t2> be the sum of the levels of t1 and of t2. That is to say, denoting the level of type t as LEVEL(t):

LEVEL(s)=1

LEVEL(p)=2

LEVEL(<t1,t2>)=LEVEL(t1)+LEVEL(t2)

So e.g.

LEVEL(TYPE(SGT(T2)(u1)(u2)))=LEVEL(p)=2

LEVEL(TYPE(SGT(T2)(u1)))=LEVEL(<s,p>)=1+2=3

LEVEL(TYPE(SGT(T2)))=LEVEL(<s,<s,p>>)=1+(1+2)=4, etc.

Now if we denote the signification function modeling the via antiqua concept of signification as SGTa and that modeling Ockham's as SGTo, then we can express their relationship by the following simple formula (provided T is not a concrete quality term):

LEVEL(TYPE(SGTo(Tn)))=LEVEL(TYPE(SGTa(Tn)))-2

which clearly shows why we can speak here of a sort of type- lowering. For example, the one-place term `homo' in the via antiqua framework was supposed to signify individual human natures of singular men, consequently:

LEVEL(TYPE(SGTa(`homo')))=LEVEL(<s,p>)=1+2=3

On the other hand, for Ockham the same term signifies directly individual men, that is:

LEVEL(TYPE(SGTo(`homo')))=LEVEL(s)=1,

which, by the way nicely shows why such a term is regarded by Ockham as absolute, i.e., not signifying its significata in relation to other things. It should also be noted here that for Ockham the significata of absolute terms constitute some subset of the whole universe, and that two absolute terms never have the same set of significata unless they are synonymous. So generally, if T is an absolute term, then SGT(T)∈U, where U is some subset of W, determined by the natural signification of the concept to which T is subordinated.38

Similarly, the two-place term `pater', in the via antiqua framework was supposed to signify an inherent relation, paternity, signified by this term in a person in respect of another, his child. Therefore:

LEVEL(TYPE(SGTa(`pater')))=LEVEL(<s,<s,p>>)=1+1+2=4

For Ockham the same term signifies individual men, in respect of others, their children, and so:

LEVEL(TYPE(SGTo(`pater')))=LEVEL(<s,s>)=1+1=2

However, as Ockham did not eliminate all inherent properties, but retained qualities, in the case of concrete quality-terms the level of the signification type of these terms remained the same.

38 As a matter of fact, I think that the need to restrict the range of the signification functions of general terms to subsets of the domain of discourse in such an Ockhamist construction of semantics is significant: this may be quite relevant to the question whether Ockham was after all really able to get rid of objectively existing universals.

137

What was changed by Ockham, however, was the type of the signification of these terms itself. For while according to the older view these terms signify qualities in substances, in Ockham's view, conversely, they signify substances connoting qualities,39 i.e., if u∈S and f∈P, then SGTa(T)(u)=f, while SGTo(f)=u, and so

TYPE(SGTa(T))=<s,p>, while

TYPE(SGTo(T))=<p,s>.

This type-change naturally leads to Ockham's move of identifying the personal supposita of these terms with their significata. If we denote a suppositum of such a term at a time t (namely the time connoted by the copula of the proposition in which the term supposits for this thing) as SUP(T)(t) and the set of things that are actual at this time as A(t), then we can write:

SUP(T)(t)=u, if SGTa(T)(u)=f∈A(t), otherwise SUP(T)(t)=0, while

SUP(T)(t)=SGTo(T)(f), if f∈A(t), otherwise SUP(T)(t)=0,

where A(t) is a part of W, 0 is a zero-entity falling outside the universe of discourse W,40 u∈S and f∈P.

And this comparison takes us immediately to a (if not the) basic problem of Ockham's semantics.

As we could see, determining the supposita of terms is vital for Ockham's logical semantics, for the truth or falsity of propositions is determined ultimately by the identity or non-identity of the supposita of their terms. The personal supposita of a simple connotative term are those things which it signifies in relation to its connotata. But the grammatical category of the term in itself says nothing about what the connotata of such a term should be. What tells us this, according to Ockham, is the term's nominal definition.

Let us take for example Ockham's "favorite" connotative term, `album' (white). According to Ockham, this term is connotative, since it has a nominal definition, for the sake of simplicity let's say: `habens albedinem' (whiteness haver). This being so, we can construct a significate of the term `album' in a semantic model out of the significates of `habens' and `albedo' in the following manner:

SGT(`album')(SGT(`albedo'))=SGT(`habens')(SGT(`albedo'))=SGT(`habens albedinem')

In this way, however, we cannot treat `album' in a semantic reconstruction as primitive, for its significata are not determined by a free-choice function, but are constructed from the significata

39 "Whether or not Ockham's criteria of primary and secondary signification are adequate, his predecessors and contemporaries thought that Ockham had the priorities exactly reversed." Adams (1985, p. 325). For detailed discussions of the niceties connected to earlier views see Ebbesen (1989), Andrews (1989) and Huelsen (1989). 40 Of course, there is nothing mystical to be supposed behind this zero-entity, which, after all, not being an element of the universe of discourse is not an entity at all. It is simply a convenient metalinguistic device for uniformly representing the cases when some expression of our object-language lacks an appropriate semantic value. Consequently I use 0 as a technical convenience to represent the case when a term supposits for nothing, or when a term signifies or connotes nothing. In these descriptions it is sometimes convenient to let metavariables range over the whole universe plus the zero-entity: in such a case I will denote this enhanced domain as W!, that is to say, W!=W∪{0}. For more on the technical advantages of introducing 0 see Ruzsa (1991) and the essays in Klima (1988a). Note also that the introduction of 0 need not affect the type-assignments given above: a mapping with a range and domain enhanced with 0 may be assigned the same type as without this enhancement, while we may stipulate that TYPE(0)=LEVEL(0)=0.

138

of expressions entering its nominal definition, even if it is simple, in the sense that syntactically it is not composed of more primitive parts evaluated separately in the semantics.

Now in this nominal definition `habens', being a relative term, is also connotative. So on Ockham's principles it also has to have a nominal definition possibly revealing even further connotata not yet taken into account in this first approach. But what can we supply here by way of such a nominal definition? And even if we are able to think up something the same question will recur, if in the proposed definition another connotative term occurs. And since according to Ockham only substance and abstract quality terms are absolute terms, the question in effect is whether we are eventually able to come up with a nominal definition that contains only substance and abstract quality terms plus syncategoremata (which, of course, in the last analysis signify also qualities, namely mental acts, the inherent qualities of the intellective soul). Indeed, this would fit in nicely with Ockham's ontological program of eliminating all apparent reference to things other than substances or qualities. But however appealing such a program may be from an ontological point of view, it has rather disastrous consequences in semantics. For, since one cannot, in principle, determine what the significata, and hence the supposita of a connotative term in a proposition are without having its nominal definition, in this framework we could not even begin the evaluation of a simple predication containing a connotative term, until this program is carried out.

Perhaps, it was something like this recognition that motivated Buridan to admit the existence of simple connotative concepts.41 Indeed, he could do so without any ontological compromise, for these simple connotative concepts may signify the same absolute things ad extra as Ockham's complex connotative concepts. The only difference is that these are not constructed out of simple absolute concepts plus syncategoremata as Ockham's putative connotative concepts, but simply they signify absolute things connoting others as adjacent or non-adjacent to what they signify.42

For example, `videns' connotes sight as adjacent, while `caecum' as non-adjacent to what it signifies. For Buridan, however, this fact alone will not determine whether these terms are

41 "Comme on le sait, Occam pense qu'il est toujours possible de donner une definitio quid nominis des termes connotatifs (SL III-2, 28. p.556. III-3, 26. pp.689-691.) La position de Buridan est différente. ... Buridan réserve explicitement la definitio exprimens quid nominis aux termes vocaux simples auxquels corresponde un terme mental complexe. (Soph. I. concl.11.; Summulae VIII, 2, f. 100ra.) Le problème de savoir si `res alba' et `nasus cavus' sont les orationes dicentes quid nominis respectivement de `album' et de `simum' s'étant posé, Buridan répond conditionaliter: si à `album' correspond dans la pensée un concept complexe, `res alba' sera sa definitio dicens quid nominis (il en est de même pour `simum' et `nasus cavus'); si au contraire, à `album' et à `simum' `correspondent in mente conceptus incomplexi quibus confuse et indistincte substantiam et albedinem, vel nasum et simitatem concipimus, et non substantiam uno conceptu et albedinem alio, nec nasum uno conceptu et simitatem alio, tunc istae definitiones non sunt dicentes quid nominis sed quid rei'. (Summulae VIII.2. 102va; cf. Meta VII, 5.)" A. Maierù (1976. pp. 110-111). For the niceties of the differences between Ockham's and Buridan's ontological views see C. Normore (1985). 42 However, in his excellent paper (Panaccio 1990) Claude Panaccio argues that Ockham also could consistently endorse the existence of simple connotative concepts, not admitting, though, that a simple connotative term is synonymous with its nominal definition. It is an open question, however, whether Ockham can consistently maintain this latter position. It may well be the case that on the basis of his general semantic principles Ockham is after all committed to holding that nominal definitions are synonymous with their definita, being subordinated to the same concepts. But this would need further inquiry. In any case, if Panaccio is right, then Ockham can indeed avoid the inconvenient consequences of the above reasoning. I am grateful to Sten Ebbesen for having called my attention to Panaccio's important paper. For a more detailed discussion and reconstruction of Buridan's theory of appellation, dealing with reference and co-reference of connotative terms, see Klima (1991a).

139

subordinated to simple or to complex concepts. This latter depends rather on the further question whether we are able to supply their nominal definition, a complex expression which signifies and connotes and in the same way all and only those things which these terms do, i.e., which are synonymous with these terms.

If so, then we cannot regard this term as primitive, but have to construct its significata and supposita as depending on its nominal definition (as we did in the case of `album' above). If, however, we cannot supply a nominal definition of this term, then we can regard it as a simple connotative term, connoting some simple quality, namely sight, as non-adjacent to what it signifies, which simply means that it will signify something only if this connotatum does not exist.43

Accordingly, we can define the signification of `caecum' as follows: SGT(`caecum')(u)∈U!, where U is a part of W, namely the set of the significata of the absolute term `animal', and U!=U∪{0}, while u∈V!, where V is another subset of W, namely the set of the significata of the absolute term `visus', and V!=V∪{0}. The negative connotation of `caecum' may be expressed by stipulating further that SGT(`caecum')(u)∈A(t), iff u∉A(t).

Hence, a suppositum of the term `caecum' in a proposition the copula of which connotes some time t is definable as:

SUP(`caecum')(t)=SGT(`caecum')(SUP(`visus')(t)),

if SGT(`caecum')(SUP(`visus')(t))∈A(t),

otherwise SUP(`caecum')(t)=0,

where

SUP(`visus')(t)=SGT(`visus') if SGT(`visus')∈A(t),

otherwise SUP(`visus')(t)=0.

That is to say, the term `caecus', in accordance with its negative connotation, refers to an animal only if what it connotes, namely the sight of the animal, purportedly referred to by the term `visus' is not actual, i.e., if the animal does not have sight. But since a simple affirmative sentence, like `Homerus fuit caecus' (`Homer was blind') is true only if its terms supposit for the same, this sentence will be true only if Homer at the time connoted by the copula of the sentence, i.e., some time earlier than the present time of its utterance, lacked sight.

Notice here, that in this sketchy reconstruction of a Buridanian account of the semantics of this sentence, `caecus' is treated as a primitive term with an appropriate negative connotation of a simple positive quality. In this way this treatment eliminates both the apparent need for entia rationis in the analysis of a sentence of this type and the apparent need for nominal definitions to achieve this purpose.

Let us suppose now that `caecum' is not primitive, but has as its nominal definition (for the sake of simplicity omitting its restriction to animals) `non habens visum'.

A significate of the term `non habens visum', then, may be constructed in the following manner:

SGT(`caecum')(SGT(`visus'))=SGT(`non habens visum')= 43 Cf. Buridan (1977, p. 61)

140

SGT(`non')(SGT(`habens')(SGT(`visus')))

where SGT(`habens')(u)∈W! and u∈W!, while

SGT(`habens')(u)∈A(t) iff u∈A(t),

SGT(`non')(u)∈W! and

SGT(`non')(u)∈A(t) iff u∉A(t),

where u∈W!, and W!=W∪{0}.44

We can construct the supposita of this term as follows:

SUP(`caecum')(t)=SGT(`caecum')(SUP(visus)(t))=

SGT(`non')(SGT(`habens')(SUP(`visus')(t)))

As can be seen, these definitions guarantee again that `Homerus fuit caecus' would be true just as above, only in this construction `caecus' is not a semantically primitive term, but its semantic values are determined by its nominal definition. Still, even though in this nominal definition another connotative term - `habens' - occurs, taking this term as primitive, we may stop here and need not go on with the elimination of connotative terms in favor of absolute ones plus syncategoremata.

So it seems that with Buridan's approach in principle we would not have to delay our semantics until we had provided nominal definitions of all connotative terms. And so it may seem that along these lines we might eventually be able to produce a working semantics incorporating Ockham's basic semantic innovations, thereby eliminating all the unwanted ontological commitments of a via antiqua-style semantics.

We must notice here, however, that if one sticks with Ockham's ontological program of reducing the number of distinct categories to two, then even with this Buridanian approach there is an enormous amount of analysis to be done before the actual semantic features of several connotative terms are established. For one still would have to provide the nominal definitions of all those terms that cannot be regarded as semantically primitive by means of absolute terms, syncategoremata and those connotative terms that are regarded as primitive, making sure all the time that the things signified or connoted by these will fall in the "permitted" ontological categories. All that this Buridanian approach achieves is to show that treating at least some syntactically simple connotative terms as also semantically primitive does not impose such severe restrictions on the vocabulary available for this analysis as Ockham's original conception. But even so the semantic theory backing Ockham's ontological program presented subsequent generations with an alternative way of construing the relationships between language, mind and reality that promised to render the ontological commitments of the older way dispensable, thereby serving as a suitable framework for a different kind of logical and metaphysical research.45

44 The significate of `non', of course is the concept of negation, a quality of mind operating on other concepts, modifying the ways they are related to external things, just as the other syncategorematic concepts. For more on this see Klima (1991b) 45 Research for this paper was done during my stay in Helsinki as a member of Simo Knuuttila's project, Ockham and the via moderna. I wish to thank the Finnish Academy for their generous financial assistance, and all the Finnish

141

friends and colleagues for their hospitality, help and encouragement. The actual writing of this paper took place during my stay in St. Andrews, Scotland, as Gifford Visiting Fellow of the Department of Logic and Metaphysics. I owe special thanks to Stephen Read, chairman of the Department, for helpful comments and correcting the English of the paper.

142

References

Abaelard, P.: 1956, Dialectica, ed. L.M. de Rijk, Van Gorcum, Assen Adams, M. M.: 1985, "Things versus `Hows'", in: Bogen et al. (1985), pp. 175-188. Adams, M. M.: 1987, William Ockham, University of Notre Dame Press, Notre Dame, Ind. Alamannus, C.: Summa Philosophiae, P. Lethielleux, Paris, 1888 Andrews, R.: "Denomination in Peter of Auvergne", in: Kretzmann (1988), pp. 91-108. Aquinas, T.: 1980, Opera Omnia, Frommann-Holzboog, Stuttgart-Bad Cannstatt Aristotle: 1962, On Interpretation: Commentary by St. Thomas and Cajetan, tr. J. T. Oesterle, Marquette University

Press, Milwaukeee, Wisconsin Ashworth, E. J.: 1974, Language and Logic in the Post-Medieval Period, D. Reidel Publishing Company, Dordrecht-

Boston. Ashworth, E. J.: The Tradition of Mediaeval Logic and Speculative Grammar, Pontifical Institute of Medieval

Studies, Toronto, 1978 Bogen, J. and McGuire, J.E. (eds.): 1985, How Things Are, D. Reidel Publishing Company, Dordrecht-Boston-

Lancaster Buridan, J.: 1964a, Kommentar zur Aristotelischen Metaphysik, Minerva G.M.B.H. Frankfurt a.M. Buridan, J.: 1964b, Kommentar zur Aristotelischen Physik, Minerva G.M.B.H., Frankfurt a.M. Buridan, J.: 1976, Tractatus de Consequentiis, ed. H. Hubien, Publications Universitaires, Louvain Buridan, J.: 1977, Sophismata, ed. T.K. Scott, Frommann-Holzboog, Stuttgart-Bad Cannstatt Burleigh, W.: 1955, De Puritate Artis Logicae Tractatus Longior with a revised edition of the Tractatus Brevior, ed.

Ph. Boehner, The Franciscan Institute, St. Bonaventure, N.Y. Cajetan, T. de Vio: 1590, "Super Librum De Ente et Essentia Sancti Thomae Aquinatis", in: Opuscula Omnia, Typis

Comini Venturae, Bergomi Cajetan, T. de Vio: 1964, Commentary on Being and Essence, transl. L.J. Kendzierski, F.C. Wade, Marquette Univ.

Press., Milwaukee, Wis. Cajetan, Thomas de Vio: 1939, Scripta Philosophica: Commentaria in Praedicamenta Aristotelis, ed. M. H. Laurent,

Angelicum, Romae Ebbesen, S.: 1988, "Concrete Accidental Terms: Late Thirteen-Century Debates About Problems Relating to Such

Terms as `Album'", in: Kretzmann (1988), pp. 107-174. Henry, D.P.: 1972, Medieval Logic and Metaphysics, Hutchinson, London Huelsen, R.: "Concrete Accidental Terms and the Fallacy of Figure of Speech", in: Kretzmann (1988), pp. 175-186. Klima, G.: 1988a, Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Institute of Philosophy,

Budapest Klima, G.: 1988b, "Existence, Quantification and the Mediaeval Theory of Ampliation" in: Klima (1988a), pp. 85-

110. Reprinted from: Doxa, 9(1987), pp. 83-112. Klima, G.: 1988c, "Understanding Matters from a Logical Angle", in Klima (1988a), pp. 111-149. Reprinted in:

Annales Universitatis Scientiarum Budapestinensis, 23(1990), pp. 37-62. Klima, G.: 1988d, "`Socrates est species': Logic, Metaphysics and Psychology in St. Thomas Aquinas' Treatment of

a Paralogism", in: Klima (1988a), pp. 165-185. Also to appear in K. Jacobi (ed.), Agumentationstheorie: Acts of the 8th European Symposium of Medieval Logic and Semantics

Klima, G.: 1990, "On Being and Essence in St. Thomas Aquinas's Metaphysics and Philosophy of Science" in: Knuuttila et al. (1990) pp. 210-221, and in Klima (1988a) pp. 150-164.

Klima, G.: 1991a, "`Debeo tibi equum': A Reconstruction of the Theoretical Framework of Buridan's Treatment of the Sophisma", in: Read (1991), pp. 333-347. Reprinted in: S-European Journal for Semiotic Studies, 4(1992), pp. 141-160.

Klima, G.: 1991b, "Latin as a Formal Language: Outlines of a Buridanian Semantics", Cahiers de l'Institute de Moyen-Age Grec et Latin 61, pp. 78-106.

Knuuttila, S. and Hintikka, J. (eds.): 1986, The Logic of Being, D. Reidel, Dordrecht Knuuttila, S. and Työrinoja, R. and Ebbesen, S. (eds.): 1990, Knowledge and the Sciences in Medieval Philosophy:

Proceedings of the Eighth International Congress of Mediaeval Philosophy, (S.I.E.P.M.), Publications of Luther-Agricola Society Series B 19, Helsinki 24-29 August 1987, vol. II. Helsinki

143

Kretzmann, N. (ed.): 1988, Meaning and Inference in Mediaeval Philosophy, Kluwer Academic Publishers, Dordrecht-Boston-London

Kretzmann, N. and Pinborg, J. and Kenny, A. (eds.): 1982, The Cambridge History of Later Mediaeval Philosophy, Cambridge University Press, Cambridge

Maierù, A.: "Significatio et Connotatio chez Buridan", in: Pinborg (1976), pp. 101-114. Matthen, M.: 1983, "Greek Ontology and the `Is' of Truth", Phronesis, 28, pp. 113-135 McInerny, R.: 1961, The Logic of Analogy, Martinus Nijhoff, The Hague Moore, W. L.: 1989, `Via Moderna', in: J.R. Strayer: Dictionary of Middle Ages, Scribner, New York, vol.12. pp.

406-409. Normore, C.: "Buridan's Ontology", in: Bogen et al. (1985), pp. 189-203. Nuchelmans, G.: 1973, Theories of the Proposition - Ancient and Medieval Conceptions of the Bearers of Truth and

Falsity, North Holland Publishing Company, Amsterdam-London Nuchelmans, G.: 1980, Late-Scholastic and Humanist Theories of the Proposition, North Holland Publishing

Company, Amsterdam-Oxford-New York Ockham, W.: 1974, Summa Logicae, ed. Ph. Boehner, Opera Philosophica, vol. I., The Franciscan Institute, St.

Bonaventure, N.Y. Ockham, W.: 1978, Expositio in Librum Perihermeneias Aristotelis, eds. A. Gambatese and S. Brown, Opera

Philosophica, vol. II., The Franciscan Institute, St. Bonaventure N.Y. Ockham, W.: 1980, Quodlibeta Septem, Oprea Theologica, Vol.VII. ed. J.C. Wey, C.S.B., The Franciscan Institute,

St. Bonaventure N.Y. Ockham, W.: 1984, Summula Philosophiae Naturalis, ed. S. Brown, Opera Philosophica, vol. VI., The Franciscan

Institute, St. Bonaventure N.Y. Panaccio, C.: 1990, "Connotative Terms in Ockham's Mental Language", Cahiers d'épistémologie, Université du

Québec à Montréal, Cahier no 9016, pp. 1-22. Peter of Spain: 1972, Tractatus, ed. L. M. de Rijk, Van Gorcum, Assen Pinborg, J. (ed.): 1976, The Logic of John Buridan, Museum Tusculanum, Copenhagen Read, S. L. (ed.): 1991, Sophisms in Mediaeval Logic and Grammar: Acts of the Ninth European Symposium of

Mediaeval Logic and Semantics, Kluwer Academic Publishers Read, S. L.: 1977, "The Objective Being of Ockham's Ficta", The Philosophical Quarterly, 27, pp.14-31. Rijk, L. M. de (ed.): 1967, Logica Modernorum, Vol. II, Part II, Van Gorcum, Assen Ruzsa, I.: 1991, Intensional Logic Revisited, Budapest Schmidt, R.W.: 1966, The Domain of Logic according to Saint Thomas Aquinas, Martinus Nijhoff, The Hague Suarez, F.: 1960, Disputaciones Metafisicas, Editorial Gredos, Madrid Weidemann, H.: 1986 "The Logic of Being in Thomas Aquinas", in: Knuuttila et al. (1986, pp. 181-200).

144

Ockham’s Semantics and Ontology of the Categories

1. Ockham’s Complaints

Ockham’s treatment of the ten Aristotelian categories1 plays a crucial role in his innovative nominalist program. One of his main complaints against “the moderns” [moderni]—as he is wont to call his opponents2—is that they treat the categories as comprising ten mutually exclusive classes of distinct entities. Indeed, the unknown author of a work written against Ockham’s logic (characteristically entitled: “A very useful and realist logic of Campsal the Englishman against Ockham”), writes as follows:

“… to such most general genera3 there are subjected individuals that are really distinct from the individuals of another most general genus of which [this genus] is properly and directly predicated; for example, we can truly assert: ‘This is [a] when’4 pointing to the relation which is caused by the motion of the first movable in the inferior things,5 so that, if that individual had a distinct proper name imposed on it, one could just as truly respond to the question: ‘What is it?’ by saying: ‘[A] when’, as one can reply to the question ‘What is it?’ asked about a man, by saying: ‘A substance’.”6

1 Namely, the category of substance, and the nine categories of accidents: quantity, quality, relation, action, passion, time, place, position, and habit. 2 Obviously, this designation is quite tendentious in Ockham’s usage: besides identifying his opponents as being relatively recent, and thus not carrying as much authority as the well-established older authors, this enables him to pose as someone who only reclaims the genuine Aristotle from his more recent distorted interpretations. 3 The “most general genera” [genera generalissima] are the ten categories listed above, which then are divided by specific differences [differentia specifica] into their species, which in turn are also divided by further differences into their species, of which they are the genera, but not the most general genera, since they are the species of some higher genus, and so on, until we reach “the most specific species” [species specialissima], which cannot be divided further by any specific differences, for the individuals contained under them are essentially the same, and are distinct from one another only by their individuating conditions. For example, descending the famous “tree of Porphyry” (or “Porphyrian tree”) in the category of substance, we get the following series of divisions: a substance is either material or immaterial, a material substance is a body (and this is how we get the essential or quidditative definition of a ‘body’, constituted by its genus, ‘substance’ and its specific difference, ‘material’); a body is either living or non-living, a living body is either sensitive or non-sensitive; non-sensitive living substances are plants, sensitive living substances are animals; an animal is either rational or irrational, irrational animals are brutes, rational animals are human beings; but human beings differ from one another only by non-essential differences, such as gender, color, height, weight, virtues and vices, etc., so the species of humans is a species specialissima, not divisible by any further essential differences, and this is how we get the essential definition of ‘man’ [homo, of course, in the sense of ‘human being’, not in the sense of ‘human male’] constituted by the genus ‘animal’ and the specific difference ‘rational’. 4 To be sure, this sentence would be as strange in vernacular Latin as it is in English. However, we must not forget that in the technical Latin of scholastic philosophy quando [‘when’], or indeed, its contrived abstract form quandoleitas or quandalitas [‘when-ness’], functioned precisely as our author describes it, namely, as the most universal, essential predicate of all temporal determinations. 5 The ‘first movable’ is the outermost sphere of the Aristotelian cosmos, the sphere of the fixed stars, the daily rotation of which was held to be the first movable cause (itself being moved by some immaterial, and hence locally immovable separate substance; for the Christian medievals: by some angel), and the first measure of every other motion of the inferior things. According to our realist author, this motion causes in inferior things a "when-ness", a certain temporal determination which is a really inherent accident, distinct from the substance as well as from its other accidents. 6 Pseudo-Campsall, R.1982, c. 38, n. 12, p. 216. Unless otherwise indicated, translations are mine.

145

As should be clear even from this brief passage, the disagreement between Ockham and his realist opponent here does not concern universals. On the contrary, regardless of the question whether there are some universal entities other than our universal terms (be they written, spoken or mental terms), the question here is whether we have to admit distinct particulars falling under our universal terms in each of the ten categories.

However, Ockham’s disagreement with this position is not simply a matter of his espousing a different ontology. For Ockham thinks that this ontological position is the consequence of an even more fundamental error in his opponents’ semantic theory: a radically mistaken conception of how our words and the concepts that render them meaningful are related to the things they represent. In general, according to Ockham, this conception would entail that “a column is to the right by to-the-rightness, God is creating by creation, is good by goodness, just by justice, mighty by might, an accident inheres by inherence, a subject is subjected by subjection, the apt is apt by aptitude, a chimera is nothing by nothingness, someone blind is blind by blindness, a body is mobile by mobility, and so on for other, innumerable cases”.7 And this is nothing, but “to multiply beings according to the multiplicity of terms... which, however, is erroneous and leads far away from the truth”.8

As we shall see, Ockham’s complaints are not entirely justified. Yet, they might appear as an entirely credible motivation for advancing his radically new approach to some basic issues in semantics and ontology. To see exactly what is and what is not justified in Ockham’s complaints, we have to start with considering at least a sketch of the semantic conception to which he objects. Then we shall have to examine whether this semantic conception does indeed have the ontological commitments Ockham claims it does, and if—as I claim—not entirely, then to what extent, and why. These considerations will then provide us with a solid basis for the analysis and brief evaluation of his alternative approach.

2. “Via Antiqua Semantics”9

The semantic conception Ockham finds fault with can be characterized at least by the following principles:

Common terms ultimately signify whatever the concepts to which these terms are subordinated directly represent.

7 Ockham, W. 1974 (SL) part 1, c. 51, p.169. 8 Ibid. p.171, where Ockham explicitly claims that this is the root (radix) of the errors of the moderns. 9 To be sure, this designation of the semantic theory under discussion is both somewhat anachronistic and simplistic in this context. Nevertheless, it is not entirely unjustified, and with the proper reservations in mind it can safely be applied to the set of semantic principles commonly endorsed both by the majority of thinkers before Ockham, and by those thinkers after Ockham who expressed their commitment to these or similar principles already in conscious opposition to Ockham’s views, or even later in opposition to the relevant views of the nominales [nominalists] in general. In any case, I find this designation potentially less misleading than the term “realist” (even despite the fact that in late-medieval debates the opponents of the nominales would often identify themselves as reales [realists]), which would inevitably suggest primarily some ontological difference in their treatment of universals. But the point here, as we shall see, is precisely that the difference between the treatment of the categories by the adherents of a “via antiqua” semantics and by Ockham is not primarily an ontological matter, and not primarily a matter of how they treat universals. For a detailed historical discussion of the late-medieval contrast between via antiqua and via moderna see: Moore, W. L. 1989, pp. 406-409.

146

Common terms, as the subject terms of categorical propositions, supposit personally for the things that are actual in respect of their ultimate significata. (Henceforth, by ‘significata’ of a common term without any further qualification I will mean its ultimate significata, and by ‘supposita’ of a common term without any further qualification I will mean its personal supposita.)

The significata and supposita of the abstract counterparts of concrete common terms are the same as the significata of the concrete terms.

Affirmative categorical propositions in the present tense are true if and only if the supposita of their subjects are actual in respect of the significata of their predicates (as required by the quantity of the proposition).10

As I have already indicated, this “minimalist” characterization of the semantic theory in question does not have the ontological commitment Ockham claims his opponents’ theory has. Indeed, I provided this “minimalist” characterization precisely because in this way it will be easier for us to see exactly what further assumptions would need to be added to these principles to yield the ontological commitment Ockham is talking about. But before discussing the issue of their ontological commitment, we need a brief clarification of these principles themselves.

The Semantic Triangle

The first of these principles, being basically a reformulation of Aristotle’s “semantic triangle” from the beginning of his On Interpretation,11 is also accepted by Ockham. Indeed, among medieval authors it was generally agreed that all our words are meaningful only in virtue of their being subordinated to our concepts. Obviously, the utterance or the inscription arbor is meaningful in Latin only because it is subordinated to the concept by which we conceive of trees in general, but since it is not thus subordinated to this concept in English, it is not meaningful in English. And since the utterance or inscription biltrix is not subordinated to any concept in either English or Latin, it is not meaningful in either of these two languages.12 To be sure, there were serious differences of opinion among medieval authors as to what concepts are, what kinds of concepts there are, and how the several kinds are related to what they represent. Nevertheless, since from our present point of view concepts are relevant only in their semantic function, we do not have to go into these questions at this point. Therefore, it is sufficient here to distinguish between the immediate and the ultimate significata of common terms by saying that the immediate significata of (written or spoken) common terms are the concepts of human minds (whatever sort of entities concepts are in themselves), and the ultimate significata of the same are 10 That is, all or only some supposita are such depending on whether the proposition is universal or particular. Also, we assume here that the proposition is interpreted as expressing some actual fact about the actually existing supposita of its subject, and not as a definitive “eternal truth”, in which case it may be true even if the supposita of its subject do not exist. According to the latter interpretation, such an affirmative proposition was analyzed by several authors in a number of different ways; either taking it to be equivalent to a hypothetical, or taking its subject to have natural supposition, or taking it to express some necessary possibility, or taking it to express a mere conceptual connection regardless of the existence of the supposita of its subject, etc. For discussion and references see Klima, G. forthcoming (b). Cf. also n. 17. 11 16a3 12 ‘Biltrix’ is one of the several standard examples of a meaningless utterance (along with ‘bu’, ‘ba’, ‘buba’, etc.) one can find in medieval commentaries on Aristotle’s relevant passage and in the corresponding sections of medieval logical treatises.

147

whatever these concepts directly represent (whatever sort of entities the things thus represented are in themselves).

Supposition of Common Terms

Supposition is the referring function of terms, which, according to most authors, they have only in propositional contexts.13 To stick with our previous example, the term arbor has signification in Latin, because in Latin it is subordinated to the concept of trees whether it is used in the context of a proposition or it is considered outside of a propositional context, say, in a dictionary. But when we use this term in the context of a proposition, its function is to stand for or to refer to14 things somehow related to this concept. According to the most commonly accepted main divisions of the kinds of supposition a term may have, depending on how the concept is related to the things thus referred to, a spoken or written term was said to have material, simple, or personal supposition. A term has material supposition if it refers to itself or to any other similar term that is subordinated to its concept. For example, in Arbor est nomen [“‘Tree’ is a noun”], the subject term stands for itself and for any other occurrence of a similar inscription or utterance subordinated to the concept of trees. The same term has simple supposition if it stands for what it immediately signifies, that is, the concept to which it is subordinated.15 For example, in Arbor est genus plantarum [‘Tree is a genus of plants’], it stands for the concept of trees.16 Finally, the same term has personal supposition if it refers to any of the things that are actual [relative to the time and modality of the proposition]17 in respect of that which the concept it is subordinated to directly represents, and thus the term ultimately signifies, namely, when it refers to the things that actually fall under the concept. For example, in Omnis arbor est planta [‘Every tree is a plant’]18 the subject refers to actual trees, because it is actual trees that are actual in respect of that which the concept of trees directly represents, whether that which is thus represented is said to be one (whether numerically or merely formally one) universal nature common to all 13 Some authors also attributed supposition to terms outside of the context of a proposition. Perhaps, the most notable example is Peter of Spain’s treatment of natural supposition. Peter of Spain 1972, p. 81. 14 The Latin technical term for this function was supponere pro, often transcribed in the secondary literature as ‘to supposit for’, just to keep the medieval theory apart from the burgeoning contemporary theories of reference. 15 Or, according to some realists, the universal nature immediately represented by the concept. For references see next note. But then many authors were also willing to call that nature an objective concept (conceptus obiectivus), insofar as it was considered as the direct, immediate object of the human mind considering the individualized natures of the particulars in abstraction from their individuating conditions. Cf.: Suarez 1960, pp. 360-361; Cajetan 1964, pp. 67-71, 121-124. For a discussion of some of the complications involved especially in the case of Aquinas, see Klima, G. 1993 (a), pp. 25-59, and Klima, G. 1993 (b), pp. 489-504. 16 Or, again, the universal nature of trees immediately represented by this concept. Cf. for example, Lambert of Auxerre, 1971, pp. 206-209; Burleigh, W. 1955, c.3. p.7. It should also be noted here that Pseudo-Campsall reserves a different kind of supposition, “formal supposition”, for reference to the nature immediately represented by the concept, to distinguish it from simple supposition, when reference is made to the concept. In fact, he attributes this formal supposition even to proper nouns, as in Sortes est unum numero primo et per se [‘Socrates is numerically one, primarily and by himself’], the term Sortes is taken to refer to Socrates’s individual difference, his haecceity, namely, Socraticity [Sorteitas]. Pseudo-Campsall, R.1982, c.51, n. 06, p. 353. 17 Modifications in the referring function of terms caused by tense and modality were usually handled by medieval logicians in the theory of ampliation. For a detailed discussion and technical reconstruction see Klima, G. forthcoming (b). Ockham’s treatment was the exception, not the rule. Cf.: Priest, G. – Read, S. 1981, pp. 274-279. Cf. also: Ockham, W. 1974 (SL) part 1, c. 72, pp. 215-216. 18 Again, taking this proposition to express some actual fact about actually existing trees, and not a definitive, “eternal truth”. Cf. n. 10.

148

individual trees, or it is numerically distinct “treenesses” inhering in, but still distinct from the individual trees, or it is nothing but the individual trees themselves.19

But again, given our present interest, we need not delve into the further complexities of medieval supposition theory. What we need here is only the semantic distinction between the ultimate significata and personal supposita of common terms, and the understanding that this semantic distinction may, but need not necessarily reflect any ontological distinction even within the framework of “via antiqua semantics”.20

Supposition of Concrete vs. Abstract Common Terms

In “via antiqua semantics” abstract terms were commonly thought to agree in their signification with their concrete counterparts (that is to say, whatever the concrete terms signify, the abstract terms also signify), but to differ from them in their mode of signification.21 The upshot of this difference was held to be that abstract terms could be used to refer to what their concrete counterparts ultimately signified. Therefore, whenever reference needs to be made to the ultimate significata of a concrete common term (as opposed to the supposita of the same, which can be referred to by the concrete term itself), the reference is supplied by the corresponding abstract term, even in cases when the vernacular does not have such a corresponding abstract term. It is this systematic need of this semantic framework that explains the proliferation of the “barbaric” coinages of the technical Latin of “the schools”, the constant target of mockery of post-medieval authors, who no longer shared this need with their medieval predecessors. But Ockham’s complaints were certainly not motivated by such humanistic squeamishness: his concern was not so much the proliferation of these terms, but rather the apparent proliferation of the alleged corresponding entities.

The Inherence Theory of Predication

Indeed, the impression of the necessary proliferation of the corresponding entities should be reinforced by the last of the above-listed principles of “via antiqua semantics”, which briefly summarizes the theory of predication often referred to in the secondary literature as the “inherence theory”.22 For if an abstract term refers to what its concrete counterpart ultimately signifies, then according to this theory the concrete term is true of a thing if and only if what its abstract counterpart refers to actually exists. For according to this theory, Socrates is a man if 19 To be sure, most medieval “realist” authors would describe the ultimate significata of spoken terms as the forms signified by these terms. However, in logical contexts they would also add the proviso that ‘form’ in such a context need not necessarily refer to something that is a form in the metaphysical sense, namely, some determination of an act of real being. Cf. Aquinas QDP, q. 7, a. 10, ad 8.; Cajetan 1939, p. 18. In fact, Domingo Soto, a late-medieval “realist” who denies any ontological distinction between the ultimate significata and personal supposita of concrete common terms in the category of substance, would still draw the semantic distinction between their formal and material significata, even though according to him ontologically these are one and the same thing. Cf. Soto 1980, lb. 1, c. 7; lb. 2, c. 10; lb. 2, c. 14. In any case, this is the reason why I tried to provide an “ontologically neutral” formulation of the general semantic rule. 20 For a more detailed discussion of this claim in connection with Aquinas see Klima G. 1996. 21 For an explicit statement of this view see Cajetan 1939, pp. 16-17. For a detailed reconstruction see Klima G. 1996. 22 Cf. e.g. L. M. de Rijk’s Introduction to his edition of Abelard, P. 1970, pp. 37-38; Henry, D. P. 1972, pp.55-56, Geach, P. T. 1972.

149

and only if he is actual in respect of humanity, which is just another way of saying that Socrates is a man if and only if his humanity exists. But then it is indeed true that he is a man by his humanity, and, by the same token, it is true that he is tall by his tallness, and that he is white by his whiteness, and he is similar to Plato by his similarity to Plato, and he is walking by his walking, and he is somewhere by his somewhere-ness, etc., which indeed does appear to involve us in multiplying entities according to the multiplicity of terms, just as Ockham claimed.

3. The Ontological Commitment of the “Via Antiqua Semantics”

Despite the apparent plausibility of Ockham’s charge, however, commitment to the above-listed semantic principles does not entail commitment to any entities other than those Ockham himself would endorse. The reason for this is the simple fact that these principles in themselves allow the identification of the semantic values of abstract and concrete terms in diverse categories just as much as Ockham’s alternative principles do. Indeed, this is precisely why Domingo Soto, who describes himself as someone who “was born among nominalists and raised by realists”,23 could make the following declaration:

“It does not escape our attention how difficult it is to ascertain that all the ten categories are really distinct in such a manner as many realists seem to contend, namely, that all of them are distinct from one another, just as whiteness is distinct from substance, which we certainly believe to exist without substance in the sacrament of the altar. However, I shall never be persuaded that relation and the last six categories are distinct in this way from substance.”24

Clearly, if the entities in the categories of substance, quantity and quality are not distinct from the entities in the other categories, then the charge of multiplying entities with the multiplicity of terms is unjustified. However, it may not be quite clear how anyone who endorses the above-mentioned semantic principles can maintain this position. After all, according to these principles, if the proposition ‘Socrates is white’ is true, then Socrates is actual in respect of the whiteness signified by the predicate, which is just another way of saying that Socrates’s whiteness exists. But Socrates’s whiteness cannot be identified with Socrates. For it is certainly possible for Socrates to exist while his whiteness does not exist, namely, when Socrates gets a tan and his whiteness ceases to exist. But then, if Socrates were identical with his whiteness, then, by substituting identicals, we would have to admit that it is possible for Socrates to exist while his whiteness, that is, he himself does not exist, which is a contradiction. Therefore, Socrates cannot be identical with his whiteness.

Apparently, the same type of reasoning can be applied to any term in all of the nine categories of accidents, since according to Porphyry’s commonly endorsed definition, an accident is something that may or may not belong to a subject without the destruction of the subject, and thus whatever is signified by any accidental predicate in a subject may or may not exist, while the subject may still stay in existence. For example, in accordance with the above-listed principles, if the proposition ‘Socrates is a father’ is true, then an entity in the category of relation, Socrates’s fatherhood exists. But it is certainly possible for Socrates to exist while his fatherhood does not exist (for in fact he existed before he became a father, and he could have existed without ever becoming a father). But then, if Socrates were identical with his fatherhood, then this would mean that it would be possible for the same thing, Socrates, who is supposed to 23 Soto 1967 (In Isagogen) p. 28H. 24 Soto1967 (In Categorias), lb. 1. q. 2. p. 181B.

150

be identical with his fatherhood, both to exist and not to exist at the same time, which is an explicit contradiction. Therefore, Socrates cannot be identical with his fatherhood either. And the same goes for all other accidents.

However, we should notice here that in these arguments we exploited a hidden assumption which is crucial concerning the issue of the distinction of the categories. To make this assumption explicit, let us consider the following, similar argument. Apparently, Socrates cannot be identified with a father, for it is certainly possible for Socrates to exist while he is not a father. Therefore, identifying Socrates with a father would entail the contradiction that it is possible for the same thing, namely, Socrates who is supposed to be identical with a father, both to exist and not to exist, which is an explicit contradiction. However, something is obviously wrong with this argument. For the assumption that Socrates is identical with a father should entail no impossibility, since when Socrates is a father, which is possible, he is identical with a father.

Clearly, what accounts for the invalidity of this argument is the fact that Socrates can be identical or non-identical with a father while continuing to exist. That is to say, the term ‘father’ refers only accidentally, but not essentially to Socrates, for in accordance with Porphyry’s definition it is an accidental predicate of Socrates.25 Therefore, it entails no contradiction to claim that it is possible for the thing that is actually a father to exist without being a father, for the thing that is actually a father may be in existence while it is not a father.

But then the previous argument concerning the alleged impossibility of the identification of Socrates with his fatherhood may equally easily be invalidated. All we have to do is to remove the implicit assumption that the term ‘fatherhood’ refers essentially to an entity in the category of relation, that is, the assumption that ‘fatherhood’ is an essential predicate of whatever it is true of. For if this assumption is removed, then no impossibility arises from identifying the entity in the category of relation referred to by this term with an entity in the category of substance, since then it is clearly possible for this same entity once to be referred to and then not to be referred to by the same term while it continues to exist. And the same goes for the other categories.

Accordingly, we can conclude that the above-listed principles of “via antiqua semantics” yield the ontological commitment Ockham claims his opponents’ theory does only if we add to them the further assumption that abstract terms in the nine categories of accidents are essential predicates of their particulars. Therefore, whoever holds at least these principles and also maintains this assumption, is indeed necessarily committed to the overpopulated ontology Ockham objects to, which is clearly the path taken by Pseudo-Campsall.

But whoever abandons this assumption clearly can hold these principles without such an ontological commitment, and this is precisely what Soto did.

Indeed, the previous arguments should make it clear that the assumption in question need not even be coupled with all the semantic principles listed above to yield the ontological commitment Ockham refuses to accept. For what we needed to exploit in these arguments besides the assumption that an abstract term in one of the categories of accidents is an essential predicate of its supposita was merely the quite generally acceptable semantic intuition that a concrete term in one of the accidental categories is true of a subject if and only if a suppositum 25 Or, in the technical parlance of modern possible worlds semantics, this term refers non-rigidly to Socrates. For a more technical exposition of the connection between the modern notion of “rigid” reference and the medieval notion of essential predication see Klima, G. forthcoming (a)

151

of the corresponding abstract term exists (which is of course entailed by these principles, but the converse entailment does not hold). So whoever wants to get rid of this ontological commitment, while maintaining this semantic intuition (regardless of whether he holds the semantic principles listed above), has to reject this assumption. And this precisely is what Ockham did.

In the Summa Logicae, in the passage corresponding to the one quoted from Pseudo-Campsall above,26 he writes as follows:

“All authors posit ten categories, but it seems to me that many moderns [moderni] disagree with the ancients [antiqui] in the way they posit them. For many moderns hold that in every category there are several items that can be ordered as superior and inferior, so that the superior ones are predicated essentially [per se primo modo]27 and in the nominative case [in recto] of any inferior one, by means of a predication such as this: ‘Every a is b’. Therefore, in order to have such predication, they make up abstract names from adverbs, as for example from ‘when’ [quando], which is an adverb, they make up the abstract name ‘when-ness’ [quandalitas], and from ‘where’ [ubi], the name ‘where-ness’ [ubitas], and so on.”28

To discredit the “moderns”, he appeals to the authority of the “ancients” to claim that it is not necessary to assume that such abstract terms are essential predicates of their supposita in every category:

“But it seems to me that the ancients did not posit such an order in every category. And so they used the name ‘category’, and similarly the names ‘genus’, ‘species’ and their likes more broadly than many moderns do. Therefore, when they said that the superior is always predicated of the inferior, and that any category has under itself species, they extended [the notion of] predication to verbs, in accordance with the way in which we say that ‘walks’ is predicated of man, in uttering ‘A man walks’, and the same goes for ‘He is shod’ and ‘He is armed’. And they also extended [the notion of] predication to the predication of adverbs and to prepositions together with the nouns they require in the appropriate cases, as we perform [the acts of predication] in propositions such as ‘This is today’, ‘This was yesterday’, ‘This is in the house’, ‘This is in the city’. And in this way there are such predications in any category. But it is not necessary that we should always have here predication in the strict sense, [predicating] a [term in the] nominative [case] of a [term in the] nominative [case]. Therefore, not every order between a superior [term] and an inferior [term] is in accordance with predication, taking predication in the strict sense, but some [order] is in accordance with entailment and predication, taking predication in a broad sense.”29

After this rejection of the critical assumption, Ockham goes on to show that this was in fact what the “ancients” meant, by analyzing two passages, one from Aristotle and another from St. John Damascene. Naturally, in the corresponding passage Pseudo-Campsall is outraged, and tries to show why these passages cannot be understood according to the “perverted” interpretation provided by Ockham.30 However, we need not go into the details of this philological disagreement. For, despite his appeal to authority here, Ockham had much more profound reasons to claim that abstract terms in the accidental categories need not be essential predicates of their supposita.

26 Cf. n. 6. Pseudo-Campsall’s work follows closely the structure of Ockham’s Summa Logicae, in accordance with the author’s intention to provide a thoroughgoing refutation of Ockham’s doctrine. 27 Cf. Ockham, W. 1974 (SL) part 3-2, c. 7, pp. 515-519. 28 Ockham, W. 1974 (SL) part 1, c.41, p.114. Cf. Ockham, W. 1980 (Quodlibeta) V, q. 22; Ockham, W. 1978 (Expositio in lib. Praedicamentorum Aristotelis) c. 7, p. 157. 29 Ockham, W. 1974 (SL) part 1, c.41, p.114. For the distinction between predication in a strict and in a broad sense see ibid. c. 31, pp. 93-94. 30 “… non ergo debet illa litera philosophi intelligi sicut isti perversores perverterunt …” Pseudo-Campsall, R.1982, p. 217.

152

4. Ockham’s Alternative Semantics

As we could see, the explicit rejection of the critical assumption concerning abstract terms in the accidental categories would have been sufficient in itself to neutralize the apparent ontological commitment of “via antiqua semantics”, much along the lines we have noted in Soto. However, for Ockham this rejection was tightly connected to his alternative semantic theory, which “automatically” eliminated all unwanted commitments from his ontology.

To facilitate the comparison with the above-sketched “via antiqua semantics”, here is a parallel summary of the relevant principles of Ockham’s semantics.

Common terms ultimately signify whatever the concepts to which these terms are subordinated represent.

Common terms, whether they are the subject terms or the predicate terms of categorical propositions, supposit personally for their actual ultimate significata, if the term is absolute, or for the things that are actually related to their connotata in the manner required by the term’s connotation, if the term is connotative.

The significata and supposita of abstract common terms are the same either as the ultimate significata, or as the connotata of their concrete counterpart, or the same as several of these significata or connotata taken together.

An affirmative categorical proposition the subject of which supposits personally is true if its predicate supposits for some or all of the same things as its predicate, depending on the quantity of the proposition.

Ockham’s Semantic Triangle

Ockham’s “semantic triangle”, as has been noted above, is the same in outline as that of the “via antiqua”. However, according to Ockham, the concepts to which categorematic written or spoken terms are subordinated fall into two classes: they are either absolute or connotative. And since these terms are meaningful only insofar as they are subordinated to such concepts, the terms themselves are also to be classified as either absolute or connotative.

The precise characterization of this distinction is a disputed question in the contemporary secondary literature. For our present purposes, however, the following characterization will certainly be sufficient. A connotative term is one that signifies any of its (ultimate) significata in respect of something, while an absolute term, ex opposito, is one that signifies any of its significata not in respect of anything, that is, absolutely.31 The major difference here from the “via antiqua” conception is that “via antiqua” authors would not accept Ockham’s conception of absolute terms as ones that signify the things that Ockham takes to be their ultimate significata directly, and not in respect of anything. Rather, they would say that the things that Ockham takes to be their ultimate significata are not the ultimate significata of these terms (but rather they are

31 Although this is not precisely the characterization Ockham gives us, I believe this formulation covers pretty well his intention. In formal terms, this formulation says that the function that would assign the significata of an absolute term in a formal semantics would be a one-place function, while the one assigning the significata of a connotative term would be a many-place function. For technical details see Klima, G. 1993 (b) and Klima, G. 1991. For detailed analyses of Ockham’s relevant texts see Spade, P. V. 1988, and Spade, P. V. 1990.

153

their personal supposita), and even if they can be said to be signified by these terms somehow (as Soto would say, materially, or as Burleigh and Pseudo-Campsall would say, secondarily), they should be said to be signified in respect of what are the direct ultimate significata of these terms (for Soto, their formal significata, or for Burleigh and Pseudo-Campsall, their primary significata).32

Consider again the example of the concept of trees, and the Latin term arbor subordinated to it. According to the “via antiqua” conception, the universal concept of trees directly represents the nature of trees in general, in abstraction from the individual trees. However, the individual trees are trees only because they are actual in respect of this nature, while for example a cat is not a tree precisely because it is not actual in respect of this nature. Now, whatever it is on account of which an individual tree is a tree (and, say, not a cat), whether it is taken to be distinct from the tree itself or not, is called the nature of this tree. The tree itself is represented by this concept only with respect to this nature, which is directly represented by the concept. Therefore, what the term arbor ultimately signifies in respect of this tree is the nature of this tree (again, regardless of whether the nature of this tree is taken to be distinct from this tree or not), but of course it represents it universally, in abstraction from this tree or from that tree (that is, not as the treeness of this tree, but as treeness in general).33 So, the immediate significate of the term arbor is the concept of trees, while the ultimate significate of it in respect of this tree is the nature of this tree, insofar as it is on account of this nature that the tree is a tree. But the tree itself, insofar as it is something which is actual in respect of this nature is not what is directly (formally or primarily) signified by this term, but rather it is something which can be said to be signified only indirectly (materially or secondarily), and which therefore can be supposited for by this term by personal supposition in the context of a proposition.

As can be seen, whether universals were regarded as real entities having numerical unity, or as existing only in their individualized instances, having some lesser-than-numerical unity that had to be recognized by the abstractive activity of the intellect, in their semantic function they were always conceived as the entities in respect of which the concepts of the mind represented the particulars falling under them, and hence as the entities in respect of which universal terms were related to these particulars as to their personal supposita. But then Ockham’s uncompromising rejection of universals even in this semantic function, inevitably led to his doctrine of absolute concepts, and the corresponding absolute terms, which represent particulars not in respect of anything. So all universal absolute terms directly signify only particulars.34 And so any other term which signifies particulars not absolutely, but in some respect, can be construed as signifying these particulars only with the connotation of some other (or occasionally the same) particulars, which again can be signified directly by absolute terms. Therefore, as far as Ockham

32 Cf. for example, Lambert of Auxerre, 1971, pp. 205-209; Burleigh, W. 1955, c.3. p.7; Soto 1980, lb. 1, c. 7; lb. 2, c. 10; lb. 2, c. 14; Pseudo-Campsall, R.1982 c. 9, n. 4, p. 101. 33 For a detailed explanation of this theory of abstraction in Aquinas in particular, see Klima, G. 1996. It should be noted here that talking about “the nature of trees in general” need not commit anyone to the existence of an entity which is numerically one, and is distinct in real existence both from individual trees and their individual treenesses. In fact, such extreme realism concerning universals was regarded even by otherwise “realist” medievals as entirely absurd, and sufficiently refuted by Aristotle, so that some even doubted whether Plato ever held the theory in this crude form. Cf. Soto, D. 1968 (In Isagogen) q. 1, p. 30. 1I; Aegidius Romanus 1968, 1SN, d.19, pars 2, q. 1, and Wyclif, J. 1985, pp. 61-69. 34 Cf. Ockham, W. 1974 (SL) part 1, c. 64, pp. 195-196. Note that I am not dealing here with Ockham’s earlier, fictum-theory. For a discussion of, and references to, that theory, see Adams, M. M. 1989, part 1, c. 3, pp.71-109.

154

is concerned, the term arbor signifies all trees (including past, present and merely possible ones) directly, and not in respect of anything, because the concept of trees equally directly (primarily) represents the same. On the other hand, connotative terms in general always signify particular things in respect of some things, which are said to be their connotata.

Common Personal Supposition of Absolute vs. Connotative Terms

In view of the previous considerations, the personal supposition of absolute terms is unproblematic for Ockham. Absolute terms signify what their concepts directly represent, namely, the particular things falling under this concept. Thus, these terms supposit for these same particulars in a propositional context, if these particulars are actual (relative to the tense and modality of the proposition). Connotative terms, on the other hand, signify particulars in respect of their connotata, so they will supposit for their significata only if these connotata are also actual, provided they are connoted positively, or, on the contrary, if these connotata are non-actual, when they are connoted negatively. For instance, the term ‘sighted’ signifies animals with respect to their sight. But, obviously, this term will supposit for an animal only if the animal in question actually has sight (relative to the tense and modality of the proposition). For example, in the proposition ‘Socrates was sighted’ the predicate term supposits for Socrates (among all animals that were sighted in the past), since Socrates actually had sight in the past. On the other hand, the term ‘blind’, which signifies animals while negatively connoting their sight, will only supposit for an animal if the animal actually does not have sight. For example, in the proposition ‘Homer was blind’ the predicate term negatively connotes Homer’s sight, and thus supposits for Homer (among all animals that lacked sight in the past), precisely on account of the fact that, since he lacked sight, Homer’s sight was not actual.35

Common Supposition of Abstract vs. Concrete Terms

Since for Ockham concrete absolute terms ultimately signify only the particulars falling under them, the abstract terms corresponding to them will signify and supposit for the same things. So, for example, the term arboreitas [‘treeness’], will also signify and supposit for individual trees, just as the term arbor [‘tree’] does.36

Abstract connotative terms, on the other hand, should be judged on a case by case basis according to Ockham. Some such terms signify and supposit for the same things that their concrete counterparts supposit for, say, the term ‘fatherhood’ supposits for the same persons that the term ‘father’ does, and the term ‘blindness’ supposits for the same blind animals that the term ‘blind’ does. Other such terms signify and supposit for the connotata of their concrete counterparts; for example, the term ‘whiteness’ supposits for the connotata of the term ‘white’, namely, the individual whitenesses of individual white things. Yet other such terms are taken to signify and stand for several connotata of the corresponding concrete terms; for example, ‘similarity’, at least in one plausible analysis according to Ockham, can supposit for the individualized qualities of those individuals that are similar to one another in respect of that

35 Ockham, W. 1974 (SL) part 1, c. 36, pp.101-103; part 2, c. 6, pp. 269-272. 36 Cf. Ockham, W. 1974 (SL) part 1, c. 6; for the theological complications inevitably cropping up for this analysis concerning ‘man’ and ‘humanity’ with respect to Christ, see also the subsequent chapters.

155

quality, say, the whiteness of Plato and the whiteness of Socrates together, in the same way as collective names such as ‘army’ stand for a number of individuals taken together. 37

The Two-Name Theory of Predication38

Ockham’s theory of predication is clearly intended to eliminate the systematic need for the inherent entities seemingly required by the “inherence theory” of the “via antiqua”. As he writes:

“Therefore, if in the proposition: ‘This is an angel’ the subject and the predicate supposit for the same thing, the proposition will be true. And so it is not denoted that this has angelity, or that there is angelity in this, or something like this, but what is denoted is that this is truly an angel; but not that he is that predicate, but that he is that for which the predicate supposits.”.39

To be sure, Ockham was not the first to propose to analyze the truth conditions of categorical propositions in terms of the identity of the supposita of their terms. For example, Aquinas explicitly uses this type of analysis side by side with the inherence theory, although remarking that the inherence-analysis is the more “proper” of the two.40 Ockham’s innovation here is rather the systematic application of this analysis to eliminate the need for the inherent entities apparently required by the inherence analysis. Indeed, together with Ockham’s rules of supposition and his account of the signification of absolute and connotative terms, it “automatically” eliminates the apparent ontological commitments of the “via antiqua”.

5. Ockham’s “Reductionist Ontology” of the Categories

With these semantic rules at hand, it is easy to see that according to Ockham’s theory all terms connoting something else than what they supposit for in a proposition are non-essential predicates of their supposita. For such a term supposits for one of its ultimate significata only if the thing in question is actually related to another thing (or to some other things) connoted by the term in the manner required by this connotation. But then, since this significatum and this connotatum (or these connotata) are supposed to be distinct entities, it is at least logically possible for them to exist or not to exist independently of one another (and hence this is always possible by God’s absolute power). Hence, it is always possible for the same term once to supposit and then not to supposit for the same thing on account of the existence (or non-existence) of this connotatum (or at least one of these connotata). And this is precisely what it means for the term to be an accidental predicate of this suppositum.

But as we have seen earlier, what was required for the ontological commitment to ten distinct entities under the ten categories was the assumption that the abstract terms in the nine accidental categories were essential predicates of their supposita, yielding together with substance the “ten distinct, tiny things [parvae res], according to the imagination of the moderns, which imagination is false and impossible”.41 So to get rid of the unwanted commitment to the “ten distinct, tiny things”, all Ockham needs to do is to show that these abstract terms are connotative, rather than absolute. But how can we decide, whether a term is connotative or absolute? Of

37 Cf. Ockham, W. 1974 (SL) part 1, c. 6; Ockham, W. 1980 (Quodlibeta) VI. q. 25, pp.681-682 38 Cf. the references in n. 22. 39 Ockham, W. 1974 (SL) part 2, c. 2, p. 250. 40 Cf. 3SN d.5, q.3, a.3; ST1 q.13, a.12 41 Ockham, W. 1980 (Quodlibeta) V, q. 22, p. 569.

156

course, since this is a question concerning the signification of terms (since an absolute term is one that signifies things absolutely, while a connotative term is one that signifies things in relation to some thing or things), we can answer it by considering the significations of terms. If, as a result of this consideration we are able to come up with a nominal definition of the term we are considering, then, according to Ockham, we can be sure that the term in question is connotative, since this is precisely what such an analysis of its signification shows. But if the term is absolute, then no such analysis is available. As Ockham writes:

“In fact, properly speaking, such names do not have a definition expressing what the name means. For, properly speaking, for a name that has a definition expressing what the name means, there is [only] one definition explicating what the name means that is, in such a way that for such a name there are not several expressions expressing what the name means [and] having distinct parts, one of which signifies something that is not conveyed in the same way by some part of the other expression. Instead, such names, insofar as what they mean is concerned, can be explicated after a fashion by several expressions that do not signify the same things by their parts. And so none of those [expressions] is properly a definition expressing what the name means.

For example, ‘angel’ is a merely absolute name (at least if it is not the name of a job, but of the substance only). For this name there is not some one definition expressing what the name means. For one [person] explains what this name means by saying “I understand by an angel a substance abstracted from matter”, another [person] by “An angel is an intellectual and incorruptible substance”, and [yet] another [person] by “An angel is a simple substance that does not enter into composition with [anything] else”. The one [person] explains what the name means just as well as the other [person] does. Nevertheless, some term occurring in the one expression signifies something that is not signified in the same way by [any] term of the other expression. Therefore, none of them is properly a definition expressing what the name means.”42

As a consequence, since any categorematic term is either absolute or connotative, to show that a term is connotative it is sufficient to show that it has a nominal definition. As Ockham writes:

“But a connotative name is one that signifies something primarily and something secondarily. Such a name does properly have a definition expressing what the name means. And often you have to put one [term] of that definition in the nominative and another [term] in an oblique case. This happens for the name ‘white’. For ‘white’ has a definition expressing what the name means, in which one word is put in the nominative and another one in an oblique case. Thus, if you ask what the name ‘white’ signifies, you will say that [it signifies] the same as [does] the whole expression ‘something informed by a whiteness’ or ‘something having a whiteness’. It is clear that one part of this expression is put in the nominative and another [part] in an oblique case.”43

Accordingly, to eliminate unwanted ontological commitment in any of the accidental categories, all Ockham has to do is to show that the abstract terms in that category are connotative, and to show this, all he has to do is to provide a nominal definition of the terms in question. Indeed, this is precisely how he treats abstract terms in the category of quantity:

“Such [connotative] names also include all names pertaining to the category of quantity, according to those who maintain that quantity is not another thing than substance and quality. For example, ‘body’, according to them, should be held [to be] a connotative name. Thus, according to them, it should be said that a body is nothing but “some thing having [one] part distant from [another] part according to length, breadth and depth”. And continuous and permanent quantity is

42 Ockham, W. 1974 (SL) part 1, c. 10, pp. 35-36. The translation is from Spade, P. V. 1995, p. 26. 43 Ibid.

157

nothing but “a thing having [one] part distant from [another] part”, in such a way that this is the definition expressing what the name means.”44

This analysis immediately allows him to treat in a similar manner even some terms in the category of quality, namely, those belonging to the species of shape (figura):

“These [people] also have to maintain that ‘figure’, ‘curvedness’, ‘rightness’, ‘length’, ‘breadth’ and the like are connotative names. Indeed, those who maintain that every thing is [either] a substance or a quality have to hold that all the contents in categories other than substance and quality are connotative names. Even certain [names] in the category of quality are connotative, as will be shown below.”45

In the passage he apparently refers to, Ockham argues as follows: “such predicables as ‘curved’ and ‘straight’ could be successively true of the same thing because of locomotion alone. For when something is straight, if the parts are brought closer together, so that they are less distant than before, by locomotion without any other thing coming to it, it is called ‘curved’. For this reason, ‘curvature’ and ‘straightness’ do not signify things (res) other than the straight or curved things. Likewise for ‘figure’, since by the mere locomotion of some of its parts a thing can come to have different figures”46

In fact, this passage provides us with a typical example of Ockham’s general “eliminative” strategy. The apparent need for positing a distinct straightness in accounting for something straight becoming non-straight is eliminated here by analyzing the concept of straightness in terms of the distance of the parts of the thing connoted by the term. Perhaps, an explicit nominal definition of the term for Ockham could be ‘a thing whose parts are maximally distant along its length’, or something like this. (To be sure, since in his merely programmatic and illustrative analyses Ockham does not care much about particular details, neither should I.) Thus, the analysis shows that the term ‘straightness’ need not be an essential predicate of whatever it supposits for. But then it can clearly become false of something that it supposited for without the destruction of this suppositum, merely on account of the change in what it connoted, namely, the distance of the parts of the thing, by locomotion. So it did not have to supposit for anything distinct from the thing whose parts were maximally distant along its length when it was straight, and whose parts are not maximally distant now, when it is curved.

In fact, it is easy to see that it is precisely this type of analysis that accounts for Ockham’s general rule:

“it is convenient to use this method for knowing when a quality should be assumed to be a thing other than a substance and when not: when some predicables can be truly asserted of the same thing successively but not simultaneously because of locomotion alone, it is not necessary for these predicables to signify distinct things ”.47

For what changes by locomotion is merely the relative positions of quantitative parts of bodies, which Ockham has already “analyzed away” by analyzing quantity-terms as denoting bodies with the connotation of the relative positions of their parts. 48

44 Ibid. Cf.: Ockham, W. 1974 (SL) part 1, c. 44, p. 137. 45 Ibid. 46 Ockham, W. 1974 (SL) part 1, c.55, p. 180; the translation is from Adams, M. M. 1989, p. 281. Cf.: Ockham, W. 1980 (Quodlibeta) VII, q. 2, p. 708. 47 Ockham, W. 1974 (SL) part 1 c. 55, p. 180. Quoted and translated by Adams, p. 281. 48 These considerations also quite clearly indicate the general reason why this strategy cannot work for Ockham in the case of the other species of quality. The concepts of those qualities for Ockham simply admit of no such

158

However, strictly speaking, all that these considerations can achieve is the elimination of the apparent ontological commitment of the theory of the categories, by removing the critical assumption of the essentiality of abstract terms in the accidental categories. That is to say, all they show is that the doctrine of the categories alone need not entail commitment to ten mutually exclusive classes of entities. But they do not show in themselves that there are in fact no distinct entities corresponding to the categories. To be sure, applying his famed “razor”,49 Ockham could get rid of any unwanted entities already on the basis of not having to posit them. But this still does not prove that they do not exist. To prove this claim, Ockham needs further arguments to show that the opposite position would entail all sorts of absurdities. Ockham’s arguments to this effect can be classified as concluding to various sorts of logical, metaphysical, physical and theological absurdities, running through the whole range of the categories of accidents. For the sake of brevity, I present here only two typical arguments concerning the category of relation to illustrate the type of difficulties that face the opposite position, represented by Pseudo-Campsall in its most extreme form.

One type of argument is based on the separability of any two really distinct entities, at least by divine power. If, for example, the fatherhood of Socrates is distinct both from Socrates and his children, then it is possible for God to create this fatherhood in Socrates without Socrates begetting any children, and thus Socrates could be a father without having any children. Indeed, by the same token, God could create a man first, and then some others, who would not be his children, nor would he be their son. However, if filiation (the relation of being somebody’s son) is distinct both from father and son, God could create it in this man, and thus he would be a son; but he certainly would not be the son of anything but a man; however, all the men there are are younger than him, so the father would have to be younger than the son, which is a contradiction.50

Another type of objections concludes to some physical absurdity. If any relation is really distinct from the things that are related, then so is the spatial relation of distance. If so, then any change of relative position by locomotion would entail the generation and corruption of an infinity of such relations in the things the are distant from one another on account of such a relation. And so whenever an ass would move over on earth, an infinity of such relations would be generated and corrupted in the heavenly bodies and their parts, since they would be related to the ass differently than they were before. But it seems physically absurd to claim that the movement of the ass could cause any change in the heavenly bodies.51

6. Conclusion: Ontological Alternatives vs. Alternative Semantics

Pseudo-Campsall was quite unmoved by these and similar arguments. Since he was explicitly committed to these distinct entities, he argued either that the alleged absurd conclusion does not

analysis. An analysis along these lines would probably have to involve explaining change in respect of these qualities in terms of the locomotion of the particles of a body, a theory dangerously close to Democritean atomism, which Ockham, following Aristotle, unequivocally rejects. For more discussion of this issue see Adams, op. cit., pp. 283-285. 49 For detailed discussions of Ockham’s actual formulations of the principle and its applications see Adams, op. cit., entry “Razor, Ockham’s” in the Index of Subjects. 50 Ockham, W. 1974 (SL) part 1, c. 50, pp. 161-162. 51 Ibid. p. 159.

159

follow from positing them, or that the conclusion is not absurd, or that the absurd conclusion follows only because of some contradictory assumption in the objection itself.52

However, whatever we should think of the merits and demerits of either Ockham’s objections, or Pseudo-Campsall’s replies, the interesting thing from our point of view is that Soto, for all his “via antiqua” semantics, is moved to reject the real distinction of relations and the remaining six categories on the basis of precisely the same type of arguments that one can find in Ockham.53 Indeed, if we look earlier, we can see that arguments of this type figured in the discussions of many authors before Ockham, especially concerning the hotly disputed issue of the real distinction of relations from their foundations.54 What is more, we can safely assert that the uncompromisingly exuberant ontology of Pseudo-Campsall was rather the exception than the rule even in pre-Ockhamist philosophy.55 So Ockham’s ontological “reductions” were hardly as radical as he himself makes them appear by his contrast with the moderni. Nevertheless, Ockham is still an innovator, not with respect to what he achieves in his ontology, but rather with respect to how he achieves it.

As we have seen, the driving force behind Ockham’s ontological program is his new semantics. In fact, if Ockham’s sole purpose had been to achieve a simplified ontology to avoid the sort of absurdities Pseudo-Campsall was bound to handle, he could have done so by simply abandoning the critical assumption of the essentiality of abstract terms in all accidental categories, as many had done before him with respect to several categories, while leaving the main semantic framework intact. But Ockham had a much more ambitious project. He set out to simplify the conceptual edifice of all theoretical sciences, by ridding them of what he perceived as unnecessary, recent accretions, which are unjustifiable both theoretically and on the grounds of “pure Aristotelian” principles.56 It is only the requirements of this overall project that can explain why Ockham could not rest content with the ontological alternatives allowed by the old semantic framework, ranging from the extreme position of Pseudo-Campsall to the much more parsimonious ontology of Soto and others. Therefore, despite whatever Ockham tells us about the ontological calamities allegedly inevitably incurred by the semantics of the “moderns”, those calamities alone would not be sufficient to justify his abandonment of the old framework and the introduction of his alternative semantics.

52 For his answers to the particular objections presented above, see Pseudo-Campsall, R.1982 c. 43, pp. 280-287. For detailed discussion of Ockham’s arguments, see Adams, op. cit., pp.169-285. 53 For Soto’s consideration of the same arguments see Soto, D. 1967 (In Categorias) c. 7, q. 2. 54 For a comprehensive historical overview of the problem see Henninger, M. 1989 55 For example, in view of Aristotle’s discussion of motion in his Physics, it was typical to identify action and passion with the same motion. See e.g. Aquinas, In Libros Metaphysicorum lb. 11, lc. 9, n.2313; cf. In Libros Physicorum lb. 3, lc. 5. Here Aquinas argues that the categories are diversified in accordance with the diverse modes of predication, and so it is not unacceptable to posit the same entity in diverse categories. On the other hand, concerning the non-relational categories of quantity and quality and (concerning relations secundum esse) Aquinas clearly commits himself to the view that the abstract terms of these categories are essential predicates, species and genera of the particulars of this genus, in the same way as Pseudo-Campsall commits himself to the same view concerning all categories. See Aquinas, De Ente et Essentia, c. 7. 56 Cf Moody, E. A. 1965, esp. pp. 26-30.

160

Bibliography

Abelard, P. 1970 Petrus Abaelardus: Dialectica, L. M. De Rijk, ed., rev. ed., (“Wijsgerige Teksten en Studies, Philosophical Texts and Studies,” vol. 1); Assen: Van Gorcum, 1970.

Adams, M. M. 1989 William Ockham, 2 vols., Notre Dame, IN: University of Notre Dame Press, 1987. 2nd rev. ed., 1989.

Aegidius Romanus 1968 In Primum Librum Sententiarum, Venice, 1521, Frankfurt/Main: Minerva, 1968

Aquinas, T. 1980 S. Thomae Aquinatis Opera Omnia, Stuttgart-Bad Canstatt: Frommann-Holzboog, 1980

Burleigh, W. 1955 De puritate artis logicae tractatus longior, with a Revised Edition of the Tractatus brevior, Philotheus Boehner, ed., (“Franciscan Institute Publications, Text Series,” vol. 9); St. Bonaventure, NY: The Franciscan Institute, 1955.

Cajetan, T. de V. 1939 Scripta Philosophica: Commentaria in Praedicamenta Aristotelis, ed. M. H. Laurent, Romae: Angelicum, 1939

Cajetan, T. de V. 1964 Commentary on Being and Essence, transl. L.J. Kendzierski, F.C. Wade, Marquette Univ. Press., Milwaukee, Wis., 1964

Geach, P. T. 1972 “Nominalism” in: Logic Matters, Berkeley and Los Angeles: University of California Press-Basil Blackwell, pp. 289-301.

Henninger, M. 1989 Relations: Medieval Theories 1250-1325, Clarendon Press: Oxford, 1989

Henry, D. P. 1972 Medieval Logic and Metaphysics, London: Routledge & K. Paul, 1972

Klima, G. 1991 “Ontological Alternatives vs. Alternative Semantics in Medieval Philosophy”, in: J. Bernard: Logical Semiotics, S - European Journal for Semiotic Studies, 3(1991), No.4,Vienna, pp. 587-618.

Klima, G. 1993 (a) “‘Socrates est species’: Logic, Metaphysics and Psychology in St. Thomas Aquinas’ Treatment of a Paralogism”, in: K. Jacobi (ed.): Argumentationstheorie: Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns, Leiden, the Netherlands: E. J. Brill Publishers, pp. 489-504.

Klima, G. 1993 (b) “The Changing Role of Entia rationis in Medieval Philosophy: A Comparative Study with a Reconstruction”, Synthese 96(1993) No. 1. pp. 25-59.

Klima, G. 1996 “The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being”, Medieval Philosophy and Theology, 5(1996), pp. 87-141.

Klima, G. forthcoming (a) “Contemporary “Essentialism” vs. Aristotelian Essentialism”, in: Thomistic Papers, 7(1996)

Klima, G. forthcoming (b) “Old Directions in Free Logic: Existence and Reference in Medieval Logic”, in: K. Lambert: New Directions in Free Logic, Sankt Augustin bei Bonn: Akademia Verlag

Lambert of Auxerre 1971 Logica (Summa Lamberti), Franco Alessio, ed., Firenze: La nuova Italia editrice, 1971

Moody, E. A. 1965 The Logic of William Ockham, Russell & Russell; New York, 1965

Moore, W. L. 1989 “Via Moderna”, in: J. R. Strayer: Dictionary of Middle Ages, New York: Scribner, 1989, vol.12. pp. 406-409.

Ockham, W. 1974 (SL) Summa logicae, Philotheus Boehner, Gedeon Gál and Stephen F. Brown, ed., (“Opera philosophica,” vol. 1), St. Bonaventure, NY: The Franciscan Institute, 1974.

Ockham, W. 1978 Epxositionis in libros artis logicae prooemium et Expositio in librum Porphyrii de praedicabilibus, E. A. Moody, ed., Expositio in librum praedicamentorum Aristotelis, Gedeon Gál, ed., Expositio in librum perihermenias Aristotelis, Angelo Gambatese and Stephen Brown, ed., Tractatus de praedestinatione et de praescientia dei respectu futuroum contingentium, Philotheus Boehner † and Stephen Brown, ed., (“Opera philosophica,” vol. 2), St. Bonaventure, NY: The Franciscan Institute, 1978.

161

Ockham, W. 1980 Quodlibeta septem, Joseph C. Wey, ed., (“Opera theologica,”vol. 9), St. Bonaventure, NY: The Franciscan Institute, 1980.

Peter of Spain. Tractatus, Called Afterwards Summule Logicales, LambertM. De Rijk, ed., Assen: Van Gorcum, 1972. Critical edition.

Priest, G. – Read, S. 1981 “Ockham’s Rejection of Ampliation”, Mind 90(1981), pp. 274-279.

Pseudo-Campsall, R.1982 Logica Campsale Anglicj, valde utilis et realis contra Ocham, in: Synan, E.A.: The Works of Richard Campsall, Vol. 2. Toronto: Pontifical Institute of Mediaeval Studies, 1982

Soto, D. 1967 In Porphyrii Isagogen, Aristotelis Categorias, librosque de Demonstratione, Commentaria, Venice, ex officina Dominici Guarraei, et Io. Baptistae, fratrum, 1587, reprint, Frankfurt: Minerva, 1967

Soto, D. 1980 Summulae, Svmmvlarvm aeditio secunda, Salmanticae: Excudebat Andreas a Portonariis, 1554, reprint, Georg Olms Verlag: Hildesheim, New York, 1980

Spade, P. V. 1988. “Ockham’s Distinctions between Absolute and Connotative Terms,” Vivarium, 13 (1975), pp. 55–76. Reprinted in Spade, Paul Vincent. Lies, Language and Logic in the Late Middle Ages, (“Collected Studies Series”), London: Variorum Reprints, 1988, item XI

Spade, P. V. 1990 “Ockham, Adams and Connotation: A Critical Notice of Marilyn Adams, William Ockham,” The Philosophical Review 99 (1990), pp. 593–612.

Spade, P. V. 1995 William of Ockham, From His Summa of Logic, Part I: Adam (of Wodeham’s) Prologue, Ockham’s Prefatory Letter and chs. 1–5 6, 8–13, 26–28, 30–31, 33, 63–66, 70, 72, with summaries of chs. 7, 29, 32; pp. 25-26; online pdf publication available at: ftp://phil.indiana.edu/pub/spade/ockham.pdf, 1995

Suarez, F. 1960 Disputaciones Metafisicas, Madrid: Editorial Gredos,1960

Wyclif, J. 1985 Tractatus de Universalibus, ed. Mueller, I. J. Oxford: Clarendon Press, 1985

162

Buridan’s Logic and the Ontology of Modes

Summary: The aim of this paper is to explore the relationships between Buridan’s logic and the ontology of modes (modi). Modes, not considered to be really distinct from absolute entities, could serve to reduce the ontological commitment of the theory of the categories, and thus they were to become ubiquitous in this role in late medieval and early modern philosophy. After a brief analysis of the most basic argument for the real distinction between entities of several categories (“the argument from separability”), I point out that despite nominalist charges to the contrary, “older realists”—that is, authors working before and around Ockham’s time—were not committed to such real distinctions, and thus to an overpopulated ontology, by their semantic principles. However, what did entail such a commitment on their part, along with the argument from separability, was treating abstract terms in several accidental categories as “rigid designators”, that is, essential predicates (species and genera) of their supposita. Therefore, although in the form of “extra-categorial” modi essendi modes were well established in earlier medieval thought, their appearance within the theory of categories was conditioned on analyzing several abstract terms in the accidental categories as non-essential predicates of their particulars, something that “older realists” would in general not endorse. (This does not mean that even “older realists” were universally committed to really distinct entities in all ten categories. See on this e.g. notes 13 and 18.) Next, I show how this type of analysis is achieved “automatically” by Buridan’s theory of “eliminative” nominal definitions (in contrast to the older “non-eliminative” theory). However, since “realist” semantic principles in themselves did not yield a commitment to really distinct entities in all categories, it was also open for later “realists” to operate with not-really-distinct modes in several categories, although using different, “non-nominalist” tactics to treat the abstract accidental terms signifying them as non-rigid designators. The conclusion of the paper is that, as a consequence, both nominalist and later “realist” thinkers were able to achieve the same degree of ontological reductions in their respective logical frameworks, and so it was not so much their ontologies as their different logical “tactics” that set them apart.

Real distinction and the argument from separability

In one of his questions on Aristotle’s Physics, Buridan invites us to consider whether an object of a certain shape (figuratum) is identical with or distinct from its shape (figura).1 Although the question in itself might not seem too exciting, the way it was handled by Buridan and other medieval philosophers has far-reaching implications concerning their general conceptions of the relationship between language, thought, and reality.

To see these implications, let us take, as philosophers so often did over the centuries, a piece of wax. First let us roll it into a ball. So now our piece of wax is spherical. Then let us shape it into a cube, so that now, say, one minute later, we have the same piece of wax as before, but with a different, cubic shape. So now it is cubical.

This much is common experience, so probably nobody would raise objections to the above description of the process of the transfiguration of our piece of wax. But here is another

1 Buridan, Quaestiones Physicorum, lb. 2. q. 3. To be sure, in the question Buridan distinguishes between taking figuratum for the substance having some shape and taking it for the quantity of the substance thus and so shaped. As he assumes the distinction of substance and quantity, he says that figuratum taken in the first way without a doubt signifies something distinct from what figura signifies, and thus the question really concerns the identity or distinction of the quantity of a substance and its shape. However, since in the following discussion the distinction between substance and quantity will not be relevant, for the sake of simplicity of expression I will ignore this nicety, and will speak freely, for example, about the identity or distinction between a piece of wax and its shape. I do not think this will do any harm if we keep in mind that what is really at stake for Buridan here is the distinction between the quantity of the wax and the shape that renders this quantity thus and so arranged in space.

163

description of the same process. Let us call our piece of wax2 W for brevity’s sake. When we rolled W into a ball, then it became spherical, that is to say, sphericity came into existence in W. Thus, if we refer to the time when W was shaped into a ball as t1, we can say that at t1 W’s sphericity existed. However, at the later time, let us call it t2, when W was shaped into a cube, W took on cubic shape, that is to say, W’s cubicity came into existence, while its sphericity perished. So at t2 W’s sphericity did not exist, while W’s cubicity did.

Now, humanist squeamishness about the barbarity of the contrived abstract terms aside, many philosophers would certainly feel uneasy about the coming and going of the strange new entities apparently referred to by these terms in this new description. After all, why should we admit such new, obscure entities into our ontology?

Apparently, we are forced to do so on the basis of the following simple argument, which henceforth I will refer to as the argument from separability.3 When W first was a sphere, this was on account of its having spherical shape. Then, after its change, W became a cube, on account of taking on cubic shape. But since spherical shape certainly cannot be the same as cubic shape, and nothing can have two different shapes at the same time, when W’s cubic shape came into existence, its spherical shape must have ceased to exist. And so, since after the change W remained in existence, while its spherical shape ceased to exist, W cannot be identified with its spherical shape before the change; indeed, by parity of reasoning, nor with its cubic shape after the change. Thus, in order to account for this change we must assume three distinct entities in our analysis: W, W’s spherical shape, and W’s cubic shape.

Ockham’s charge

This is, however, precisely the kind of consideration William Ockham would reject as arising from a mistaken, what we might call “realist”, conception of the relationship between language and reality, according to which — says Ockham — “a column is to the right by to-the-rightness, God is creating by creation, is good by goodness, just by justice, mighty by might, an accident inheres by inherence, a subject is subjected by subjection, the apt is apt by aptitude, a chimera is nothing by nothingness, someone blind is blind by blindness, a body is mobile by mobility, and so on for other, innumerable cases”.4 And this is nothing, but “to multiply beings according to the multiplicity of terms ..., which, however, is erroneous and leads far away from the truth”.5

2 Or, rather, its quantity: see previous note. 3 Perhaps, it is interesting to note here that Scotus referred to the same type of argument as via separationis. In any case, this seems to indicate that by his time this type of argumentation was considered as one of the basic types of argument to decide issues of ontological distinctness. Cf. Joannis Duns Scoti Opera Omnia, t. 7, Quaestiones subtilissimae super libros Metaphysicorum Aristotelis, Parisiis, apud Ludovicum Vivès, 1893, lb. 7, q, 1, pp. 350-355. 4 Ockham, Summa Logicae:169. 5 Ibid. p.171.

164

Despite Ockham’s accusation (to be echoed by later nominalists over and over again),6 the “realists” Ockham attacks were not committed to an overpopulated ontology by their semantic principles. First of all, it should be clear that the “obscure entities” purportedly referred to by these contrived abstract terms are not the universal, eternal beings of some Platonic heaven of ideas. The entities to be considered here are just as individual and just as temporal as the things we are all familiar with in our everyday experience.7 Secondly, and this is more to the present point, as far as “realist” semantic principles are concerned, these entities need not even be “new”, that is, they need not even be distinct from the other, “familiar” entities, such as the piece of wax we started out with.

The main principles of a “realist” semantics

To see this in more detail, let us consider the following. The “realist” semantics Ockham attacks can be characterized at least by the following assumptions:

1. Concrete as well as abstract common terms signify ultimately whatever their concepts represent as their formal objects. I shall call what they ultimately signify their significata.8

6 “the realists are those who contend that things are multiplied according to the multiplicity of the terms,” whereas “those doctors are called nominalists, who do not multiply the things principally signified by terms according to the multiplicity of the terms.” This is from the manifesto of the Parisian nominalist doctors of 1474, printed in Franz Ehrle, Der Sentenzenkommentar Peters von Candia, Münster, 1925, p. 322. Quoted and translated by Menn: Forthcoming. 7 In fact, the theory of ideas in the crude form in which it is usually presented was regarded by late medieval philosophers as so absurd that some even doubted Plato would have ever held it in that form. “Adeo opinio Platonis apparet impossibilis, ut fuerint nonnulli suspicati Aristotelem id imposuisse Platoni. Et certe Augustinus, qui fuit Platonicus, lib. 83 Quaestiones, q. 46, dicit, quasi interpretans Platonem, ideas non esse nisi rationes in mente Creatoris, nec esse distinctas ab essentia divina, sed essentiam Dei esse Ideam omnium rerum, quia est quodam modo omnia, atque adeo Deus se intuens ut exemplar res extra producit, quae est concors sententia theologorum. […] At vero creditu est difficillimum Aristotelem, tempore ipso Platonis, euisque discipulis viventibus rem tam absurdam imposuisse Platoni, nisi Plato dixisset.” D. Soto: In Isagogen, q. 1, p. 30. 1I. Cf. Aegidius Romanus, 1SN, d.19, pars 2, q. 1, and Wyclif: 61-69. 8 Both from primary sources and from secondary literature we usually get a characterization according to which these ultimate significata are the forms of particulars. However, that the ultimate significata of common terms need not necessarily be regarded metaphysically as forms in all cases was a commonplace among thinkers who otherwise would provide such a characterization. As St. Thomas wrote: “...dicendum est quod illud a quo aliquid denominatur non oportet quod sit semper forma secundum rei naturam, sed sufficit quod significetur per modum formae, grammatice loquendo. Denominatur enim homo ab actione et ab indumento, et ab aliis huiusmodi, quae realiter non sunt formae.” QDP, q. 7, a. 10, ad 8. Cf. also e.g. Cajetan: “Verum ne fallaris cum audis denominativum a forma denominante oriri, et credas propter formae vocabulum quod res denominans debet esse forma eius quod denominatur, scito quod formae nomine in hac materia intelligimus omne illud a quo aliquid dicitur tale, sive illud sit secundum rem accidens, sive substantia, sive materia, sive forma.” Cajetan, In Praedicamenta: 18. In general, it is precisely this point that lies at the bottom of the distinction between extrinsic vs. intrinsic denomination. In fact, Buridan attributes the original idea of the distinction between semantic and metaphysical considerations to Averroes: “Nam, sicut dicit Commentator, duodecimo Metaphysicae, grammaticus videt in multis differre dispositionem et dispositum, et sic movetur ad imponendum eis nomina diversa, ut ‘albedo’ et ‘album’; et quia non est ejus inquirere an in omnibus vel in quibus sic differant dispositio et dispositum, ipse secundum similitudinem ad illa in quibus manifeste differunt imponit etiam aliis nomina per modum dispositionis et dispositi, seu determinationis et determinabilis, vel etiam determinati, derivando ab abstracto concretum vel e converso, relinquens metaphysico considerationem an illa nomina supponant pro eodem vel pro diversis, propter quem diversum modum significandi grammaticalem illa nomina habent diversos modos praedicandi.” Buridanus, Lectura

165

2. As the subject of a proposition, a common term supposits personally for (i.e., refers to) whatever is in actuality in respect of its significata (relative to the time and modality of the copula of the proposition, taking into account the possible ampliative force of the propositional context).9 What is thus supposited for by a term in the context of a proposition I shall briefly call here the term’s supposita.

3. On account of their different mode of signifying (modus significandi), the supposita of abstract terms are the same as their significata, whereas the supposita of concrete terms may or may not be the same as their significata. In any case, the supposita (and hence also the significata) of abstract terms are always the same as the significata of their concrete counterparts. So, this semantic principle specifies only that the significata and supposita of abstract terms are the same, and that they are the same as the significata of their concrete counterpart, but it leaves open the question whether the supposita of a concrete term are the same as its significata. Using our example of W and its sphericity, this is shown in the following figure:

sphaera

W’sspherical

shape

W

sphaericitassphaera

significatio

suppositio

= ?

4. An affirmative categorical proposition is true if and only if the supposita of its subject are actual in respect of the significata of its predicate (relative to the time and modality of the copula, taking into account the possible ampliative force of the propositional context) as determined by the quantity of the proposition. (This, of course, is just a general formulation of the familiar inherence theory of predication.)

These semantic principles in the form listed here, of course, appear nowhere in the works of medieval logicians. Still, I think it can be claimed with a justifiable degree of confidence that they provide a fair characterization of the kind of semantic theory that was at work in the logical doctrines Ockham attacked.10 However, on the basis of this characterization it should also be clear that Ockham’s attack, as far as the issue of the ontological commitment of this semantic theory is concerned, was rather unjustified.

de Summa Logicae: De Praedicabilibus, c. 7, n. 4. 9 Thus, album in album currit refers to whatever is actual at the time of the utterance of this proposition in respect of what is signified in it by album (whatever it is in itself), that is, all things that are white at that time. However, say, in album currebat, owing to the past tense of the verb, the same term refers to whatever is or was actual in the same respect, that is, whatever is or was white at that time. For further details and reconstruction of the theory of ampliation see Klima: Forthcoming. 10 For references to justify the historical correctness of these formulations, especially in St. Thomas Aquinas’s case, see Klima 1996.

166

Ockham’s charge disproved

Ockham’s charge, which Buridan shares,11 is that the “realists” posit distinct entities for each term in each category as their significata. In view of 3, however, we can see that, as far as the semantic theory is concerned, this need not be the case at all. In fact, using the previous example, it is easy to see that these semantic principles leave open the question whether we should regard W and its shape as the same entity or as distinct entities. For concerning our example this theory states only the following. At t1 W was a sphere, so at t1 the proposition ‘W is a sphere’ was true. Hence, by 4, the theory is committed to holding that at t1 W was actual in respect of the significate of the predicate ‘sphere’, which, by 3, is what can be referred to in another proposition by the corresponding abstract term, namely, ‘sphericity’. Thus, the theory is committed to holding that at t1 W was actual in respect of sphericity, which is just another way of saying that W’s sphericity existed, whence we can conclude further that the theory is committed to holding that at t1 the proposition ‘A sphericity exists’ was true. However, again, in virtue of 3, this commitment does not imply a further commitment to a “new” entity besides W, for W’s sphericity, namely, what was supposited for by the term ‘sphericity’ in this existential claim, as far as the semantic theory is concerned, may or may not be identical with W, namely, with one of the supposita of the term ‘sphere’ at t1 in the proposition ‘A sphere exists’.

But then, what can we make of the fact that at t2 W still existed, whereas its sphericity ceased to exist? Again, as far as the above-described semantic theory is concerned, this fact need not imply the distinction between W and its sphericity. For in terms of this theory, if we assume the identity of W and W’s sphericity, all this means is that whereas the term ‘W’ at t2 still supposited for W in the context of the proposition ‘W exists’, the term ‘sphericity’ no longer supposited for the same thing in the context of the proposition ‘A sphericity exists’ at the same time.

In fact, if we take a look at Buridan’s reply to the same type of argument we can see that his solution is essentially the same: despite the fact that, in virtue of its transmutation, W’s sphericity ceased to exist, while W remained in existence, we need not thereby be committed to their distinction, for we may analyze the description of this change solely in terms of the change of the supposition of the term ‘sphericity’. What happened need not be regarded as one entity ceasing to be while the other remained in existence. Rather, what we had here was just one and the same entity staying in existence, which before the change could be referred to both by the name ‘W’ and by the name ‘sphericity’, but which after the change could be referred to only by the name ‘W’, but no longer by the name ‘sphericity’.

“Rigid designators” and the argument from separability

This analysis, however, immediately gives rise to at least two further questions. First, if it is not the ceasing to be of W’s sphericity that accounts for the fact that the term ‘sphericity’ can no longer refer to W’s sphericity, then what is it? Something, after all, did change here! Second, if 11 “Notandum est quod de actione et passione et de aliis quattuor ultimis praedicamentis ego non intendo sequi doctrinam auctoris Sex Principiorum. Quia puto quod erravit ex eo quod credidit nullos terminos diversorum praedicamentorum supponere pro eodem, et ideo credidit quod actio esset una forma et passio alia, et quod passio esset effectus actionis; quod est totum falsum, ideo dicta ejus fecerunt multos errare.” Buridanus, Lectura de Summa Logicae: De Praedicamentis, c. 6, n. 1.

167

Buridan’s solution was in principle available to the upholders of the older semantic theory attacked by Ockham, then why is it that they, in fact, would maintain a distinction between W and W’s sphericity? Was there some further (semantic, or perhaps other) reason besides these simple semantic principles on account of which they were in fact committed to such a distinction?

It is the answer to the first question that for Buridan, and, most significantly, for late-medieval “realists” as well, gives rise to the ontology of modes. (To be sure, talk about modi, especially, about “extra-categorial” modi essendi, was nothing new in Buridan’s time.12 The novelty in the treatment of modi in late-medieval philosophy, therefore, seems to be rather their systematic introduction into the theory of the categories.13) However, to see why the same new ontological scenario should emerge for an uncompromising nominalist and for late-medieval “realists” alike, we have to deal first with the second question.

Let us, therefore, consider again the original argument for the distinction of W from its sphericity. Very simply stated, the reason why we concluded that W had to be distinct from its sphericity was that during the transmutation W remained in existence, while its sphericity did not. Now why does this seem to be a sufficient reason for our conclusion? The answer is simple: if W and its sphericity are one and the same entity, then the assumption that W exists at t2 while its sphericity does not implies the contradiction that one and the same entity both exists and does not exist at the same time. Therefore, W and its sphericity cannot be the same entity. This argument is simple and conclusive. But then how can Buridan deny its conclusion?

We have to notice here that the validity of this argument rests on a tacit assumption, which is so simple that it is quite easily overlooked, although almost everything else depends on it in this question. When in the argument we make the assumption to be refuted, namely, that W and its sphericity are one and the same entity, we also make the tacit assumption that the terms ‘W’ and

12 In fact, such an “old realist” as Giles of Rome, felt it inevitable to introduce modi essendi as the esse essentiae (as opposed to the esse existentiae) of the forma partis (as opposed to the forma totius) and of accidental forms. (Aegidius Romanus, Theoremata, th. VIII.) Indeed, he even goes on to explain that such a modus is not a third thing besides the accidental form and its subject. (Theoremata, th. XV.) Yet, he insists that the accidental form itself can never be the same as its subject, for from the union of an accident and its subject there can never result one nature. Also, he insists that, since whatever is in a category is there on account of its nature, nothing can be in two categories. (Theoremata, th. XIII-XIV.) So, since these modi essendi are not categorial entities, despite the fact that outside of the categories Giles recognizes modi and along with them some distinction that is not a distinction of one thing from another, he does not find such considerations applicable to the per se entities he acknowledges within the categories. And, most importantly from the point of view of our present argument, apparently he does so precisely because he regards the abstract terms of the nine accidental categories as the direct, essential predicates (species and genera) of their particulars in linea praedicamentali. 13 An interesting “transitional” figure in this regard seems to be Durand de Saint Pourçain. See Durandus de Sancto Porciano, 1SN d. 33, q. 1, where he makes a special point of the denominative character of the predicates signifying modi (among which he also considers tangere and tangi). Cf. also his 1SN d. 30, q. 2. n. 15, approvingly referred to by Suarez (Suarez, Disputationes, disp. 7, sect. 1. n. 19.) Another, perhaps even more important figure seems to be Henry of Ghent, who explicitly talks about categorial relations as modes. See Henninger, 1989, pp. 40-58. (I am grateful for this reference to Russ Friedman.) Indeed, Henry apparently utilized modes to account also for the last six categories, which, despite the fact that he is chronologically “older”, would doctrinally place him among the “later realists”. I think this observation may have enormously interesting historical implications concerning the formation and interaction of nominalist and realist trends in later-medieval philosophy and theology, but pursuing these issues lies far beyond the scope of this paper. Further interesting remarks concerning the emergence of categorial modi in the works of Peter Olivi and Jean de Mirecourt can be found in Maier 1958. Cf. also n. 18.

168

‘W’s sphericity’ — to borrow an expression from modern semantics — designate rigidly whatever they designate.14 If a term designates rigidly whatever it designates, then it designates its designatum or designata in any possible circumstances in which this designatum exists or these designata exist. Now, in fact, it is only with something like this assumption in mind that we can conclude from the transmutation of W that the entity that was designated by the term ‘W’s sphericity’ at t1 does not exist at t2. For otherwise, if we do not assume this rigidity, then nothing prevents the same entity that was designated by this term at one time from persisting and still ceasing to be designated by the same term at another time. But it is easy to see that this is precisely the point also of Buridan’s solution.

This is most obvious in Buridan’s reply to the argument, which he posited earlier in his quaestio in the following form:

Again, tomorrow this magnitude which now is spherical will exist, and tomorrow the sphericity will not exist, because the magnitude will not be spherical, but cubical; therefore, this magnitude is not the same as this sphericity.15

His response points out that without the assumption of the rigidity of designation, the argument is formally invalid:

To the other [argument] I reply that the argument is formally invalid, for we could argue in the same way that this man is not the same as this white thing, pointing to the same thing, for tomorrow this man will exist, but this white thing will not exist.16

The reason why the comparison with the case of the white man who gets separated from his whiteness is justified is explained more clearly in the next reply:

To the other [argument] I reply that it is in the same way and not otherwise that this magnitude can be separated from this sphericity as a man from this white thing, provided that this man is white; for this separation cannot occur so that this magnitude would exist at a certain time when this sphericity will not exist. But the separation can occur so that this magnitude exists at a certain time, when, however, it is not a sphericity, so this sphericity will exist, when it [i.e. the magnitude] will not be a sphericity.17

However, this last, crucial remark, namely that the sphericity of the wax will still exist when the magnitude will no longer be a sphericity, expresses precisely the denial of the claim that the term ‘sphericity’ rigidly designates whatever it designates, that is, the claim that the term ‘sphericity’ is an essential predicate of anything of which it is true at all.

So it seems that the difference between the upholders of the older theory on the one hand, and Buridan, as well as late-medieval realists, such as Soto, Fonseca, and Suárez on the other, boils down to this, namely, that while the former would consider abstract terms in the accidental

14 See Kripke 1980: passim. 15 “Item cras erit hec magnitudo que nunc est sperica et cras non erit spericitas quia magnitudo non erit sperica sed cubica, ergo non est eadem hec magnitudo et spericitas.” Buridanus, Quaestiones Physicorum, lb. 2. q. 3. 16 “Ad aliam dico quod forma argumenti non valet, sic enim argueretur quod non est idem homo et iste albus demonstrando eodem, quia cras erit iste homo, sed non erit iste albus.” Ibid. 17 “Ad aliam dico quod eodem modo et non aliter potest haec magnitudo separari ab hac sphericitate sicut hic homo ab hoc albo, posito quod iste homo est albus; non enim potest sic esse separatio quod haec magnitudo sit aliquando quando ista sphericitas non erit. Sed sic potest esse separatio quod sit ista magnitudo aliquando quod tamen non sit sphericitas, unde haec sphericitas erit quando illa non erit sphericitas.” Ibid., emphasis mine.

169

categories to be essential predicates of their particulars, the latter would reject this assumption.18 But if so, then what accounts for this “change of mind”? Indeed, who is right? Or is this just a matter of changing conventions?

Now, this point, as it obviously affects the distinction of the categories, was certainly not regarded as a matter of convention by the “realists”. Indeed, it was not regarded as such by Buridan either. He remarks:

Neither can the distinction of the categories be taken simply from the distinction of utterances, for we should not change the number [of categories] commonly given by the philosophers on account of different languages. Also, we impose utterances to signify by convention. Therefore, the number of categories would be a matter of convention, which is unacceptable.19

On the other hand, it is not just the distinction of things either that accounts for this distinction, for the same things may be supposited for by terms that belong to different categories:

… we should know that the distinction of these categories cannot be taken from the [distinction of] things for which the terms in the categories supposit, for, as was argued earlier, the same calidity is action and passion, and quantity, and quality, and relation; and the same Socrates is a man, and white, and three cubits, and father, and agent, etc.20

However, what is regarded by Buridan as accounting for the distinction of the categories is the difference between the connotations of the various concepts by which we conceive of possibly the same things:

But [the distinction of the categories] is taken from the diverse intentions according to which terms are connotative or even non-connotative in different ways. It is from these diverse connotations that the diverse modes of predication of terms about first substances derive; and thus [the

18 What seems to be at the bottom of the “older realist” commitment, then, is interpreting abstract accidental terms as the genera and species, that is, essential predicates, of their particulars. To be sure, even those authors who can justifiably be regarded as “older realists” in the sense of working within the semantic framework outlined above plus endorsing the view that abstract terms in the accidental categories are essential predicates of their supposita (such as Thomas Aquinas or Giles of Rome, or even such a chronologically later — yet, doctrinally “older” — figure as Cajetan, indeed, anyone who held that abstract accidental terms could be arranged on “predicamental trees” analogous to the familiar one in the category of substance) were prepared to regard several abstract terms as non-essential predicates of their supposita. But then they either had to regard such terms as not being (properly) in a category, or deny that all abstract accidental terms are essential predicates of their supposita, in which case, of course, it was open to them to identify entities across categories. (For this point see n. 30 below.) So, perhaps, in the strict sense of holding that all abstract terms in all nine accidental categories should be essential predicates of their supposita, and consequently holding the distinctness of these supposita from the supposita of substance terms and from those of terms from other categories, only Ockham’s possibly merely imaginary opponent could be considered an absolute “older realist”. On the other hand, it is also interesting to observe that the unidentified author of the Logica Campsale Anglicj, valde utilis et realis contra Ocham (Pseudo-Richard of Campsall, 1982), being a staunch defender of the real distinction of the entities in all ten categories, actually fits very well the description of Ockham’s opponent(s), so this opponent (or these opponents) may not have been entirely imaginary after all. In any case, a comprehensive account of which authors and to what extent could be regarded as “older realists” in this doctrinal sense is beyond the scope of this paper. 19 “Nec potest eorum [sc. praedicamentorum] distinctio sumi simpliciter ex parte vocum, quia non oportet propter diversa idiomata mutare numerum quem communiter ponunt philosophi. Et voces etiam imponuntur ad significandum ad placitum. Ideo plurificarentur praedicamenta ad placitum nostrum, quod est inconveniens.” Buridanus, Quaestiones in Praedicamenta, q. 3, pp.17-18. 20 “… sciendum, quod non potest distinctio horum praedicamentorum sumi ex parte rerum, pro quibus termini praedicamentales supponunt, quia sicut prius arguebatur, eadem caliditas est actio et passio et quantitas et qualitas et ad aliquid; et idem Sortes est homo et albus et tricubitus et pater et agens, etc.”. ibid.

170

categories] are distinguished directly and immediately in accordance with the diverse modes of predication about primary substances.21

Again, this much, as far as concrete terms are concerned, is common doctrine both for Buridan and for the older as well as the later “realists”. However, there is one particular aspect of Buridan’s treatment of the categories which brings him together with later “realists”, and distinguishes both his and the latter’s approach from that of the older “realists”. This is his treatment of several abstract terms from the nine accidental categories as being connotative, and thus as being non-essential predicates of their particulars.22 But, as we could see, this is precisely what allows him to reduce the number of the kinds of really distinct entities, while formally keeping the distinction of the ten categories.

Nominal definitions and the semantic complexity of abstract terms

Treating several abstract terms as connotative rather than absolute terms, and hence regarding them as accidental rather than essential predicates of their particulars, is not just a capricious innovation on Buridan’s part. He has serious theoretical reasons for doing so, rooted in the very principles of his philosophy of mind and language.

For Buridan what a term signifies is determined by the kind of concept the term is subordinated to, but the syntactic features of spoken or written terms do not provide us with a safe guide to decide whether they are subordinated to simple or complex concepts. In particular, the syntactic simplicity of a spoken or written term may conceal just any sort of conceptual, and hence semantic complexity. But then the way for us to find out about this sort of hidden complexity is conceptual analysis: by providing the exact nominal definition of such a simple term we reveal precisely this hidden semantic complexity, when the grammatical construction of the nominal definition faithfully mirrors the conceptual construction hidden by the syntactic simplicity of the spoken or written term.23 Therefore, as Buridan himself explicitly concludes, if a term has a

21 “Sed [distinctiones praedicamentorum] sumuntur ex diversis intentionibus, secundum quas termini sunt diversimode connotativi vel etiam non connotativi. Ex quibus diversis connotationibus proveniunt diversi modi praedicandi terminorum de primis substantiis; et ita directe et immediate distinguuntur penes diversos modos praedicandi de primis substantiis.” Ibid. 22 Cf.: “De prima dubitatione secundum dicta alias manifestum est, quod multi sunt termini vocales non habentes in mente conceptus simplices sibi correspondentes, sed quod terminus vocalis habet conceptum sibi correspondentem complexum ex multis simplicibus. Et sic ille terminus vocalis indiget diffiniri diffinitione explicante quid nominis per orationem complexam ex multis dictionibus saepe ad diversa praedicamenta pertinentibus. Et sic talis terminus dicitur esse de unoquoque illorum praedicamentorum; non tamen simpliciter, sed secundum quid, scilicet cum additione, loquendo ut quia est de tali praedicamento quantum ad talem terminum, quem includit, et de alio praedicamento quantum ad alium talem terminum. Sed tamen ego credo, quod simpliciter sine additione debeat dici de illo praedicamento, cujus magis retinet modum praedicandi secundum suam totalem aggregationem. Verbi gratia licet prandium significet comestionem de mane et cena comestionem in vespere, tamen prandere et cenare pertinent ad praedicamentum ‘agere’ et non ad praedicamentum de quando, quia si quaeratur, quid Sortes facit, dicimus quod ipse prandet vel quod ipse cenat. Sed si quaeramus, quando comedet Sortes vobiscum respondetur forte, quod cras, et tunc quaeritur magis specifice, scilicet quando cras, et respondetur: in prandio, vel respondetur: in cena. Et sic illud praedicatum ‘in cena’ est de praedicamento ‘quando’, et non de praedicamento actionis simpliciter loquendo. Unde licet ‘in cena’ et ‘cenare’ bene habeant aliquas easdem significationes, tamen cum illis habent diversas connotationes, propter quas habent diversos modos praedicandi. Et similiter reponitur hoc in uno praedicamento et illud in alio.” Buridanus, Quaestiones in Praedicamenta, q. 14: 103. 23 For more on this see Klima 1991.

171

nominal definition, then the term has to be subordinated to a complex concept.24 However, a complex concept corresponding to a nominal definition has to be connotative. The reason for this is that the only complex absolute concepts are those corresponding to quidditative definitions, which can be given only of absolute terms.25 But absolute terms do not have nominal definitions, since they are subordinated to simple concepts.26 Therefore, any term that has a nominal definition is subordinated to a complex concept which has to be connotative, and so the term has to be connotative too. So, if we are able to provide a nominal definition of an abstract term, then the abstract term in question “automatically” comes out from this analysis as connotative, and thus, if its connotata are distinct from its supposita, as an accidental predicate of its particulars.27 Therefore, providing nominal definitions of abstract terms referring to these particulars can be used to “eliminate” these particulars as distinct entities, for such an analysis will at once invalidate the principal argument for their distinction from entities referred to by absolute terms.

However, at this point it is very important to note a fundamental difference between the way Buridan treats nominal definitions, and the way “realists” treat them. The difference can be most clearly seen if we compare Buridan’s treatment with what Cajetan says about nominal definitions in his commentary on Aquinas’s De Ente et Essentia:

Just as the quid rei is the quiddity of the thing, so the quid nominis is the quiddity of the name: but a name, as it is the sign of the passions that are objectively in the soul (from bk.1. of Aristotle’s Perihermeneias), does not have any other quiddity than this, namely that it is a sign of a thing understood or thought of. But a sign, as such, is in a relation to what is signified: so to know the

24 “In secunda clausula manifestatur quorum terminorum sunt tales diffinitiones. Propter quod sciendum est quod dictiones vocales impositae sunt ad significandum conceptus immediate, et mediantibus eis res conceptas significant. Sunt autem conceptus nostri aliqui simplices, aliqui ex pluribus simplicibus complexi, prout alias dictum est. Si ergo imponatur dictio aliqua ad significandum conceptum simplicem, sive incomplexum, tunc talis dictio non est interpretabilis, sed si alicui sit ignota ejus significatio, notificabitur sibi aliquando per aliam dictionem synonymam, sicut puero gallico per idioma gallicum docetur idioma latinum, aliquando docetur hoc per ostensionem rei significatae et vocis expressionem, sicut infanti a matre docetur suum idioma, aliquando etiam docetur hoc per dictionis descriptionem vel quidditativam diffinitionem. Sed si dictio imposita fuerit ad significandum conceptum ex pluribus simplicibus conceptibus complexum, tunc indiget interpretatione per plures dictiones significantes seorsum illos conceptus simplices ex quibus est in mente complexio. Sic enim ‘philosophus’ interpretatur ‘amator sapientiae’ (dicitur enim ‘philosophus’ a ‘philos’ graece, quod est ‘amator’ latine, et ‘sophos’, quod est ‘sapientia’, quasi ‘amator sapientiae’), et ideo nihil plus vel nihil aliud debet nobis significare ista dictio ‘philosophus’ quam ista oratio ‘amator sapientiae’, et e converso. Notandum est autem quod aliquando conceptum complexum ex pluribus simplicibus imponimus ad significandum per unam simplicem dictionem vocalem, sicut possumus facere ad placitum nostrum, et expedit saepe ad brevius loquendum. Et aliquando conceptus complexus ex determinatione et determinabili pro aliquo supponit, et aliquando pro nullo, sicut dictum est alias, sicut ‘animal album’ pro aliquo supponit, aut etiam ‘animal non album’, sed ‘homo hinnibilis’ pro nullo supponit, vel etiam ‘equus non hinnibilis’. Si ergo conceptum complexum significatum complexe per hanc orationem vocalem ‘animal album’ ego volo significare per dictionem incomplexam, ut per hanc vocem ‘A’, et similiter conceptum ‘hominis hinnibilis’ per hanc vocem ‘B’, tunc haec dictio ‘A’ pro aliquo supponit, sicut ‘animal album’, et haec dictio ‘B’ pro nullo supponit, sicut nec ‘homo hinnibilis’. Et utraque dictio habet diffinitionem dicentem quid nominis; nam haec oratio ‘animal album’ est diffinitio hujus dictionis ‘A’ et haec oratio ‘homo hinnibilis’ hujus dictionis ‘B’.” Buridanus, Lectura de Summa Logicae: De Demonstrationibus c.2, n. 4. 25 “Quinta clausula apponit etiam istam aliam proprietatem, scilicet quod termini connotativi, sicut sunt termini accidentales concreti et multi tales abstracti, non habent diffinitiones proprie dictas quidditativas.” ibid. 26 “Unde solus terminus vocalis cui non correspondet conceptus simplex, sed complexus, habet proprie diffinitionem dicentem quid nominis, scilicet praecise significantem quid et quo modo ille terminus significat.” Buridanus, Lectura de Summa Logicae: Sophismata c. 1, conclusio 11a. 27 Cf. Buridanus: Quaestiones in Praedicamenta, q.2: 9-12.

172

quid nominis is precisely to know what the name is related to, as a sign [is related to] what is signified. Such knowledge, however, can be acquired through the accidental properties of what is signified, as well as through its common, or essential properties, or simply by a gesture, or whatever else you like. For example, if we ask a Greek about the meaning of anthropos, if he points to a man, at once we know the quid nominis, and similarly in other cases. But to those asking about the quid rei, it is necessary to indicate what belongs to the thing in virtue of its essence. And this is the essential difference between the quid nominis and the quid rei: namely, that the quid nominis is the relation of the name to what it signifies; but the quid rei is the essence of the thing related or signified. All the other differences that are usually claimed follow from this difference: namely, that the quid nominis is of non-entities, complexes, [defined] by accidental, common, and external [properties]; while the quid rei is of incomplex entities [defined] by their proper, essential [properties]. For a spoken word’s relation can be terminated to non-existents, and it can be clarified by accidental and similar properties, but the thing’s essence can be known only by proper, essential properties of incomplex things.28

As can be seen, Cajetan’s nominal definitions, in contrast to Buridan’s, need not at all be synonymous with their diffinita, whence they do not serve any sort of conceptual analysis that Buridan had in mind with his nominal definitions. For Cajetan a nominal definition can be just any sort of indication of a sample of the supposita of a term, indeed, it may have nothing to do with the signification of its diffinitum. But then, giving a nominal definition of a term need not reveal anything about the simplicity or complexity of the concept it is subordinated to. Thus, for those who hold such a conception of nominal definitions there is nothing in giving a nominal definition that would make them conclude that the concept of the term thus defined must be complex, and that, as a consequence, the term itself should be an accidental predicate of its particulars.29

Conclusion: separability, modes, and the disintegration of scholastic discourse

As we have seen, despite nominalist charges to the contrary, “realist” semantic principles in themselves did not determine the distinctness of the semantic values of abstract and concrete terms, and so by these principles alone “realists” were not committed to the distinctness of the semantic values of abstract terms in the nine accidental categories either. The principal argument for the distinctness of these semantic values, the argument from separability, however, does

28 “Sicut quid rei est quidditas rei, ita quid nominis est quidditas nominis: nomen autem, cum sit nota earum quae sunt obiective in anima passionum (ex primo Perihermeneias), non habet aliam quidditatem nisi hanc, quod est signum alicuius rei intellectae seu cogitatae. Signum autem ut sic, relativum est ad signatum: unde cognoscere quid nominis nihil est aliud, quam cognoscere ad quid tale nomen habet relationem ut signum ad signatum. Talis autem cognitio potest acquiri per accidentalia illius signati, per communia, per essentialia, per nutus, et quibusvis aliis modis. Sicut a Graeco quaerentibus nobis quid nominis anthropos, si digito ostendatur homo iam percipimus quid nominis, et similiter de aliis. Interrogantibus vero quid rei oportet assignare id quod convenit rei significatae in primo modo perseitatis adaequate. Et haec est essentialis differentia inter quid nominis et quid rei, scilicet quod quid nominis est relatio nominis ad signatum; quid rei vero est rei relatae seu significatae essentia. Et ex hac differentia sequuntur omnes aliae quae dici solent: puta quod quid nominis sit non entium, complexorum, per accidentalia, per communia, per extranea; quid rei vero est entium incomplexorum per propria et essentialia. Relatio enim vocis potest terminari ad non entia in rerum natura, et complexa, et declarari per accidentalia et huiusmodi, essentia autem rei non nisi per propria essentialia habetur de entibus incomplexis.” Cajetanus, Super Librum De Ente et Essentia: 290. 29 In fact, Cajetan in his Commentary on the Categories insists that Aristotle’s theory concerns entities as conceived by simple concepts. So in his conception such eliminative analyses of categorial concepts would be excluded from the start. See Cajetanus, In Praedicamenta, Prologus: 1-7.

173

imply such a commitment, if these abstract terms are regarded as “rigid designators”, that is, as essential predicates of their particulars. In fact, the main reason for this type of commitment in the case of “older realists” seems to be precisely their treating (most, not necessarily all) abstract accidental terms as signifying the species and genera of particular accidents in linea recta praedicamentali, and hence as being their essential predicates.30

But then, anyone who wishes to get rid of this type of commitment obviously has to eliminate the “rigidity” of abstract accidental terms in some way or another. A powerful nominalist tactic to this effect was conceptual analysis in terms of nominal definitions. Such analysis eliminates the apparent semantic simplicity of abstract accidental terms, thereby showing that the abstract term in question is not absolute, but connotative, and so it is not essentially true of its particulars. As a result, a nominalist can justifiably claim that such a term may become false of its particulars without the perishing of its particulars. But then in the case of such a term the argument from separability does not work, and so apparently nothing prevents the identification of its semantic values with those of other, absolute terms.

Thus, if we say that the nominal definition of ‘sphericity’ is ‘a quantity whose outermost points are equidistant from a given point’, then it may seem obvious that a quantity which is now a sphericity may remain in existence without remaining a sphericity, on account of simply changing the distance of its outermost points from a given point in space. However, this of course will not cause its perishing, it will only change the way it is arranged in space, its modus. But this modus does not have to be another thing over and above the quantity of a body thus and so arranged in space. Indeed, if it were something really distinct from the quantity thus and so arranged, then it could be separated from this quantity by divine power, which means that there could be a quantity with definite dimensions, but no shape, or, conversely, there could be a shape, but no quantity so-shaped, which is absurd.31 Thus the spherical shape is just a quantity 30 Cf. St. Thomas Aquinas, De Ente et Essentia, c. 7; see also Aegidius Romanus, Theoremata, theorems XIII-XIV, and Cajetanus, In Praedicamenta: 188-92. For the qualification that “most, not necessarily all” accidental terms were so treated, see in particular the alternative opinions Cajetan refers to in this passage, and the way Soto uses the old distinction between relativa secundum esse vs. secundum dici. Indeed, even Aquinas allows the possibility of one and the same entity belonging to different categories: “Sed si actio et passio sunt idem secundum substantiam, videtur quod non sint diversa praedicamenta. Sed sciendum quod praedicamenta diversificantur secundum diversos modos praedicandi. Unde idem, secundum quod diversimode de diversis praedicatur, ad diversa praedicamenta pertinet. Locus enim, secundum quod praedicatur de locante, pertinet ad genus quantitatis. Secundum autem quod praedicatur denominative de locato, constituit praedicamentum ubi. Similiter motus, secundum quod praedicatur de subiecto in quo est, constituit praedicamentum passionis. Secundum autem quod praedicatur de eo a quo est, constituit praedicamentum actionis.” In Meta. lb. 11, lc. 9, n. 2313. See also n. 34. below. 31 Of course, “older realists”, such as Scotus, were also quite aware of the possibility of this type of argumentation (for example, in the case of real relations), which Stephen Menn calls the “voluntaristic argument”. See Menn: Forthcoming. Their solution was to refer to the essential dependency of one thing on another, which, despite their real distinction, would render their separation contradictory, and hence not possible even by divine power. In a different context, Henry of Ghent also talks about the inseparability of real relations from their foundations on account of their essential dependency on them: “De relativis etiam secundum esse dictum erat, quod quaedam erant relativa per se secundum duos modos, scilicet modo numerorum et modo potentiarum. Quae sunt verissima relativa, quia referuntur per essentialem dependentiam fundatam in aliquo quod per se pertinet ad utrumque eorum, in quantum refertur ad reliquum, ita quod singulum sit relativorum per se, et id quod habet in se, per se refertur ad suum correlativum. Ita quod, si desinat referri, hoc est quia deficit per se in ipso illud super quod fundatur ille respectus, et si de novo incipit referri, hoc est quia de novo incipit esse in eo id super quod ille respectus fundatur, sive fuerit ipsa essentia eius super quam fundatur, sive aliquid aliud.” Henricus de Gandavo, Quodl. III, q. 10. But then, it seems that Henry’s more radical solution was eventually to opt for the real identity and merely intentional

174

thus and so arranged, and it ceases to be this quantity when the quantity ceases to be thus and so arranged. So the modus referred to by the term ‘sphericity’ is nothing but the thing referred to by the absolute term ‘quantity’. Still, it is not the same thing as this quantity, absolutely speaking, for the same thing may go on existing without its continuing to be this modus. So the modus cannot be said to be the same thing, absolutely speaking, yet it cannot be said to be a distinct thing absolutely speaking either. So it has to be distinct just somehow [aliqualiter], in a qualified sense, namely, as Suárez would call such a qualified distinction, modally.32

On the basis of this reconstruction I think it is easy to see how naturally the ontology of modi arises in such a framework.33 But, as a matter of fact, not all elements of this framework are necessary for the emergence of modi. As we could see, to invalidate the argument from separability it was enough to regard abstract accidental terms as non-rigid, that is, as non-essential predicates of their particulars. Buridan’s method to show that such a term is non-essential is conceptual analysis in terms of nominal definitions. But this is not the only possible way to arrive at the same conclusion. In fact, the “older realists” already had appropriate tools for treating several abstract accidental terms as non-essential predicates of their particulars, and so, as not necessarily picking out really distinct entities. As Domingo Soto’s work shows, the traditional distinction between relationes secundum esse and relationes secundum dici, combined with identifying relations with their foundations, can achieve exactly the same result in ontology as the different, nominalist tactic.34 But, instead of using Buridan’s eliminative nominal definitions, Soto uses these “old tricks” to eliminate real distinctions between the semantic values of terms belonging to several categories, especially of those belonging to the last six categories, containing the Pseudo-Porretanus’s by then infamous “six principles”. Indeed, quite characteristically, he expresses astonishment at the fact that others think nominal definitions could not be given of absolute terms, a direct consequence of Buridan’s understanding of the function of nominal definitions. As he says:

Furthermore, a nominal definition is what explicates the quiddity of a name, and the quiddity of a name is its signification: that definition, therefore, which explicates what a name signifies, is the nominal definition. And this, as Aristotle says in bk. 1. of his Posterior Analytics, is presupposed from the beginning of each science. For example, if we set out to deal with the science about man, we have to presuppose what the name ‘man’ signifies. And the phrase which explains what it signifies is the nominal definition, even if it would not explain the nature of man at all, as if you were to say, “man signifies the animal than which none is higher”. And so I do not know from where recent authors [iuniores] took it that an absolute name cannot be defined by a nominal

distinction of relations and their foundations. See n. 13 above. 32 Cf. Suarez, Disputaciones, disp. VII, sect. I. 33 For further details concerning Buridan, see Normore 1985. For comparisons with Ockham, see Adams 1985. 34 “Est ergo conclusio quod sex ultima praedicamenta sunt relativa secundum dici, quae non sunt vere relativa, sed res absolutae, quae tamen explicari non possunt nisi per respectum ad res a quibus dependent”. Soto, In Categorias, 237 b. Cf.: “Cum enim substantia omnium sit fundamentum, tria in rebus est considerare, scilicet, aut id quod est substantia, aut accidens quod formaliter est in substantia, aut res quae extrinsecus sunt circa substanciam. Res primi generis sunt in praedicamento substantiae. Res secundi generis sunt in tribus proximis praedicamentis; si enim accidens quod formaliter est in substantia est absolutum, aut est quantitas aut qualitas, et si relativum, est ad aliquid. Res tertii generis pertinent ad sex ultima praedicamenta.” ibid. In fact, since Soto also argues that even relationes secundum esse properly in the category of relation are not really distinct from their fundamenta, precisely because, as we would say, they are not rigid designators of their particulars, his ontology is basically the same as Buridan’s. See ibid.: 213-17.

175

definition, for what is signified by an absolute name, such as ‘elephant’, is just as well explained, as [what is signified by] the name ‘white’.35

Nevertheless, despite this difference with regard to nominal definitions, both Soto and Buridan are able to regard the semantic values of several abstract accidental terms as not really distinct entities from the semantic values of absolute terms on account of the fact that they treat these abstract terms as connotative, although on different grounds.

“Nominalists”, in their theory of signification, make the fundamental distinction between absolute and connotative terms, which establishes only absolute terms as essential predicates of their particulars, or as we would say, rigid designators, and hence the only carriers of ontological commitment to really distinct entities. Combining this semantics with the eliminative nominal definitions of abstract terms, the desired ontological reductions are “automatically” achieved.

Later “realists” remain “realists” insofar as they stick to old semantic principles as well as to old reductionist tactics. But at the same time, apparently prompted by the “nominalist” charges, they are also eager to show that they are no more committed to an unreasonably overpopulated ontology than the nominalists are. A natural consequence of this program was the consistent use of modi — not only in the form of “extra-categorial” modi essendi, as they appeared in the works of “older realists”, but also in the form of “categorial” entities — culminating in Suárez’s systematic treatment of the theory of distinctions. However, this systematic use of modi apparently opened up the conceptual possibility of eliminating all really distinct accidents, “which — as Descartes puts it — would be added to substances (like little souls to their bodies), and could be separated from them by divine power”.36 Indeed, since aside from considerations concerning the theology of the Holy Eucharist, the main reason for assuming the distinct existence of inherent accidents was the mostly implicit assumption that their abstract names were their essential predicates, the elimination of this assumption, both by the nominalists and by the later realists in their own ways, naturally led to the elimination of really distinct accidents in favor of the modes of substances in most categories by both groups of thinkers. But then it should come as no surprise that it was precisely the possibility of this sort of elimination, by whatever conceptual means available, that was to be eagerly seized upon by the representatives of the emerging modern science and philosophy, who in this way could do away with all the “obscure entities” purportedly referred to by the “barbaric” abstract terms of “the schools”.37

35 “Rursus definitio quid nominis est illa quae explicat quidditatem nominis, & quidditas nominis est eius significatio: illa ergo definitio, quae explicat quid nomen significet, est quid nominis. Quae (ut auctor est Aristo.i.post.) praesupponitur in initio cuiusque scientiae: vt aggredienti investigare scientiam de homine, supponendum est quid significat ly, homo. Et illa oratio qua declaratur quid significat, est definitio quid nominis, licet nullam naturam hominis explicaret. Vt si diceres, homo significat illud animal, quo nullum est praestantius. Et ideo nescio unde collegerunt iuniores, quod nomen absolutum non potest definiri definitione quid nominis, postquam ita bene explicatur, quid significat nomen absolutum, elephas, sicut nomen album.” Soto: Summulae, f. 22c. For this usage of iuniores cf. f. 214 i. 36 AT 3: 648, quoted and translated in Menn 1995: 185. 37 Research for this paper and travel to the Copenhagen meeting was partly supported by an NEH grant (“Buridan’s Summulae”, grant No. NEH-RL-22270-95). I owe thanks to Sten Ebbesen and Russell Friedman for helpful comments on an earlier version of this paper.

176

Bibliography

Primary Literature

Aegidius Romanus, Theoremata De Esse et Essentia, ed. E. Hocedez, S.J. Museum Lessianum: Louvain, 1930. Aegidius Romanus, In Primum Librum Sententiarum, Venice, 1521, Minerva, Frankfurt/Main, 1968. Buridan, J. Quaestiones super octo libros Physicorum Ariostotelis, Paris, 1509, reprint Minerva G.M.B.H: Frankfurt

a.M, 1964. Buridan, J. Lectura de Summa Logicae, H. Hubien’s unpublished edition. Buridan, J. Quaestiones in Praedicamenta, ed. Johannes Schneider, Verlag der Bayerischen Akademie der

Wissenschaften: München, 1983. Cajetan, T. de Vio. Scripta Philosophica: Commentaria in Praedicamenta Aristotelis, ed. M. H. Laurent,

Angelicum: Romae, 1939. Cajetan, T. Super Librum De Ente et Essentia Sancti Thomae, in: Opuscula Omnia, Bergomi, Typis Comini

Venturae, 1590. Durandus de Sancto Porciano, In Petri Lombardi Sententias Theologicas Commentarium Libri IIII, Venice, 1571,

reprint Gregg Press Incorporated: Ridgewood, N.J., 1964. Henry of Ghent, Quodlibeta, Paris(?), 1518, reprint Bibliothèque S. J.: Louvain, 1961. Ockham, W. Summa Logicae, St. Bonaventure N.Y., 1974. Pseudo-Richard of Campsall, Logica Campsale Anglicj, valde utilis et realis contra Ocham, in: Synan, E.A. The

Works of Richard Campsall, Vol. 2. Pontifical Institute of Mediaeval Studies: Toronto, 1982. Scotus, Johannes Duns, Joannis Duns Scoti Opera Omnia, t. 7, Quaestiones subtilissimae super libros

Metaphysicorum Aristotelis, Parisiis, apud Ludovicum Vivès, 1893 Soto, D. Summulae, Svmmvlarvm aeditio secunda, Salmanticae: Excudebat Andreas a Portonariis, 1554, reprint,

Georg Olms Verlag: Hildesheim, New York, 1980 Soto, D. In Porphyrii Isagogen, Aristotelis Categorias, librosque de Demonstratione, Commentaria, Venice, ex

officina Dominici Guarraei, et Io. Baptistae, fratrum, 1587, reprint Frankfurt: Minerva, 1967. Suarez, F. Disputaciones Metafisicas, (Latin-Spanish bilingual edition), ed. and tr. Romeo, S. R.-Sánchez. S. C.-

Zanón, A. P. Editorial Gredos: Madrid, 1960 Wyclif, J. Tractatus de Universalibus, ed. Mueller, I. J. Clarendon Press: Oxford, 1985.

Secondary Literature

Adams, Marilyn. 1985. “Things versus ‘Hows’, or Ockham on Predication and Ontology”, in: Bogen, James and McGuire, James E. (eds.). 1985: 175-188.

Bogen, James and McGuire, James E. (eds.). 1985. How Things Are, D. Reidel Publishing Company: Dordrecht-Boston-Lancaster.

Henninger, Mark, SJ. 1989. Relations: Medieval Theories 1250-1325, Clarendon Press: Oxford. Klima, Gyula. 1991. “Latin as a Formal Language: Outlines of a Buridanian Semantics”, CIMAGL, 61: 78-106. Klima, Gyula. 1996. “The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being”,

Medieval Philosophy and Theology 5, pp. 87-141. Klima, Gyula. Forthcoming. “Old Directions in Free Logic: Existence and Reference in Medieval Logic”, in:

Lambert, Karel (ed.). New Directions in Free Logic, Akademia Verlag: Sankt Augustin bei Bonn, forthcoming.

Kripke, Saul. 1980. Naming and Necessity, Harvard University Press: Cambridge, Mass. Maier, Anneliese. 1958. “Bewegung ohne Ursache”; in: Zwischen Philosophie und Mechanik, Edizioni di Storia e

Letteratura: Roma, 1958: 286-339. Menn, Stephen. Forthcoming. “Suárez, Nominalism, and Modes”; in: Hispanic Philosophy in the Age of Discovery,

Catholic University of America Press: Washington, D.C. Menn, Stephen. 1995. “The Greatest Stumbling-Block: Descartes’ Denial of Real Qualities”; in: Ariew, Roger and

Grene, Marjorie (eds.). Descartes and his Contemporaries: Meditations, Objections, and Replies, University of Chicago Press: Chicago, 1995.

Normore, Calvin. 1985. “Buridan’s Ontology”, in: Bogen, James and McGuire, James E. (eds.). 1985: 189-203.

177

‘DEBEO TIBI EQUUM’: A Reconstruction of the Theoretical Framework of Buridan’s Treatment of the Sophisma

1. Introduction

In this paper my main aim is to sketch a formal reconstruction of the theoretical framework of Buridan’s treatment of the famous sophisma. In this way I hope to show not only that Buridan’s treatment is an organic part of his general semantics and philosophy of language and mind,1 but also that the theoretical framework of his treatment, namely his theory of appellation, can be given such a rigorous formulation as to make it a genuine rival to contemporary theories too.2 But in order to have a better understanding of Buridan’s theory, we have first to take a closer look at what paved the way for it, namely Ockham’s theory of connotation.

2. Denomination, Connotation and Ockham’s Innovation in the Theory of Signification

As is well-known, Buridan’s theory of appellation owes much to and has many features in common with Ockham’s theory of connotation. Ockham’s theory, on the other hand, may best be understood starting from considerations connected with the Aristotelian conception of paronymy, i.e., denomination. Indeed, as is pointed out by Marilyn McCord Adams in her recent book on Ockham, one of Ockham’s main semantic innovations was his reversal of the traditional priorities of the significates of denominative terms.3 As she writes:

1 In respectful opposition to the judgment of L. M. de Rijk, who wrote: “As a matter of fact, Buridan himself seems to feel quite uneasy about his ‘debeo tibi equum’ case (see Scott, pp.141-142). It must be considered an intruder, indeed. The last case of appellation (‘equus’ in ‘debeo tibi equum’) is not a correct one, since it is just a case of supposition. Buridan’s extending the ‘venientem’ case to the ‘equum’ case (i.e. the adjective noun cases to the substantive noun cases) seems to be rather abortive.” “Buridan’s Doctrine of Connotation”, in: J. Pinborg (ed.): The Logic of John Buridan, Copenhagen, 1976, p.100. For a more sympathetic evaluation of Buridan’s doctrine see A. Maierù: “Significatio et connotatio chez Buridan”, in the same volume. Cf. also Joël Biard: “Le cheval de Buridan: Logique et philosophie du langage dans l’analyse d’un verbe intentionnel”, in: Olaf Pluta (ed.): Die Philosophie im 14. und 15. Jahrhundert, Bochumer Studien zur Philosophie, Amsterdam, 1989. 2 For a critical assessment of Buridan’s solution by the lights of contemporary logic see P. T. Geach: “A Mediaeval Discussion of Intentionality”, in his Logic Matters, Oxford, 1972. My claim is that if we go further with our reconstructions and take Buridan’s own semantic ideas seriously, then his theory works well, indeed even better than modern theories like those of Quine and Montague, taking refuge in “easier” paraphrases, leaving the semantics of the original problematic sentences simply unexplained. Indeed, Buridan himself considers and rejects as “superficial” such evasive attempts. See his Sophismata, (ed. T. K. Scott) Stuttgart-Bad Cannstatt, 1977, p.87. For more criticism of and references to the modern theories see S. L. Read: “‘I promise a penny that I do not promise’: The Realist/Nominalist Debate over Intensional Propositions in Fourteenth-Century British Logic and its Contemporary Relevance”, in: The Rise of British Logic, ed. P. Osmund Lewry, O.P., Papers in Mediaeval Studies 7 (Toronto: Pontifical Institute of Mediaeval Studies, 1985), pp.335-359, and G. Klima: “Approaching Natural Language via Mediaeval Logic”, in: J. Bernard-J. Kelemen (eds.): Zeichen, Denken, Praxis, Budapest-Vienna, 1990. 3 That this tradition was far from being uniform can be seen from the extensive discussion of the earlier positions concerning denominatives by Sten Ebbesen: “Concrete Accidental Terms: Late Thirteenth-Century Debates About Problems Relating to Such Terms as ‘Album’”, in: N. Kretzmann (ed.): Meaning and Inference in Mediaeval Philosophy, Kluwer Academic Publishers, 1989. See also the related papers by R. Andrews and R. Huelsen in the same volume.

178

Whether or not Ockham’s criteria of primary and secondary signification are adequate, his predecessors and contemporaries thought that Ockham had the priorities exactly reversed. For example, in De Grammatico, Anselm says that the per se signification of ‘literate’ is literacy, while ‘literate’ appellates, or signifies per aliud, one who is literate. Since the name ‘literate’ is imposed on Socrates through something else - viz., literacy - Anselm suggests that literacy is the primary and the one who is literate the secondary signification of ‘literate’ and not vice versa.4 Burleigh takes a similar line in De Puritate Artis Logicae.5

Of course, this reversal of priorities, as Burleigh clearly sees in his criticism of Ockham’s views, is closely connected with Ockham’s reductionist ontological program. For by this reversal Ockham could claim that what a general term primarily signifies is not some common nature that can be found individualised in the singulars falling under this term, but the singulars themselves. So what these terms signify are just their possible supposita, i.e., the things they refer to in several propositions. Accordingly, it comes as no surprise that it is precisely over this point that Burleigh feels especially at odds with Ockham.

However, although I agree with Adams’ characterisation of Ockham’s innovation as a reversal of priorities, I think that anyone reading Burleigh’s argumentation may get completely false impressions as to exactly what was exchanged by Ockham for what. For from Burleigh’s words it is quite clear that what he takes to be the primary significate of a general term is a universal, whatever the ontological status of that universal is, whether it is something outside the soul, or it is a concept existing in the soul.6 So in view of Burleigh’s line of argument, Ockham’s ‘reversal of priorities’ should amount to his claiming that the secondary significates of denominative terms are universals, which he definitely identifies with concepts or intentions of the soul.7 Consequently, he would have to claim that a denominative term, say, ‘white’ primarily signifies its supposita, the things falling under it, that is, white things, and secondarily signifies the concept of whiteness existing in the soul. However it is definitely not this concept that Ockham takes to be the secondary significate of ‘white’ as opposed to its primary significate, namely the white thing.

For he says that ‘a denominative term in the strictest sense is one to which there corresponds an abstract term importing an accident that exists formally inhering in something else’,8 namely in a thing having this accident as its form, like whiteness in a white thing. But of course in the case of a white thing it is not anybody’s concept of whiteness that exists as a form of the white thing, for this concept, being a quality of the mind either distinct from or identical with the mental act itself by which one thinks of a white thing, is an accident formally inhering in one’s mind, and not in the white thing that is thought of.9 What inheres in the white thing is this thing’s whiteness, by which the thing is denominated ‘white’. Consequently, it is this whiteness which, in Ockham’s

4 Cf. sect.3. of D. P. Henry: The Logic of Saint Anselm, Oxford, 1967. (Adams’ note.) 5 M. McCord Adams: William Ockham, Notre Dame, 1987, Vol.I. p.325. The reference to Burleigh is Walter Burleigh: De Puritate Artis Logicae Tractatus Longior with a revised edition of the Tractatus Brevior, (ed. Ph. Boehner) St. Bonaventure, N.Y., 1955, c.3. pp.7-10. 6 “Sed sive illud commune sit res extra animam sive sit conceptus in anima non curo quantum ad praesens; sed tantum sufficit, quod illud quod hoc nomen primo significat est species.” Burley, ibid. p.8. 7 See e.g. cc. 12, 14-15. of Ockham: Summa Logicae, St. Bonaventure N.Y., 1974, (hereafter SL). 8 Ockham: Expositio in Librum Praedicamentorum Aristotelis, Opera Philosophica II, St. Bonaventure, N.Y., 1978. (hereafter OP-II) p.147. 9 Cf. Adams, op.cit., p.74.n.10.

179

view, is the secondary significate of the term ‘white’. But, to be sure, this whiteness is not a universal. For the whiteness of this white thing is as individual as the thing itself, being numerically distinct from other things as well as from the whitenesses of other white things.10

As a matter of fact, if we take a closer look at the theory of signification of the antiquiores defended by Burleigh against Ockham, we find explicit reference to such individualised forms as what are signified by general terms in the individuals. So it seems that also in the framework of the older theory we have to make a distinction between the form signified by a general term immediately, in an absolute sense, the ‘forma in communi’ on the one hand, and the forms signified by the same term ultimately, in the individuals falling under it, on the other.11

So such a term signifies these individualised properties in respect of the individuals in which they inhere, i.e., it signifies such a property for this individual, and another for that one, etc. But then, signification being a semantic relation, we may represent the signification of a general term as a semantic function assigning inherent properties to individuals. A significate of a one-place general term, therefore, can be denoted as the value of the signification function of this general term for an individual, like this:12

SGT(P)(u)=v

(Read: a significate of P in respect of u is v, where u and v range over elements of the universe of discourse W, plus 0, a zero-entity falling outside the universe of discourse. The case v=0, of course, represents the situation when P signifies nothing in respect of u.13)

The usefulness of this move will turn out immediately if we consider how easy it renders the explanation of the nature of Ockham’s innovative ‘reversal of priorities’ between the significata of denominatives.

For with this formulation at hand we can say that both on Ockham’s and on the older view there is something that such a term primarily signifies, whatever it is, that takes the place of v, and there is something that is signified secondarily by the same term, whatever it is, that takes the place of u in the above equation. Ockham’s ‘reversal’, then, simply consists in his claiming that, e.g. in the case of ‘white’, what takes the place of v is the white thing, not the thing’s whiteness, 10 See e.g. Ockham: Expositio in Librum Porphyrii de Praedicabilibus, OP-II, pp.24-25. 11 Such an individualised form is what e.g. St. Thomas Aquinas refers to as “forma in supposito singulari existens per quod individuatur”. ST1.q.13.a.9. This distinction is made also very clearly by St. Thomas in his De Ente et Essentia, c.4. For a reconstruction of this distinction in St. Thomas see “‘Socrates est species’: Logic, Metaphysics and Psychology in St. Thomas Aquinas’ Treatment of a Paralogism”, in my Ars Artium: Essays in Philosophical Semantics, Mediaeval and Modern, Budapest, 1989, also forthcoming in: K. Jacobi (ed.): Acts of the 8th European Symposium of Mediaeval Logic and Semantics. Cf. also William of Sherwood, Introductiones in Logicam, (ed. M. Grabmann), Sitzungsberichte der Bayerischen Akademie der Wissenschaften, 1937, 10, p.78; Peter of Spain: Tractatus, (ed. L.M. de Rijk), Assen, 1972, pp.83-88. See also Ebbesen, op. cit. pp.133-134. 12 Of course, by describing a semantic relation occurring in a mediaeval theory as a semantic function, we do not ascribe anachronistically the possession of the concept of a semantic function to the mediaevals, no more, than one describing someone else’s argumentation as a case of ignoratio elenchi thereby attributes to him possession of the concept of ignoratio elenchi. 13 Notice here that SGT is not a two-place function, with a term in its first, and a thing in its second argument-place, but a one-place function, which for a one-place term in its argument-place yields another one-place function, which for a thing in its argument-place yields an individualised property (the property signified by this term in this thing). In this way, applying the same trick, we can give a uniform treatment of the signification of general terms of any arity, and so, generally speaking, we can denote a significate of an n-place general term like this: SGT(Tn)(u1)...(un). For further technical details and the role of 0 see n.22. below.

180

while what takes the place of u is, conversely, the thing’s whiteness, not the white thing. So we can bring out the contrast between Ockham’s and the older view by the following instances of the above equation:

Older view: SGT(‘album’)(Socrates)=albedo Socratis

Ockham’s view: SGT(‘album’)(albedo Socratis)=Socrates

But Ockham’s innovations, of course, did not concern only denominative terms, a subclass of the class of connotative terms, but connotative terms in general, i.e., terms which have both primary and secondary significata, indeed, in Ockham’s view all terms belonging in categories other than substance and quality.14

For example, the relative term ‘father’ signifies those men who have sons in relation to their sons:15

SGT(‘father’)(son)=father

In contrast to this, on the older view, heavily criticised by Ockham,16 the term ‘father’ was taken to signify a relation, “fatherhood”, holding between two persons, the son and his father:

SGT(‘father’)(son)(father)=fatherhood of father

Indeed, this formulation immediately shows why the question whether the same person’s having several sons multiplies his fatherhoods so naturally arises in this context.17

On the other hand, it also shows why Ockham did not have to worry about such questions: for him what such a term signifies are just the things which it can stand for in propositions, namely its possible supposita, signified in relation to other things, the term’s connotata. This is why he could define personal supposition in terms of signification, thereby incurring the charges raised by Burleigh of challenging the opinion of the antiquiores.18

Clinging much less to older views, however, Buridan willingly adopted this conception of Ockham’s in his own semantic theory.

3. Buridan’s Theory of Appellation

Indeed, in line with T. K. Scott’s characterisation of Buridan’s relation to Ockham, according to which “if Ockham initiated a new way of doing philosophy, Buridan is already a man of the new way”,19 Buridan defines the personal supposita of a term as its significata as a matter of course.20 14 See e.g. SL, pp.37-38. 15 Cf. e.g. Guillelmi de Ockham: Quodlibeta Septem, ed. J.C.Wey, Opera Theologica, vol.IX., St. Bonaventure N.Y., 1980. V.25, VI.20-25. 16 Cf. e.g. SL, cc.50-54. 17 A theologically more intriguing question of this kind was whether Christ’s being the son of both the Holy Mother and the Heavenly Father multiplies his filiations. See e.g. St. Thomas Aquinas, ST III, q.35.a.5. 18 Cf. SL, p.195-196. 19 T. K. Scott: John Buridan, Sophisms on Meaning and Truth, New York, 1966. n.1. p.13, quoted at greater length also by J. Pinborg in discussing in more detail this relationship in his “John Buridan, The Summulae, Tractatus I De Introductionibus”, in: J. Pinborg: Mediaeval Semantics, Variorum Reprints, London, 1984. 20 “Et vocatur suppositio personalis quando subiectum vel praedicatum propositionis supponit pro suis ultimatis significatis vel pro suo ultimato significato.” Buridan: Tractatus de Suppositionibus, (ed. M. E. Reina), Rivista Critica di Storia della Filosofia, 1957, pp.175-208, pp.323-352. p.201.

181

He finds no difficulty either in defining appellative terms as those that connote other things beyond the ones which they are apt to supposit for:

... omnis terminus connotans aliud ab eo pro quo supponit dicimus quod est appellativus et appellat illud quod connotat per modum adiacentis ei pro quo supponit, ut ‘album’ appellat albedinem tanquam adiacentem ei pro quo supponit21

Buridan explains the notion of ‘adjacency’ used here in the following manner in his Sophismata: ... terminus appellat illud quod appellat per modum adiacentis aliquo modo vel per modum non adiacentis ad illud pro quo supponit vel est natus supponere. Dico per modum adiacentis, si appellat illud positive, et dico per modum non adiacentis, si appellat illud privative, ut ‘album’ appellat albedinem positive, tanquam inhaerentem ei quod est album ... Sed ‘caecum’ supponens pro oculo appellat visum privative per modum non adiacentis illo oculo.22

This adjacency or non-adjacency of the appellata of a term has a prominent role in determining the supposition of appellative terms and, consequently, in determining the truth-conditions of categorical sentences formed with them. For an appellative term supposits only for those of its significata in a proposition to which its appellata are adjacent (or non-adjacent, as the meaning of the term requires) relative to the time connoted by the copula of the proposition.23 But since according to Buridan an indefinite affirmative categorical is true only if its terms supposit for the same thing or same things, the sentence: ‘a man is white’ is true, only if both ‘man’ and ‘white’ supposit in it for the same thing or things.24 However, a thing can be a suppositum of the term ‘white’ in this proposition only if it actually possesses whiteness at the time connoted by the copula, namely the present time of the formation of the proposition. On the other hand, in the sentence: ‘a man will be white’ the same term supposits for only those things that will possess whiteness in some future time relative to the present time of the formation of the proposition.

21 Ibid. p.343. Although as far as I know he never says so explicitly, it seems that for Buridan being appellative or non-appellative are properties of terms independent of context, but appellation is a property of terms only in propositions. On the other hand, we find explicit statement of this in the work of his pupil, Marsilius of Inghen. See Marsilius of Inghen: Treatises on the Properties of Terms, (ed. E.P. Bos), D. Reidel Publishing Company, 1983. pp.128-136. So we may say that while supposition is reference in a proposition to a term’s signifcata, appellation is (oblique) reference in a proposition to a term’s connotata. 22 Buridan: Sophismata, (ed. T.K. Scott) Stuttgart-Bad Cannstatt, 1977. p.61. This means that if an appellative term connotes something positively, say as ‘videns’ connotes sight, then it signifies what it is apt to supposit for in relation to its connotatum only if the connotatum belongs to its significatum, while an appellative term connoting something privatively, as ‘caecum’ connotes sight, conversely, signifies what it is apt to supposit for only if its connotatum does not belong to its significatum. Otherwise these terms signify nothing in relation to these connotata. Making use of our previously introduced notation we may reconstruct this difference between positive and negative adjacence in the following way: SGT(‘videns’)(u)∈W, if u∈W, and SGT(‘videns’)(u)=0, if u=0, while SGT(‘caecum’)(u)=0 if u∈W, and SGT(‘caecum’)(u)∈W, if u=0. Accordingly, a suppositum of the term ‘videns’ in a proposition the copula of which connotes some time t is definable as: SUP(‘videns’)(t)=SGT(‘videns’)(SUP(‘visus’)(t)), where, ‘visus’ being an absolute term, SUP(‘visus’)(t)=SGT(‘visus’), if SGT(‘visus’) is actual at t, otherwise SUP(‘visus’)(t)=0. (Here, of course, SGT(‘visus’) is an element of a subset of the universe of discourse determined by the natural signification of the concept, or ratio signified immediately by this term, namely the set of individual sights that there were, are, will be or can be.) That is to say, the term ‘videns’ will supposit for someone in this proposition only if the term ‘visus’ may successfully refer to his sight, i.e., if he actually has sight (at t), while the term ‘caecus’, in accordance with its negative connotation, would refer to this person only if he did not have sight. 23 Cf. Tractatus de Suppositionibus, pp.184-185, pp.347-351. 24 See Sophismata, p.43. Duodecima conclusio

182

As Buridan notes, there is a substantial difference between the appellation of the subject and of the predicate terms of such a proposition. For although the predicate term appellates what it connotes strictly for the time connoted by the verb, or even determined more by some explicit temporal adverb, the subject term always appellates “under disjunction to the present”:

Nam praedicatum appellat rem suam pro tempore verbi solum, quantumcumque tempus verbi fuerit restrictum. Et si pro isto tempore non correspondet modus adiacentiae rei appellatae ei pro quo terminus est natus supponere, non supponit pro illo, quamvis bene correspondeat modus adiacentiae pro tempore praesenti. Verbi gratia si dico ‘Socrates heri fuit albus’, iste terminus ‘albus’ in ista propositione non supponit pro Sorte nisi heri albedo ei adiacebat, quamvis etiam modo ei adiaceat et quamvis ante ei adiaceret. Et sic propositio esset falsa. Sed subiectum appellat rem suam indifferenter modo disiunctivo pro tempore praesenti et pro tempore verbi, sicut etiam est de suppositione. Unde haec est vera ‘Album fuit heri nigrum’, si ei quod heri fuit nigrum nunc adiaceat albedo, licet heri non adiacebat sibi. Propter quod exponitur ‘Album fuit heri nigrum’, idest ‘Quod est album vel fuit heri album fuit heri nigrum’.25

As Buridan adds later, this difference between the mode of appellation of the subject and predicate does not mean that only one of them, namely the predicate would have appellation in such a proposition. On the contrary, both terms have appellation, provided they are both appellative, but in a different manner: the subject under disjunction to the present, while the predicate only for the time of the verb.

So appellative terms always appellate the things in a proposition that they connote as being determinant of the things they refer to, and consequently whether they refer to this thing or that thing in the given proposition depends on whether what they appellate as the determination of the thing in question does (or does not, as the meaning of the term requires) actually belong (in the appropriate manner) to the thing relative to the time connoted by the verb of the proposition.

The case is different, however, with absolute terms, which do not connote anything as a determination of the things they signify, but simply supposit for those things which they signify, like substance-terms or abstract terms from the category of quality.26 Since the type of appellation discussed above is a kind of secondary reference in a proposition to what a term connotes also outside a proposition, this kind of appellation can belong only to appellative terms, which do have connotation, or secondary signification.27

On the other hand, also absolute terms can have appellation, i.e., oblique reference to what is not supposited for in a proposition. Obviously, this is the kind of reference they have as oblique parts of complex terms.28 But they also can have a peculiar type of appellation in the special context created by intentional verbs like the one in our problem-sentence, the kind of appellation that Buridan and his followers called appellatio rationis.

25 Sophismata, pp.62-63. 26 See Tractatus de Suppositionibus, p.184. 27 This is the type of appellation that Marsilius de Inghen calls appellatio formalis significati, which he sharply distinguishes from the other type of appellation, the appellatio rationis. From this doctrinal point of view it is quite evident that in the otherwise excellent edition (see n.21. above) of Marsilius’ text all occurrences of the phrase ‘rationem suam’ on pp.150-152. should read as ‘rem suam’, the standard traditional expression for what he calls ‘significatum formale’. 28 “terminus obliquus substantivus appellat illud pro quo rectus suus supponeret per modum adjacentis ei pro quo rectus regens ipsum supponit.” Tractatus de Suppositionibus, p.347.

183

4. A Reconstruction of Buridan’s Treatment and his Theory of Appellatio Rationis

Nevertheless, despite its specific character, Buridan’s appellatio rationis is justly called appellation, insofar as it is a sort of oblique reference to something in a proposition which is not supposited for in that proposition. However, this is not something connoted by a connotative term, but something signified immediately by every vocal term, namely the concept to which this vocal term is subordinated, due to which it is a meaningful term at all.29 For according to Buridan a term, or in general, any meaningful vocal expression of some language has meaning only insofar as it is associated to some cognitive act of a human mind, a conceptus, intentio, or ratio, whether it is simple or complex, by which we conceive things in some way, and it is only through this association, or subordination as Ockham and Buridan call it, that vocal terms can signify the things we conceive by the concepts to which they are subordinated.

Now Buridan’s treatment of our sophisma rests on his claim that intentional verbs and other terms deriving from them which signify some mental act force the terms following them to appellate their rationes according to which they were imposed to signify the things conceived by these rationes.

He also gives a short explanation for this peculiarity of these verbs in contradistinction to other, extensional verbs: namely that the terms constructed with these verbs have to appellate their concepts because “we think of things by these concepts, but it is not by these concepts that fire heats water or a stone hits the ground”.30 So since a mental act concerns its object only through the concept by which the thing is conceived (since unless it were conceived by some concept it could not be an object of a mental act altogether), it is no wonder that a verb signifying such a mental act makes the term signifying the object of this act appellate the concept by which the term signifies the object; and it is equally no wonder that other verbs which do not signify such mental acts do not force such an appellation.31

So Buridan’s theory can already be said to have scored a point over several others in that it is able to give a plausible philosophical explanation for the peculiar behaviour of these verbs.

29 On the other hand, we may say that the only difference between a case of appellatio rationis and the appellatio an oblique term has in a complex term is that what the oblique term appellates is what would be its personal suppositum, while what a term having appellatio rationis appellates is what would be its material (or simple, according to earlier terminology) suppositum, if it itself were a whole term of a proposition. (Cf. previous note.) Hence Buridan’s comparison of the latter case (without, however, subsuming it!) to material supposition: “isti accusativi quodammodo videntur participare suppositionem materialem, quia appellant conceptus suos, licet non supponant pro eis.” Tractatus de Suppositionibus, p.335. Cf. n.1. above. 30 Tractatus de Suppositionibus, p.335. 31 Cf. “...sciendum est quod ista verba ‘intelligo’ cognosco’, ‘scio’ et huiusmodi de quibus post dicemus, et participia et nomina inde descendentia, ut ‘intelligens’, ‘cognoscens’, ‘intellectio’, ‘cognitio’, etc., faciunt in terminis cum quibus construuntur quosdam modos speciales appellationum. ... Postea notandum est quod nomina imponimus ad significandum mediantibus rationibus quibus res intelligimus. Ideo etiam istud verbum ‘significo’ tales facit appellationes, sicut ‘intelligo’ vel ‘cognosco’, et ita etiam hoc verbum ‘apparet’, et haec verba ‘scio’, ‘opinor’, ‘puto’, ‘credo’, etc. Praeterea etiam quia appetitus nostri fiunt in nobis mediante cognitione, ideo sequitur quod similes appellationes faciunt nobis ista verba, scilicet ‘volo’, ‘appeto’, et ‘desidero’. Et adhuc etiam quia sub aliquibus conceptibus facimus nostras promissiones et obligationes, sequitur quod etiam ista verba ‘debeo’, ‘promitto’, ‘obligo’, etc. et alii termini ex ipsis descendentes faciant huiusmodi appellationes.” Sophismata, pp.73-74.

184

However, the further question is whether Buridan’s theory also works as a logical theory, in that it is able to justify the intuitively acceptable, and invalidate the unacceptable logical relations of our problem-sentence to others, and/or to provide compelling arguments to accept possible unintuitive results.

But in order to know this first we have to see how this kind of appellation affects the truth-conditions of sentences in which it occurs. Buridan writes about this as follows:

Nam quia eandem rem possum cognoscere secundum multas diversas rationes, et isti rei secundum diversas rationes diversa nomina imponere ad significandum eam, ideo talia verba faciunt terminos cum quibus construuntur appellare rationes secundum quas imposita sunt nomina ad significandum, et non solum res cognitas ad extra, sicut faciunt alia verba. Aliter tamen a parte ante et a parte post. Nam a parte post, illi termini appellant determinate suas rationes proprias. Sed a parte ante appellant eas indifferenter sub disiunctione ad alias rationes quibus res significatae possunt significari et intelligi. Propter quod iste propositio non est vera ‘Cognosco venientem’, proprie loquendo, nisi cognoscam eam secundum eam rationem, secundum quam dicitur veniens, licet cognoscerem bene secundum alias rationes. Et sic non sequitur, cognosco Sortem, et sit veniens; ergo cognosco venientem. Quia licet cognoscam illum secundum illam rationem secundum quam dicitur Sortes, non tamen cognosco illum secundum illam rationem secundum quam dicitur veniens. Sed a parte subiecti, bene sequitur, Sortem cognosco, et Sortes est veniens; ergo venientem cognosco. ... Non ergo sequitur, venientem cognosco, ergo cognosco venientem. Immo est possibile quod ignoro venientem. Sed bene sequitur, cognosco venientem, ergo venientem cognosco; sicut in aliis appellationibus non sequebatur, album erit, ergo erit album, sed bene econverso, erit album, ergo album erit.32

Now since according to Buridan the “canonical form” of such sentences as ‘Cognosco venientem’ or ‘Debeo tibi equum’ is obtained by analysing their verbs into copula and participle, and the result is true if the terms so obtained supposit for the same, the question of the truth-conditions of such sentences reduces to the question whether the terms ‘cognoscens venientem’ or ‘debens tibi equum’ supposit for me in the sentences ‘Ego sum cognoscens venientem’ or ‘Ego sum debens tibi equum’. But in these terms the intentional participle makes the oblique term following it appellate its own ratio, whether this term is appellative or not, and so these complex terms can supposit for me only if their participles signify me in relation to this ratio and, of course, their other connotata required by their signification.

So if we return to the notation previously introduced for representing the significata of connotative terms we can spell this out quite simply in the following manner:

SUP(‘cognoscens venientem’)(t) =

= SGT(‘cognoscens’)(RAT(‘veniens’))(SUP(‘veniens’)(t))(t)

SUP(‘debens tibi equum’)(t) =

= SGT(‘debens’)(SUP(‘te’))(RAT(‘equus’))(SUP(‘equus’)(t’))(t)

where, taking into account the ampliative force of ‘debens’, t≤t’ (but henceforth I disregard from this complication), RAT is a function assigning to terms the concepts they are subordinated to and SUP is a function assigning to terms their supposita.33

32 Sophismata, pp.73-74. 33 Cf. n.22. above. To be sure, in view of equivocations there is no such simple functional connection between words and their rationes, i.e., concepts to which they are subordinated. But by adding a further argument-place for several impositions, associating the same words with possibly different rationes like this: RAT(T)(i), where i ranges over

185

Now the question of the truth of ‘Cognosco venientem’ and ‘Debeo tibi equum’, as I said, boils down to the question whether I am one of the above defined supposita of the terms concerned. But as we can see these supposita are functionally dependent on the rationes appellatae of the names following these verbs. So changing the name may change the ratio appellata, and this may change the supposita of the terms in question, which changes the truth-conditions of the corresponding propositions. So this is why the passage from ‘Cognosco Socratem’ to ‘Cognosco venientem’ does not preserve truth-value despite the identity of the supposita of ‘Socrates’ and ‘veniens’, and so the inference from the first to the second is not valid.

On the other hand, since when the noun in question precedes the verb, or the participle deriving from the verb, it does not determinately appellate its own ratio, but appellates it under disjunction to other rationes, we can determine the supposita of the corresponding complex terms in question in the following manner:

SUP(‘venientem cognoscens’)(t) =

= SGT(‘cognoscens’)(RAT(X))(SUP(‘veniens’)(t))(t)

SUP(‘equum tibi debens’)(t) =

= SGT(‘debens’)(SUP(‘te’))(RAT(X))(SUP(‘equus’)(t))(t)

where X is some expression that can take the place of ‘venientem’ or ‘equum’ in the above complex terms.34

different acts of imposition, we may approximate better the real situation. Furthermore, since these rationes are individualised qualities of individual minds, we might even add another argument-place reserved for individual minds like this: RAT(T)(i)(m), where m ranges over human minds. Nevertheless, as from our present point of view both equivocations and individual conceptual differences may be neglected, to simplify the formulation I omit these argument-places. But we should keep well in mind that these have theoretical significance in Buridan’s discussions of significatio ad placitum, as e.g. in cc.1. and 6. of his Sophismata, or qq.2. and 3. of his Questiones Longae super Librum Perihermeneias, (ed. R. van der Lecq), Utrecht, 1983. On the other hand, even this simplified formulation well represents the case when two expressions are synonymous: in this case RAT has the same value for both expressions. This immediately shows why synonyms are interchangeable salva veritate even in such contexts. 34 Note that here we quantify over expressions, not the rationes themselves. So in this context we need not worry much about the identity-criteria of rationes. The theory only says that if two expressions have the same ratio, then their interchange in intentional contexts a parte post does not affect the truth of the sentence in which they occur, but the same interchange involving non-synonymous expressions does, while the case is different a parte ante, where the interchange of any terms suppositing for the same thing or things leaves the truth-value of the sentence unaltered. (Cf. note above.) As P.T. Geach in his paper mentioned above correctly points out, for quantifying over rationes we would need some criterion of identity for them. However, it is simply not true that “we have not even one example <from Buridan> of the same ratio differently expressed, from which we might divine a criterion of identity.” (op. cit. pp.132-133.) Of course, all synonyms are different expressions of the same ratio, and, in particular, all definitiones exprimentes quid nominis, are different expressions of the ratio expressed by the nouns they define, as Buridan carefully explains in several places. (E.g. Sophismata, pp.24-35.) So from these explanations we may “divine” the following criterion of identity: different expressions express, or are subordinated to, the same ratio if and only if the sum total of their significata and connotata, in the case of connotative terms, is the same, whether these are things outside the mind or concepts existing in the mind (e.g. in the case of complex expressions containing syncategoremata). So the identity-conditions of rationes are definable in terms of the sets of significata and connotata of the terms subordinated to them. But sets are quite well-behaved entities with respect to identity even on modern standards. So along these lines, in the framework of a thoroughgoing model-theoretical reconstruction of Buridanian semantics we may eventually appease our modern qualms concerning quantification over rationes.

186

This formulation immediately justifies Buridan’s claim that with this type of appellation ‘Cognosco venientem’ implies ‘Venientem cognosco’ and ‘Debeo tibi equum’ implies ‘Equum tibi debeo’, but not conversely. For if I am one among the supposita of ‘cognoscens venientem’ with the determinate appellation of the concept of ‘veniens’, then I also have to be among the supposita of ‘venientem cognoscens’ with the appellation of some concept, one among these possible appellata being the concept of ‘veniens’, but not conversely, just as if I see Socrates, I see someone, but if I see someone, it does not follow that I see Socrates.

There is, however, a further, at the first sight rather unintuitive claim made by Buridan with respect to the implications of ‘Debeo tibi equum’. For he does not only claim that ‘Debeo tibi equum’ implies ‘Equum tibi debeo’, but even further that ‘Equum tibi debeo’ implies ‘Omnem equum tibi debeo’, on the basis that my obligation concerns particular horses through the general concept of ‘horse’, which, in turn, concerns equally every horse, whence my obligation, through the general concept of ‘horse’, concerns equally every horse. On the other hand, according to Buridan, this does not mean that I owe you every horse, for you can claim from me only what is signified by the term under which the obligation was made, but I did not oblige myself to give you every horse, only a horse. (In ‘I owe you every horse’ the ratio appellata would be that corresponding to ‘every horse’, not only that corresponding to ‘horse’. Hence, since change of appellation changes truth-conditions, the passage from ‘I owe you a horse’ to ‘I owe you every horse’ does not preserve truth.)

Without going into detailed discussion of the matter, I only wish to show here very briefly what kind of further semantic considerations may prompt such a conclusion.

But to this end, first we have to see in general what effect the addition of a distributive sign to an oblique term in a complex term may have on the supposition of the complex term. For example, it is clear that the term ‘videns asinum’ supposits for me if I actually see an ass, but the term ‘videns omnem asinum’ supposits for me only if I see every ass, i.e., every suppositum of the term ‘asinus’. But this means that I am a suppositum of the term ‘videns omnem asinum’, only if for any choice of a suppositum of ‘asinus’ the term ‘videns’ signifies me in relation to that suppositum, that is, in general, a suppositum of this complex term is a thing that is signified by ‘videns’ for any choice of a suppositum of ‘asinus’.

This may be formulated as follows:

SUP(‘videns omnem asinum’)(t) =

= SGT(‘videns’)(SUP’(‘asinus’)(t))(t), for any SUP’,

if there is a v∈W such that SGT(‘videns’)(u)(t)=v for any u, otherwise

SUP(‘videns omnem asinum’)(t)=0

where u∈{w: for some SUP’, w=SUP’(‘asinus’)(t)}, i.e., u is a suppositum of ‘asinus’ at time t, and, adding the clause familiar from quantification theory, SUP’ is the same as SUP except for the value assigned by it to ‘asinus’, which makes it clear that SUP functions here as an ordinary value-assignment, and ‘asinus’ and the other general terms as restricted variables in many-sorted quantification.35

35 Concerning this topic see my earlier reconstructions in my Ars Artium (see n.11. above). See also Sophismata pp.191-196, 347-348. Concerning SUP(‘asinus’)(t) see the similar case of SUP(‘visus’)(t) in n.22. above.

187

But regarding Buridan’s claim concerning ‘Omnem equum tibi debeo’ this amounts to saying that if this sentence is true, then for any choice of an individual suppositum of the term ‘equus’, the term ‘debens’ signifies me with respect to that horse considered under any concept whatever.

Making use of our notation:

SUP(‘equum tibi debens’)(t)=SUP(‘omnem equum tibi debens’)(t)=

=SGT(‘debens’)(SUP(‘te’))(RAT(X))(SUP’(‘equus’)(t))(t), for any SUP’

But this assumption is indeed quite plausible: after all it is something like this that we mean by owing just any horse in general, no matter which one in particular. But this plausible semantic assumption does have as its consequence the above-mentioned unintuitively sounding implication. However, despite its rather unintuitive sounding, on seeing that it is a consequence of a plausible semantic assumption, one may eventually accept the conclusion that ‘I owe you a horse’ implies ‘Every horse I owe you’, without, however, implying ‘I owe you every horse’, of which Buridan’s arguments also try to convince us.

5. conclusion

In conclusion I wish to give only a brief illustration of the explanatory power of Buridan’s theory and remark on its consistency with his more general philosophical ideas in the light of the above reconstruction.

In particular, I would like to show that with a minimal modification of its starting assumptions Buridan’s theory is also able to account for the intuitions backing Ockham’s treatment of sentences with intentional verbs.36 To see this, we only have to notice that Ockham’s contrary claim (namely, that the proposition ‘Equum tibi promitto’ is not true in the posited case because the term ‘equum’, being preposited to the verb, supposits in it determinately) may be obtained in Buridan’s theory from the assumption that if the term is preposited to (the participle derived from) the intentional verb, then, instead of having a disjunctive appellation, it does not have appellatio rationis at all, but simply stands for some of its supposita. With this assumption, contrary to his own claim, Buridan’s theory predicts that ‘Promitto tibi equum’ does not imply ‘Equum tibi promitto’.

For with this assumption it may well be the case that although in the complex term ‘promittens tibi equum’ the participle ‘promittens’ signifies me in relation to the ratio of ‘equus’, and so the complex term supposits for me with the appellation of this ratio in ‘Ego sum promittens tibi equum’, in which case this sentence is true, still, ‘equum tibi promittens’ does not supposit for me without any appellation of the ratio of ‘equus’, or of any other term in ‘Ego sum equum tibi promittens’, in which case this sentence is false. For if we determine the supposita of ‘equum tibi promittens’ in the following manner:

SUP(‘equum tibi promittens’)(t)=

=SGT(‘promittens’)(SUP(‘te’))(SUP(‘equus’)(t))(t),

36 For Ockham’s treatment of the similar case of ‘Promitto tibi equum’ see: SL P.I.c.72., pp.219-221. cf. P.II.c.7. Cf. also Guillelmi de Ockham Scriptum in librum primum Sententiarum Ordinatio, St. Bonaventure N.Y., 1967-1979; d.2.q.4., pp.145-148.

188

then I may be one among its supposita only if I am signified by ‘promittens’ in relation to this horse, or in relation to that horse, and so on, that is, if I promise you some horse determinately, which is not the case when only ‘Promitto tibi equum’ is true.

So Buridan’s theory is able to account for the intuitions of those who feel uneasy about his actual solution: these intuitions dictate that we take ‘equus’ as standing determinately and without any appellatio rationis in ‘Equus tibi promittitur’, in which sense this proposition is, of course, false, if no determinate horse was promised to you, but only a horse in general. So those who share their intuitions with Ockham and claim that no horse is promised to you in such a situation may respect at least Buridan’s theory, even if they dislike his actual solution, insofar as it is this theory that may account even for their intuitions.

On the other hand, in this case it is their task to account for the other, epistemologically important cases of ‘Cognosco triangulum’ and ‘Triangulum cognosco’ where it would indeed be valde durum, to use Buridan’s phrase, to accept ‘Nullum triangulum cognosco’. As we know, Buridan’s solution was also motivated by these epistemological considerations.37 We also know that his rationes play a prominent role in his general theory of significatio ad placitum. Finally, we know that since these rationes are individualised qualities of individual human minds, they fit in nicely with Buridan’s nominalistic metaphysics and philosophy of mind. So whatever particular misgivings we may have concerning his actual treatment of the case of ‘Debeo tibi equum’, we cannot but respect the consistency of Buridan’s theory with his more general philosophical considerations.

37 See Sophismata, p.86, pp.76-78, and Tractatus de Suppositionibus, pp.333-335.

189

Thomistic Semantics and Metaphysics

190

The Semantic Principles Underlying Saint Thomas Aquinas's Metaphysics of Being

Introduction: Semantics and Metaphysics

As I hope the title clearly indicates, this paper is not intended to contribute its ounces to the tons of literature on Aquinas's metaphysics of being. On the contrary, the primary motivation for this paper is the perhaps deplorable, but certainly not negligible fact that the very form of discourse within which the substantive claims of that literature as well as Aquinas's own claims are formulated is radically different from that of contemporary philosophical discussions.1 Faced with this different form of discourse, modern readers are either willing/able to "join in", and then they may become "players" of the relevant "language game", or they are unwilling/unable to "join in", and then they will be left ultimately "intellectually intact" by these claims. In either case, without careful reflection on the general principles governing "the game", this willingness/ability on the part of the modern reader will be determined mostly by vague intuitions and more or less articulated sympathies or antipathies, rather than by serious philosophical considerations.

As we know, metaphysics studies the first principles of all knowledge.2 But even the metaphysical investigation of first principles presupposes that we understand what is meant by these principles and their terms, that is to say, even metaphysical principles presuppose certain semantic principles. As Aristotle advises us in the fourth book of the Metaphysics concerning disputations about first principles, in all such disputations the ultimate appeal should be to what both ourselves and our opponents mean, indeed, to maintain mutual understanding in the framework of rational discourse, should mean by our phrases.3 On the other hand, such an 1 For pregnant expressions of the keen awareness of isolation in many contemporary Thomists see the numerous essays devoted to this problem in Hudson, D. W.-Moran, D. W. (eds.): The Future of Thomism, American Maritain Association Publications, University of Notre Dame Press, Notre Dame IN, 1992. On the other hand, of course, one cannot ignore the tremendous amount of good work done by philosophers, apparently also of some analytic background (e.g., Bochenski, Henry, Geach, Kenny, Kretzmann, McInerny, Stump, Veatch, Weidemann, etc., just to name a few, without aiming at completeness), to overcome this "language barrier". However, as far as I know, no comprehensive attempt has been made so far to state those formal semantic principles which, as such, regardless of the metaphysical contents of their particular instances, by reason of their formality constitute the very form of discourse presupposed in Aquinas's (and I would add, also his contemporaries') metaphysical discussions. I hope the statement and discussion of these principles below will also shed some more light on exactly how I conceive of the separation of metaphysical from formal semantic principles. 2 For this point, which of course does not define the proper subject matter of metaphysics, but is a consequence of metaphysics' being the study of being qua being, see in Meta lb. 4, lc. 5. (References to Aristotle are given by referring to Aquinas' commentaries. For St. Thomas's works I used the supplemental volumes to Father R. Busa's Index Thomisticus, S. Thomae Aquinatis Opera Omnia, Frommann-Holzboog: Stuttgart-Bad Canstatt, 1980.) 3 Cf. in Meta lb. 4, lc. 7. It is important to realize in this connection that the main thrust of Aristotle's arguments is that those who deny the first principle (i.e., the principle of non-contradiction) cannot possibly mean what they say. It is also important in this regard to consider what Aristotle and St. Thomas (in his commentary on the Posterior Analytics and in several other places) say about the order of questions to be answered by a demonstrative science. The question of what a thing is [quid est?] is preceded by the question of whether the thing is [an est?], but even this question presupposes that we know what is meant by the name of the thing in question [quid significatur per nomen]. Cf.: "... antequam sciatur de aliquo an sit, non potest sciri proprie de eo quid est: non entium enim non sunt definitiones. Unde quaestio, an est, praecedit quaestionem, quid est. Sed non potest ostendi de aliquo an sit, nisi

191

appeal, especially nowadays, after the "linguistic turn" in philosophy, when just everyone seems to have their own "philosophy of language" and "theory of meaning and/or reference", is far from being compelling or even unambiguous.4 The primary aim of this paper, therefore, is to spell out with clarity and precision the underlying semantic principles of the very form of discourse presupposed by Aquinas's substantive metaphysical claims concerning being, clearly distinguishing the former from the latter, so that the contemporary reader's willingness/ability to participate in the "language game" of competently evaluating the substantive metaphysical arguments for, or against, the relevant metaphysical claims will not depend eventually on unexamined intuitions, but rather on a careful consideration of these underlying principles themselves.

To be sure, in this paper I cannot undertake a presentation of these underlying semantic principles as ones that we absolutely have to accept; I will only try to articulate as clearly as possible what it is that we have to accept for a competent evaluation of the substantive metaphysical arguments. On the other hand, of course, even within the framework of this more modest enterprise I will have to show that these semantic principles are at least acceptable, that is to say, that they are consistent in themselves and do not commit anyone willing to maintain them to some manifest falsity or even nonsense.

In the next section, therefore, I will begin the discussion with the introduction of the basic concepts we need for the clear formulation of the relevant semantic principles. I start with Aquinas's concept of meaning, or—using a transliteration of medieval terminology to distinguish it from contemporary conceptions—signification. However, as we shall see, we run into difficulties already at the very beginning, given the fact that Aquinas's Aristotelian concept of signification apparently commits him to some "mysterious", nonexistent objects of signification. So in section 3. I point out how Aquinas's distinctions between different senses5 of 'being' might be used to eliminate our misgivings concerning such objects. However, this solution will leave us with a set of further, rather disturbing questions concerning the conceptual apparatus utilized in this discussion itself. So in section 4. I provide a systematic account of this conceptual apparatus as it functions in Aquinas's theory of signification and predication, addressing various ontological and epistemological concerns contemporary philosophers may have regarding these semantic theories. Having thus placed Aquinas's notions of signification and existence into their proper theoretical context, in section 5. I finish the introduction of the basic conceptual apparatus by a brief discussion of Aquinas's account of the relationship between the signification and reference, or—again, using the transliteration of medieval terminology—supposition of concrete as well as of abstract common terms.6 Section 6. will present the formulation of the relevant

prius intelligatur quid significatur per nomen. Propter quod etiam Philosophus in iv Metaphysicae, in disputatione contra negantes principia docet incipere a significatione nominum." in PA lb. 1, lc. 2, n. 5. For the significance of this order in the proofs for God's existence see: ST1, q. 2, a. 2; ScG lb. 1, c. 12. 4 Cf. "the double indexical definition of meaning" provided by William Lycan: "meaning=df.whatever aspect of linguistic activity happens to interest me now", quoted by Devitt, M.: "The Methodology of Naturalistic Semantics", The Journal of Philosophy, 91(1994), p. 545-572, p. 548. 5 Fregean connotations aside, throughout this paper by a sense of an analogical term I simply mean one of its several, but related significations. The clarification of the notion of "signification", on the other hand, is going to be one of the tasks of the subsequent discussion. 6 Thus, in this paper I am not going to deal per se with the medieval theory of supposition in general, or Aquinas's version of it particular. I am going to touch on Aquinas's (and his contemporaries') conception of the relationship between signification and supposition only to the extent we shall need an account of this relationship in

192

semantic principles themselves, providing a brief comment on each. On this basis in section 7. I will show how we can interpret in this framework all predications about substance as predications of some act of being either absolutely (simpliciter) or with qualification (secundum quid). Finally, in section 8. I will argue that in this theoretical setting the metaphysical idea of an objective hierarchy of being not only makes good sense, but is even quite plausible, even if we may not be able to determine off-hand the exact place of any given entity in this overall hierarchy.

Signification and Existence

As is well-known, what set the stage for all semantic considerations in the Middle Ages was Aristotle's "semantic triangle", the conception sketched at the beginning of his On Interpretation, according to which words immediately signify the concepts of the mind and it is by the mediation of these concepts that they signify the things. Aquinas comments on the relevant passage as follows:

Therefore 'passions of the soul' must be understood here as conceptions of the intellect, and names, verbs, and speech signify these conceptions of the intellect immediately according to the teaching of Aristotle. They cannot immediately signify things, as is clear from the mode of signifying, for the name 'man' signifies human nature in abstraction from singulars; hence it is impossible that it immediately signify a singular man. The Platonists for this reason held that it signified the separated idea of man. But because in Aristotle's teaching man in the abstract does not really subsist, but is only in the mind, it was necessary for Aristotle to say that vocal sounds signify the conceptions of the intellect immediately and things by means of them.7

So signification is dependent on acts of human thought: by our words we signify whatever we can think of, whether it actually exists or not. For there is no doubt that we can think of something that does not exist, whence, on this conception, it follows that our words also can signify something that does not exist. Thus it is no wonder that at another place Aquinas writes as follows:

In response we have to say that there is a three-fold diversity between things signified by names. For some are in total, complete being outside the soul; and such are complete beings, as a man or a stone. Some have nothing outside the soul, as dreams or the imagination of a chimera. And some have some foundation in the reality outside the soul, but their formal account [ratio] is completed by the operation of the soul, as is clear in the case of universals. For humanity is something in reality, but there it is not universal, for there is no some humanity outside the soul common to many, but as it is conceived by the intellect, by the intellect's operation a further concept [intentio] is adjoined to it, on account of which it is called a species.8

understanding Aquinas's treatment of the notion of being. Cf. n. 54. below. 7 Aristotle: On Interpretation: Commentary by St. Thomas and Cajetan, tr. J. T. Oesterle, Marquette University Press, Milwaukeee, Wisconsin, 1962, p. 25. Unless otherwise indicated, as in this case, translations in this paper will be mine. 8 "Respondeo dicendum, quod eorum quae significantur nominibus, invenitur triplex diversitas. Quaedam enim sunt quae secundum esse totum completum sunt extra animam; et hujusmodi sunt entia completa, sicut homo et lapis. Quaedam autem sunt quae nihil habent extra animam, sicut somnia et imaginatio chimerae. Quaedam autem sunt quae habent fundamentum in re extra animam, sed complementum rationis eorum quantum ad id quod est formale, est per operationem animae, ut patet in universali. Humanitas enim est aliquid in re, non tamen ibi habet rationem universalis, cum non sit extra animam aliqua humanitas multis communis; sed secundum quod accipitur in intellectu, adjungitur ei per operationem intellectus intentio, secundum quam dicitur species." SN1 d.19,q.5,a.1.

193

However, this conception of signification immediately gives rise to a swarm of rather disturbing questions. For even granting that we can think of and thus speak about these mysterious, since non-existent, objects of signification, the first question that immediately arises is: what are, then, these objects that we are thus speaking about, if they are none of the things in the world? And, in any case, how is our ability to signify these objects by our words, as sketched by Aquinas's remarks, exactly related to our ability to speak about, that is, to refer to them? What is Aquinas's conception of the relationship between meaning, signification, and reference, supposition? Also, what can we make of Aquinas's three-fold distinction above of objects of signification? If chimeras and humanity as such are equally non-existent, whatever they are in themselves, what is that 'foundation in reality' the having or lacking of which is supposed to set them apart? And, after all, what does this whole tangled issue of nonexistent objects of signification have to do with Aquinas's metaphysics of being, the semantic principles of which we are supposed to elucidate here?

Ens Reale vs. Ens rationis as Ens simpliciter vs. secundum quid

Given the possibility of signifying objects of thought that do not exist (on the basis of their thinkability and the relationship between thought and signification), it is natural to ask about the nature of, and the relationships between, the members of the resulting classifications. In fact, Aquinas's famous distinctions of the various senses of 'being' (based on Aristotle's), which serve as the semantic foundation of his metaphysics of being, are part of the response to such questions.

The primary distinction concerns the notions of what in the scholastic tradition came to be known as real beings (entia realia) and beings of reason (entia rationis). Besides numerous shorter characterizations scattered all over Aquinas's works,9 the fullest account of this distinction is provided by the following passage:

By way of answer we have to say that the Philosopher shows that 'being' is predicated in many ways. For in one sense 'being' is predicated as it is divided by the ten genera. And in this sense 'being' signifies something existing in the nature of things, whether it is a substance, as a man, or an accident, as a color. In another sense 'being' signifies the truth of a proposition; as when it is said that an affirmation is true when it signifies to be what is, and a negation is true when it signifies not to be what is not; and this 'being' signifies composition produced by the judgment-forming intellect. So whatever is said to be a being in the first sense is a being also in the second sense: for whatever has natural existence in the nature of things can be signified to be by an affirmative proposition, e.g. when it is said that a color is, or a man is. But not everything which is a being in the second sense is a being also in the first sense: for of a privation, such as blindness, we can form an affirmative proposition, saying: 'Blindness is'; but blindness is not something in the nature of things, but it is rather a removal of a being: and so even privations and negations are said to be beings in the second sense, but not in the first. And 'being' is predicated in different manners according to these two senses: for taken in the first sense it is a substantial predicate, and it pertains to the question 'What is it?' [quid est?], but taken in the second sense it is an

9 Cf. 2SN d. 34, q. 1, a. 1; 1SN d. 19, q. 5, a. 1, ad 1, d. 33, q. 1, a. 1, ad 1.; 2SN d. 37, q. 1, a. 2, ad 1 & ad 3; De Ente c. 1; QDP q. 7, 2, ad 1; QDM q. 1, a. 1, ad 19.; QDL 9, q. 2, a. 2; In Meta lb. 4, lc. 1, lb. 5, lc. 9, lb. 6, lc. 2, lb. 6, lc. 4, lb. 9, lc. 11, lb. 11, lc. 8; ST1 q. 3, a. 4, ad 2, q. 16, a. 3, ad 2, q. 48, a. 2, ad 2; ST1-2 q. 36, a. 1; ScG lb. 1, c. 12, lb. 1, c. 58, lb. 3, c. 9, lb 3, c. 8, n. 13. Cf. also Cajetan, T. de Vio: Commentary on Being and Essence, transl. L. J. Kendzierski, F. C. Wade, Marquette Univ. Press., Milwaukee, Wis., 1964, c. 1; Alamannus, C.: Summa Philosophiae, P. Lethielleux, Paris, 1888, Tom.1. sect. II, 5, 1; Schmidt, R.W.: The Domain of Logic according to Saint Thomas Aquinas, Martinus Nijhoff, The Hague, 1966, Part II, ch. 4, and Part III, ch. 8.

194

accidental predicate, ... and it pertains to the question 'Is there [such and such a thing]?' [an est?].10

This distinction derives primarily from Aristotle's discussion of the concept of being in the fifth book of his Metaphysics, where St. Thomas starts his comments on the relevant passages with the following remarks:

[Aristotle] first divides being that is outside the soul, which is perfect being, by the ten categories. Secondly he considers another mode of being, according to which it is only in the mind [...]. Thirdly he divides being by potentiality and actuality: and being thus divided is more common than perfect being. For a being in potentiality is only a being with qualification [secundum quid] and is imperfect.11

But the same distinction is considered even earlier by St. Thomas, in his comments on book 4 of the Metaphysics, where he embeds this distinction into the broader context of his famous doctrine of the analogy of being.12 Having discussed the ways in which the various analogous senses of 'healthy', in which it can be predicated even of food and of urine, are related to each other, namely, the various ways in which its secondary senses are related to its primary sense, which signifies the health of an animal, Aquinas says that 'being' is analogous in the same way in that all of its secondary senses are related to a primary sense, the sense in which 'being' is predicated of substance. He summarizes his discussion in the following passage:

We should know that the above-mentioned modes of being can be reduced to four. For one of them, which is the weakest, is only in reason, namely, negation and privation, which we say are in reason because reason considers them as if they were some beings, when it affirms or denies of them something. [...] Another [mode of being], which is the closest to this one in weakness, is according to which generation and corruption and motions are said to be beings. For they have some privation and negation mixed with them. For motion is imperfect actuality, as is said in book 3 of the Physics. [A being] in the third sense has nothing of non-being mixed with it, but it has a weak existence [habet esse debile], for [it has existence] not by itself, but in something else, as [do] qualities, quantities and properties of substance. The fourth kind is which is the most perfect, namely, which has existence in nature without any admixture of privation, and has firm and solid existence, as it exists by itself, as do substances. And it is to this [last one], as primary and principal, that all the others are related. For qualities and quantities are said to be insofar as they are in a substance; motions and generations are said to be insofar as they tend to substance or

10 2SN d. 34, q. 1, a. 1. 11 "Primo distinguit ens, quod est extra animam, per decem praedicamenta, quod est ens perfectum. secundo ponit alium modum entis, secundum quod est tantum in mente, ibi, amplius autem et esse significat. tertio dividit ens per potentiam et actum: et ens sic divisum est communius quam ens perfectum. nam ens in potentia, est ens secundum quid tantum et imperfectum, ibi, amplius esse significat et ens." in Meta lb. 5, lc. 9. 12 Of course, Aquinas's doctrine of analogy in general is in itself a huge, and hotly debated topic. Nevertheless, the details of that doctrine, describing exactly how the various analogous senses of an analogous term are related to each other and to the things named analogously, need not be considered in the present paper. As we shall see below, all we need in the present context is to realize that a secondary sense of an analogous term may be expressed also by adding some diminishing qualification to the same term in its primary sense, i.e., that a secondary sense of an analogous term is the result of some modification of the primary sense. However, we need not consider in detail exactly how such modifications can occur, that is to say, we need not consider what are the different modes of analogy, which is in the focus of the debates. For a masterly exposition of the issues involved see McInerny, R.: The Logic of Analogy, Martinus Nijhoff: The Hague, 1961. Recently Professor McInerny has also kindly provided me with the opportunity to consult the manuscript of his new book under preparation (Aquinas and Analogy) which presents a detailed, although also debatable criticism of Cajetan's interpretation of analogy. Cf. also: Ashworth, E. J.: "Analogical Concepts: The Fourteenth-Century Background to Cajetan", Dialogue, 31(1992), p. 399.; Ashworth, E. J.: "Analogy and Equivocation in Thirteenth-Century Logic: Aquinas in Context", Mediaeval Studies, (54)1992, p. 94.

195

to some other of the above-said [beings]; and privations and negations are said to be insofar as they remove some of the above-said three. 13

Thus, as we can see, the distinction between ens reale and ens rationis is regarded by St. Thomas as forming part of the division of the common term ens, i.e., 'being', into its various, though related, analogical senses. Concerning this kind of division in general, as opposed to the division of a genus into its species, St. Thomas writes the following:

... there are two ways in which something common can be divided into what are under it, just as there are two ways in which something is common. For there is the division of a univocal [term] into its species by differences by which the nature of the genus is equally participated in the species, as animal is divided into man and horse, and the like. Another division is that of something common by analogy, which is predicated according to its perfect concept [ratio] of one of those that divide it, and of the other[s] imperfectly and with qualification [secundum quid], as being is divided into substance and accident, and into being in actuality and in potentiality ...14

Accordingly, however obscure the details of the divisions of the notion of being may appear at first, the first thing to realize about the distinction between real beings and beings of reason is that it does not constitute a division of a class into its subclasses, as, for example, the distinction between rational vs. non-rational animals constitutes the division of the class of animals into two kinds of animals, namely, humans and brutes. Real beings and beings of reason do not constitute in this way two subclasses, or two kinds of beings, indeed, not any more than real money and forged money would constitute two kinds of money. Just as it is only real money that is money simpliciter, that is, without qualification, so it is only a real being that is a being simpliciter, without qualification. As medieval logicians, as well as Aquinas himself, would say, the qualifications 'of reason' as added to 'being', or 'forged' as added to 'money' are examples of a "diminishing" qualification or determination, determinatio diminuens, whereas the qualification 'real' in both cases is a "non-diminishing" qualification, determinatio non diminuens. The origin

13 "Sciendum tamen quod praedicti modi essendi ad quatuor possunt reduci. Nam unum eorum quod est debilissimum, est tantum in ratione, scilicet negatio et privatio, quam dicimus in ratione esse, quia ratio de eis negociatur quasi de quibusdam entibus, dum de eis affirmat vel negat aliquid. Secundum quid autem differant negatio et privatio, infra dicetur. Aliud autem huic proximum in debilitate est, secundum quod generatio et corruptio et motus entia dicuntur. Habent enim aliquid admixtum de privatione et negatione. Nam motus est actus imperfectus, ut dicitur tertio Physicorum. Tertium autem dicitur quod nihil habet de non ente admixtum, habet tamen esse debile, quia non per se, sed in alio, sicut sunt qualitates, quantitates et substantiae proprietates. Quartum autem genus est quod est perfectissimum, quod scilicet habet esse in natura absque admixtione privationis, et habet esse firmum et solidum, quasi per se existens, sicut sunt substantiae. Et ad hoc sicut ad primum et principale omnia alia referuntur. Nam qualitates et quantitates dicuntur esse, inquantum insunt substantiae; motus et generationes, inquantum tendunt ad substantiam vel ad aliquid praedictorum; privationes autem et negationes, inquantum removent aliquid trium praedictorum." In Meta lb. 4, lc.1, n. 15. 14 "Respondeo dicendum, quod est duplex modus dividendi commune in ea quae sub ipso sunt, sicut est duplex communitatis modus. Est enim quaedam divisio univoci in species per differentias quibus aequaliter natura generis in speciebus participatur, sicut animal dividitur in hominem et equum, et hujusmodi; alia vero divisio est ejus quod est commune per analogiam, quod quidem secundum perfectam rationem praedicatur de uno dividentium, et de altero imperfecte et secundum quid, sicut ens dividitur in substantiam et accidens, et in ens actu et in ens potentia: et haec divisio est quasi media inter aequivocum et univocum." 2SN d. 42, q. 1, a. 3, in corp. Cf. "... non ens dicitur multipliciter sicut et ens. Uno enim modo dicitur quod est secundum compositionem et divisionem propositionis. Et hoc, cum non sit in rebus, sed in mente, non potest moveri. Alio modo dicitur ens et non ens secundum potentiam et actum. Et id quod est actu est simpliciter ens. Quod autem est secundum potentiam tantum, est non ens." (in Meta lb. 11, lc. 11, nn. 2368-9.) Cf. also: "Unum enim eodem modo dicitur aliquid sicut et ens; unde sicut ipsum non ens, non quidem simpliciter, sed secundum quid, idest secundum rationem, ut patet in 4o Metaphysicae, ita etiam negatio est unum secundum quid, scilicet secundum rationem." in Peri lb. 2, lc. 2, n. 3.

196

of the theory of these two kinds of determination goes back to Aristotle's Sophistical Refutations¸ in particular, to his treatment of the fallacy referred to by the schoolmen as secundum quid et simpliciter.15

According to the medieval analysis of this fallacy, the fallacy consists in dropping a diminishing qualification in an inference from a proposition in which a predicate is applied to a subject with some qualification, secundum quid, to a proposition in which the same predicate is applied to the same subject absolutely, without qualification, i.e., simpliciter. In his De Fallaciis,16 Aquinas characterizes this fallacy in the following manner:

Next, about the fallacy secundum quid and simpliciter. In this context that is [said to be] predicated simpliciter what is predicated without any modification [modus] added to it, as when we say: 'Socrates is white' or 'Socrates runs'; and that is [said to be] predicated secundum quid what is predicated with adding something to it, as in 'He runs well' or in 'Socrates is white with respect to his teeth'. What is added may be related in two ways to that to which it is added: for sometimes it does not diminish the concept [ratio] of that to which it is added, and then it is possible to proceed from what is secundum quid to what is simpliciter, as when we say: 'He runs fast; therefore, he runs', for speed does not take away anything from the concept [ratio] of running. [...] Sometimes, however, what is added takes away something from the concept [ratio] of that to which it is added, as when it is said: 'A black man is white with respect to his teeth'. For the qualification 'with respect to his teeth' takes something away from the concept of what is said to be white, since nobody can be said to be white, except who is totally white, or with respect to most or the principal parts. Therefore, if someone were to conclude: 'A black man is white with respect to his teeth; therefore, he is white', then this is a sophistic argument, or an instance of the fallacy secundum quid et simpliciter, and the deception derives from taking what is predicated secundum quid as if it were predicated simpliciter.17

Thus, when the qualification is diminishing, then its omission yields an invalid inference, however, when it is non-diminishing, i.e., when the qualification added to the predicate does not specify any conditions for the applicability of the predicate other than those included in the meaning of the predicate in itself, then its omission preserves the truth of the original proposition. As Aquinas somewhat later, in discussing the several modes in which this fallacy can occur, explains:

15 For a more comprehensive discussion of, and further references to, the medieval literature of this fallacy (in connection with St. Thomas's use of the related theoretical apparatus in his theology of the Incarnation) see Klima, G.: "Libellus pro Sapiente: A Criticism of Allan Bäck's Argument against St. Thomas Aquinas' Theory of the Incarnation", The New Scholasticism, 58(1984), pp. 207-219. 16 A minor work whose authenticity recently has been vindicated. See Father Busa's note at the end of the list of works included in the supplements (very conveniently printed at the end of each volume) of his monumental Index Thomisticus, S. Thomae Aquinatis Opera Omnia, Frommann-Holzboog: Stuttgart-Bad Canstatt, 1980. 17 "Sequitur de fallacia secundum quid et simpliciter. Simpliciter autem hic dicitur quod nullo modo addito dicitur, ut cum dicitur: Socrates est albus, vel Socrates currit; secundum quid autem dicitur quod cum aliquo addito dicitur, ut: iste currit bene, vel Socrates est albus secundum dentem. Hoc autem quod additur, dupliciter se habet ad id cui additur: nam quandoque non diminuit de ratione eius cui additur, et tunc potest procedi ab eo quod est secundum quid ad hoc quod est simpliciter, ut cum dicitur: iste currit velociter, igitur currit: velocitas enim nihil diminuit de ratione cursus. Et est in praedicto argumento locus a parte in modo. Quandoque vero id quod additur diminuit aliquid de ratione eius cui additur; ut cum dicitur: aethiops est albus secundum dentem. Nam haec determinatio dentem diminuit aliquid de ratione eius quod dicitur albus: non enim potest dici albus, nisi qui totus est albus, vel secundum plures et principaliores partes. Et ideo si concludatur: aethiops est albus secundum dentem, ergo est albus; est locus sophisticus, vel fallacia secundum quid et simpliciter, et est deceptio proveniens ex eo quod dictum secundum quid accipitur ac si esset dictum simpliciter." De Fallaciis, c. 13.

197

We should know, however, that if a whole is aptly denominated from its part, then there is no fallacy, as is clear in this case: 'He is curly with respect to his hair; therefore, he is curly'. This correctly follows, for a man is denominated curly with respect to his hair. And this mode covers also other [sorts of] parts, namely, [parts] of place, of time, or of other [sorts of] wholes. If, however, something is added to a whole in place by the mediation of a part in place, from which part it is not aptly denominated, the fallacy occurs in such inferences, as [in the following]: 'This diet is good in unhealthy places, so it is good'. This does not follow, for 'in unhealthy places' signifies a part in place. The case is similar with a whole and part in time, as here: 'Drinking wine is bad for the sick; therefore, it is bad'. And the same goes for all similar cases.18

Therefore, since 'real' as added to 'being' is a non-diminishing qualification, a real being is simply a being; on the other hand, since 'of reason' as added to 'being' is a diminishing qualification, a 'being of reason' is not necessarily a being, except secundum quid.19 But then we can easily see that our first question at the end of the previous section, asking about the nature of nonexistent objects of signification was based on a category mistake. For the question about the nature of anything presupposes that it has a nature. But this, again, presupposes that it exists, that is to say, that it is a being simpliciter, a real being:

Since a non-being does not have a quiddity or essence, of that which is not, nobody can know what it is; but one can know the signification of the name, or the description composed of several names; as for example one can know what the name 'tragelaphus', or 'goatstag', signifies, which is the same, since it signifies an animal composed of a goat and a stag. But it is impossible to know what a goatstag is, for nothing is like this in the nature of things.20

Therefore, asking the question: 'What are nonexistent beings of reason?', understood as asking about the nature of a curious kind of beings, namely, beings that do not exist, is just as misguided as asking about the actual legal currency rate between, say, yen and forged dollars. But, again, this of course does not mean that we cannot understand what we mean by the phrase 'beings of reason', on the contrary, as we just explained, such beings of reason are what certain expressions signify in virtue of the fact that we can think of them when we understand the expressions in question, whether they actually exist in rerum natura or not.

So far, so good. But even if by this response we may have dulled somewhat the critical edge of this disturbing question, I hardly think any contemporary philosopher would be absolutely satisfied by the explanations given so far, and apparently for good reasons. For weren't these 18 "Sciendum tamen quod si a parte sit natum denominari totum, non accidit fallacia, ut patet in hoc processu: iste est crispus secundum capillos. Ergo est crispus. Bene sequitur: quia homo denominatur crispus secundum capillos. Et hic modus se extendit ad alias partes, scilicet loci, vel temporis, vel aliorum totorum. Si vero aliquid additur toti in loco mediante parte in loco, a qua parte totum non est natum denominari, accidit fallacia in his processibus, ut: haec diaeta est bona in locis aegrotativis, ergo est bona. Non sequitur: quia hoc quod dicit in locis aegrotativis significat partem in loco. Similiter est de toto et parte in tempore, sicut hic: bibere vinum est malum aegrotanti. Ergo est malum. Et eadem ratio est in omnibus similibus." ibid. 19 Cf.: "Unum enim eodem modo dicitur aliquid sicut et ens; unde sicut ipsum non ens, non quidem simpliciter, sed secundum quid, idest secundum rationem, ut patet in 4o Metaphysicae, ita etiam negatio est unum secundum quid, scilicet secundum rationem." in Peri lb. 2, lc. 2, n. 3. 20 "Quia enim non entis non est aliqua quidditas vel essentia, de eo quod non est nullus potest scire quod quid est; sed potest scire significationem nominis, vel rationem ex pluribus nominibus compositam: sicut potest aliquis scire quid significat hoc nomen tragelaphus vel hircocervus, quod idem est, quia significat quoddam animal compositum ex hirco et cervo; sed impossibile est scire quod quid est hircocervi, quia nihil est tale in rerum natura." in PA lb. 2, lc. 6, n. 2. Cf. in PA lb. 1, lc. 2, n. 5.: " ... antequam sciatur de aliquo an sit, non potest sciri proprie de eo quid est: non entium enim non sunt definitiones. Unde quaestio, an est, praecedit quaestionem, quid est. Sed non potest ostendi de aliquo an sit, nisi prius intelligatur quid significatur per nomen. Propter quod etiam Philosophus in iv Metaphysicae, in disputatione contra negantes principia docet incipere a significatione nominum."

198

explanations just a series of obscura per obscuriora, vain attempts to elucidate some obscure distinctions by other, even more obscure ones? After all, we started out answering the disturbing questions concerning existent vs. nonexistent objects of signification at the end of the previous section by presenting St. Thomas's quite obscure distinction between the two senses of 'being'. This immediately turned out to be just a part of a more comprehensive distinction between the various analogous senses of the same. The explanation of this latter distinction in its turn led only to even further distinctions, namely those between predication simpliciter vs. secundum quid and determinatio diminuens vs. non-diminuens, just to pave the way for dismissing one of our initial questions as mistaken. But then, the dubious result of eliminating this question by this procedure was achieved at the expense of introducing distinctions that are bound to give rise to even further, and even more disturbing questions. For how are we supposed to understand St. Thomas's claims in his distinction of the two notions of being? Why would blindness be a non-being, or a being only in the second sense? But even if it is, why would this rather obscure fact be expressed by a copula of an affirmative proposition? And what should we make of the claim that the concept of being applicable to blindness is a result of somehow "diminishing" the concept of being applicable to sight, which in turn is a concept of being that results from another "diminishing" of the concept of being applicable to substances, i.e., ordinary things, such as animals that can be sighted or blind? Indeed, what does the fact that an animal is sighted, or blind, have to do with the existence (in any sense) of such spurious entities as blindness or sight?

Signification and the Inherence Theory of Predication

To provide acceptable replies to these questions as well as to the previous ones, we have to start with a systematic account of Aquinas's conception of signification. As we have already seen, for Aquinas our words have two sorts of signification, immediate and ultimate. What a word immediately signifies is a human concept, the possession and actual exercise of which makes a human being aware of something.

Note here that by this claim Aquinas is not committed to any particular "philosophy of mind and language" (although, of course, he has one), or to any particular psychological or psycholinguistic theory. For such theories would certainly have to involve answering the question of what human concepts in themselves are, i.e., characterizing the nature of these acts of human awareness, and the nature of their relationship to their subject, the human mind, which in turn would demand a characterization of the nature of the human mind itself, etc. Aquinas's claim in itself, however, determines nothing concerning such issues, instead, it merely introduces a certain terminology to speak in a fairly general fashion about things familiar just to anyone. For of course anyone who speaks any language at all is familiar with the fact that the intelligent use and understanding of a meaningful word necessarily involves the ability to think or be aware of what the word is used for by the users of the language in which the word is meaningful, that is to say, the ability to think or be aware of what other users of the same language think or are aware of when they use the word with understanding. It is only the same familiar fact that is expressed otherwise by saying that words, that is, certain meaningful utterances or inscriptions of a language, immediately signify concepts of the users of the language, that is, they are meaningful to users of the language precisely because they are conventionally attached to concepts, i.e., certain acts of human awareness or understanding of the users of the language in question. To know this much, however, we do not have to know what thinking or awareness or understanding is or what these acts of awareness or concepts are. Whatever it is that accounts for a human

199

being's ability to think of what a word is used for in a linguistic community, i.e., whatever it is that accounts for a human being's ability to use a meaningful word with understanding, be it a brain process, a spiritual modification, or whatever else a philosopher can think up, that is what we call here a concept immediately signified by the word in question. Thus, whatever it is that makes me (or you) aware of human beings in general when I (or you) use the word 'man' in English (say, in the sentence: 'I'm looking for a good man') that is what is called here the concept of human beings signified immediately by the word 'man' in the minds of those who understand English (or at least this much of English).

But of course by saying that words immediately signify concepts of the human mind Aquinas was not claiming that words are simply the signs of these concepts. Words are ultimately the signs of the objects of these concepts, that is to say, (categorematic)21 words signify ultimately what the concepts they immediately signify make us aware of. It is such a concept that St. Thomas calls the ratio of the things it makes us aware of. But, perhaps curiously to the modern reader, according to St. Thomas this ratio is not only in the intellect, but somehow also in the thing thought of:

... the ratio of any thing is what its name signifies, as the ratio of a stone is what its name signifies. But names are the signs of intellectual conceptions, whence the ratio of any thing signified by a name is the conception of the intellect that the name signifies. And this conception of the intellect is in the intellect as in its subject, but it is in the thing thought of as in that which is represented: for the conceptions of the intellect are certain similitudes of the things thought of. But if the conception of the intellect were not assimilated to the thing, then the conception would be false of that thing; for example, if the intellect would think something that is not a stone to be a stone. So the ratio of the stone is in the intellect as in its subject, but it is in the stone as in that which causes truth in the conception of the intellect thinking the stone to be such and such.22

In another passage, in connection with the question of how the attributes we predicate of God may apply to Him, Aquinas explains in more detail in what sense we can say that the ratio is in the thing:

... we should know that a ratio, as taken here, is nothing else, but what the intellect apprehends from the signification of some name, and this in the case of those things that have definition is the definition of the thing itself, in accordance with what the Philosopher says: 'the ratio signified by the name is the definition'.23 But some things, which are not defined, are [also] said to have a ratio in this way, e.g., things such as quantity or quality, which are not defined because they are

21 Of course, syncategorematic terms do not have such ultimate significata in themselves, as their function is not to signify but only to co-signify (consignificare). See n. 68. of Ashworth, E. J.: "Signification and Modes of Signifying in Thirteenth-Century Logic: A Preface to Aquinas on Analogy", Medieval Philosophy and Theology 1(1991), pp. 39-67. For a formal treatment of syncategorematic terms along these lines see Essay V. of Klima, G.: Ars Artium: Essays in Philosophical Semantics, Medieval and Modern, Budapest: Institute of Philosophy of the Hungarian Academy of Sciences, 1988. But we are not concerned here with syncategorematic terms. 22 "Primo considerandum est, quod ratio cuiuslibet est quam significat nomen eius, sicut ratio lapidis est quam significat nomen eius. Nomina autem sunt signa intellectualium conceptionum: unde ratio uniuscuiusque rei significata per nomen, est conceptio intellectus, quam significat nomen. Haec autem conceptio intellectus est quidem in intellectu sicut in subiecto, in re autem intellecta sicut in repraesentato: nam conceptiones intellectuum sunt similitudines quaedam rerum intellectarum. Si autem conceptio intellectus non assimilaretur rei, falsa esset conceptio de re illa, sicut si intelligeret esse lapidem quod non est lapis. Ratio igitur lapidis est quidem in intellectu sicut in subiecto, in lapide autem sicut in eo quod causat veritatem in conceptione intellectus intelligentis lapidem talem esse." Resp. ad lect. Vercell. de art. 108 q. 1. Cf.: "Ratio enim quam significat nomen, est conceptio intellectus de re significata per nomen." ST1 q. 13, a. 4. 23 in Meta lb. 4, lc. 16, n. 733.

200

most general genera. Nevertheless, the ratio of quality is what is signified by the name of quality; and it is that from which quality has it that it is quality. Thus it makes no difference whether those things that are said to have a ratio have a definition. And so it is clear that the ratio of wisdom predicated of God is what is conceived of in the signification of this name, even if divine wisdom itself cannot be defined. Nevertheless, the name 'ratio' does not signify this conception itself, because that is signified by the name of wisdom, or by some other name of the thing, but it signifies the intention of this conception, just as the name 'definition' and other names of second imposition. And thus the second point, namely, the one concerning how the ratio is said to be in the thing, is also clear. For this does not mean that the intention itself which is signified by the name 'ratio' would be in the thing, nor even that the conception to which this intention applies would be in the thing outside the soul, for it is in the soul as in its subject; but it is said to be in the thing insofar as there is something in the thing outside the soul that corresponds to the conception of the soul, as what is signified [corresponds] to the sign.24

There are two points in this passage that we should very clearly understand for the subsequent discussion. The first is that the name 'ratio' is a name of second imposition. The second is that to know the ratio of a thing, and hence the meaning of its name, we need not know the essential definition of whatever is conceived of in that ratio, that is to say, that we can clearly know what a name signifies without knowing what the thing signified by the name is in itself.25

24 "... sciendum est, quod ratio, prout hic sumitur, nihil aliud est quam id quod apprehendit intellectus de significatione alicujus nominis: et hoc in his quae habent definitionem, est ipsa rei definitio, secundum quod philosophus dicit: ratio quam significat nomen est definitio. Sed quaedam dicuntur habere rationem sic dictam, quae non definiuntur, sicut quantitas et qualitas et hujusmodi, quae non definiuntur, quia sunt genera generalissima. Et tamen ratio qualitatis est id quod significatur nomine qualitatis; et hoc est illud ex quo qualitas habet quod sit qualitas. Unde non refert, utrum illa quae dicuntur habere rationem, habeant vel non habeant definitionem. Et sic patet quod ratio sapientiae quae de deo dicitur, est id quod concipitur de significatione hujus nominis, quamvis ipsa sapientia divina definiri non possit. Nec tamen hoc nomen ratio significat ipsam conceptionem, quia hoc significatur per nomen sapientiae vel per aliud nomen rei; sed significat intentionem hujus conceptionis, sicut et hoc nomen definitio, et alia nomina secundae impositionis. Et ex hoc patet secundum, scilicet qualiter ratio dicatur esse in re. Non enim hoc dicitur, quasi ipsa intentio quam significat nomen rationis, sit in re; aut etiam ipsa conceptio, cui convenit talis intentio, sit in re extra animam, cum sit in anima sicut in subjecto: sed dicitur esse in re, inquantum in re extra animam est aliquid quod respondet conceptioni animae, sicut significatum signo. Unde sciendum, quod ipsa conceptio intellectus tripliciter se habet ad rem quae est extra animam. Aliquando enim hoc quod intellectus concipit, est similitudo rei existentis extra animam, sicut hoc quod concipitur de hoc nomine homo; et talis conceptio intellectus habet fundamentum in re immediate, inquantum res ipsa, ex sua conformitate ad intellectum, facit quod intellectus sit verus, et quod nomen significans illum intellectum, proprie de re dicatur. Aliquando autem hoc quod significat nomen non est similitudo rei existentis extra animam, sed est aliquid quod consequitur ex modo intelligendi rem quae est extra animam: et hujusmodi sunt intentiones quas intellectus noster adinvenit; sicut significatum hujus nominis genus non est similitudo alicujus rei extra animam existentis; sed ex hoc quod intellectus intelligit animal ut in pluribus speciebus, attribuit ei intentionem generis; et hujusmodi intentionis licet proximum fundamentum non sit in re sed in intellectu, tamen remotum fundamentum est res ipsa. Unde intellectus non est falsus, qui has intentiones adinvenit. Et simile est de omnibus aliis qui consequuntur ex modo intelligendi, sicut est abstractio mathematicorum et hujusmodi. Aliquando vero id quod significatur per nomen, non habet fundamentum in re, neque proximum neque remotum, sicut conceptio chimerae: quia neque est similitudo alicujus rei extra animam, neque consequitur ex modo intelligendi rem aliquam naturae: et ideo ista conceptio est falsa. Unde patet secundum, scilicet quod ratio dicitur esse in re, inquantum significatum nominis, cui accidit esse rationem, est in re: et hoc contingit proprie, quando conceptio intellectus est similitudo rei." 1SN ds. 2, q. 1, a. 3. in corpore 25 Or, using medieval terminology, we can know the quid nominis without knowing the quid rei. The distinction itself is most aptly characterized by Aquinas's famous commentator, Cajetan, in the following way: "Just as the quid rei is the thing's quiddity, so the quid nominis is the quiddity of the name: but a name, as it is the sign of the passions that are objectively in the soul (from bk. 1. of Aristotle's Perihermeneias), does not have any other quiddity but this, namely, that it is a sign of a thing understood or thought of. But a sign, as such, is relative to what is signified: so to know the quid nominis is nothing, but to know what the name, as a sign, is related to, as what is signified. Such a

201

As to the first point, we should know that St. Thomas applies a common medieval distinction here, roughly comparable to the contemporary distinction between expressions of object language vs. metalanguage. However, for the medievals this distinction did not concern two distinct, and in themselves complete languages, one of which is designed to speak about things other than its own expressions, while the other is designed to speak about the expressions of the former. On the contrary, here we have expressions of the same language distinguished with respect to their function in speaking about different types of objects, namely, either about concepts or the objects of these concepts. As we have seen, for Aquinas a word is meaningful on account of the fact that it immediately signifies some concept of the human mind. But the word is imposed to signify ultimately the object of this concept, i.e., what the actual exercise of this concept makes a human being aware of. However, some concepts make us aware not of objects of external reality, but of concepts of the mind. So just as, say, the concept that makes us aware of human beings in general is the concept of human beings, so the concept that makes us aware, say, of concepts that make us aware of things that differ only numerically but not by essential differences (as does the concept of human beings, or the concept of horses, or the concept of oak trees) is the concept of species. Concepts that have as their objects things other than concepts in this comparison are called first intentions, intentiones primae, and, correspondingly, their names are called names of first imposition, nomina primae impositionis. On the other hand, concepts that have concepts as such as their objects are called second intentions, intentiones secundae, and, correspondingly, their names are called names of second imposition, nomina secundae impositionis.

The qualification 'as such' is needed here for the reason that of course there are concepts that have both concepts and things other than concepts as their objects. For example, the concepts of knowledge, however, can be acquired by the accidental properties of what is signified, as well as by its common, or by its essential properties, or simply by a gesture, or whatever else you like. For example, if we ask a Greek about the meaning of anthropos, if he points to a man, at once we know the quid nominis, and similarly in other cases. But to those asking about the quid rei, it is necessary to give what belongs to the thing adequately, in the first mode of perseity [i.e., in virtue of its essence–for the four modes of "perseity", i.e., of predication per se, see in PA lb. 1, lc. 10.–G.K.]. This is the essential difference between the quid nominis and the quid rei: namely, that the quid nominis is the relation of the name to what it signifies; but the quid rei is the essence of the thing related or signified. And from this difference follow all the rest that are usually enumerated: namely, that the quid nominis is of nonentities, complexes, by accidental, common, and external properties; while the quid rei is of incomplex entities [grasped] by their proper, essential properties. For a word's relation can be terminated to non-existents, and complexes, and it can be clarified by accidental and similar properties, but the thing's essence can be known only by proper, essential properties of incomplex things."–"Sicut quid rei est quidditas rei, ita quid nominis est quidditas nominis: nomen autem, cum sit nota earum quae sunt obiective in anima passionum (ex primo Perihermeneias), non habet aliam quidditatem nisi hanc, quod est signum alicuius rei intellectae seu cogitatae. Signum autem ut sic, relativum est ad signatum: unde cognoscere quid nominis nihil est aliud, quam cognoscere ad quid tale nomen habet relationem ut signum ad signatum. Talis autem cognitio potest acquiri per accidentalia illius signati, per communia, per essentialia, per nutus, et quibusvis aliis modis. Sicut a Graeco quaerentibus nobis quid nominis anthropos, si digito ostendatur homo iam percipimus quid nominis, et similiter de aliis. Interrogantibus vero quid rei oportet assignare id quod convenit rei significatae in primo modo perseitatis adaequate. Et haec est essentialis differentia inter quid nominis et quid rei, scilicet quod quid nominis est relatio nominis ad signatum; quid rei vero est rei relatae seu significatae essentia. Et ex hac differentia sequuntur omnes aliae quae dici solent: puta quod quid nominis sit non entium, complexorum, per accidentalia, per communia, per extranea; quid rei vero est entium incomplexorum per propria et essentialia. Relatio enim vocis potest terminari ad non entia in rerum natura, et complexa, et declarari per accidentalia et huiusmodi, essentia autem rei non nisi per propria essentialia habetur de entibus incomplexis." Cajetanus, T. de Vio: "Super Librum De Ente et Essentia Sancti Thomae", in: Opuscula Omnia, Bergomi, Typis Comini Venturae, 1590, p. 299.

202

'being', 'thing' and the like are certainly such concepts. Still, these concepts are not second intentions, since, even if they do represent concepts as well as other things, they do not represent concepts qua concepts, i.e. qua acts, whatever they are in themselves, that make humans aware of something, but qua beings, or qua things in their own right, regardless of whatever their function in human cognition may be. Indeed, even if there were intentions that would have only concepts as their objects, but would not represent them qua concepts, those intentions would not be second intentions. For example, even if it turned out that what we call here concepts are brain processes, this stunning discovery would not turn the concept of a brain process into a second intention, for it does not characterize whatever makes a human aware of something in terms of the relationship of this act of awareness to the object of this act, but otherwise, as some natural phenomenon in its own right, some bioelectric changes in a particular sort of grayish stuff.26

On the other hand, for example, the concept of species, as interpreted by the medievals, is a concept of a concept qua a concept, because it characterizes or represents concepts as such, i.e., in their function of making humans aware of certain sorts of things in a particular manner.27 In the same way, as Aquinas explains in the passage quoted above, the concept of ratio is a second intention, and hence its name is a name of second imposition, because it represents concepts of other things qua concepts, i.e., insofar as these concepts are related to their objects, naturally representing them in a certain manner. Hence, what the name 'ratio' immediately signifies is the intention of ratio, a second intention, which represents concepts in their function in human cognition. But then the intention of ratio applies to concepts that represent their own objects, and hence the name 'ratio' refers to these concepts.

However, as Aquinas goes on to explain, we can also say that the ratio is in the thing. But this is not intended in the sense that the concept by which the thing is conceived of would be in the thing, for the concept is in the human mind as in its subject.28 What this means is that there is something in the thing corresponding to the ratio, on account of which the concept applies to this thing at all, called the form or nature of the thing.29 For example, if the concept in question is a universal concept of many particulars, as the concept of man30 is a specific concept representing

26 Which is basically what accounts for the futility of all reductionist attempts to explain away talk about mental acts in terms of a purely physicalisitc language, regardless of whether what we speak about as mental acts are in fact only brain processes, i.e., modifications of matter, or something else, distinct from such material modifications. 27 In any case, this is how Aquinas, among many other medieval authors, would interpret the standard Porphyrean definition: species est praedicabile in quid de pluribus solo numero differentibus, insofar as the relation of predicability of many things is what definitively characterizes a universal as such, whereas a universal as such is nothing, but an abstract, universal concept, which, again, as such, is an act of human awareness that makes humans aware of the nature of particulars in abstraction from the individuating conditions with which it only can exist in the particulars. Cf. De Ente c. 4. 28 For a discussion and formal semantic reconstruction of the details of Aquinas's rather intricate doctrine of concepts (which, again, we need not consider here), especially with respect to their relationships to their subjects, their objects, and to what St. Thomas calls natura absolute considerata, see: Klima, G.: "'Socrates est species': Logic, Metaphysics and Psychology in St. Thomas Aquinas's Treatment of a Paralogism", in: K. Jacobi (ed.): Argumentationstheorie: Scholastische Forschungen zu den logischen und semantischen Regeln korrekten Folgerns, Brill: Leiden, the Netherlands, 1993, pp. 489-504. 29 This is why the form of the thing corresponding to the concept or ratio of the mind is also called a ratio: "Forma vero quae et ratio nominatur, quia ex ipsa sumitur ratio speciei, dicitur substantia quasi ens aliquid actu, et quasi ens separabile secundum rationem a materia." in Meta lb. 8, lc. 1, n. 1678. 30 In the sense of human being—in general, the medieval concept of homo, as signifying the species of humans, was not regarded as gender-specific.

203

humans in abstraction from their accidental, individuating features, then the ratio in the mind is this concept itself, but the ratio in the thing is what is represented by this concept in the thing, and that is what is referred to as human nature, or humanity, on account of which the thing represented is a human being. Indeed, what accounts for the intellect's being able to think of humans in this manner is its capacity to think or be aware of humans precisely qua humans, that is, to be aware of them only with respect to what makes them humans, their human nature, disregarding whatever other features they may have, such as color, gender, weight, height, virtues or vices, etc. It is precisely this capacity, the capacity to abstract the natures or forms of things from their individualizing conditions, that accounts for the very possibility for humans to have universal concepts. As St. Thomas explains:

When we speak about an abstract universal, we imply two things, namely the nature of the thing itself, and abstraction or universality. So the nature itself to which it is accidental that it is thought of, or that it is abstracted, or that the intention of universality applies to it, exists only in the singulars, but the nature’s being abstracted or its being thought of or the intention of universality is in the intellect. And we can see this by the similar situation in perception. For sight sees the color of an apple without its smell. Thus, if it is asked: Where is the color that is seen without the smell?–it is obvious that it is nowhere else, but in the apple. But that it is perceived without the smell happens to apply to it [accidit ei] on account of sight, insofar as in sight there is a similitude of color but not of smell. Similarly, humanity that is thought of exists only in this or in that man; but that humanity is apprehended without its individuating conditions, which is nothing but for it to be being abstracted, which confers on it the attribute of universality, is an accidental feature of humanity [accidit humanitati] in virtue of its being perceived by the intellect, in which there is a similitude of the nature of the species but not of the individuating principles.31

But then, as to the second point mentioned above, we should clearly realize that even if by having such a concept in our minds we necessarily are aware of human nature without its individuating conditions, this does not mean that we necessarily have to be able to say what this human nature is. For to have this concept means only to be able to think or to be aware of humans in this abstract and hence universal manner. But the ability to think of humans in this way is nothing but the ability to think of humans only qua humans, only in terms of what it is necessary for something to have so that it be a human (regardless of any other features it may have), and this is precisely what is called a human nature, or a humanity, namely, what makes the thing in question a human being, regardless of whether we are able to spell it out what this nature is in terms of other concepts, by providing an essential definition of human beings. Therefore, by having this concept of human beings we necessarily are aware of human nature as such, in abstraction from its individualizing conditions in particular humans, whether we are able to give any other characterization of this nature in terms of other concepts or not. Of course, if we do know the essential definition of the thing in question, then we are in a position to give an answer also in terms of other concepts to the question asking about the nature of the thing: we can tell what the thing is, what it is that it has to have so that it be the kind of thing it is. But as 31 "Cum dicitur universale abstractum, duo intelliguntur, scilicet ipsa natura rei et abstractio seu universalitas. Ipsa igitur natura cui accidit vel intelligi vel abstrahi vel intentio universalitatis non est nisi in singularibus; sed hoc ipsum quod est intelligi vel abstrahi vel intentio universalitatis est in intellectu Et hoc possumus videre per simile in sensu. Visus enim videt colorem pomi sine eius odore. Si ergo quaeratur ubi sit color qui videtur sine odore, manifestum est quod color qui videtur non est nisi in pomo; sed quod sit sine odore perceptus, hoc accidit ei ex parte visus, inquantum in visu est similitudo coloris et non odoris. Similiter, humanitas quae intelligitur non est nisi in hoc vel in illo homine; sed quod humanitas apprehendatur sine individualibus conditionibus, quod est ipsam abstrahi, ad quod sequitur intentio universalitatis, accidit humanitati secundum quod percipitur ab intellectu, in quo est similitudo naturae speciei et non individualium principiorum." ST1 q. 85, a. 2, ad 2.

204

concerning divine wisdom St. Thomas insisted above, this is not required of us in order to have a ratio or concept of the thing, an act of simple apprehension by which we can be aware of the thing with respect to its form or nature represented by this ratio, namely, that feature of the thing which is conceived of in this concept, whatever it is, disregarding the thing's other features. Indeed, since it is this ability to think of particular things in this abstract universal manner that is for us to have the abstract concepts or rationes of particular things, and our words signify immediately our concepts, on account of which they signify ultimately what we conceive of in these concepts, it is precisely this human ability that accounts for there being universal terms in human languages at all, signifying things in the same universal manner, with respect to the natures of particular things conceived of in their concepts without their individualizing features. But since this applies to all sorts of universal terms (and in all sorts of human languages, for that matter), we can state in general that a universal term immediately signifies an abstract and hence universal concept of the human mind, on account of which it ultimately signifies whatever is conceived of by this concept in the particulars (without conceiving their individualizing features), namely, the individualized natures or forms of particulars, which render them such as to fall under this concept. For despite our ability to think of particulars in this abstract, universal manner, and hence our common terms' ability to signify them in the same way, the form or nature signified by a general term in this particular thing is of course a numerically distinct entity from the form or nature signified by the same term in that particular thing. As St. Thomas writes:

... it is not necessary that if this is a man and that is a man, then they both have numerically the same humanity, just as two white things do not have numerically the same whiteness; but [it is necessary] that the one be similar to the other in that it has humanity just as the other: whence the intellect, considering humanity not as belonging to this thing, but as humanity, forms an intention that is common to all.32

Thus, the abstractive consideration of the intellect is able to conceive of these particular, individualized forms in a universal manner (considering, say, this whiteness or that whiteness only as whiteness, but not considering this whiteness as belonging to this thing or that whiteness as belonging to that thing) and it is therefore able to confer universal meaning on certain sounds and inscriptions as parts of a human language. However, it is only this humanity, say the humanity of Socrates, or that humanity, say the humanity of Plato, or this whiteness of this white sheet of paper, or that whiteness of that white sheet of paper that exists in rerum natura. For even if, say, this whiteness or that whiteness can be considered without considering whether it belongs to this thing or to that thing, no whiteness can be without being the whiteness of this thing or of that thing, i.e., without belonging to this thing or to that thing. And this is necessarily so, because for this whiteness to be is nothing but for this thing to be white and vice versa, and of course it is only some particular thing that can be white. Thus, in this semantic conception, for some particular thing to be white is nothing but for its particular whiteness (the particular quality that is represented in a universal manner by the human concept that renders the term 'white' in English meaningful) to be. But then this is why, according to St. Thomas, we use the verb of existence even when we want to express only the simple fact that a thing actually is white:

32 "Non enim oportet si hoc est homo, et illud homo, quod eadem sit numero humanitas utriusque, sicut in duobus albis non est eadem albedo numero; sed quod hoc similetur illi in hoc quod habet humanitatem sicut illud: unde intellectus, accipiens humanitatem non secundum quod est huius, sed ut est humanitas, format intentionem communem omnibus." 2SN d. 17, q. 1, a. 1.

205

Since actuality, what is principally signified by the verb 'is', is in general the actuality of all forms, whether substantial or accidental actuality, when we want to signify any form or actuality to be actually in a subject, we signify this by the verb 'is'.33

Of course, this is just one of several of Aquinas's formulations of the theory of predication that historians of medieval logic duly dubbed the inherence theory.34 Stated as a general, formal semantic principle, the inherence theory claims that

(I) the predication of a common term F of an individual u is true if and only if the form ultimately signified by F in u actually is, i.e., exists.35

Again, I have to stress that despite possible modern worries to the contrary, this claim, as a formal semantic claim, does not involve the introduction of any sorts of "mysterious" or spurious entities. For this apparently atavistic talk about "forms" and "natures", clearly of the same breed as Molière's mocked talk about dormative powers, in this semantic interpretation need not commit us to any curious sorts of entities other than those familiar to anyone, nor to any sort of epistemological nonsense, such as having to have some "metaphysical intuition" into the ordinarily hidden natures of things.

For by saying that a general term ultimately signifies a form in the particulars that render those particulars such that they actually fall under the concept immediately signified by the term in question we do not need to posit some new sort of "mysterious" entities in the thing, indeed, not any more than by talking about concepts in this semantic context did we have to posit any sorts of further, "mysterious" entities, other than those anyone would agree to be familiar with. (Remember, talk about concepts in itself neither implies nor excludes the possibility that the acts of awareness that, in relation to their objects, we talk about as concepts are in themselves just brain processes. On the other hand, there being such acts of awareness in the intended sense is just such a familiar fact of human existence that denying their existence would yield a self-defeating claim.)36 Thus, just as we could start talking about concepts without having to commit ourselves to any particular theory as to what concepts in themselves are, so we can start talking about the 'forms' of things as the ultimate significata of our words, without having to take a metaphysical stance as to what these 'forms' in themselves are. Of course, talking about these ultimate significata as forms, rather than anything else, indicates the close historical relationship 33 "... nam est, simpliciter dictum, significat in actu esse; et ideo significat per modum verbi. Quia vero actualitas, quam principaliter significat hoc verbum 'est', est communiter actualitas omnis formae, vel actus substantialis vel accidentalis, inde est quod cum volumus significare quamcumque formam vel actum actualiter inesse subiecto, significamus illud per hoc verbum 'est', vel simpliciter vel secundum quid: simpliciter quidem secundum praesens tempus, secundum quid autem secundum alia tempora." in Peri lb. 1, lc. 5, n. 22. 34 Cf. e.g. L. M. de Rijk's Introduction to his edition of Abaelard, P.: Dialectica, Assen, 1956, pp. 37-38; Henry, D. P.: Medieval Logic and Metaphysics, London, 1972, pp.55-56, Geach, P.T.: "Nominalism", in Geach, P. T.: God and the Soul, London, 1969. 35 Cf., e.g.: "Oportet enim veritatem et falsitatem, quae est in oratione vel opinione, reduci ad dispositionem rei sicut ad causam. Cum autem intellectus compositionem format, accipit duo, quorum unum se habet ut formale respectu alterius: unde accipit id ut in alio existens, propter quod praedicata tenentur formaliter. Et ideo, si talis operatio intellectus ad rem debeat reduci sicut ad causam, oportet quod in compositis substantiis ipsa compositio formae ad materiam, aut eius quod se habet per modum formae et materiae, vel etiam compositio accidentis ad subiectum, respondeat quasi fundamentum et causa veritatis, compositioni, quam intellectus interius format et exprimit voce. Sicut cum dico, Socrates est homo, veritas huius enuntiationis causatur ex compositione formae humanae ad materiam individualem, per quam Socrates est hic homo: et cum dico, homo est albus, causa veritatis est compositio albedinis ad subiectum: et similiter est in aliis." in Meta lb. 9, lc. 11, n. 1898. 36 For more on this see the comments on rule 1. in section 6.

206

between this semantic conception and a hylomorphist metaphysics. This, however, does not mean that this semantic approach in itself logically implies a hylomorphist metaphysics in general, 37 or any specific version of it in particular. In fact, such an implication would leave no room for metaphysical disagreements to be disputed within the same semantic framework. But of course many of the great metaphysical disputes of high-scholasticism can be construed as revolving precisely around the distinctions vs. identities of the semantic values commonly assigned to several expressions within basically the same semantic framework.

This is the most obvious in the famous debate concerning the unicity vs. plurality of substantial forms. Recapitulated in semantic terms, the point of the debate was to decide whether the ultimate significata of the substantial predicates of the same individual are the same or distinct, a question left open by the semantic principles of signification and predication, but one that has far-reaching ramifications both in metaphysics and in theology.38 Again, the same semantic framework leaves the question whether the significata of such substantial predicates should be regarded as identical with or distinct from the significatum of the predicate 'is' in the same individual undetermined. Hence the need for Aquinas to deploy several metaphysical arguments for his famous thesis of the real distinction between essence and existence, i.e., between the significata of substantial predicates and the significata of the verb 'is', in creatures, while, of course, the same semantic principles allow him to state the identity of these significata in the case of God.39 But the same semantic principles do not determine even whether the significatum of a predicate in an individual is distinct from this individual itself, so again, anyone having ontological, that is, metaphysical qualms about "multiplying entities" is free to construe the significata of predicates with respect to the particulars as being the particulars themselves, at least, as far as the semantics is concerned.40 However, of course, such a decision will again have 37 In fact, that the ultimate significata of common terms need not necessarily be regarded metaphysically as forms in all cases was a commonplace also for thinkers who otherwise were committed to a hylomorphist metaphysics. As St. Thomas wrote: "...dicendum est quod illud a quo aliquid denominatur non oportet quod sit semper forma secundum rei naturam, sed sufficit quod significetur per modum formae, grammatice loquendo. Denominatur enim homo ab actione et ab indumento, et ab aliis huiusmodi, quae realiter non sunt formae." QDP, q. 7, a. 10, ad 8. Cf. also e.g. Cajetan: "Verum ne fallaris cum audis denominativum a forma denominante oriri, et credas propter formae vocabulum quod res denominans debet esse forma eius quod denominatur, scito quod formae nomine in hac materia intelligimus omne illud a quo aliquid dicitur tale, sive illud sit secundum rem accidens, sive substantia, sive materia, sive forma." Cajetan, Thomas de Vio: Scripta Philosophica: Commentaria in Praedicamenta Aristotelis, ed. M. H. Laurent, Angelicum: Romae, 1939, p. 18. In general, it is precisely this point that lies at the bottom of the distinction between extrinsic vs. intrinsic denomination. Cf. also: "Nam, sicut dicit Commentator, duodecimo Metaphysicae, grammaticus videt in multis differre dispositionem et dispositum, et sic movetur ad imponendum eis nomina diversa, ut 'albedo' et 'album'; et quia non est ejus inquirere an in omnibus vel in quibus sic differant dispositio et dispositum, ipse secundum similitudinem ad illa in quibus manifeste differunt imponit etiam aliis nomina per modum dispositionis et dispositi, seu determinationis et determinabilis, vel etiam determinati, derivando ab abstracto concretum vel e converso, relinquens metaphysico considerationem an illa nomina supponant pro eodem vel pro diversis, propter quem diversum modum significandi grammaticalem illa nomina habent diversos modos praedicandi." Jean Buridan: Lectura de Summa Logicae: De Praedicabilibus, c. 7, n. 4, H. Hubien's unpublished edition. 38 An excellent historical summary of the debate with ample further references is provided by Callus, D. A.: "Forms, Unicity and Plurality of ", in: New Catholic Encyclopedia, Prepared by an editorial staff at the Catholic University of America, McGraw-Hill: New York, 1967-79. 39 See, e.g., De Ente c. 5. 40 Without intending to go too much into technicalities, let me just give here a brief indication of how this claim can be made exact in a formal semantic system. If P is a common predicate, then the ultimate significate of P in respect of an individual u at a time t may be assigned by the semantic function SGT in a model in the following way:

207

its metaphysical consequences, so anyone wishing to do so will have to face, among others, Aquinas's metaphysical arguments to the effect that in material beings such an identification is impossible, whereas in the case of God it is more than justified.41 Finally, not only do these formal semantic principles, namely the inherence theory of predication and the corresponding theory of signification, leave the questions of the identity vs. distinction of the ultimate significata and supposita of common predicates undetermined, but also the question whether there really is in actual being something, an actually inherent form, in the thing corresponding to a predicate, even when the predicate is true of this thing. For certain predicates, namely, negative or privative predicates, which in their very concept involve the lack of what their opposite signifies, are true of something precisely because the opposite significatum is lacking in this thing. So for the former to be is for the latter not to be. But then the being of the significatum of the negative or privative predicate is nothing but the non-being of the significatum of the opposite positive predicate. Therefore, since nothing can be both being and non-being in the same sense, the significatum of the privative or negative predicate cannot be said to be in the same sense as the significatum of the opposite positive predicate. Indeed, this is precisely what seems to be the primary motivation for the Aristotelian distinction between the two senses of 'being' with which we started our discussion. As in a different context Aquinas writes: SGT(P)(u)(t)∈W∪{0}, where W is the domain of the model, t is some time, and 0 is a zero-entity (0∉W). The case SGT(P)(u)(t)=0 represents the situation that P signifies nothing in u, as for example the predicate 'red' signifies nothing in respect of the number 2. It is also reasonable to stipulate that SGT(P)(0)(t)=0. Then, if the set of things that are actual at a certain time t, A(t), is a subset of W, in accordance with the inherence theory of predication we can say that the predication of P of an individual u at a certain time t in a present tense sentence (i.e., the copula of which consignifies the time t of the utterance) is true if and only if SGT(P)(u)(t)∈A(t). Now this much of semantics can certainly stay in place whether in a particular model SGT(P)(u)(t)=u or SGT(P)(u)(t)≠u. But the former case represents precisely the simple ontology in which the significate of P in u at t is not an entity distinct from u, but is u itself. In such an ontology, for example, the predicate 'round' in respect of a round thing, say, a billiard ball, would signify the ball itself, but in respect of, say, a cube, it would signify nothing. (SGT('round')(ball)(t)=ball, SGT('round')(cube)(t)=0) Nevertheless, in general, in this paper I do not intend to go into technicalities. I will only indicate in the notes how the semantic principles discussed here could be given exact formulations in a model-theoretical framework. For a complete semantic system constructed along these lines to represent St. Thomas's ontology see Klima, G.: "On Being and Essence in St. Thomas Aquinas’s Metaphysics and Philosophy of Science", S. Knuuttila-R.Työrinoja-S. Ebbesen (eds.): Knowledge And The Sciences In Medieval Philosophy: Proceedings of the Eighth International Congress of Medieval Philosophy (S.I.E.P.M.), Helsinki 24-29 August 1987, Vol. II, Publications of Luther-Agricola Society Series B 19, Helsinki, 1990, pp. 210-221. For the issue of the independence of this semantic construction from that particular ontology see Essay V. of my Ars Artium. 41 See, e.g., ST1 q. 3, a. 3; Quodl. 2, q. 2, a. 2[4]. However, I think it is also interesting to note here that the possibility of identifying everything with substance even in the case of material substances was considered already even by a medieval philosopher, John of Mirecourt, who denied all sorts of metaphysical distinctions corresponding to semantic distinctions in rebus, even the distinction between substance and accident. In fact, it is somewhat ironical that it took an "arch-nominalist" like Jean Buridan, someone who himself reduced the number of distinct ontological categories to two (namely, to substance and quality), to deploy several metaphysical arguments against this "obscure and dangerous" doctrine. Cf. Adams, M. M.: "Things versus 'Hows'", in: Bogen, J. and McGuire, J. E. (eds.): How Things Are, D. Reidel Publishing Company, Dordrecht-Boston-Lancaster, 1985, pp. 175-188, esp. pp. 179-180. Of course, there are substantial differences between Aquinas' and Buridan's (and probably also Mirecourt's) approach to semantics. The point, however, is that for both of them, semantics does not dictate to ontology: however differently we may pick out things for our consideration, whether we do pick out distinct things or just the same thing differently is not determined by semantics, and so this has to be determined by careful metaphysical considerations. For more on this issue and the particular differences between Aquinas's and Buridan's approach to semantics, see: Klima, G.: “Ontological Alternatives vs. Alternative Semantics in Medieval Philosophy”, in: J. Bernard: Logical Semiotics, S - European Journal for Semiotic Studies, 3(1991), No. 4, Vienna, pp. 587-618.

208

... as was said above, 'being' is predicated in two ways. In one way it signifies the essence of a thing existing outside of the soul; and in this way the deformity of sin cannot be said to be a being, for it is a certain privation, but privations do not have an essence in the nature of things. In the second way ['being'] signifies the truth of a proposition; and in this way a deformity is said to be, not that it has being in the thing, but because the intellect compounds a privation with its subject as if it were some form. Therefore, just as from the composition of a form with a subject or with matter there results some substantial or accidental being; so does the intellect signify the composition of a privation with a subject by some being. But this being is only being of reason, for in the thing it is rather non being ... 42

Thus, whatever common predicate we substitute for F in (I) above, (I) will hold, only the sense of 'is' or 'exists' in it may vary, depending on the kind of significatum F has in u. In fact, on the basis of this point one may already surmise how the different senses of 'being' distinguished by Aquinas are related to the different kinds of predicates that can occur in actual predications. However, before considering this relationship we have to consider the function of common terms in the other necessary component of an actual predication in a proposition, namely, the subject term, which supplies the referent, or suppositum, for the predication.

Supposition and signification of abstract vs. concrete terms

So far I have been gathering and discussing Aquinas's semantic ideas only concerning common terms as they are predicable of individuals. As we could see, according to this conception, a common term in an actual predication, i.e., as the predicate of a categorical proposition, ultimately signifies some individualized property of the individual (or individuals) of which it is predicated, i.e., which is (or are) referred to by the subject of the proposition. But common terms can function also as subjects themselves, and then, according to medieval logicians, they also have the function to refer to, or to use the modern transliteration of medieval terminology, supposit for the individuals that fall under them. 43 In this referring function, then, despite the fact that they signify what we called the forms of the particulars (i.e., their ultimate significata in the particulars, whatever those ultimate significata are in themselves), they normally refer to, or supposit for, the particulars themselves. As St. Thomas says:

In respect of any name we have to consider two things, namely that from which the name is imposed, what is called the quality of the name, and that on which the name is imposed, what is called the substance of the name. And the name, properly speaking, is said to signify the form, or quality, from which the name is imposed, and is said to supposit for the thing on which it is imposed.44

42 "Ad tertium dicendum, quod, ut supra dictum est, ens dicitur dupliciter. Uno modo quod significat essentiam rei extra animam existentis; et hoc modo non potest dici ens deformitas peccati, quae privatio quaedam est: privationes enim essentiam non habent in rerum natura. Alio modo secundum quod significat veritatem propositionis; et sic deformitas dicitur esse, non propter hoc quod in re esse habeat, sed quia intellectus componit privationem cum subjecto, sicut formam quamdam. Unde sicut ex compositione formae ad subjectum vel ad materiam, relinquitur quoddam esse substantiale vel accidentale; ita etiam intellectus compositionem privationis cum subjecto per quoddam esse significat. Sed hoc esse non est nisi esse rationis, cum in re potius sit non esse; et secundum hoc quod in ratione esse habet, constat quod a Deo est." 2SN d. 37, q. 1, a. 2. 43 For formal reconstructions of the relevant medieval ideas, and ample references to and discussion of the enormous amount of contemporary literature they generated see Essays II-IV. of my Ars Artium. 44 "... in quolibet nomine duo est considerare: scilicet id a quo imponitur nomen, quod dicitur qualitas nominis; et id cui imponitur nomen, quod dicitur substantia nominis: et nomen, proprie loquendo, dicitur significare formam sive qualitatem a qua imponitur nomen; dicitur vero supponere pro eo cui imponitur." 3SN d. 6, q. 1, a. 3. It is important

209

So, for example, the term 'man' signifies human nature in abstraction from the singulars immediately, and signifies individual human natures ultimately, but normally, say, in the proposition 'A man is white', it supposits for the things actually bearing the nature it signifies, namely individual humans.45 But then this proposition is true if and only if the form ultimately signified by its predicate term in at least one of the supposita of the subject term actually exists, that is, if and only if the individual whiteness of at least one of the individuals actually having humanity (i.e., the whiteness of a human being) actually exists.

But here we should note again that this semantic distinction between suppositum and significatum, as such, need not posit any real distinction between what is signified and what is supposited for by a common term in a proposition. For even if according to Aquinas's metaphysical views, to this semantic distinction, in the case of material beings there corresponds a real distinction, and thus, for example, a human being is not his or her humanity, or a wise person is not his or her wisdom, in the case of God, while the semantic distinction is still in force, that is, for example, the predicate 'wise' is still related to divine wisdom as to its significatum, and to God as to its suppositum, there is no corresponding real distinction between what is signified and what is supposited for, since, as a consequence of divine simplicity, God is identical with divine wisdom.46 Thus, at least as far as common concrete terms are concerned,

to note here that although St. Thomas sometimes also contrasts id a quo with id ad quod nomen imponitur to distinguish the etymology of a name from its proper signification (the stock-example being "lapis", cf., e.g., ST1. q. 13, a. 2, ad 2. ), we must not confuse the two distinctions. As St. Thomas himself pointed out: "...nomen dicitur ab aliquo imponi dupliciter: aut ex parte imponentis nomen, aut ex parte rei cui imponitur. Ex parte autem rei nomen dicitur ab illo imponi per quod completur ratio rei quam nomen significat; et haec est differentia specifica illius rei. Et hoc est quod principaliter significatur per nomen. Sed quia differentiae essentiales sunt nobis ignotae, quandoque utimur accidentibus vel effectibus loco earum, ut VII Metaphys. dicitur; et secundum hoc nominamus rem; et sic illud quod loco differentiae essentialis sumitur, est a quo imponitur nomen ex parte imponentis, sicut lapis imponitur ab effectu, qui est laedere pedem. Et hoc non oportet esse principaliter significatum per nomen, sed illud loco cuius hoc ponitur." QDV. q. 4, a. 1, ad 8. Thus, id a quo nomen lapidis imponitur, ex parte rei, is the ratio seu natura lapidis, i.e., the nature of stones, sometimes also referred to as lapideitas, namely, what is signified by the term lapis, whatever it is, and whether we know it in terms of an essential definition or not; whereas id a quo nomen lapidis imponitur, ex parte imponentis, is the accidental property of stones that they tend to hurt the foot (laedere pedem), which may have provided the motivation for so naming them. (Whether Isidore of Seville's etymology is actually correct or not is irrelevant here.) For a more detailed discussion of the two distinctions and references to their earlier history see Ashworth, E. J.: "Signification and Modes of Signifying in Thirteenth-Century Logic: A Preface to Aquinas on Analogy", Medieval Philosophy and Theology 1(1991), pp. 39-67, esp. pp. 47-50. 45 I say, "normally", because it is only in some special context that a term is made to refer to what it normally signifies. As Aquinas says: "Quia enim forma significata per hoc nomen 'homo', idest humanitas, realiter dividitur in diversis suppositis, per se supponit pro persona; etiamsi nihil addatur quod determinet ipsum ad personam, quae est suppositum distinctum. Unitas autem sive communitas humanae naturae non est secundum rem, sed solum secundum considerationem, unde iste terminus 'homo' non supponit pro natura communi, nisi propter exigentiam alicuius additi, ut cum dicitur, 'Homo est secies'." ST I. q. 39, a. 4, cf. ST III. q. 16, a. 7. Of course, those familiar with medieval logic will immediately recognize here a case of simple supposition, as opposed to personal supposition. However, as I said before, in this paper I do not intend to go into the technicalities of supposition theory. Following Aquinas's practice, when I will speak about a term's supposita without any qualification, I will intend the term's personal supposita. 46 Cf.: "Respondeo dicendum, quod natura et suppositum naturae in quibusdam differunt re et ratione, sicut in compositis; in quibusdam autem ratione et non re, sicut in divinis." 3SN d. 11, q. 1, a. 4, in corp. Cf.also: "... propter divinam simplicitatem, consideratur duplex realis identitas in divinis eorum quae differunt in rebus creatis. Quia enim divina simplicitas excludit compositionem formae et materiae, sequitur quod in divinis idem est abstractum et concretum, ut deitas et deus. Quia vero divina simplicitas excludit compositionem subiecti et accidentis, sequitur quod quidquid attribuitur deo, est eius essentia, et propter hoc sapientia et virtus idem sunt in deo, quia ambo sunt in

210

their mode of signification (modus significandi) is such that they signify their ultimate significata in the particular things (whether these significata are actual or merely potential), but as subjects of categorical propositions they supposit for those particular things in which their ultimate significata actually exist.47 Nevertheless, what they ultimately signify and what they supposit for may or may not be identical, depending on the nature of the things signified and supposited for, whence the question of the identity or distinction of their supposita and significata is a metaphysical question, not determined by the semantic distinction. On the other hand, the abstract counterparts of these concrete terms differ from the concrete terms precisely in their mode of signification, insofar as abstract terms both signify and supposit for what their concrete counterparts signify, but they do not supposit for the supposita of their concrete counterparts, except when these supposita are identical with the significata. This is why we can refer to the significata of concrete terms by their abstract counterparts, and say, for example, that the term 'man' signifies humanity, whereas it supposits for humans, and that a man is not identical with his humanity, whereas God (the suppositum of the term 'God') is identical with deity, i.e., the significatum of the term 'God', and the suppositum (and significatum) of the term 'deity'.48

Note here that in the previous sentence the term 'humanity' is used to refer to what the term 'man' signifies. Indeed, in general, the function of abstract terms seems to be precisely this, namely, to afford us the linguistic means to refer in a proposition to the significata of their concrete counterparts, for the concrete terms do not refer to their significata, but to the things actually having their significata. Thus, whenever we need to refer not to the supposita but to the significata of a concrete term, we need an abstract term, corresponding to the concrete term. But then we can see how this semantic framework generated in scholastic philosophy and science the need for abstract terms even in cases where ordinary usage did not supply any. It was this systematic need of this semantic framework that yielded all the 'barbarisms' (such as 'lapideitas', 'asininitas', or even 'Sorteitas', and the Scotists' famous 'haecceitas' and their likes) that later on were to evoke the contempt of an emerging new, non-scholastic intelligentsia, which originally just refused, and a couple of centuries later simply forgot to think in terms of the semantic principles governing scholastic discussions. But, of course, this is already a different, and enormously complicated story, which we cannot go into here. Still, it is important to keep in mind that it is only as a result of this 'historical amnesia' that now we are in a situation in which it takes this meticulous gathering and arranging bits and pieces of Aquinas' thought to piece together his semantic conception, consisting of principles that constitute a certain form of divina essentia." ST1 q. 40, a. 1, ad 1. 47 We should also add: "relative to the time and modality of the copula". But we need not consider these complications here. Cf., however, the text referred to in n. 53. below, and the related discussion in the body of the paper. In any case, using the notation introduced in n. 40. we could state this rule concerning assertoric (i.e., non-modal, non-ampliative) propositions in a formal system as follows: SUP(P)(t)∈{u: SGT(P)(u)(t)∈A(t)}, provided {u: SGT(P)(u)(t)∈A(t)}≠∅, otherwise SUP(P)(t)=0, where t is the time connoted by the copula of the proposition. From this, and from the rules of n. 40, it can be seen that an affirmative proposition whose subject supposits for nothing will have to be false. 48 Accordingly, if [P] is the abstract counterpart of P, then we can say that SGT([P])(u)(t)=SGT(P)(u)(t), and SUP([P])(t)=SGT(P)(SUP(P)(t))(t), if SGT(P)(SUP(P)(t))(t)∈A(t), otherwise SUP([P])(t)=0. But then, in a model representing Aquinas's metaphysics the following will hold: SGT('God')(SUP('God')(t))(t)=SUP('deity')(t)=SUP('God')(t); whereas SGT('man')(SUP('man')(t))(t)=SUP('humanity')(t)≠SUP('man')(t). But of course other models may represent different metaphysics. In particular, the same semantic system permits even the case when SGT('man')(SUP('man')(t))(t)=SUP('humanity')(t)=SUP('man')(t).

211

discourse, which was common in his time, but which for various reasons was gradually abandoned by subsequent generations. In any case, by now we have gathered enough of these bits and pieces to state at least some of the most general semantic principles underlying Aquinas's thought.

Aquinas's semantic principles

What follows, of course, will not be an exhaustive statement of what might be dubbed "Aquinas's semantics". Here I only summarize, and briefly comment on some of the most general principles we could glean from the foregoing discussion, so that on this basis I shall be able to answer all the questions and doubts that have emerged in the course of this discussion.

1. Common terms signify human concepts immediately, and the forms of particulars represented by these concepts ultimately.

The point of this principle is that the signification of a common term is something it has on account of its being associated with some act of human understanding. An utterance or an inscription becomes a term of a language precisely on account of this association with, or subordination to such a mental act. Once by an act of imposition, or name-giving, this conventional relation of subordination or immediate signification is established, the utterance or inscription becomes a term. Such a term, then, ultimately signifies the features, or forms, of the particular things represented by the concept to which it is subordinated.49

Note that what we call here concepts are just certain acts of the human understanding on account of which a human being is able to use the terms of a language with understanding, whatever those acts are in themselves. Again, what we call here forms are just the features of the things represented by these acts of understanding, whatever those features are in themselves. Thus, concepts and forms, as just the immediate vs. ultimate significata of our terms, are to be understood here in such a noncommittal way that to deny their existence in the intended sense should yield self-defeating claims. In this way, to claim, for example, that "I'm sure I have no such concepts in my head" in the intended sense of 'concept' would amount to the admission that "I can't use a single word with understanding, not even the words I'm just uttering". Again, if someone were to say: "Things just don't have such forms", then, in the intended sense of 'form', his claim would imply the admission that "Nothing is characterized by anything, and so neither the proposition I just uttered was characterized by truth".

On the other hand, admitting such concepts and forms as the immediate vs. ultimate significata of our terms need not involve any knowledge of what these significata are in themselves, for, in general, we can think of, and hence signify and refer to things without knowing their nature. In fact, of most of the things we talk about we don't know what they are, whereas, of course, we know what we signify by their names; we are only unable to give an essential definition of what is thus signified. For example, we can know what we signify by the term 'diamond' in English, without knowing that for something to be a diamond is for it to be a tetrahedrally crystallized

49 Formally, if CON(m,t)(P) is the concept to which P is subordinated in a mind m at a certain time t, i.e. the immediate significate of P in m at t, and CON(m,t)(P)(u)(t) is what is represented by this concept in respect of the particular u at time t, then the ultimate significate of P in u at t can be defined as follows: SGT(P)(u)(t)=CON(m,t)(P)(u)(t). Notice how this formulation allows for conceptual change and hence for change of meaning of P. For details in this regard see Essay V. of my Ars Artium.

212

allotrope of carbon. To know the latter is to know that the form signified by the term 'diamond' is the same as the form signified by the phrase 'tetrahedrally crystallized allotrope of carbon'. (Provided this is indeed what it is for something to be a diamond, but that is a question to be answered by natural scientists.) But whether or not we are in possession of this piece of knowledge, by the term 'diamond' we signify this form, which we are certainly entitled to baptize by coining an abstract term, say, 'diamondhood', to be able to refer to it in the further discussion. Of course, later on, it just might turn out that what we referred to as 'diamondhood' is nothing, but the tetrahedral arrangement of carbon atoms held together by covalent bonds, which we may further identify as the carbon atoms themselves thus and so arranged, etc. But none of these later results should affect the validity of the original, semantic principle, which only specifies how our terms are related to what they signify, but says nothing about what these significata are in themselves, that is, to what ontological category they belong, or by what combination of other terms we would be able to pick out precisely the same significata.

2. A concrete common term P is true of a particular thing u iff the form (ultimately) signified by P is actual in u. 50

This principle is just a reformulation of the inherence-theory: 'is actual' is meant to be taken in the same sense as 'is' or 'exists', the actual sense of which is determined by the signification of the actual substituents of P. For example, if P signifies a privation, then, of course, its significata can be actual only in the sense in which privations can be actual,51 not positing any entity in reality, indeed, indicating the lack of some real being in actual reality. Thus, for example, if 'bald' is construed as a privative term signifying the lack of hair where there should be hair by nature, then the predication of 'bald' of a bald man is true on account of the lack of hair on the bald man's head, i.e., it is the actuality of his baldness, the actual lack of hair on his head, that verifies the predicate 'bald' of him. But of course the actuality of this lack of hair does not make his baldness a real being superadded to the other, real entities of the world. Such a superadded real being would be the hair (or a wig, for that matter). But since it is precisely the actual lack of this superadded entity that is the actuality of baldness, the latter cannot be regarded as another such being, adding to the number of entities of the same kind. Hence, even if baldness is actual, it is in a different sense than those real entities. Indeed, even among real entities, which are not privations or just other beings of reason, there are further differences in their modes of being, reflected in the analogous senses of 'being' distinguished by Aristotle and Aquinas, which will be discussed in more detail in the next section.

3. A concrete common term P supposits for (refers to) a particular thing u as the subject of a proposition iff the form signified by P in u is actual (relative to the time and modality of the copula of the proposition and to the ampliation of the predicate).52

The actuality of the significata of a common term is what makes it true of particular things, and so, if the term in question occurs as the predicate term of an affirmative categorical proposition, this will render the proposition true of the individuals referred to in it. But if the term in question is the subject term of a proposition, then its function is not to state something of the things referred to in the proposition, but to refer, to supply the referents, or supposita for the predicate

50 Cf. n. 40. above. 51 Cf.: "et sicut in rebus, quae extra animam sunt, dicitur aliquid in actu et aliquid in potentia, ita in actibus animae et privationibus, quae sunt res rationis tantum." in Meta lb. 5, lc. 9, n. 13. 52 Cf. n. 47. above.

213

term to be true of. However, even in this referring function, what determines whether a certain particular is actually supposited for by the common term as the subject term of a proposition is whether the form signified by the term in the particular is actual at the time consignified53 by the copula (or the verb implying the copula) of the proposition. For example, in the sentence 'A dinosaur is running', the subject term 'dinosaur' should supposit for actual dinosaurs, i.e., things that actually have the nature of a dinosaur, for the sentence would be true only if the things actually having the significate of the subject would also actually have the significate of the predicate at the present time of the utterance of the proposition. But, since by all probability there is no such thing in actuality (nothing has a dinosaur nature in actuality, i.e., nothing is a dinosaur), no such thing has the significate of the predicate in actuality, whence the sentence is actually false. On the other hand, in the proposition 'A dinosaur was running', the time consignified by the copula is some past time relative to the present time of the utterance of the proposition. So this proposition is true if the things which have or had the significate of the subject in actuality also had the significate of the predicate in actuality at some past time relative to the utterance of the proposition. But then, since some things did have dinosaur nature in the past, i.e., there were dinosaurs, and by all probability some of them were actually running at some past time (i.e., they had the significate of the predicate, the act of running, in actuality), this proposition is probably actually true. Similar considerations would apply to other tenses, modalities, and special predicates habentes vim ampliandi, as medieval logicians would put it, i.e., predicates that have the force of extending the range of reference of their subject terms beyond the set of things that actually exist at the time of the utterance of the proposition, such as verbs and participles signifying mental acts (say, 'think', 'imagine', etc.), but we need not go into those details here.54 All we need to note here is that while reference depends on signification, for it is its having or not having the significate of a common term that ultimately determines whether a particular thing is supposited for in a proposition or not, nevertheless, this determination takes place in a propositional context, which further determines how these significata contribute to the determination of supposition.55

4. The significata of the abstract counterpart [P] of a concrete common term P are the same as those of P, but as the subject of a proposition [P] supposits for the ultimate significata of P (which are also the significata of [P], of course), provided they are actual relative to the time and modality of the copula of the proposition.56

53 Cf. e.g., in Peri lb. 1. lc. 5. 54 Especially, since St. Thomas never addressed the issue of suppositio, the medieval theory of reference, ex professo. However, that he knew well and applied consciously the theoretical apparatus of the sophistae, the teachers of logic of the Faculty of Arts, is obvious from his references to their doctrine in the following places: 1SN d. 21, q. 1, a. 1a, ad 2-um; ST1 q. 31, a. 3, ad 3-um; ST1 q. 39, a. 4, obj. 1; ST1 q. 39, a. 5, ad 5-um. For a discussion of Aquinas's doctrine in relation to the logical theory of his contemporaries, see: Ashworth, E. J.: "Signification and Modes of Signifying in Thirteenth-Century Logic: A Preface to Aquinas on Analogy", Medieval Philosophy and Theology 1(1991), pp. 39-67. Also, for a discussion of ampliatio in particular see Klima, G.: "Old Directions in Free Logic: Existence and Reference in Medieval Logic", in: K. Lambert: New Directions in Free Logic, Akademia Verlag, Sankt Augustin bei Bonn, (forthcoming). 55 Although Peter of Spain, e.g., regards natural supposition as the kind of supposition a term has absolutely [per se], apparently even outside of the context of a proposition. But even according to him, within a propositional context the actual (what he calls accidental) supposition of a term is determined by the context. See: Peter of Spain: Tractatus, ed. L. M. de Rijk, Van Gorcum, Assen, 1972, p. 81. For some discussion and further references see again my paper referred to in the previous note. 56 Cf. n. 48.

214

The ultimate significata of abstract and concrete terms (and, hence, also their significations) are the same. Both 'white' and 'whiteness' signify the same forms, the individual whitenesses of particular things,57 whether they are actually, or merely potentially white. (There are, of course, things which cannot possibly be white, say, numbers, which are extra genus coloris, i.e., for which color predicates are simply not interpreted. In such things color predicates signify nothing.58) However, while concrete terms supposit for the things that have their significata in actuality, abstract terms supposit for their significata in actuality (of course, also relative to the conditions required by the propositional context). So whereas 'white' supposits for white things, 'whiteness' supposits for whitenesses, etc. But of course, this does not tell us what kind of entity a whiteness is, or indeed, whether it is something distinct from a white thing. 59

5. An affirmative categorical proposition is true iff its predicate is true of (all, or some, depending on the quantity of the proposition, of) the supposita of its subject.

The truth of an affirmative categorical proposition, i.e., a proposition in which two common terms are joined by an affirmative copula, is ultimately determined by whether its predicate is true of the thing(s) supposited for by its subject term. Note that the terms here may be of any complexity, so the theory of categorical propositions need not be thought of as covering only simple cases like 'A man is an animal'. But here we need not deal with those complexities.60 Also, of course, the truth of a categorical is determined by its quantity, i.e., the determiner of its subject term, which determines how many of the supposita of the subject term should be considered in determining the truth of the proposition. In fact, this analysis of the categoricals allows for a uniform treatment of all sorts of determiners in the framework of a logical theory the expressive capacity of which matches that of generalized quantification theory, but again, such technicalities need not be considered here.61 The only really important point in the present discussion is that in accordance with this principle the truth of a categorical proposition ultimately depends on whether its predicate is true of the supposita of its subject. But whether the predicate is true of these supposita depends on the actual inherence of its significata in these supposita. And so, since the actual inherence of these significata is nothing, but their actuality, i.e., their actual being, this point directly takes us back to the starting point of our discussion: the various analogical senses of 'being' distinguished by St. Thomas in accordance with the various modes of predication.

57 Cf., e.g., the detailed discussion of denomination by Cajetan: "... non debet denominativum differre a nomine formae denominantis in significatione. Hoc enim esset differre non solo casu sed significatione. [interpunction mine–G.K.] Et consequenter diffinitione et essentia idem significat album et albedo, quum (ut infra docet Aristoteles) album puram qualitatem significat. [cf. with this in Meta lb. 5, lc. 9, n. 894.] Differentia autem in modo significandi inventa inter denominativum et denominans non excluditur per ly solo casu, quoniam talis differentia comes est differentiae secundum casum." Cajetan, Thomas de Vio: Scripta Philosophica: Commentaria in Praedicamenta Aristotelis, ed. M. H. Laurent, Angelicum: Romae, 1939, pp. 16-17. 58 For this point see again n. 40. 59See again nn. 47, 48. 60 For a detailed discussion of these complexities see Klima, G.: "Latin as a Formal Language: Outlines of a Buridanian Semantics", Cahiers de l’Institut du Moyen-Âge Grec et Latin, Copenhagen, 61(1991), pp. 78-106. 61 Nevertheless, see Essay IV. of my Ars Artium; or Klima, G. and Sandu, G.: "Numerical Quantifiers in Game-Theoretical Semantics", Theoria, 56(1990), pp. 173-192.

215

Being simpliciter vs. secundum quid

As we could see, the theory of truth and predication outlined above in itself seems to require a systematic correspondence between the different kinds of significata of several sorts of predicates and the various analogical senses of 'being' distinguished by Aristotle and Saint Thomas. We could also see, however, that according to St. Thomas's theory of the copula, the copula of an affirmative categorical proposition invariably signifies the truth of the proposition in which it occurs.

To see in more detail the relationships between the sense of the copula and the various senses in which the significata of several predicates can be said to be, let us take a more careful look again at the various formulations of the inherence theory of predication provided above. All of these formulations are equivalences, the left-hand-side of which states the truth of a predication, while the right-hand-side states the actual existence of the significata of the predicate in the supposita of the subject of the predication. But a predication itself is performed by a categorical proposition, the formal element of which is the copula, which joins the terms to form a proposition (for without the copula, whether it is expressed in the surface structure of a language or not, a mere sequence of terms does not form a proposition).62 This is why we can say that what is invariably signified by the copula is the truth of the proposition in which it occurs, which is precisely the reason why St. Thomas also often speaks about the mode of being signified by the copula as ens ut verum, being as truth.63 But stating the truth of the proposition is nothing, but stating the obtaining of the state of affairs expressed by the proposition as a whole, which in English can be referred to by a that-clause, while in Latin either by a clause beginning with a corresponding 'quod' or 'quia' or by an accusative with infinitive construction.64 Consider the following, equivalent sentences:

S is P

'S is P' is true

It is true that S is P

That S is P is true

62 Of course, verbs in this theory are to be analyzed into a copula and a participle. In fact, even in languages like Russian or Hungarian, in which no copula is needed for the formation of present tense categoricals (although the two languages belong to different families of languages), the well-formedness of sentences in the past and future tenses requires the addition of the appropriate forms of the verb corresponding to the verb 'be', which indicates that on the conceptual level a copula is present even in the present tense sentences, even if it is unmarked in their surface syntax. 63 Cf.: "Deinde cum dicit amplius autem ponit alium modum entis, secundum quod esse et est, significant compositionem propositionis, quam facit intellectus componens et dividens. Unde dicit, quod esse significat veritatem rei. Vel sicut alia translatio melius habet quod esse significat quia aliquod dictum est verum. Unde veritas propositionis potest dici veritas rei per causam. Nam ex eo quod res est vel non est, oratio vera vel falsa est. Cum enim dicimus aliquid esse, significamus propositionem esse veram. Et cum dicimus non esse, significamus non esse veram; et hoc sive in affirmando, sive in negando. In affirmando quidem, sicut dicimus quod Socrates est albus, quia hoc verum est. In negando vero, ut Socrates non est albus, quia hoc est verum, scilicet ipsum esse non album. Et similiter dicimus, quod non est diameter incommensurabilis lateri quadrati, quia hoc est falsum, scilicet non esse ipsum non commensurabilem." in Meta lb. 5, lc. 9, n. 895. 64 For the early medieval theory of such sentential nominalizations, called appellatio dicti, see: Rijk, L. M. de (ed.): Logica Modernorum, II-1-2, Van Gorcum, Assen, 1967.

216

That S is P is

That S is P is a being

Aquinas's point seems to be precisely that all occurrences of 'is' (or rather the corresponding occurrences of 'est' in Latin), as well as the occurrence of 'being' in (6), above express the same sense of 'being', which, however, is not the primary sense, but is somehow analogically related to the primary sense of 'being'. That is, all occurrences of 'is' above, both as a copula and as an absolute predicate, express the same sense in which something can be said to be, indeed, the same sense as that expressed by the predicate 'being' in (6), as well as, say, in the sentence 'A blindness is a being'.65 In fact, any of the above formulations could stand on the left-hand-side of an equivalence stating the inherence theory of predication. However, on the right-hand-side we would have to have formulations like the following (where [P] is the abstract form of P):

A significate of P in a suppositum of S is (is actual/exists)

A [P] of an S is (is actual/exists)

A [P] of an S is a being

Note that here it is only the italicized copulae of these schemata that express the same sense as the occurrences of 'is' in (1)-(6). The other occurrences of 'is', as well as occurrences of 'actual', 'exists' and 'being', express different senses of 'being', depending on what sort of entity is signified by P in a suppositum of S. For example, taking 'blind' as the privative opposite of 'sighted', and 'blindness' and 'sight' as their respective abstract forms, consider the following instances of a scheme expressing the inherence theory of predication:

A man is sighted if and only if the sight of a man is (is a being)

A man is blind if and only if the blindness of a man is (is a being)

St. Thomas's point seems to be that here the italicized occurrences of 'is' (and 'being') signify being in the same sense:

We should know that this second mode is compared to the first as effect to cause. For it is from there being something in the nature of things that the truth or falsity of a proposition follows,

65But how is it possible, one might ask, for both the copula and the predicate of 'A blindness is a being' to express the same sense? How could any absolute predicate have the same sense as the copula? Well, using 'is2' to distinguish the usage of 'is' when it is used in the ens-rationis-sense, and using 'being2' to distinguish the usage of 'being' when it is used in the ens-rationis-sense, we can say first, in general, that 'is2' signifies the same whether it is used as a copula of a proposition or as the absolute predicate of a significate of the predicate of the same proposition: SGT('is2')(SGT(P))(SUP(S)(t))(t)=SGT('is2')(SGT(P)(SUP(S)(t))(t))(t), that is, given that, in accordance with rule 4, SGT(P)(SUP(S)(t))(t)=SUP([P])(t), SGT('is2')(SGT(P))(SUP(S)(t))(t)=SGT('is2')(SUP([P])(t))(t), which is precisely to say that 'is2' both in 'An S is2 P' and in 'A [P] is2' signifies the same, or has the same sense. But then, further, we can say that SGT('is2')(SUP([P])(t))(t)=SGT('being2')(SUP([P])(t))(t), which is nothing, but to claim that 'is2' and 'being2' as absolute predicates of the supposita of [P] signify the same. But then, in general, SGT('is2')(SGT(P))(SUP(S)(t))(t)=SGT('being2')(SUP(S)(t))(t). Whence, in particular, SGT('is2')(SUP('blindness')(t))(t)=SGT('is2')(SGT('being2'))(SUP('blindness')(t))(t)= =SGT('being2')(SUP('blindness')(t))(t). So, since 'blindness' supposits for a privation, we say that blindness is and it is a being, but it is and it is a being precisely and only in this sense, namely in the sense which is also expressed by the copula of an affirmative proposition. For the different case of 'sight' see n. 69. Indeed, even further, SGT('is2')(SUP('blindness')(t))(t)=SGT('is2')(SGT('blind'))(SUP(S)(t))(t), that is, when we say that a blindness is, the predicate of this sentence signifies the same as what is signified by the copula of the sentence by which we assert that an S is blind, precisely as Aquinas says (see quote in next note).

217

which the intellect signifies by the verb 'is' as it is a verbal copula. But, since something which in itself is not a being, as a negation and the like, is considered by the intellect as some being, sometimes that it is is said of something in this second way, but not in the first. For it is said that blindness is, in the second way, because the proposition by which something is said to be blind is true; but it is not said that this is true in the first way. For blindness does not have some being in the things, but it is rather a privation of being.66

On the other hand, the non-italicized occurrence of 'is' (as well as that of 'being') in (10) signifies being in the sense contrasted with the ens-rationis-sense, as expressing real being, ens reale, which itself comprises both the primary sense and several other secondary senses:

We have to say that 'being' is predicated in two ways [...] In one way as it is a verbal copula signifying the composition of any proposition that the soul forms: whence this being is not something in the nature of things, but only in the act of the judgment-forming intellect. And in this way being is attributed to everything of which a proposition can be formed, whether it is a being or a privation of being: for we say that blindness is. In the other way being [esse] is said to be the act of being [ens] insofar as being, that is, that by which something is denominated as a being in the nature of things. And being in this way is attributed only to the things themselves which are contained in the ten categories, whence 'being' [ens] predicated on account of such [an act of] being [esse] is divided by the ten categories. But this [act of] being [esse] is attributed to something in two ways. In one way as to that which [quod] properly and truly has being, or is. And thus it is attributed only to a per se subsisting substance; whence that which truly is is said to be a substance in bk. 1. of the Physics. All those [things], however, which do not subsist per se, but in others and with others, whether they are accidents or substantial forms or any sorts of parts, do not have being [esse] so that they themselves would truly be, but being [esse] is attributed to them in another way, namely, as to something by which [quo] something is; as whiteness is said to be, not that it itself would subsist in itself, but because it is by it that something has it that it is white. Being, therefore, is properly and truly attributed only to a per se subsisting thing. To this, however, two kinds of being are attributed. The one is that results from those from which its unity is integrated, which is the proper substantial being of a suppositum. Another being is attributed to a suppositum besides those that integrate it, which is an additional being, namely, accidental being; as being white is attributed to Socrates when it is said: Socrates is white.67

66 "Sciendum est autem quod iste secundus modus comparatur ad primum, sicut effectus ad causam. Ex hoc enim quod aliquid in rerum natura est, sequitur veritas et falsitas in propositione, quam intellectus significat per hoc verbum est prout est verbalis copula. Sed, quia aliquid, quod est in se non ens, intellectus considerat ut quoddam ens, sicut negationem et huiusmodi, ideo quandoque dicitur esse de aliquo hoc secundo modo, et non primo. Dicitur enim, quod caecitas est secundo modo, ex eo quod vera est propositio, qua dicitur aliquid esse caecum; non tamen dicitur quod sit primo modo vera. Nam caecitas non habet aliquod esse in rebus, sed magis est privatio alicuius esse." Meta lb. 5. lc. 9. n. 896. 67 "Respondeo. Dicendum, quod esse dupliciter dicitur, ut patet per Philosophum in v Metaph., Et in quadam glossa Origenis super Principium Ioan.Uno modo, secundum quod est copula verbalis significans compositionem cuiuslibet enuntiationis quam anima facit: unde hoc esse non est aliquid in rerum natura, sed tantum in actu animae componentis et dividentis. Et sic esse attribuitur omni ei de quo potest propositio formari, sive sit ens, sive privatio entis; dicimus enim caecitatem esse. Alio modo esse dicitur actus entis in quantum est ens, idest quo denominatur aliquid ens actu in rerum natura. Et sic esse non attribuitur nisi rebus ipsis quae in decem generibus continentur; unde ens a tali esse dictum per decem genera dividitur. Sed hoc esse attribuitur alicui dupliciter. Uno modo ut sicut ei quod proprie et vere habet esse vel est. Et sic attribuitur soli substantiae per se subsistenti: unde quod vere est, dicitur substantia in i Physic.. Omnia vero quae non per se subsistunt, sed in alio et cum alio, sive sint accidentia sive formae substantiales aut quaelibet partes, non habent esse ita ut ipsa vere sint, sed attribuitur eis esse alio modo, idest ut quo aliquid est; sicut albedo dicitur esse, non quia ipsa in se subsistat, sed quia ea aliquid habet esse album. Esse ergo proprie et vere non attribuitur nisi rei per se subsistenti. Huic autem attribuitur esse duplex. Unum scilicet esse resultans ex his ex quibus eius unitas integratur, quod proprium est esse suppositi substantiale. Aliud esse est supposito attributum praeter ea quae integrant ipsum, quod est esse superadditum, scilicet accidentale; ut esse album attribuitur Socrati cum dicitur: Socrates est albus." QDL 9. q. 2, a. 2, in corp.

218

So, if in

(i) An S is P

P signifies a privation (or negation or relation of reason68) then in the corresponding

(ii) A [P] of an S is

'is' signifies being in the secondary, ens-rationis-sense, inasmuch as the two propositions are equivalent. Of course, nothing prevents anyone from asserting, say, that [a] blindness is, or [an] evil exists, intending to signify that blindness and evil are real beings, i.e., taking 'is' or 'exists' in the sense in which they signify the actuality of real being. But if the terms 'blindness' and 'evil' are genuinely privative, in the way they were interpreted by St. Thomas, these assertions simply will not be true. On the other hand, if P signifies a real being, then, while the copula of (i) will still express being in the ens-rationis-sense, 'is' in (ii) will signify some real being. For example, if the proposition 'A man is sighted' is true, then 'A man's sight is' will also be true, so that while the occurrence of 'is' as the copula of the first proposition signifies being in the ens-rationis-sense, the occurrence of 'is', as the predicate of the second proposition, signifies being in an ens-reale-sense.69 Again, of course, one may wish to claim that a man's sight is, or exists, or that there is such a thing as a man's sight, in the ens-rationis-sense, in which sense the claim thus made will also be true, since whatever is a real being also exists in this weaker, ens-rationis-sense according to St. Thomas. But the point is that, unlike the case of 'A man is blind' and 'A man's blindness is', if 'A man is sighted' is true, then 'A man's sight is' will also be true even taking 'is' in the latter in an ens-reale-sense. However, as we could see, given that a man's sight is not a substance, even this is not the primary sense of being, but only one of the several senses of real being analogically related to its primary sense, namely, the sense in which we can say of a substance that it is.

Perhaps, in view of what has been said so far, now it will be easy to see how Aquinas is able to base this distinction between the primary and the secondary senses in which a real being can be said to be on the distinction between that which is, quod est, and that by which something is, quo

68 Although here I take only privations as my examples of beings of reason, it is not only privations that were regarded as such by St. Thomas. Indeed, according to him, the proper subject matter of logic consisted of beings of reason of a different sort: relations of reason. For a thoroughgoing discussion of St. Thomas's conceptions of the subject of logic, see Schmidt, R.W.: The Domain of Logic according to Saint Thomas Aquinas, Martinus Nijhoff: The Hague, 1966. For a discussion of various sorts of entia rationis and their systematic role in medieval semantics see: Klima, G.: "The Changing Role of Entia rationis in Medieval Philosophy: A Comparative Study with a Reconstruction", Synthese 96(1993), No. 1, pp. 25-59. 69 Of course, the absolute predicate 'is', expressing an ens-reale-sense could be analyzed further into 'is a being'. In this case 'is' would express the ens-rationis-sense whereas 'being' an ens-reale-sense. Using 'is1/2' and 'being1/2' to distinguish the usage of 'is' and 'being' respectively, in which they express the sense in which they are truly predicated of really inherent accidental forms, but not of mere beings of reason, we can say that SGT('is1/2')(SUP('sight')(t))(t)=SGT('being1/2')(SUP('sight')(t))(t), but SGT('being1/2')(SUP('sight')(t))(t)≠SGT('is2')(SGT('being1/2'))(SUP('sight')(t))(t), whereas, of course, SGT('is2')(SGT('being1/2'))(SUP('sight')(t))(t)=SGT('is2')(SUP('sight')(t))(t). So, what 'is' signifies in a secondary ens-reale-sense in a suppositum of 'sight' at the time of uttering 'A sight is' is the same as what 'being' signifies in the same sense in respect of the same at the same time in the utterance 'A sight is a being', but this is not identical with what the copula of this latter utterance signifies at the same time in respect of the signification of the predicate ('being') and the suppositum of 'sight' at the same time, which is nevertheless nothing, but what would be signified by 'is2' in the sentence 'A sight is2', claiming the existence of sight in the ens-rationis-sense. Cf. with this the analysis of 'A blindness is a being' above, in n. 65.

219

aliquid est, which, in turn, is based on a distinction between what he regards as the predication of 'being' or 'is' simpliciter and secundum quid. The clue, of course, lies in the inherence theory of predication and in the related theories of signification and supposition. In accordance with these, when a substance u is said to be, say, white, this is equivalent with saying that the whiteness of u exists. But then we can say that for u's whiteness to be is nothing, but for u to be white, which is, further, for u to be, not absolutely, simpliciter, but with respect to something, secundum quid, namely, with respect to its whiteness. As St. Thomas says:

... substance is the first being, and is being absolutely [simpliciter], and not being with respect to something, i.e., with qualification [secundum quid], as is the case with accidents. For to be white is not to be absolutely [simpliciter esse], but with qualification [secundum quid]. And this is clear from the fact that when something begins to be white, we don't say that it begins to be, absolutely, but that it begins to be white. For when Socrates begins to be a man, we say absolutely that he begins to be. Whence it is clear that to be a man signifies to be, absolutely. But to be white signifies to be with qualification.70

Thus we can see exactly how Aquinas can interpret all predications as predications of being, either with or without qualification. Just as in "ordinary predications" we can attach various qualifications to the predicate, so these "ordinary predications" themselves may be regarded as various qualifications of the predication of being. So according to this analysis, when we say: 'A man is blind', this is equivalent with saying: 'A man's blindness is', which, in turn, is further equivalent with saying: 'A man is with respect to his blindness'.

70 "... substantia est primum ens, et ens simpliciter, et non ens secundum aliquid, idest secundum quid, sicut est in accidentibus. Esse enim album non est simpliciter esse, sed secundum quid. Quod ex hoc patet, quia cum incipit esse albus, non dicimus quod incipiat esse simpliciter, sed quia incipiat esse albus. Cum enim Socrates incipit esse homo, dicitur simpliciter quod incipit esse. Unde patet quod esse hominem significat esse simpliciter. Esse autem album significat esse secundum quid." in Meta lb. 7, lc. 1, n. 1256. Cf.: "Nota quod qoddam potest esse licet non sit, quoddam vero est. Illud quod potest esse dicitur esse potentia; quod iam est dicitur esse actu. Sed duplex est esse: scilicet esse essentiale rei, sive substantiale, ut hominem esse, et hoc est esse simpliciter. Est autem aliud esse accidentale, ut hominem esse album, et hoc est esse aliquid. Ad utrumque esse est aliquid in potentia. Aliquid enim est in potentia ut sit homo, ut sperma et sanguis menstruus; aliquid est in potentia ut sit album, ut homo. Tam illud quod est in potentia ad esse substantiale, quam illud quod est in potentia ad esse accidentale, potest dici materia, sicut sperma hominis et homo albedinis. Sed in hoc differt: quia materia quae est in potentia ad esse substantiale, dicitur materia ex qua; quae autem est in potentia ad esse accidentale dicitur materia in qua. Item, proprie loquendo, quod est in potentia ad esse accidentale dicitur subiectum, quod vero est in potentia ad esse substantiale dicitur proprie materia. Quod autem illud quod est in potentia ad esse accidentale dicatur subiectum, signum est, quia dicuntur esse accidentia in subiecto, non autem <dicitur> quod forma substantialis est in subiecto. Et secundum hoc differt materia a subiecto: quia subiectum est quod non habet esse ex eo quod advenit, sed per se habet esse completum, sicut homo non habet esse ab albedine, sed materia habet esse ex eo quod ei advenit, qui de se habet esse incompletum. Unde simpliciter loquendo, forma dat esse materiae, sed subiectum accidenti, licet aliquando unum sumatur pro altero scilicet materia pro subiecto et econverso. Sicut autem omne quod est in potentia potest dici materia, ita omne a quo aliquid habet esse, quodcumque esse, sive accidentale sive substantiale, potest dici forma; sicut homo, cum sit potentia albus, fit actu albus per albedinem, et sperma, cum sit potentia homo, fit actu homo per animam. Et quia forma facit esse in actu, ideo forma dicitur esse actus. Quod autem facit esse actu esse substantiale, est forma substantialis, et quod facit esse actu esse accidentale, dicitur forma accidentalis. Et quia generatio est motus ad formam, duplici formae respondet duplex generatio: formae substantiali respondet generatio simpliciter, formae vero accidentali generatio secundum quid. Quando enim introducitur forma substantialis, dicitur aliquid fieri simpliciter. Quando autem introducitur forma accidentalis , non dicitur aliquid fieri simpliciter, sed fieri hoc; sicut quando homo fit albus, non dicimus simpliciter hominem fieri vel generari, sed fieri vel generari album. Et huic duplici generationi respondet duplex corruptio, scilicet simpliciter et secundum quid. Generatio vero et corruptio simpliciter non sunt nisi in genere substantiae; sed generatio et corruptio secundum quid sunt in aliis generibus." De Principiis Naturae c. 1.

220

It is this last formulation which shows explicitly why we can say that the attribution of blindness to a man is an attribution of being to him (insofar as we say that he is with respect to something), although not simpliciter, but secundum quid (insofar as we say that he is with respect to something), and that this attribution is at the same time an attribution of being to his blindness (insofar as what is signified by the complex predicate 'is with respect to blindness' in him is identical with what is signified by 'is' in his blindness, and which, in turn, is identical with what is signified in him by 'is blind').71 However, given the privative character of the predicate 'blind', the being thus attributed is, and can only be, being in the ens-rationis-sense, which is nothing, but the lack-of-real-being being conceived by the intellect as a form signified by the predicate 'blind'. So we can see how we should understand that the being of a privation (or of any other ens rationis, for that matter) is being in the intellect, having some foundation in reality. For being in the intellect is nothing, but being conceived by the human intellect, which we can express by predicates signifying acts of human awareness, as in saying that a chimera is thought of. In fact, even this predication can be construed as a predication of being secundum quid (which may be expressed by saying that thus a chimera is with respect to its being thought of) but the sense of being that is predicated in this case is not even the ens-rationis-sense, which Aquinas says is the sense in which we can answer a question asking whether there is such and such a thing. For of course to the question whether there are chimeras it would not be an appropriate answer to say that yes, there are insofar as they are thought of. On the other hand, to the question whether there is blindness it is an appropriate answer to say that yes, there is, insofar as some animals that should have sight by nature actually lack sight, which is precisely what is conceived of in the concept of blindness. Note here that for the being of blindness both conditions are required: both the lack of some sight and the activity of the human intellect to conceive of this lack of sight by forming the concept of blindness. Were there no humans to form the concept of blindness, there would be no blindness, even if there were animals lacking sight, for the actuality of blindness consists in the actual lack of sight conceived by humans by applying the concept of negation to the concept of sight (in forming the concept of blindness as an animal's lacking, i.e., not having sight).72 By contrast, the actuality of sight does not involve any such activity of the human mind,

71 Using 'is2' again in the same way as above, and using 'is1' to distinguish the usage of 'is' in which it is truly predicable in its primary sense of substances, we can state this formally as follows: SGT('is2 blind')(SUP('man')(t))=SGT('is2')(SGT('blind'))(SUP('man')(t))= =SGT('is1 with-respect-to blindness')(SUP('man')(t))(t)=SGT('is2')(SUP('blindness'))(t))(t). Here, of course, the signification of the complex, qualified predicate can (and, to comply with the requirement of compositionality, should) be analyzed further as follows: SGT('is1 with-respect-to blindness')=SGT('with-respect-to')(SGT('is1'))(SUP('blindness')(t)). (The phrase 'with-respect-to' need not be analyzed, as it functions as a single modifier. Indeed, in Latin the one-word-phrase respectu, as in homo est respectu caecitatis, or secundum, as in homo est secundum caecitatem, would do the same job.) 72 But at this point one might object that if there are animals lacking sight, then there must be blindnesses also, even if there are no minds to conceive of them, given that for a blindness to be is nothing but for a sight not to be. (In fact, I received this objection from Scott MacDonald.) Well, it is true that for a blindness to be is for a sight not to be, in the sense privations and negations can be, that is, SGT('is2')(SUP('blindness')(t))(t)=SGT('not')(SGT('is2'))(SUP('sight')(t))(t). Here, of course, SGT('not')(SGT(P))(SUP(S)(t))(t)∈A(t), if SGT(P)(SUP(S)(t))(t)∈W-A(t), SGT('not')(SGT(P))(SUP(S)(t))(t)∈W-A(t), if SGT(P)(SUP(S)(t))(t)∈A(t), and SGT('not')(SGT(P))(SUP(S)(t))(t)=0 if SGT(P)(SUP(S)(t))(t)=0 (Note how these rules provide the conditions for an internal negation, the truth of which presupposes that the negated predicate is interpreted for the subject of which it is denied. This is how we can do justice to the intuition that, say, the number 2 is neither sighted nor blind.) Still, even if there are no blindnesses, that is, SGT('is2')(SUP('blindness')(t))(t)∉A(t), it is quite possible that there are no sights either:

221

for if there were sighted animals, there would be sights in actual reality, even if there were no humans to conceive of them. The difference is that what we conceive of by the concept of blindness in its very concept involves some mental act (in this case negation), whereby it can be said to be only if the relevant mental act exists. On the other hand, even if, of course, the concept of sight is a mental act in itself, it does not involve any mental act in what is conceived of by it, whence what is conceived of by it can exist whether there are any mental acts in reality or not. Thus, the difference between a real being and a (mere) being of reason is the mind-dependence of the latter. On the other hand, the difference between a being of reason and a mere object of thought (and hence an object of signification and reference) is precisely the former's having some foundation in reality, namely, the way real beings are, as conceived of in the concept of the being of reason in question. So we can say that for a mere object of thought to be is nothing but for it to be thought of, but for a being of reason to be in the sense in which, say, a privation is, is for it to be thought of and for something that is conceived of in its concept also to obtain in the realm of real beings, as in the case of a privation for it to be is for it to be thought of and for its real opposite not to be.73

Thus, Aquinas's "universe of discourse" consists primarily of objects of thought, that is, whatever human beings can think of and hence by external, spoken or written words signify, or refer to in the context of a proposition. Therefore, since a chimera can be thought of, 74 and hence the proposition: 'A chimera is thought of' can be true, in which reference is made to a chimera, a chimera can be said to be one of the things that can be thought of, signified or referred to. Still, of course, it is not true to say that what is thought of when a chimera is thought of, or what is referred to in the proposition: 'A chimera is thought of', is a chimera. For nothing is a chimera. Thus a chimera cannot be said to be at all, except, perhaps, in the very thin sense of possibly being thought of, in the sense of 'being' Walter Burleigh called 'ens maxime transcendens'.75

SGT('is1/2')(SUP('sight')(t))(t)∉A(t). So even if there are no sights in the sense sights could be, because, say, all animals lack sight, still, it is quite possible that there are no blindnesses either, in the sense blindnesses could be (that is, in the sense that they are conceived and have the foundation in reality required by their concept), because there are no minds to form the concept of negation and hence to be able to conceive of them. In fact, we can say that in the case when there are no minds to form the concept of negation SGT('is2')(SUP('blindness')(t))(t)=SGT('not')(SGT('is2'))(SUP('sight')(t))(t)=0. But of course with this it is compatible that SGT('is1/2')(SUP('sight')(t))(t)∉A(t), and even that SGT('is2')(SUP('sight')(t))(t)∉A(t). In brief, whenever there is no sight, there is no being of a sight either, but this does not mean that then there also has to be the being of the non-being of sight conceived by an intellect. 73 Thus, the actuality of a being of reason is conditioned both on the side of reality and on the side of the activity of the intellect. So if either of these two fails to obtain, a being of reason will not be in actuality, just as it was technically detailed in the previous note. 74 Of course, insofar as we construe ‘chimera’ as referring to a possible imaginary animal, and not an implicitly contradictory term, in the way 14th century logicians used this term. For more on this issue see Ashworth, E. J.: “Existential Assumptions in Late Medieval Logic”, American Philosophical Quarterly, 10(1973), pp.141-147. Cf. Klima, G.: "Old Directions in Free Logic: Existence and Reference in Medieval Logic", in: K. Lambert: New Directions in Free Logic, Akademia Verlag, Sankt Augustin bei Bonn, (forthcoming). 75 "... ens potest accipi tripliciter. Uno modo ut est maxime transcendens et commune omni intelligibili. Et sic est adaequatum obiectum intellectus. Et sic non sequitur: Hoc est ens, ergo hoc est. Secundo modo accipitur pro ente, cui non est esse prohibitum, et sic omne possibile est ens. Et sic etiam non sequitur: Hoc est ens, ergo hoc est. Tertio modo accipitur pro ente actualiter existente, et sic est participium descendens ab hoc verbo 'est'. Ens primo modo dictum dicitur ens in intellectu, quia est obiectum intellectus; et ita est in intellectu obiective. Ens secundo modo dictum dicitur ens in suis causis vel ens quod est in sua causa. Sed ens tertio modo dictum dicitur esse ens in se." Burleigh, W.: De Puritate Artis Logicae Tractatus Longior, (ed. P. Boehner), The Franciscan Institute, St.

222

But this is not the sense of 'being' in which St. Thomas calls something a being of reason, the sense in which to say of something that it is answers the question whether there is such a thing. Thus the domain of beings of reason forms a subdomain of Aquinas's universe of discourse, comprising both real beings and mere beings of reason, but excluding mere objects of thought. A being of reason can properly be said to be in the sense in which a being of reason can be at all, i.e., in the sense which is signified by the copula of an affirmative proposition. But we could see that the being that is signified by a copula is not signified only by a copula, for being is signified in the same sense by 'is' as the predicate, say, in the sentence: 'A blindness is' (or by 'being' in 'A blindness is a being'), as this sentence is true.76 This sense of 'is' or 'being' is analogically related to the sense in which really existing substances are said to be. But then, just as any analogical sense of a common term is derived from its primary sense by some determination or qualification of its primary sense, so is this, as well as any other, analogical sense of 'being' derived from its primary sense by some qualification of its primary sense. But then, in general, the predication of being (by means of predicating 'is' or 'being' or 'is P') in any of its analogical, secondary senses is the predication of being in its primary sense with some determination or qualification. And since in view of the inherence theory of predication every predication is a predication of being, either in its primary or in one of its analogical senses, just every predication is a predication of being either without or with some qualification, either simpliciter or secundum quid. 77

To see this relationship between predication and the predication of the several analogous senses of being in general, consider the following scheme:

(EP) (i) An S is2 P iff (ii) An S's [P] isx iff (iii) An S is1 with respect to [P]78

In this scheme the subscripts to 'is' are designed to distinguish the various senses in which being is signified in the given propositional context, insofar as the proposition is or can be true (for, of course, anyone may intend to use 'is' in a different sense in a given context, but then, in that use, his or her proposition may be necessarily false or even ill-formed). Accordingly, in (i) 'is2' signifies being in the ens-rationis-sense, the sense uniformly expressed by the copula, as well as by 'is' or 'exists' as absolute predicates, as they are true of beings of reason; in (ii) 'isx' signifies being in any of the analogical senses of being (including the ens-rationis-sense); and, finally, in (iii) 'is1' signifies being in the primary sense, the sense in which it can truly be stated of substances as an absolute predicate, to signify their actuality absolutely speaking, as well as a predicate with some qualification, to signify their actuality in some determinate respect.

Let us see, then, exactly how the various kinds of substitutions of P affect what sense of being is expressed by 'isx' in (ii) insofar as it is true. If we substitute for P a term that signifies an ens rationis (which is not a real being), such as the term 'blind', then the equivalences of (EP) will hold if we take 'isx' to be 'is2', i.e., if we take 'isx' in (ii) to express the ens-rationis-sense of being

Bonaventure, N.Y, 1955, pp. 58-59. 76 See nn. 65, 69. above. 77 Cf. n. 71. Note that when I am talking about 'the predication of being' in a certain 'sense of being', I mean the act of predicating either the absolute predicate 'is' or the predicate 'being' or 'is a being' or the complex 'is P' or 'is with respect to P' in the sense of 'is' or 'being' required by the context for the truth of the predication. 78 In such a "chain" of equivalences, the logically squeamish would certainly look for parentheses (as in 'p iff (q iff p)'), but in vain. Such "chains" of equivalences are only intended to abbreviate a series of proper equivalences. Thus, '(i) iff (ii) iff (iii)' abbreviates '(i) iff (ii) and (ii) iff (iii)', i.e., this is just a brief expression of the idea that each member of the chain is equivalent with any other member. Of course, the same applies to such "chains" of any number of members.

223

as it was contradistinguished by St. Thomas from the ens-reale-sense. Thus, substituting 'blind' for P and 'animal' for S, we get the following valid instance of (EP):

(E2P) (i) An animal is2 blind iff (ii) The blindness of an animal is2 iff (iii) An animal is1 with respect to blindness

Note that in (ii) 'is2' could be analyzed further as 'is2 a being2', which in turn is equivalent with 'is2 a being1 of reason'.79 This is how the secondary, ens-rationis-sense of being can be shown to be derivable from the primary sense by the addition of the appropriate, in this case diminishing qualification, which is why, of course, the inference from 'A blindness of an animal is2', i.e., 'A blindness of an animal is2 a being1 of reason' to 'A blindness of an animal is1', i.e. 'A blindness of an animal is2 a being1' would be invalid, whence Aquinas can justifiably claim that a (mere) being of reason is not a being, except secundum quid.

But then one might ask why the secundum quid ad simpliciter inference in the case of (iii) would be valid. For, certainly, from (iii) we can infer that an animal is, indeed, absolutely and in the primary sense of being, for according to the above equivalences (iii) is equivalent with (i), and (i) certainly implies than an animal is, for no animal can be blind unless it exists. But then, if the above equivalences also show how this secondary sense of being is derivable from the primary sense by adding the appropriate, diminishing qualification, then this means that the act of being signified by the predicate of (ii) is the same as the act of being signified by the qualified predicate of (iii), indeed, that it is precisely this qualification which so modifies the sense of the predicate that instead of what it would signify without this qualification, an act of being in the primary sense, it rather signifies an act of being in this secondary sense, namely, in this case the actuality of the blindness of an animal. However, in the case of (ii) from the actuality of the act of being signified by the predicate of (ii) we could not conclude to the actuality of the act of being signified by 'is1' absolutely. So why can we in (iii)?

Of course, the answer is simple, if we consider these inferences themselves.80 In the case of (ii) the conclusion stated in itself would state the existence of a blindness of an animal in the primary sense of being, in which sense this claim could not be true. On the other hand, the conclusion in the case of (iii) in itself states the actual being of an animal in the primary sense, which of course is implied by the existence (in the secondary sense) of its blindness. So although it is indeed the same act of being that is signified both by the predicate of (ii) and by the qualified predicate of (iii) (a very important point to which I shall return soon), the subjects of the conclusions of these secundum quid ad simpliciter inferences are not the same, so the two inferences have nothing to do with each other.

Still, one might insist that the validity of the secundum quid ad simpliciter in the case of (iii) seems to invalidate the general rule concerning such inferences, namely, that if the qualification added to the predicate is diminishing, then the inference is invalid, whereas the equivalences above show precisely that the qualification in (iii) is diminishing.

79 In fact, SGT('being1 of reason')=SGT('is2)=SGT('being2'). Cf. n. 65. and n. 69. 80 Namely, 'The blindness of an animal is2; therefore, a blindness is1', and 'An animal is1 with respect to blindness; therefore an animal is1'. The question is why the first inference is invalid while the second is valid, given that SGT('is2')(SGT('blind')(SUP('animal')(t))(t))(t)=SGT('is1 with-respect-to blindness')(SUP('animal')(t))(t), where, of course, SGT('is1 with-respect-to blindness')= =SGT('with-respect-to')(SGT('is1'))(SGT('blind'))=SGT('is2')(SGT('blind')). Cf. n. 71.

224

But this objection would rest on a misunderstanding of what a formal rule of inference is. For of course, even if an inference is not valid in its form, nothing prevents it from being valid on the basis of the actual meaning of its terms. For example, even if an inference of the form: 'an S is M, and an M is P; therefore an S is P' is formally invalid, as can be shown by substituting 'man', 'animal' and 'donkey' for S, M and P, respectively; if we substitute 'man', 'animal' and 'living being' for S, M and P, respectively, the resulting inference is valid on account of the meaning of these terms. But then, in the same way, although an inference of the form 'An S is2 P with respect to [Q]; therefore an S is2 P' is formally invalid if 'with respect to [Q]' is a diminishing qualification of P, but formally valid if 'with respect to [Q]' is a non-diminishing qualification of P, nothing prevents an inference of this form from being valid on account of the meaning of its terms, even if it is formally invalid, i.e., even if the qualification of the predicate is diminishing. Indeed, the particular reason why in the case of (iii) such an inference (i.e., the one resulting from substituting 'is1' or 'is2 a being1' for 'is2 P', and, 'blindness' for [Q], namely: 'An animal is1 with respect to blindness; therefore an animal is1') would be valid, despite the fact that the qualification is diminishing, is that a privation is a lack of a property in a determinate subject, so if the privation is actual, then the subject has to be actual too.81 But that the inference is still formally invalid if the qualification is diminishing is shown by the fact that substituting 'is1' or 'is2 a being1' for 'is2 P', and, say, 'being thought of' for [Q] in this rule of inference, the resulting inference, 'An animal is1 with respect to being thought of; therefore an animal is1', is invalid.

So, if in (EP) for P we substitute a predicate signifying a being of reason, the qualification added to 'is1' in (iii) modifies its sense in such a way that the resulting complex, qualified predicate will signify the same act of being as that signified by 'is2' as an absolute predicate in (ii), or by the equivalent phrases: 'is a being in the secondary, ens-rationis-sense', 'is a being of reason', 'is a being in thought having some foundation in reality', etc., all signifying being in the same, diminished, qualified sense. So the qualification in this case yields a sense of being in which it is predicable even of objects of thought that exist neither in the primary sense of subsisting, nor in the secondary sense of being some really inherent property of a subsistent being, but only in the sense of being conceived by the human mind and having for their actuality some foundation in reality, some particular way real beings actually are, as was explained above.

But on this basis we can perhaps have a better understanding also of what it is for a qualification to be diminishing, and how the addition of diminishing qualifications is related to analogical predication in general. The first interesting thing to note about a diminishing qualification is that, to put it in contemporary terms, while it is intensionally diminishing, it is extensionally "enlarging". The point of this is that a diminishing qualification is one that takes away some of the conditions of the strict applicability of the term to which the qualification is added, whence the term with the qualification added becomes applicable even to things to which in its strict usage, without the diminishing qualification, it could not apply. For example, if to the predicate 'white' we add the qualification 'with respect to its one half', then the qualified predicate will apply even to things which strictly speaking and without this qualification could not be called white, since without the addition, properly, and strictly speaking only that thing can be said to be white which is totally white, with respect to its whole surface. Indeed, this also shows immediately that the qualification 'with respect to its whole surface' is a non-diminishing

81 Cf. n. 72.

225

qualification of 'white',82 whence in a predication it can be added or dropped without affecting the truth conditions of the predication, from which it follows that a secundum quid ad simpliciter inference that drops this qualification from 'white' will be valid. (It should be noted though, that the same qualification which is non-diminishing of one predicate may be diminishing of another: for example, 'with respect to its whole surface', is a diminishing qualification of 'hot', for something can be called strictly and properly hot only if it is hot in its every part, not only on its surface.) However, in ordinary usage we do not always bother adding even diminishing qualifications, instead, we apply the same term without qualification, intending it with some qualification which should be clear from the actual context.83 But then, if such a usage is quite clearly related to the primary usage and is generally received, we get exactly an analogical, extended usage of the same term, i.e., a usage of the term in which it applies to things to which it would not apply in this strict, primary usage, but on account of the implied qualification relating it to its primary usage it is still properly applicable in this secondary usage even without explicitly adding the relevant qualification. This is, then, the reason why St. Thomas said that a division of a common term with respect to its analogata, i.e., distinguishing a term's usage in its primary sense from its usage in its secondary, analogical senses, yields a distinction between the sense in which the term can be predicated simpliciter, and several other senses in which it can be predicated only secundum quid.84 And this is how, according to St. Thomas, 'being' is predicated simpliciter, in its primary sense, of substance, i.e., of that which is simpliciter, a subsistent being,85 and secundum quid, in one of its secondary senses, of substantial forms, i.e., of beings by which a substance is, and of accidents, i.e., of beings by which a substance is somehow, and of beings of reason, and of beings in potentiality, and perhaps even of mere objects of thought.86

82 That is to say, SGT('white1 with-respect-to a-part-of-surface)=SGT('white2')≠ ≠SGT('white1')=SGT('white1 with-respect-to whole-surface'). Here 'white1' indicates the strict usage of 'white', in which it is true only of those things which are totally white, whereas 'white2' indicates a broader, less stringent usage of 'white', say, in which the white pages of the phone book can be called 'white' (as opposed to the yellow pages), despite the black letters covering a part of their surface. Of course, in a complete semantics the hyphenated qualifications could (and should) be analyzed further, but that is irrelevant here. 83 Indeed, most things we normally call white, even if they are white all over their whole surface, could not be called absolutely and totally white in the strictest sense; namely, in the sense in which the definition of whiteness would absolutely and a hundred percent be satisfied by the property of the thing called white. For, on the basis of contemporary physical optics we could reasonably define that property, whiteness, as the reflective capacity of a surface measurable by what is called albedo (Latin for whiteness) in modern science, i.e., the percentage of the reflected light relative to the incident light (which is, by the way, just one of the nicest illustrations, pace Molière, of modern science's unabashed usage of "scholastic barbarisms", when they come in handy). But then we can also quite reasonably say that only that thing can be called absolutely white that has a hundred percent albedo. So any object with a lesser albedo is only white to a certain degree, but not strictly and absolutely white, without any qualification, even if we normally would not add any qualification in ordinary usage. But then this example also shows very nicely that it is precisely this phenomenon, namely, the omission of several sorts of implied qualifications, that accounts for much of the vagueness or "fuzziness" of everyday usage, represented in contemporary "fuzzy logics" by assigning "fuzzy" or "diminished" truth values to predications, i.e., truth values between (and including) 0 and 1, instead of the classical 0 and 1. However, in treating this "fuzziness", instead of assigning "fuzzy", qualified truth, to unqualified, absolute predicates, medieval Aristotelian logicians assigned absolute, unqualified truth to either explicitly or implicitly qualified, "fuzzy" predicates. But vagueness is an issue beyond the scope of this paper. 84 See n. 14. 85 "Non enim ens dicitur proprie et per se, nisi de substantia, cuius est subsistere. Accidentia enim non dicuntur entia quasi ipsa sint, sed inquantum eis subest aliquid, ut postea dicetur." in De Hebd. lc. 2. 86Cf. text quoted in n. 13.

226

Thus, then, it should also be clear why St. Thomas would claim that there is a distinction between the attribution of being to something as to that which is and the attribution of being to something as to that by which something else (namely, a substance) is, even if we are talking about real beings in both cases, and not about mere beings of reason.87 For, as was pointed out above, the act of being signified by 'isx' in (ii) in (EP) is the very same act of being as that signified by the qualified predication of being in (iii). But then, if in (EP) for P we substitute an accidental predicate, 'isx' will be true of the supposita of [P] only in a qualified sense, namely, in the same sense which is expressed by the qualified predication of being in (iii), but not in the primary sense, signifying the subsistence of a substance, which would be expressed by an unqualified predication of being in (iii).88

But then, if it is only the absolute predication of 'is' of a substance that can express the primary sense of being, it might appear that 'isx' in (ii), insofar as it is true, can never be 'is1', i.e., it cannot express the primary sense of being for any substitution of P, whether P is an accidental or a substantial predicate. For the subject term of (ii) supposits for the significata of P in the supposita of S by means of the abstract counterpart of P, namely [P]. However, according to St. Thomas, those that are signified in abstracto are signified as something by which something else is, not as that which is.89 But it is only that which is by itself, namely, what subsists, a per se existing substance, that is said to be in the primary sense. So, even if the act of being signified by 'isx' in the significatum of a substantial predicate of a substance is the same act of being that is signified by 'is1' in the same substance, 'isx' cannot be the same as 'is1'. Indeed, in the passage quoted from St. Thomas's Quodlibeta above he includes even substantial forms, i.e., the significata of substantial predicates, among the things that can be said to be only in the qualified sense, as that by which something is. But then, since every predicate that signifies some real being is either substantial or accidental, it seems that nothing that is signified in abstracto can be said to be in the primary sense, whence for no substitution of P would 'isx' in (ii) be 'is1', i.e., 'is' signifying the primary sense of being, insofar as (ii) is true.

But St. Thomas would say that this reasoning involves confusing modi significandi with modi essendi, that is, confusing semantic distinctions with ontological distinctions.90 For although it is true that abstract terms are imposed to refer to what concrete terms signify, and in the case of material beings what are thus signified are inherent forms of material substances, for which to be is only for them to inform the matter of these substances, i.e., to render these material substances actual in some respect, this does not exclude the possibility of there being forms for which to be is not for them to make something else actual in some respect, but just to be, absolutely, in actuality. In the case of such a subsistent form, therefore, there is no real distinction between what is supposited for by the concrete and by the abstract term, whence, 'is' or 'exists' or 'being' can equally truly be predicated of both, in the same, primary sense of being, signifying the

87 See n. 67. 88 Cf. n. 70. 89 "... quod significatur concretive, significatur ut per se existens, ut homo vel album. Similiter de ratione abstracti duo sunt, scilicet simplicitas, et imperfectio; quia quod significatur in abstracto, significatur per modum formae, cujus non est operari vel subsistere in se, sed in alio." 1SN d. 33, q. 1, a. 2. in corp. Cf. in Meta. lb.7, lc. 1, nn. 1252-1256. 90 For St. Thomas's principled insistence on keeping the two apart, see both his numerous discussions of what he took to be Plato's fundamental error concerning universals and of how the modi significandi of the names we attribute to God do not correspond to some matching modi essendi in Him.

227

subsistence of a substance.91 Thus, whereas the semantic distinction, as to the difference between the mode of signification of an abstract term and that of a concrete term, is in force even concerning such an immaterial form,92 the lack of a corresponding ontological or real distinction, as to what is signified by these terms, is expressed precisely both by the fact that the abstract and concrete terms signifying and suppositing for such a subsistent form are truly predicable of each other, and by the fact that existence can be attributed to the thing thus signified and supposited for in the primary sense, whether the thing is referred to in concreto or in abstracto.93

Indeed, this also shows why, adapting D. P. Henry's happy phrase, the "aloofness"94 of Aquinas's semantic theory from ontology is so important, not only from the point of view of its acceptability by others of a different metaphysical persuasion, but also from the point of view of his own metaphysics.95 For it is precisely this "aloofness" of the semantic theory, not prescribing anything concerning the ontological categories of the semantic values of our phrases, that makes it possible for Aquinas to admit subsistent forms into his ontology, i.e., forms which exist not only as something by which something else, namely, a substance, is, but which exist also as that which is.

So if in the scheme above we substitute 'God' for P (and, for the sake of simplicity, for S too) and we take 'divinity' (or 'godhead', if you prefer a Saxon word in the abstract form too) as the abstract counterpart of 'God', then we get the following:

(E1P) (i) God is2 God iff (ii) God's divinity is1 iff (iii) God is1 with respect to divinity

On the other hand, if we substitute, say, 'tree' for P (and, again, for S too) and 'is[1]' for 'isx' to distinguish the sense in which 'is' can be truly predicated of non-subsistent substantial forms, and if we baptize the significata of 'tree' in individual trees 'arboreity' (or 'treeness', if you prefer), then we get:

(E[1]P) (i) A tree is2 a tree iff (ii) A tree's arboreity is[1] iff (iii) A tree is1 with respect to arboreity

91 "Respondeo dicendum, quod natura et suppositum naturae in quibusdam differunt re et ratione, sicut in compositis; in quibusdam autem ratione et non re, sicut in divinis." 3SN ds. 11, q. 1, a. 4. "Et quia in huiusmodi creaturis, ea quae sunt perfecta et subsistentia sunt composita; forma autem in eis non est aliquid completum subsistens, sed magis quo aliquid est, inde est quod omnia nomina a nobis imposita ad significandum aliquid completum subsistens, significant in concretione, prout competit compositis; quae autem imponuntur ad significandas formas simplices, significant aliquid non ut subsistens, sed ut quo aliquid est, sicut albedo significat ut quo aliquid est album. Quia igitur et deus simplex est, et subsistens est, attribuimus ei et nomina abstracta, ad significandam simplicitatem eius; et nomina concreta, ad significandum subsistentiam et perfectionem ipsius, quamvis utraque nomina deficiant a modo ipsius, sicut intellectus noster non cognoscit eum ut est, secundum hanc vitam." ST1 q. 13, a. 1, ad 2-um. Cf. ST1 q. 32, a. 2. 92 "Ad decimum dicendum, quod abstractum et concretum in divinis non differunt secundum rem, cum in deo non sit accidens neque materia, sed solum secundum modum significandi; ex quo modo procedit quod intelligimus divinitatem ut constituentem deum, et deum ut habentem deitatem; et similiter est de paternitate et patre: nam licet sint idem secundum rem, differunt tamen secundum modum significandi." QDP q. 8, a. 3. Cf. SN1 d. 22, q. 1, a. 2. 93 Cf. ScG lb. 1, c. 30; 1SN d. 22, q. 1, a. 2; De Ente c. 5. See also n. 41. 94 For D. P. Henry's own Principle of Logical Aloofness see: Henry, D. P.: That Most Subtle Question - (Quaestio Subtilissima): The Metaphysical Bearing of Medieval and Contemporary Linguistic Disciplines, Manchester University Press: Manchester, 1984. (See entry "aloofness" in the index.) 95 Again, we should note here that the question whether there are such subsistent forms or not is a metaphysical question, not determined by these semantic considerations. All these semantic considerations determine is what it means to claim that there are such subsistent forms. But, of course, it is only on the basis of the proper understanding of this claim that one can set about determining its truth.

228

The point of the comparison is that even if we suppose that 'tree' is a substantial predicate of trees as well as 'God' is of God, if the form signified by 'tree' in trees, i.e., the substantial form of trees is not a subsistent form, then (ii) can be true only in a diminished, qualified sense, even if for a tree to be, absolutely, and in the primary sense, is nothing but to have this substantial form in actuality, i.e., to be in actuality with respect to that form. Nevertheless, it is only the substance that has this actuality as that which is (quod est), while the form, if it is not a substance itself, exists only insofar as that by which the substance of which it is the form has being (quo aliquid est), even if the form's act of being, provided the form is a substantial form, is the very same act of being that the substance itself has.96 However, should it turn out that arboreity, the substantial form of trees is not only an inherent form, but also a substance that for some reason should be regarded as having subsistent being, this would mean that, instead of (ii) in (E[1]P), 'A tree's arboreity is1' would be true. In fact, showing that the rational soul is precisely such a substantial form on account of the fact that it has an operation that is not the actuality of the body is the most crucial step in Aquinas's proof of the immortality of the human soul.97 But again, from our present, semantic point of view, the important point is that whether this claim is true or false is not determined by the semantic theory itself, whereas of course, it is these semantic considerations that tell us what such a claim means, and so what evidence can be regarded as relevant for or against it.

Anyhow, these comparisons between the various senses of being in which it may be attributed to different kinds of things I think should also show that it is precisely these different senses of being, once carefully distinguished, that can be used to express the basic ontological differences between various kinds of beings. Accidents are the kind of beings for which to be is to make substances actual in some respect, i.e., for which to be is for their subject to be actual in some respect, that is, actual by an act of being that does not make them actually be, simpliciter. So, the act of being truly attributable to an accident is just an act of being secundum quid of the substance whose accident it is, whence the sense in which accidents can be said to be is only a sense of being secundum quid, analogically related to the primary sense, in which something is called a being simpliciter. Again, substantial forms are the kind of beings for which to be is to make a substance actual in respect of what it is, whence the act of being of a substantial form is the act of being of the substance itself, which is why the actuality of the substantial form makes the substance actual simpliciter, and not only secundum quid. Still, unless the substantial form is

96 Formally, the point is that if P is a substantial predicate of a substance u, then SGT('is1')(u)(t)=SGT('is[1]')(SGT(P)(u)(t))(t); still, of course SGT('is1')≠SGT('is[1]'), for if P signifies a non-subsistent substantial form, then, if u is actually P (i.e., SGT(P)(u)(t)∈A(t)), then SGT('is[1]')(SGT(P)(u)(t))(t)∈A(t), nevertheless, SGT('is1')(SGT(P)(u)(t))(t)=0, and also SGT('is[1]')(u)(t)=0. For the general definition of what it is for a predicate P to be substantial to an individual substance u see n. 99. below. 97 Cf. QDA q. 14. Indeed, this is precisely the point that Siger of Brabant, unable to separate modi essendi from modi significandi in the way Thomas did, found unacceptable from Thomas's conception of the intellective soul: "Praeterea, alia est ratio essendi formae materialis et compositi seu formae per se subsistentis. Ratio enim essendi formae materialis est secundum quam est aliquid aliud, ut ratio compositionis est secundum quam habet esse compositum, et ratio figurae secundum quam habet esse figuratum unde ratio essendi formae materialis est quod sit unita alii. Ratio autem essendi compositi vel formae liberatae a materia est quod sit ens per se et separate, non unum ens cum alio. ... Et sunt istae rationes essendi, qua aliquid habet esse unite ad materiam et qua aliquid habet rationem subsistentis per se et separate, oppositae adeo ut eidem inesse non possunt. Unde anima intellectiva non potest habere rationem per se subsistentis et, cum hoc, unum facere cum materia et corpore in essendo." Siger of Brabant: De Anima Intellectiva, in: Bazán, B.: Siger de Brabant, Louvain-Paris, 1972, pp. 79-80. Cf. also St. Thomas's De Unitate Intellectus nn. 37-38.

229

itself a substance, either being the whole substance itself or being a substantial part of a composite substance, this act of being cannot be attributed to it as to that which is, but only as to that by which the substance is. Finally, it is only substances that can be said to be absolutely and without qualification, in the primary sense of being.

But in these comparisons we could already see that even among substances there are important differences with respect to their being. For even if all sorts of substances can be said to be without qualification, in the primary sense of being, we could also see that the being of these various sorts of substances was at the same time the being of their substantial forms which, making them be what they are, are what distinguish these various sorts from each other, determining their specific and generic kinds. But then, their actuality simpliciter being nothing but their actuality in respect of their substantial form, also their being is determined to that form:98 they can only be actual inasmuch as their form permits them to be, for this is precisely, namely, to be in respect of their substantial forms, what it is for them just to be, simpliciter. But then these determinations of being in the determinate kinds of substances are also limitations on the actuality in principle available to a substance of a given, determinate kind. But if this is true, then different determinations yield different limitations, which, in turn, imply different degrees.

It is in this way, then, that from the analysis of the various analogical senses of being in their relation to the primary sense, in which it is predicable of substance, we can arrive at a not only comprehensible but even plausible idea of the different degrees of being even among different kinds of substances themselves, whether we are actually able to identify (let alone measure) correctly these various degrees or not. In any case, the semantic question, again, is not whether what is said in particular in arranging different kinds of substances according to different degrees of being is true (i.e., whether, say, humans are indeed a higher form of being than e. g. worms, for that is a question of metaphysics); the semantic question is whether what is thus said makes good sense, and if so, then what sense it makes, which has to be understood well before the inquiry into its truth, under pain of ignoratio elenchi.

The Great Chain of Being

We could see how the different analogous senses of being are all related to the primary sense (signifying the subsistence of a substance), namely, how these secondary senses are interpretable in the framework of the inherence theory of predication and the corresponding theories of signification and supposition as signifying being in some qualified sense, deriving from the primary sense by the addition of some diminishing qualification. However, we could also see that even within the range of application of this primary sense of being it is possible to make sense of distinguishing different degrees of being, insofar as different kinds of substances are different precisely on account of their different substantial forms, which in turn, may be regarded as just further, not properly diminishing, but in a certain way limiting qualifications on some even more central, more absolute sense of being, yielding differences that we may characterize as constituting different degrees of being.

Let us take a closer look at this idea, and let us see how we can say that, despite the fact that the actuality of a substantial form is an act of being attributable to the substance having this form in the primary, absolute sense, the form itself imposes some limitation on this absolute being, 98 "quaelibet forma est determinativa ipsius esse" in De Hebd. lc. 2, n. 34.

230

determining it to a certain degree in comparison to others. Our starting point, again, should be a comparison of the various instances of the scheme (EP):

(EP) (i) An S is2 P iff (ii) An S's [P] isx iff (iii) An S is1 with respect to [P]

So far we have seen that the act of being signified by the qualified predicate in (iii) is the same act of being as that signified by 'isx' in (ii). We have also seen that if the subject term (i.e., the phrase S's [P]) of (ii) supposits for an inherent, as opposed to a subsistent, form, then 'isx' can be truly predicated of it only if it is not 'is1', because in this case being can be attributed to the form supposited for by this term only as to that by which something else (namely, the substance supposited for by S in (iii)) is, and not as to that which is. However, if P is a substantial predicate, then the act of being signified by 'isx' in (ii) is the very same act as that by which the substance itself is, absolutely, and in the primary sense, for this is precisely what it is for P to be a substantial predicate of the supposita of S.99 Therefore, we can supplement (EP) as follows:

(EP*) (i) An S is2 P iff (ii) An S's [P] isx iff (iii) An S is1 with respect to [P] iff (iv) An S is1

provided P is a substantial predicate of the supposita of S.

But then, since the act of being signified by the predicate of (ii) is the same as the act of being signified by the predicate of (iii), which, in turn, is the same act of being signified by 'is1' as an absolute predicate of S in (iv), we can see that even the absolute predication of 'is1' in (iv) involves an implied determination or qualification, namely the qualification of being provided by the substantial form signified by P in the supposita of S. So, if the predication of 'is1' in (iv) is true at all, it can be true only in the sense in which the predication of 'is1 with respect to [P]' is true in (iii).100 But this means that an S can be only in the way things having the substantial form signified by P can be, but not in any other way. So, what is, say, a diamond (provided 'diamond' is a substantial predicate of diamonds) can be only in the way a diamond can be, localized in space and time, and characterized by certain capacities and incapacities, such as being capable of scratching other solid bodies, but, say, not being capable of self-propagation, whereas what is a tree, provided 'tree' is a substantial predicate of trees, can only be in the way trees are, also localized in space and time, but characterized by different capacities and incapacities, etc. It seems, then, that whatever substantial predicate we substitute for P in the above scheme, the substantial form signified by that predicate will always impose some determination, and thereby a certain limitation on the act of being signified by 'is1' in (iv). However, what if we can find a predicate that signifies a substantial form which, not being distinct from this act of being itself, does not impose any determination or limitation on the kind of being signified by 'is1' in (iv)? Suppose we find such a predicate and we find that there is a being whose substantial form signified by this predicate is the very act of being that is signified in it by the predicate 'is1'.101 Such an act of being then would truly be called infinite, in the sense of not being determined to the capacity of some form distinct from it. Therefore it is only an entity having such an act of being that could be said truly, and genuinely absolutely to be, without any, whether explicit or implicit, restriction or limitation imposed on what is signified in it by the verb 'is' or by the predicate 'being'. So it is only such an entity to which these terms would the most properly, absolutely and maximally apply, without any limitation of a particular kind or degree. But 99 For, in general, a predicate P is substantial to a substance u iff SGT('isx')(SGT(P)(u)(t))(t)=SGT('is1')(u)(t); otherwise P is accidental to u. Cf. n. 96. 100 That is, if P is a substantial predicate of u, then SGT('is1')(u)(t)=SGT('is1 with-respect-to [P]')(u)(t). 101 That is, suppose we find a P such that for a substance u, SGT(P)(u)(t)=SGT('is1')(u)(t).

231

Aquinas's metaphysical proofs are designed to show precisely that there is such an entity, God, because God's nature, the "form" signified by the term 'God' is identical with the act of being signified by the term 'being' in Him. But then this is why Aquinas can claim that 'He Who IS' (qui est) is the most proper name of God, expressing most clearly the unlimited character of Divine Being, and that even among substances, which all are beings in the primary sense, it is God to whom this term most properly and maximally applies.102

But such a being, the nature of which is nothing but its act of being, can be only one. For there could be two such beings only if the one would be different from the other. So one of them would have to have something, some form, that somehow qualifies, and thereby restricts its being. But then the nature of that being would not be the pure, unlimited, unqualified act of being. So that other being would not be the kind of being of which we assumed to have two.103 So, different kinds of beings, which are different on account of their different forms, have their acts of being qualified and limited differently by their forms, and thus these acts of being are either more or less removed from the fullness of absolute being, thereby constituting different degrees of being.104

But even this overall hierarchy of being necessarily generated by the different substantial forms of different kinds of substances (which are different precisely because they are nothing, but more

102 "Respondeo dicendum quod hoc nomen qui est triplici ratione est maxime proprium nomen Dei. Primo quidem, propter sui significationem. Non enim significat formam aliquam, sed ipsum esse. Unde, cum esse dei sit ipsa eius essentia, et hoc nulli alii conveniat, ut supra ostensum est, manifestum est quod inter alia nomina hoc maxime proprie nominat deum, unumquodque enim denominatur a sua forma. Secundo, propter eius universalitatem. Omnia enim alia nomina vel sunt minus communia; vel, si convertantur cum ipso, tamen addunt aliqua supra ipsum secundum rationem; unde quodammodo informant et determinant ipsum. Intellectus autem noster non potest ipsam dei essentiam cognoscere in statu viae, secundum quod in se est, sed quemcumque modum determinet circa id quod de deo intelligit, deficit a modo quo deus in se est. Et ideo, quanto aliqua nomina sunt minus determinata, et magis communia et absoluta, tanto magis proprie dicuntur de deo a nobis. Unde et Damascenus dicit quod principalius omnibus quae de deo dicuntur nominibus, est qui est, totum enim in seipso comprehendens, habet ipsum esse velut quoddam pelagus substantiae infinitum et indeterminatum." ST1 q. 13, a. 11. 103 "Id autem erit solum vere simplex, quod non participat esse, non quidem inhaerens, sed subsistens. Hoc autem non potest esse nisi unum; quia si ipsum esse nihil aliud habet admixtum praeter id quod est esse, ut dictum est impossibile est id quod est ipsum esse, multiplicari per aliquid diversificans: et quia nihil aliud praeter se habet admixtum, consequens est quod nullius accidentis sit susceptivum. Hoc autem simplex unum et sublime est ipse Deus." in De Hebd. lc. 2, n. 33. ScG lb. 1, c. 42, n. 10. 104 "Ex diversitate autem formarum sumitur ratio ordinis rerum. Cum enim forma sit secundum quam res habet esse; res autem quaelibet secundum quod habet esse, accedat ad similitudinem Dei, qui est ipsum suum esse simplex: necesse est quod forma nihil sit aliud quam divina similitudo participata in rebus; unde convenienter Aristoteles, in i Physic., de forma loquens, dicit quod est divinum quoddam et appetibile. Similitudo autem ad unum simplex considerata diversificari non potest nisi secundum quod magis vel minus similitudo est propinqua vel remota. Quanto autem aliquid propinquius ad divinam similitudinem accedit, perfectius est. Unde in formis differentia esse non potest nisi secundum quod una perfectior existit quam alia: propter quod Aristoteles, in viii Metaphys., definitiones, per quas naturae rerum et formae significantur, assimilat numeris, in quibus species variantur per additionem vel subtractionem unitatis, ut ex hoc detur intelligi quod formarum diversitas diversum gradum perfectionis requirit. Et hoc evidenter apparet naturas rerum speculanti. Inveniet enim, si quis diligenter consideret, gradatim rerum diversitatem compleri: nam supra inanimata corpora inveniet plantas; et super has irrationalia animalia; et super has intellectuales substantias; et in singulis horum inveniet diversitatem secundum quod quaedam sunt aliis perfectiora, in tantum quod ea quae sunt suprema inferioris generis, videntur propinqua superiori generi, et e converso, sicut animalia immobilia sunt similia plantis; unde et Dionysius dicit, vii cap. De Div. Nom., quod divina sapientia coniungit fines primorum principiis secundorum. Unde patet quod rerum diversitas exigit quod non sint omnia aequalia, sed sit ordo in rebus et gradus." ScG lb. 3, c. 97, n. 3.

232

or less restrictive qualifications of the absolute, unqualified being105) allows for further, even finer degrees of being, on the level of individuals in which the same substantial nature may be more or less perfectly realized in the actualization of the individuals' accidents.

How should we understand this claim? What does the accidental being of a substance's accidents have to do with the degree of the substantial being of the substance itself? Even granting that different kinds of substances can be arranged into a hierarchy with regard to the perfection of their substantial being (even if we may not be able to determine the exact position of any given kind in this hierarchy), isn't it just so that any given individual of any given kind either simply is or simply is not, at the degree determined by its kind?

Well, the answer to this last question, as one may expect, is 'Yes', absolutely speaking, but 'No', with qualification. For, of course, absolutely speaking, any substance of any given kind either is or is not, but if it is at all, absolutely speaking, it can still be more or less, i.e., it can still be or not be with some qualification (it can still be to a certain extent or not be to that extent).

But, again, isn't this just sheer play with words? Of course, if a substance already is by its substantial being it may or may not have several sorts of accidental being, but why would the actuality or non-actuality of any such accidental being have anything to do with the degree or intensity of its substantial being?

To this we can say first of all that we must not forget that even if an accidental act of being of a substance is not identified with its substantial act of being, that accidental act is a certain act of the substance itself, an act of being secundum quid, on account of which it is the substance that is in actuality in some respect. Indeed, it is only such actualities secundum quid that manifest the degree of a given substantial being in the first place in the overall hierarchy of beings determined by the substantial form of the kind of the substance in question. For the degree of a given sort of substantial being determines, and thereby manifests itself precisely in, the range of actualities that are in principle available to or attainable by any particular substance holding that degree of substantial being by belonging to its kind, i.e., having the kind of substantial form determining that degree of substantial being. So, for example, supposing with Aquinas that living is a sort of substantial being that is of a higher degree than sheer lifeless existence,106 we can say that this is so because the notion of the mode of being which is living imposes a lesser restriction (or maybe even no restriction at all)107on the notion of absolutely unqualified being than does the notion of a lifeless existence, which manifests itself precisely in the fact that the actualities in principle available to or attainable by a living being are in principle unavailable to or unattainable by a lifeless being, just because of the difference between what it is for something to live and what it is for something just to be but not to live.

But isn't there still some problem here? For even granting that a living being can do things that a lifeless being cannot, which may be regarded as the manifestation of a higher degree of substantial being, isn't the converse also possible, indeed, actually true, namely, that a lifeless being can do things that a living being cannot? And if so, isn't this latter capacity a manifestation of a higher degree of substantial being as well? But then don't we have to conclude that the same 105 For this point see Wippel, J. F.: "Thomas Aquinas and Participation", in: Wippel, J. F. (ed.): Studies in Medieval Philosophy, The Catholic University of America Press: Washington D.C., 1987. 106 Whether this is indeed so is a metaphysical question, again, left undetermined by our formal, semantic considerations, but for the sake of the example it is a quite plausible assumption in any case. 107 Cf. e.g. ST1 q. 18, a. 3; ScG lb. 1, cc. 97-98.

233

lifeless being has a higher degree of substantial being than the living being, in contradiction to what we just conceded?

Well, of course it is true that lifeless things can do several things living things cannot do; for example, a diamond can scratch glass, that a tree or a cat cannot do. (In fact, properly speaking, a diamond cannot scratch glass by its own activity either, but this is beside the point. The point is that the body of a tree or a cat lacks the capacity that a diamond has, namely to scratch glass when it is rubbed against it, even if this requires the action of an external force.) But we should realize that the mere difference in the range of available capacities does not automatically translate into differences in the degree of substantial being. For if a capacity is available precisely on account of the unavailability of some other capacity or a whole range of other capacities which, in its turn, is directly an indication of a higher degree of substantial being, then of course the availability of the former is an indication not of a higher, but of a lesser degree of substantial being. But this is the case in the example. For a diamond has the capacity to scratch glass precisely because it has such a molecular structure that prevents it from performing all sorts of activities in which the degree of being we call life manifests itself, whence this capacity is precisely an indication of a more limited form of being.108

But of course from our present point of view such an example, or any other, 109 perhaps less trivial, but particular case is relevant only to the extent it helps illustrate how the general semantic principles concerning the concept of being should be applied in the particular discussions of these particular cases. These principles themselves, however, being presupposed by the discussion of particular cases, should be regarded as valid regardless of the outcome of any particular discussion, provided they are consistent in themselves and with each other.110

108 Note that in this argument we already assumed with Aquinas that life is a kind of being of a higher degree than lifeless existence. This argument only shows that the fact that lifeless entities can have certain capacities that living beings do not have does not contradict this assumption. Of course, it is a further issue whether and why we are justified in this assumption. For this see Aquinas's texts referred to in n. 107. 109 Consider the following, more drastic example. God cannot scratch His nose. This is not an incapacity, absolutely speaking, for this is an incapacity only insofar as a higher capacity excludes the presence of the limiting opposite capacity. My capacity to scratch my nose is a capacity that directly involves the limitation on the form of being I have, namely, the limitation that it is a sort of bodily existence, restricted to a portion (a rather small portion at that!) of space and time. So I can have this particular, limited capacity only and precisely on account of the obviously restricted mode of being I have. So despite possible appearances to the contrary, this capacity is obviously an indication of a lower degree of being, whence the lack of this capacity in, or rather its sheer inapplicability to, Divine Being is just a further indication of the absolute perfection of that Being. See Thomas on why we cannot truly and properly predicate of God terms that signify perfections, but also necessarily involve limitations of being. Cf. ST1 q. 13, a. 3; 1SN d. 22, q. 1, a. 2. 110 Research for this paper was completed during my Morse Fellowship exempting me from teaching duties at the Philosophy Department of Yale University in the academic year 1994/95. I owe thanks to Desmond Paul Henry, John Jenkins, Heikki Kirjavainen, Eleonore Stump and Jack Zupko, who read and commented on earlier drafts of this paper. I would also like to thank my new colleagues at the University of Notre Dame for a very lively and thorough discussion of the same material during my first visit here. But my special thanks go to Scott MacDonald for his detailed and perceptive comments as well as for his general suggestions to improve the presentation of the material. My original plan was to provide a non-technical exposition of the semantic principles underlying Aquinas's metaphysics of being and goodness. I had to realize, however, both that if I do not want to compromise precision I cannot completely abandon technicalities (though I tried to relegate them mostly to the footnotes), and that the further considerations linking the notion of being to the notion of goodness would already exceed the limits of a single research paper. A full account of these further considerations, as well as the technicalities only outlined here will be provided in my book under preparation: Meaning, Nature, Concept. Nevertheless, I do hope that the

234

foregoing considerations will already prove useful in interpreting the passage most clearly relating the notion of being to the notion of goodness, while also explaining the difference of their predication simpliciter vs. secundum quid: ST1 q. 5, a. 1.

235

Aquinas on One and Many

Introduction: The Systematic ambiguity of the notions of One and Being

As is well-known, St. Thomas regarded the notion of one as a transcendental notion, convertible with the notion of being, and thus, as surpassing the boundaries of individual categories. On the other hand, the notion of one is also obviously a numerical notion, and so it should belong to the category of quantity, in particular, to the species of discrete quantity. This apparent conflict can easily be resolved by St. Thomas’s distinction between the notion of the one that is the principle of number and the notion of the one that is convertible with being, provided that the distinction itself is clear enough. However, despite the fact that the notion of one in the context of performing simple arithmetical operations, such as adding one, subtracting one, multiplying or dividing by one, is clear, familiar, and absolutely unambiguous and precise, in a metaphysical context it becomes disturbingly vague, or, in any case, as Aquinas’s need to make this distinction shows, far from unambiguous.

Therefore, in an attempt to clarify this puzzling aspect of this notion, I will first show that upon Aquinas’s conception such vagueness and ambiguity of our notion of one is inevitable, arising of necessity from the analogical character of this notion.

To show the essentially analogical character of this notion, I will begin the discussion in the next section with Aquinas’s distinction, starting with the more familiar and more precise member of this distinction, namely, the one as the principle of number. However, despite the fact that the one as the principle of number may be more familiar in our arithmetical practice, it will soon turn out that the more basic, more primary notion is still that of the one that is convertible with being. But given the analogical character of Aquinas’ notion of being, it is no wonder that the latter member of St. Thomas’s distinction will also turn out to be analogical in itself. Indeed, the subsequent semantic discussion of the analogical predication of both the notion of being and that of the one will show the interdependence of the analogical character of both notions: anything that speaks for the analogical character of being eo ipso speaks for the analogy of unity and vice versa.

These considerations will inevitably lead us to the further discussions of the relationships between the notions of being and one, and those of substantiality, identity and simplicity. As these discussions will show, the systematic ambiguities of these latter notions are necessarily entailed by the primarily analogical character of the notions of being and one.

On the basis of these considerations it will be a natural conclusion that the systematic ambiguity of these notions, rather than being their defect, is precisely what allows us to capture the idea of a metaphysical hierarchy of beings of various degrees of perfection. But then the further inevitable conclusion will be that with respect to this hierarchy of beings we have to make a distinction between beings that are more familiar to us (notiora quoad nos) and those that are not such. To those that are more familiar to us we can apply these notions without qualification, with the presumption of the primacy of our ordinary common-sense conceptual framework. However, once we recognize this hierarchy of beings, we shall also have to recognize that considering this hierarchy in itself, regardless of which beings in this hierarchy are more familiar to us, it is only the absolutely simple One on the top of this hierarchy to which these notions can apply in an absolutely unqualified manner. Or rather we should say that they could apply in this way, were it

236

not for the realization that that absolute simplicity cannot really be captured by any one of these notions.

The One that is the Principle of Number, and the One that is Convertible with Being

The most elementary application of our notion of a unit occurs in the simple process of counting. For example, when we have the task of counting the number of people in a room, we take the persons one by one, raising the number of persons we have already counted by one at each step, until we reach the last person. In this process, if we “do not lose count”, that is, if we make sure that we never take the same person twice and we do not leave out any one of them, we have to arrive at a definite and precise result. Apparently, nothing can be more exact and unambiguous than this.

But then suppose we need to count the words on this page. Here the word ‘one’ occurs twice in the subtitle. Should we take these occurrences as one word or two words? Clearly, in this case the result of counting will depend on what we take to be the criteria of identity for words, namely, whether we are supposed to be counting type-words, in which case two occurrences of a similar string of letters should be counted as one word, or token-words, in which case such distinct occurrences should be counted as two words1. But once the criteria of identity are fixed, again, we have to arrive at a precise, definite result.

However, what if we need to deal with “fuzzier” entities? What if we have to count, say, the number of the clouds in the sky? Obviously, in this case first we need to know just where one cloud ends and the other begins, and then we have to make sure that during the process of counting no two clouds will merge into one, no one cloud will split into two or more clouds, and that no cloud will vanish, nor a new one will come into existence.

As can be seen from this simple example, even if counting in itself is a simple and entirely unambiguous operation, it has some rather complex and far from unambiguous presuppositions. For even if whenever we count something as one, its addition increases the number of the items counted up to that point exactly and unambiguously by one, it is far from being a simple and unambiguous issue just what we can count as one. So, clearly, in this way the precise and unambiguous arithmetical notion of the unit (that serves as the measure of the number of things when we count them one by one), which Aquinas appropriately describes as the principle of number, presupposes the far from unambiguous notion of some being which is undivided in itself and is divided from others, which is the notion of the one that St. Thomas describes as that which is convertible with being. As he says:

«We should realize that there are two sorts of one [duplex est unum]. Namely, there is the one which is convertible with being, which adds nothing to being except being undivided; and this

1 Actually, even distinct occurrences of type-words should probably be counted as one only if the two occurrences express the same meaning. For example, in the sentence: ‘She hit the bat with a baseball bat’ we should not count the two occurrences of ‘bat’ as the same type-word. Indeed, the two occurrences of this word belong to distinctly numbered dictionary entries. So perhaps also the two occurrences of ‘one’ in the subtitle should be counted as two type-words in accordance with their two intended meanings. But then it would be a further issue to decide how analogical terms, whose meanings according to Cajetan are partly (secundum quid) the same and partly diverse, should be counted. THOMAS DE VIO CARDINALIS CAJETANUS: De Nominum Analogia, Rome: Angelicum, 1934, c. 2, n. 8, p. 12.

237

deprives multitude, insofar as multitude is caused by division, however, it does not deprive extrinsic multitude, which the one constitutes as its part, but the intrinsic multitude that is opposed to unity. For just because something is said to be one, it is not denied that there is something outside of it with which it constitutes a multitude, but what is denied is its own division into a multitude. The other sort of one is that which is the principle of number, which to the notion of being adds measurement; and the multitude of this sort of one is a privation, for a number comes to be by the division of the continuum. Nevertheless, multitude does not entirely deprive unity, for after the division of the whole, the part still remains undivided, but it does remove the unity of the whole2.»

The reason why the presupposed, transcendental notion of the one is, indeed, has to be ambiguous, despite the precision of the consequent arithmetical notion, should be clear if we consider the inherent ambiguity of the notion of division. For suppose we have managed sufficiently to separate and distinguish the individual clouds that serve as the units for our counting. But are those alleged units really one? For what is a cloud? A visible aggregate of tiny droplets of water suspended in midair. So one cloud, which we treated as one in the process of counting clouds, upon closer inspection turns out to be just so many droplets of water. Clearly, these many droplets each are distinct, spatially separated individuals, undivided in themselves and divided from each other. So if the clouds appeared to have some sort of unity merely on account of the relative closeness of their parts, namely of the droplets constituting them, we have to say that the droplets themselves have a greater unity, on account of their continuity.

But then, one of course may go further and ask about the unity of those droplets themselves, which after all are just rather densely packed collections of water molecules. And then, in the same way, one may further ask about the molecules, and then the atoms, which, despite their name, are not indivisible, and then the particles of atoms, until we reach the limits of our knowledge, but perhaps still not the limits of divisibility. But, in fact, those further details are already irrelevant from our point of view. Not only because St. Thomas did not and could not have any idea about these lower levels of the organization of matter, but also because no matter what further details modern physicists may come up with, the metaphysical principles constituted by our most universal notions concerning the unity of a whole and the multiplicity of its parts are the same, regardless of such details3.

But even from this point of view, one may find the idea of these changing perspectives rather disturbing. For the breaking up of what appeared to be units on a certain level into multitudes on a lower level, and, conversely, the recognition of units on a higher level constituted by a multitude of entities on a lower level is clearly dependent on our perspective, on the “degree of resolution” we apply in distinguishing one thing from another, and taking this thing as one, and not as a multitude of several things. But how can it depend on our perspective what counts as one

2 «Sciendum autem, quod duplex est unum; quoddam scilicet quod convertitur cum ente, quod nihil addit supra ens nisi indivisionem; et hoc unum privat multitudinem, in quantum multitudo ex divisione causatur; non quidem multitudinem extrinsecam quam unum constituit sicut pars; sed multitudinem intrinsecam quae unitati opponitur. Non enim ex hoc quod aliquid dicitur esse unum, negatur quin aliquid sit extra ipsum quod cum eo constituat multitudinem; sed negatur divisio ipsius in multa. Aliud vero unum est quod est principium numeri, quod supra rationem entis addit mensurationem; et huius unius multitudo est privatio, quia numerus fit per divisionem continui. Nec tamen multitudo privat unitatem totaliter, cum diviso toto adhuc remaneat pars indivisa; sed removet unitatem totius.» QDP q. 3, a. 16, ad 3-um 3 For detailed discussions of the medieval notions and principles concerning parts and wholes, see HENRY, D. P. 1991, Medieval Mereology, Bochumer Studien zur Philosophie, Band 16, B. R. Gruener, Amsterdam-Philadelphia; for a discussion of Aquinas’s views in particular see especially pp. 218-328.

238

entity or many entities? For even if there may be some sort of ambiguity in how we divide up things into various units depending on our perspective, isn’t reality supposed to be something definite, determinate, regardless of how we look at it?

Analogy and Predication secundum quid

It is at this point that St. Thomas’s insight concerning the convertibility of one and being turns out to be of particular importance. As he writes:

«… nothing prevents some things from being many in some respect [secundum quid] and being one in another. Indeed, all sorts of things that are many are one in some respect, as Dionysius says in the last chapter of On Divine Names. But we have to be aware of the difference that some things are many absolutely [simpliciter], and one in some respect, while the case is the reverse with others. Now something is said to be one in the same way as it is said to be a being. But a being absolutely speaking is a substance, while a being in some respect is an accident, or even [only] a being of reason. So whatever is one in substance, is one absolutely speaking, yet many in some respect. For example, a whole in the genus of substance, composed of its several integral or essential parts, is one absolutely speaking, for the whole is a being and a substance absolutely speaking, while the parts are beings and substances in the whole. Those things, however, which are diverse in substance, and one by accident, are diverse absolutely speaking, and one in some respect, as many humans are one people, or many stones are one heap; and this is the unity of composition or order. Likewise, many individuals that are one in genus or species are many absolutely speaking, and one with respect to something, for to be one in genus or species is to be one with respect to reason4.»

So the status of the unity of a thing is dependent on the ontological status of the thing itself. That thing is said to be one absolutely speaking which is a being absolutely speaking. Therefore, even if we may find some unity on a “higher level” of organization, such as the unity of a heap of stones or an army of people, or some multitude on a “lower level”, such as the multitude of the parts of individual stones or of individual humans, if individual stones and individual humans are beings in the absolute sense, then they also are units in the absolute sense, whereas their collections are units only in some respect, and their parts constitute a multitude only in some other respect, with some qualification.

Now, in general, whenever we have to distinguish the predication of some common term simpliciter and secundum quid, that is, without and with some qualification, then this is a sure sign that the term is being predicated analogically of its inferiors. St. Thomas makes this quite clear in the following passage:

«... there are two ways in which something common can be divided into those that are under it, just as there are two ways in which something is common. For there is the division of a univocal

4 «Respondeo dicendum quod nihil prohibet aliqua esse secundum quid multa, et secundum quid unum. Quinimmo omnia multa sunt secundum aliquid unum, ut dionysius dicit, ult. Cap. De div. Nom.. Est tamen differentia attendenda in hoc, quod quaedam sunt simpliciter multa, et secundum quid unum, quaedam vero e converso. Unum autem hoc modo dicitur sicut et ens. Ens autem simpliciter est substantia, sed ens secundum quid est accidens, vel etiam ens rationis. Et ideo quaecumque sunt unum secundum substantiam, sunt unum simpliciter, et multa secundum quid. Sicut totum in genere substantiae, compositum ex suis partibus vel integralibus vel essentialibus, est unum simpliciter, nam totum est ens et substantia simpliciter, partes vero sunt entia et substantiae in toto. Quae vero sunt diversa secundum substantiam, et unum secundum accidens, sunt diversa simpliciter, et unum secundum quid, sicut multi homines sunt unus populus, et multi lapides sunt unus acervus; quae est unitas compositionis, aut ordinis. Similiter etiam multa individua, quae sunt unum genere vel specie, sunt simpliciter multa, et secundum quid unum, nam esse unum genere vel specie, est esse unum secundum rationem.» ST1-2 q. 17, a. 4.

239

[term] into its species by differences by which the nature of the genus is equally participated in the species, as animal is divided into man and horse, and the like. Another division is that of something common by analogy, which is predicated according to its perfect concept [ratio] of one of those that divide it, and of the other[s] imperfectly and with qualification [secundum quid], as being is divided into substance and accident, and into being in actuality and in potentiality ...5»

This general feature of analogical predication (regardless of the details of how an analogical concept is formed, and consequently what sorts of analogy may or need be distinguished6) betrays a common feature of analogical concept-formation. This common feature is that our analogical notions presuppose a primary, univocal concept arrived at by ordinary abstraction; it is this primary concept which is then further modified somehow in the process of some analogical concept-formation, yielding those further, qualified senses of the term subordinated to this concept which allow the term to be extended and analogically applied to things to which in its primary sense it could not apply without qualification.

If, therefore, the primary, unqualified concept of being is the one that applies to material substances of ordinary human experience, then, in view of the convertibility of the transcendental notion of being with the transcendental notion of one, it is substances of this kind that can be said to be one in the primary, unqualified sense. In general, then, on this account, the primary units in reality, that is, the things that can be said to be one without qualification, should be precisely these substances. Therefore, whenever it takes some further cognitive operation to discover either some further unity that they constitute, or some multitude of other units that constitute them, the units thus discovered can be said to be one only with qualification, just as St. Thomas said7.

5 «Respondeo dicendum, quod est duplex modus dividendi commune in ea quae sub ipso sunt, sicut est duplex communitatis modus. Est enim quaedam divisio univoci in species per differentias quibus aequaliter natura generis in speciebus participatur, sicut animal dividitur in hominem et equum, et hujusmodi; alia vero divisio est ejus quod est commune per analogiam, quod quidem secundum perfectam rationem praedicatur de uno dividentium, et de altero imperfecte et secundum quid, sicut ens dividitur in substantiam et accidens, et in ens actu et in ens potentia: et haec divisio est quasi media inter aequivocum et univocum.» 2SN d. 42, q. 1, a. 3, in corp. Cf.: «Unum enim eodem modo dicitur aliquid sicut et ens; unde sicut ipsum non ens, non quidem simpliciter, sed secundum quid, idest secundum rationem, ut patet in 4o Metaphysicae, ita etiam negatio est unum secundum quid, scilicet secundum rationem.» in Peri lb. 2, lc. 2, n. 3. 6 Since here we need not consider in detail exactly how an analogical concept is formed, we need not consider what are the different modes of analogy, which is in the focus of the debates concerning Aquinas’s theory of analogy. See MCINERNY, R.: The Logic of Analogy, Martinus Nijhoff: The Hague, 1961, and MCINERNY, R.: Aquinas and Analogy, Washington, D.C.: Catholic University of America Press, 1996. Cf. also: ASHWORTH, E. J.: Analogical Concepts: The Fourteenth-Century Background to Cajetan, «Dialogue», 31, 1992, p. 399.; ASHWORTH, E. J.: Analogy and Equivocation in Thirteenth-Century Logic: Aquinas in Context, «Mediaeval Studies», 54,1992, p. 94. 7 Cf.: «Ad secundum dicendum quod nihil prohibet id quod est uno modo divisum, esse alio modo indivisum; sicut quod est divisum numero, est indivisum secundum speciem, et sic contingit aliquid esse uno modo unum, alio modo multa. Sed tamen si sit indivisum simpliciter; vel quia est indivisum secundum id quod pertinet ad essentiam rei, licet sit divisum quantum ad ea quae sunt extra essentiam rei, sicut quod est unum subiecto et multa secundum accidentia; vel quia est indivisum in actu, et divisum in potentia, sicut quod est unum toto et multa secundum partes, huiusmodi erit unum simpliciter, et multa secundum quid. Si vero aliquid e converso sit indivisum secundum quid, et divisum simpliciter; utpote quia est divisum secundum essentiam, et indivisum secundum rationem, vel secundum principium sive causam, erit multa simpliciter, et unum secundum quid; ut quae sunt multa numero et unum specie, vel unum principio. Sic igitur ens dividitur per unum et multa, quasi per unum simpliciter, et multa secundum quid. Nam et ipsa multitudo non contineretur sub ente, nisi contineretur aliquo modo sub uno. Dicit enim dionysius, ult. Cap. De div. Nom., Quod non est multitudo non participans uno, sed quae sunt multa partibus, sunt unum toto; et quae sunt multa accidentibus, sunt unum subiecto; et quae sunt multa numero, sunt unum specie; et quae sunt

240

Indeed, the unity such primary substances constitute is either the unity of their collections or the unity of their genera and species. The cognitive operation required to realize the unity of their collections is counting them together, or some other way of viewing them together collectively, based on their order, connections or common function, while the mental operation required to realize the unity of their species and genera is abstraction8. On the other hand, the cognitive operation required to recognize the multitude of the parts that constitute primary substances is the discernment of their parts. In this way, since on this conception the account of unity is based on the primary ontological status of primary substances, it will clearly not depend on us what the primary units of reality are, despite the fact that the ways of carving out our units from reality obviously depend on our cognitive faculties.

However, at this point one may object that despite appearances to the contrary, this account in fact ties the issue of what the primary units of reality are even more closely to our cognitive faculties. For the only reason why Aristotelian primary substances are singled out as the primary beings, and thus as the primary units, seems to be that these are the things that are most familiar to us, insofar as they are the primary objects of our cognitive faculties. But, then, if the objects of ordinary human experience are the beings in the primary sense only and precisely because they are the primary objects of our cognitive faculties, then it is apparently the nature of our cognitive faculties that determines what should be regarded as primary beings. However, this may have nothing to do with how things really are in themselves, apart from our cognitive faculties. Indeed, as we get increasingly familiar with objects that are not objects of our ordinary experience through the advance of natural science, we may have more and more evidence to suggest that objects of our ordinary experience may not be the primary units of reality, but rather they are more like the clouds relative to the droplets that constitute them.

Being, Substance, Identity, Unity and Simplicity

Now is it really the case that it is Aristotelian primary substances that are beings in the primary, unqualified sense? And if so, does it really depend on our cognitive faculties what should count as a primary substance?

In a way the issue whether primary substances are the primary beings and thus the primary units is trivial. Primary substances are the primary beings and vice versa, because this is how the two concepts are related, and that is that. A being in the primary sense is one that has an act of being [esse] without qualification. This means that it has its act of being in such a manner that its act of being is not the act of being of something else with qualification. For instance, by this criterion the wisdom of Socrates is not a primary being, for its act of being is the act of being of something else with qualification, namely the act of Socrates’s being wise, that is, Socrates’s being with respect to his wisdom9. On the other hand, by the same criterion, Socrates himself has speciebus multa, sunt unum genere; et quae sunt multa processibus, sunt unum principio.» ST1 q. 11, a. 1, ad 2-um 8 Note that in modern logic and set theory it is the former operation of forming collective wholes by lumping individuals together that is rather improperly called abstraction, whereas the original Aristotelian notion of abstraction of forming universal wholes by disregarding the individuating conditions of singulars is discussed rather in historically oriented philosophical studies. In fact, the whole issue would deserve separate treatment, but here I cannot go into further details. 9 Cf.: KLIMA, G. The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being, «Medieval Philosophy and Theology», 5, 1996, pp. 87-141. The gist of the criterion can be summarized in the following formula: esse simpliciter entis secundum quid est esse secundum quid entis simpliciter.

241

to count as a primary being, since his act of being is not the act of being of something else with qualification, which is shown by the fact that Socrates’s coming to be and ceasing to be simpliciter is not the coming to be and ceasing to be of something else secundum quid. However, the act of being which is the act of being of something else with qualification is what is usually described as the act of something’s being in something else, esse in alio, that is, as accidental being. By contrast, the kind of being that something has absolutely speaking and which is not the act of being with qualification of something else is what is usually described as esse per se, that is, as substantial being. But this is precisely the way in which primary substances are described, namely, as beings whose nature demands this kind of act of being10. So whatever is a primary being is a primary substance and vice versa.

The non-trivial issue, however, is just which entities should count as primary beings and hence as primary substances in this sense. Now since primary substances are primary beings, which have their own act of being without qualification, they will also be beings which, if they are generable and corruptible, will have generation and corruption without qualification. Again, this means that their coming to be and ceasing to be is not the coming to be and ceasing to be of something else with qualification. By contrast, the coming to be and ceasing to be of their accidents is their coming to be or ceasing to be with qualification, that is, their change. But then, since their coming to be and ceasing to be with qualification is not their coming to be or ceasing to be simpliciter, these are the entities that are permanent through change. However, permanence through change is nothing but identity across time, or indeed, with respect to merely possible changes, it is identity across possible situations, or as modern philosophers would have it, across “possible worlds”. But since identity is nothing but unity in substance according to Aristotle11, a changeable primary substance is something that preserves its unity through actual or merely possible changes.

However, with this last remark we seem to have come full circle. For I started the discussion with trying to clarify the notion of primary unit with reference to the notion of primary being. This then turned out to be equivalent to the notion of primary substance, which however turns 10 «Ad secundum dicendum, quod secundum Avicennam in sua Metaph., esse non potest poni in definitione alicuius generis et speciei, quia omnia particularia uniuntur in definitione generis vel speciei, cum tamen genus vel species non sit secundum unum esse in omnibus. Et ideo haec non est vera definitio substantiae: substantia est quod per se est; vel: accidens est quod est in alio. Sed est circumlocutio verae descriptionis, quae talis intelligitur: substantia est res cuius naturae debetur esse non in alio; accidens vero est res, cuius naturae debetur esse in alio. Unde patet quod, quamvis accidens miraculose sit non in subiecto, non tamen pertinet ad definitionem substantiae; non enim per hoc eius naturae debetur esse non in alio; nec egreditur definitionem accidentis, quia adhuc natura eius remanet talis ut ei debeatur esse in alio.” QDL 9, q. 3, ad 2-um. Cf. “Ad secundum dicendum, quod sicut probat Avicenna in sua Metaph., per se existere non est definitio substantiae: quia per hoc non demonstratur quidditas ejus, sed ejus esse; et sua quidditas non est suum esse; alias non posset esse genus: quia esse non potest esse commune per modum generis, cum singula contenta in genere differant secundum esse; sed definitio, vel quasi definitio, substantiae est res habens quidditatem, cui acquiritur esse, vel debetur, ut non in alio; et similiter esse in subjecto non est definitio accidentis, sed e contrario res cui debetur esse in alio; et hoc nunquam separatur ab aliquo accidente, nec separari potest: quia illi rei quae est accidens, secundum rationem suae quidditatis semper debetur esse in alio. Sed potest esse quod illud quod debetur alicui secundum rationem suae quidditatis, ei virtute divina agente non conveniat; et sic patet quod facere accidens esse sine substantia, non est separare definitionem a definito; et si aliquando hoc dicatur definitio accidentis, praedicto modo intelligenda est definitio dicta: quia aliquando ab auctoribus definitiones ponuntur causa brevitatis non secundum debitum ordinem, sed tanguntur illa ex quibus potest accipi definitio.» 4SN, d. 12, q. 1, a. 1a, ad 2-um 11 Cf. «Philosophus dicit: unum in substantia facit idem, in quantitate aequale, in qualitate simile.» 1SN d. 8, q. 4, a. 3, 2.

242

out to be describable in terms of identity, and hence of unity, through change. So, apparently, to explain primary unity we have to resort to the notion of primary substance, while in explaining primary substance we have to appeal to the same notion of unity.

But there is nothing vicious in this apparent circularity. For there is a vicious circle of definitions only if a defining term cannot be understood without the term it defines, whereas the latter cannot be understood without the defining term in question. However, this is certainly not the case here. In fact, there is no circularity here at all. The primary distinction is still that between an act of being without and with qualification, which grounds the distinction between substance and accident. The rest, namely, permanence, identity and hence unity through change, is merely a consequence of this primary distinction, indeed, not even concerning all beings or even all substances, but only concerning generable and corruptible substances. These consequences, however, provide further, occasionally better-known indications which may help us to tell substances from non-substances in particular cases. For instance, in some cases it may be evident that certain kinds of things have generation and corruption without qualification, as in the case of living things, while in other cases it may be more obvious what constitutes the unity of a given thing, as in the case of continuous non-living substances.

But of course other cases may still leave us with a number of hard-to-decide questions. For example, consider the question whether the turning of a piece of graphite into a diamond crystal is a substantial or an accidental change. In this case, the answer obviously depends on whether being graphite or diamond are accidental modifications of the same underlying substance, namely, carbon, which never loses its existence and unity during such a metamorphosis, or graphite and diamond should be regarded as substances in their own right, consisting of differently configured carbon atoms, which however, do not preserve their distinct existence and unity in the wholes they constitute. The former solution would tie the identity of a piece of carbon, whether it is in the form of diamond or graphite, to the unity of the collection of carbon atoms that make it up, treating their differences in configuration on a par with a simple accidental rearrangement of individual units in space, analogous to the rearrangement of a flight of aircraft taking up a new formation in the sky. On the other hand, the latter solution would regard a piece of carbon in the form of a diamond crystal as a unified whole in which there are no distinct carbon atoms as such, but which could be generated by unifying previously distinct carbon atoms in the tetrahedral crystalline structure characteristic of diamonds.

Now I certainly do not want to decide this particular question here, which is not so interesting after all. To be sure, modern quantum chemistry speaks rather for the latter position, as opposed to the rather primitive mechanistic picture underlying the former. But then the further details concerning the distinct vs. indistinct character of the carbon atoms making up the whole should rely on further specific considerations belonging to quantum chemistry. What is important from our point of view is that the clarification of the conceptual relations between being, unity, identity and substance gives us important clues as to what are the relevant considerations in discussing particular cases. Whenever it is clear that a certain kind of thing has generation and corruption simpliciter, then that should be the decisive factor. On the other hand, as could be seen in the particular case of the allotropes of carbon, when the question of substantiality needs to be determined on the basis of considerations concerning unity, then the relevant issue will have to be the relative distinction and unity of the parts making up the whole. The less distinct are the parts, the more unified is the whole; but the more unified is the whole, the more it has to

243

be regarded as having its own substantial being, and the less its parts can be regarded as having their own unity and substantial being12.

So, if we recognize this type of unity in the realm of objects of ordinary human experience, then we have to recognize those objects as primary substances without further ado. Still, even though on this basis we can recognize such objects as primary substances and hence as the primary beings and primary units in an unqualified sense as they present themselves in our experience, this still need not mean that these substances are the absolutely ultimate units and entities in an even further, more basic sense.

For given that the distinctness and multiplicity of the constitutive parts is what is opposed to the simplicity and unity of the whole, which we have just acknowledged to go hand in hand with substantiality and unqualified being, if we recognize that even within the realm of primary substances there are various degrees of the multiplicity of parts and thus of the opposite simplicity of the whole, then we should also acknowledge that even within the realm of primary substances there have to be several degrees in the applicability of the notion of unity. As St. Thomas writes:

«In response we have to say that God is maximally and most truly one. For just as something is related to being undivided, so it is related to unity; since, according to the Philosopher, a being is said to be one insofar as it is not divided. And so those things which are undivided per se are more truly one than those things that are undivided per accidens, as Socrates and a white thing, which are one per accidens. But among the things that are one per se, those which are undivided absolutely speaking are more truly one than those which are undivided in respect of a genus, or species, or some analogy [proportio]. Hence they are not even said to be one absolutely speaking, but one in genus, or in species, or by analogy; but what is absolutely undivided is said to be absolutely one, and that is numerically one. But even among such things there are degrees. For there is something which is such that even though it is actually undivided, still it is potentially divisible, either by a division of quantity, or by an essential division, or by both: by the division of quantity, as something which is one by continuity; by an essential division, as those things which are composed of matter and form, or from the act of being and that which is; or by both divisions as the natural bodies. And that some of these are not actually divided derives in them from something outside of the nature of composition or division, as is obvious in the case of the body of the heavens and the like, which are such that although they are not actually divisible, they are nevertheless divisible by the intellect. But there are things which are indivisible both actually and potentially, and such are of various kinds. For some involve something else in their concept besides the concept of indivisibility, as a point, which besides being undivided involves also position. But there is something which involves nothing else, but is its own indivisibility, as is the unity which is the principle of number; yet this inheres in something which is not this unity itself, namely, in its subject. Whence it is clear that that in which there is no composition of parts, no continuity of dimension, no variety of accidents, and which inheres in nothing, is maximally and most truly one, as Boethius concludes. And hence follows that His unity is the principle of all unity and the measure of all things; for that which is the maximal is the principle in every genus, just as that which is maximally hot is the [principle] of all hot things, as is said in bk. 2 of the Metaphysics, and that which is the simplest is the measure in any genus, as is said in bk. 10 of the Metaphysics13.»

12 Cf. Aquinas's De Mixtione Elementorum, where it is precisely along these lines that Thomas distinguishes what we would describe as a chemical reaction from the simple physical mixing of imperceptibly small parts. 13 «Respondeo dicendum, quod deus summe et verissime unus est. Secundum enim quod aliquid se habet ad indivisionem, ita se habet ad unitatem; quia, secundum philosophum, ens dicitur unum in eo quod non dividitur. Et ideo illa quae sunt indivisa per se, verius sunt unum quam illa quae sunt indivisa per accidens, sicut albus et socrates quae sunt unum per accidens; et inter illa quae sunt unum per se, verius sunt unum quae sunt indivisa simpliciter

244

However, if there are degrees in unity even within the domain of primary substances, that is, primary beings, then there also have to be degrees of being within the same domain. But how can this come about? How can we interpret degrees of being within this domain, once we have agreed that all primary substances are primary beings, that is, things that are said to be beings without any qualification?

Absolute Being and Absolute Unity

To respond to this question we have to consider how we can say both that any primary substance is one and being in the primary, unqualified sense and that only God can be said to be one and being in an absolutely unqualified sense.

The primary, unqualified sense of being is that on account of which any primary substance can be said to be a being without qualification insofar as it is. But for a primary substance to be is for it to have its essence in actuality, that is, for a primary substance to be, absolutely speaking, is at the same time for it to be with respect to its essence. So even the primary, unqualified predication of being implies a certain implicit qualification, namely, the determination of a thing’s substantial being to its own essence14. But isn’t this equally true in the case of God? Couldn’t we say that even for God to be is for Him to be with respect to the divine essence, and so also in this case there is a certain implicit qualification, namely, the determination of divine being by divine essence?

To answer this question, we should consider it in the general context of Aquinas’s analysis of the difference between predication secundum quid and simpliciter, distinguishing between diminishing and non-diminishing determinations15. To use the common medieval example, if I say: ‘This shield is white with respect to its one half’, this obviously does not entail that the

quam quae sunt indivisa respectu alicujus vel generis vel speciei vel proportionis. Unde etiam non dicuntur simpliciter unum, sed unum vel in genere vel in specie vel in proportione; et quod est simpliciter indivisum, dicitur simpliciter unum, quod est unum numero. Sed in istis etiam invenitur aliquis gradus. Aliquid enim est quod quamvis sit indivisum in actu, est tamen divisibile potentia, vel divisione quantitatis, vel divisione essentiali, vel secundum utrumque. Divisione quantitatis, sicut quod est unum continuitate; divisione essentiali, sicut in compositis ex forma et materia, vel ex esse et quod est; divisione secundum utrumque, sicut in naturalibus corporibus. Et quod aliqua horum non dividantur in actu, est ex aliquo in eis praeter naturam compositionis vel divisionis, sicut patet in corpore caeli et hujusmodi; quae quamvis non sint divisibilia actu, sunt tamen divisibilia intellectu. Aliquid vero est quod est indivisibile actu et potentia; et hoc multiplex est. Quoddam enim habet in sui ratione aliquid praeter rationem indivisibilitatis, ut punctum, quod praeter indivisionem importat situm: aliquid vero est quod nihil aliud importat, sed est ipsa sua indivisibilitas, ut unitas quae est principium numeri; et tamen inhaeret alicui quod non est ipsamet unitas, scilicet subjecto suo. Unde patet quod illud in quo nulla est compositio partium, nulla dimensionis continuitas, nulla accidentium varietas, nulli inhaerens, summe et vere unum est, ut concludit boetius. Et inde est quod sua unitas est principium omnis unitatis et mensura omnis rei. Quia illud quod est maximum, est principium in quolibet genere, sicut maxime calidum omnis calidi, ut dicitur 2 metaphysic., Et illud quod est simplicissimum, est mensura in quolibet genere, ut 10 metaphysic. dicitur.» 1SN d. 24, q. 1, a. 1. 14 For this point see WIPPEL, J. F.: Thomas Aquinas and Participation, in: WIPPEL, J. F. (ed.): «Studies in Medieval Philosophy», The Catholic University of America Press: Washington D.C., 1987. For the significance of using the preposition ‘to’ in this context, see R.A. TE VELDE: Participation and Substantiality in Thomas Aquinas, Brill: Leiden-New York-Köln, 1995, p. 152. 15 For a more comprehensive discussion of the logical doctrine behind Aquinas’s analysis of this difference (in connection with St. Thomas’s use of the related theoretical apparatus in his theology of the Incarnation) see KLIMA, G.: Libellus pro Sapiente: A Criticism of Allan Bäck’s Argument against St. Thomas Aquinas’ Theory of the Incarnation, «The New Scholasticism», 58, 1984, pp. 207-219.

245

shield is white, absolutely speaking, for its other half may be black. So in this case the qualification is diminishing [determinatio diminuens], in the sense that it “diminishes”, that is, takes away from, the conditions of the absolute, unqualified applicability of the predicate, and this is why the predicate so qualified can apply to something which is not absolutely white, but only in its half. So precisely because the qualification is intensionally diminishing, it is extensionally enlarging. By contrast, if I say: ‘This shield is white with respect to its whole surface’, then the qualification added to the predicate is not diminishing, for this qualification states that the shield is white all over, which is precisely what the absolute, unqualified predicate would say, namely, that the shield is white, so this qualification does not take away anything from the conditions of the strict applicability of the unqualified predicate and hence it applies only to what is white all over, without qualification.

But, further, if I say: ‘This shield is white with respect to its whiteness’, then, again, the qualification added to the predicate does not take away anything from the conditions of its strict, unqualified applicability, whence it applies only to something that is absolutely white, without any limitation. The reason for this clearly is that when the qualification refers to what is signified by the predicate, then the qualification is not diminishing; on the contrary, since the predicate can apply to the subject only in respect of what it signifies anyway, the predicate so qualified can apply only to that to which it applies also in itself, absolutely, without any qualification16. So a diminishing qualification has to refer to something which is distinct from what is signified by the predicate, but when there is no such a distinction, then the qualification is not diminishing. But this is precisely the case in the predication: ‘God exists with respect to His divinity’, for God’s existence being the same as His essence, the qualification refers to what the predicate signifies, namely, divine existence, which is divinity, the divine essence. On the other hand, in everything else, i.e., in every created thing, the nature of the thing is not the same as the existence of the thing, and this is why the created nature imposes a certain diminishing, limiting qualification and determination upon the existence of the thing. As St. Thomas says:

«For a created spiritual substance has to contain two [principles], the one of which is related to the other as potency to act. And this is clear from the following. It is obvious that the first being, which is God, is infinite act, namely, having in Himself the whole plenitude of being not contracted to the nature of some genus or species. Therefore it is necessary that His being itself should not be an act of being that is, as it were, put into a nature which is not its own being, for in this way it would be confined to that nature. Hence we say that God is His own being. But this cannot be said about anything else; just as it is impossible to think that there should be several separate whitenesses, but if a whiteness were separate from any subject and recipient, then it would be only one, so it is impossible that there should be a subsistent act of being, except only one. Therefore, everything else after the first being, since it is not its own being, has being received in something, by which its being is contracted; and thus in any created being the nature of the thing that participates being is other than the act of being itself that is participated17.»

16 According to the medieval logical literature concerning the fallacy secundum quid et simpliciter, the general rule for distinguishing diminishing vs. non-diminishing qualifications is that a qualification is non-diminishing if and only if it refers to a part of the subject which is such that the predicate would apply to the whole subject without qualification only in respect of that part anyway. For references see my paper referred to in the previous note. 17 De spir. creat. q. un., a.1: «Oportet enim in substantia spirituali creata esse duo, quorum unum comparatur ad alterum ut potentia ad actum. Quod sic patet. Manifestum est enim quod primum ens, quod Deus est, est actus infini-tus, utpote habens in se totam essendi plenitudinem non contractam ad aliquam naturam generis vel speciei. Unde oportet quod ipsum esse eius non sit esse quasi inditum alicui naturae quae non sit suum esse; quia sic finiretur ad illam naturam. Unde dicimus, quod Deus est ipsum suum esse. Hoc autem non potest dici de aliquo alio: sicut

246

So although all created substances are beings in the primary, unqualified sense, this unqualified sense of being is still not, indeed, cannot be, the absolutely unlimited sense of being according to which only God can be said to exist. The reason for this is that everything is said to exist with respect to its essence, for the substantial existence of every thing is precisely the actuality of its essence. But it is only God whose essence is His own existence, so everything else’s essence, being distinct from its existence imposes some diminishing qualification, some limitation upon the sense of being in which only God can be said to exist. So the substantial being of created substances, on account of which the predicate ‘is’ or ‘exists’ applies to them without qualification, for it is the act of being by which they exist simpliciter, is at the same time an act of being which can be signified by the predicate ‘is’ or ‘exists’ only in a sense which can be derived by some diminishing qualification of the sense of the same predicate in which it applies only to God. Therefore, what accounts for the difference between the senses of ‘exists’ in which a creature and God can be said to exist is precisely God’s absolutely undivided unity, that is, God’s absolute simplicity, as opposed to the necessary intrinsic multiplicity of the constitutive parts of any creature. Indeed, it is precisely this intrinsic multiplicity that distinguishes creatures from God as well as from one another, thereby causing the extrinsic multiplicity of the number of creatures, for created substances differ from one another in their essence insofar as their essences are different determinations of their acts of being. Furthermore, when their essence itself is composite, because it comprises both matter and form, the determination it imposes upon the substantial act of being of material substances also allows the numerical multiplicity of individuals within the same species, divided from one another by their designated matter, that is, their matter informed by their dimensions18.

Now it is individuals of this kind that are the most familiar to us, and so it is the unity and being of these individuals that provides for us the primary, unqualified notions of being and unity. So first it is relative to these individuals that we have to recognize that their integral parts (whether quantitative parts, other accidental parts or even essential parts), their collections, and their species and genera also exhibit some sort of unity and being which is analogous to the unity and being of these primary substances19.

But once we recognize the analogical character of the applicability of these notions in the realm of created substances, their parts, species, genera and collections, and we also recognize how the created order of these primary beings is determined by their metaphysical unity, on account of which they approach more or less the absolute unity of divine simplicity, we also have to admit that even the being of these is subject to certain qualification and limitation in comparison to the being of He who IS, without any limitation.

And this is why, when he discusses whether ‘He who is’ [qui est] is the most appropriate name of God, St. Thomas says the following:

impossibile est intelligere quod sint plures albedines separatae; sed si esset albedo separata ab omni subiecto et recipiente, esset una tantum; ita impossibile est quod sit ipsum esse subsistens nisi unum tantum. Omne igitur quod est post primum ens, cum non sit suum esse, habet esse in aliquo receptum, per quod ipsum esse contrahitur; et sic in quolibet creato aliud est natura rei quae participat esse, et aliud ipsum esse participatum.» 18 Cf. WIPPEL, J. F.: Thomas Aquinas on the Distinction and the Derivation of the Many from the One: a Dialectic between Being and Nonbeing, «The Review of Metaphysics,» 38, 1985, pp. 563-590. 19 See again the text quoted in n. 4.

247

«… all other names say something determinate and particularized, as ‘[to be] wise’ says [to be] something20. But the name ‘He who is’ says being absolutely, not determined by something added [to it] and this is why Damascene says that it does not signify what God is, but it signifies a certain infinite ocean of substance, as it were, something not determinate. Therefore, when we move toward God in the way of removal, first we deny of Him corporeal [attributes], and secondly even intellectual ones, in the way they are found in creatures, such as goodness and wisdom; and then it remains in our understanding only that He is, and nothing more, whence He is there in a sort of confusion. And finally we remove even this being itself, according to the way it is in the creatures; and then He remains there in a sort of shadow of ignorance, and by this ignorance, as it pertains to our present state, we are most appropriately tied to God, as Dionysius asserts, and this is a sort of haze, in which God is said to dwell21.»

So if we try to capture this absolute being in its simplicity, the notion of absolute being we arrive at leaves us with a certain confusion, because of a lack of determinate understanding. On the other hand, as soon as we try to reach a more determinate understanding of divine nature, it is precisely the determinate character of our concepts, and their resulting multiplicity, which will be incompatible with the absolutely unlimited nature and simplicity of divine being. Indeed, even when a determinate concept represents some absolute perfection which in its absolute, unlimited form is nothing but the plenitude of divine being, but which we can find in the creatures only in a limited and determinate manner, the very determinacy of the concept matches the determinacy, and so also the limited character of the perfection in question as it is found in the creatures. For even though the perfection represented by the concept in itself is absolute insofar as by its own nature it does not demand any determination, the way in which it is represented by the concept, as being a perfection which is distinct from other creaturely perfections, involves a multiplicity that is not compatible with the absolute divine simplicity.

But this is precisely the reason why St. Thomas has to claim that although those names which signify such absolute perfections apply primarily to God quantum ad rem significatam, still, quantum ad modum significandi they apply primarily to creatures. As he says:

«We should consider, therefore, that because [the] names [we apply to God] are imposed by us, and we do not know God except from the creatures, [these names] are always defective in their representation with respect to their mode of signifying [quantum ad modum significandi], for they signify divine perfections in the way in which they are participated by the creatures. But if we consider the thing signified [res significata] by the name, which is that which the name is imposed to signify, we find that some names are imposed to signify primarily the perfection itself exemplified by God absolutely, not implying some [determinate] mode in their signification, while others [are imposed] to signify a perfection in accordance with such a mode of participation. For example, every cognition is [primarily] exemplified by divine cognition, and every knowledge by divine knowledge. The name ‘sense’, however, is imposed to signify cognition in the manner in which it is received materially by a power of an organ. But the name ‘cognition’ does not signify a mode of participation in its principal signification. Therefore, we have to say that all those names

20 Cf. In Boethii De Hebdomadibus, lc. 2. nn. 20-35. 21 «Ad quartum dicendum, quod alia omnia nomina dicunt esse determinatum et particulatum; sicut sapiens dicit aliquid esse; sed hoc nomen qui est dicit esse absolutum et indeterminatum per aliquid additum; et ideo dicit Damascenus quod non significat quid est deus, sed significat quoddam pelagus substantiae infinitum, quasi non determinatum. Unde quando in deum procedimus per viam remotionis, primo negamus ab eo corporalia; et secundo etiam intellectualia, secundum quod inveniuntur in creaturis, ut bonitas et sapientia; et tunc remanet tantum in intellectu nostro, quia est, et nihil amplius: unde est sicut in quadam confusione. Ad ultimum autem etiam hoc ipsum esse, secundum quod est in creaturis, ab ipso removemus; et tunc remanet in quadam tenebra ignorantiae, secundum quam ignorantiam, quantum ad statum viae pertinet, optime deo conjungimur, ut dicit dionysius, et haec est quaedam caligo, in qua deus habitare dicitur.» 1SN d. 8, q.1, a. 1, resp. 4

248

which are imposed to signify some perfection absolutely are properly said of God, and they apply to Him primarily as far as the thing signified is concerned, although not as far as the mode of signifying is concerned, such as ‘wisdom’, ‘goodness’, ‘essence’ and the like22.»

So, divine simplicity necessarily defies any adequate characterization by us. The only name that could most appropriately express this absolute simplicity by its indeterminacy, the name qui est, leaves us in confusion precisely because of its indeterminacy. On the other hand, any other name that gives us a more determinate concept is inappropriate in its mode of signifying to express divine simplicity precisely because of the determinacy of the concept in question.

Therefore, since the names signifying some absolute perfection apply primarily and absolutely to God only with respect to what they signify, but none of them can properly apply to Him with respect to their mode of signifying, these names can also absolutely be denied of Him:

«… since a name has both a mode of signifying and the thing signified itself, it can always be denied of God either on account of one of these or on account of both; but it cannot be said of God except on account of only of one them. And since the truth and appropriateness of an affirmation requires that all be affirmed, whereas for the appropriateness of a negation it is sufficient if only one of them is lacking, this is why Dionysius says that negations are absolutely true, but affirmations only in some respect [secundum quid]: for only with respect to what is signified, but not with respect to the mode of signifying23.»

Therefore, on the basis of these considerations we have to recognize the following paradox: these names could be predicated only of God in an absolutely unqualified sense (for the perfection they signify can be found only in God in an absolutely unqualified manner), and not of the creatures (for they apply to creatures in an unqualified sense only because it is from them that we abstracted the primary concepts of the perfections these names signify); still, because of the inherent multiplicity in their mode of signifying, reflecting their origin from the multiplicity of creaturely perfections, we can more appropriately deny them than affirm them of God. But it is

22 «Considerandum est igitur, quod cum nomina sint imposita a nobis, qui deum non nisi ex creaturis cognoscimus, semper deficiunt a divina repraesentatione quantum ad modum significandi: quia significant divinas perfectiones per modum quo participantur in creaturis. Si autem consideremus rem significatam in nomine, quae est id ad quod significandum imponitur nomen, invenimus, quaedam nomina esse imposita ad significandum principaliter ipsam perfectionem exemplatam a deo simpliciter, non concernendo aliquem modum in sua significatione; et quaedam ad significandum perfectionem receptam secundum talem modum participandi; verbi gratia, omnis cognitio est exemplata a divina cognitione, et omnis scientia a divina scientia. Hoc igitur nomen sensus est impositum ad significandum cognitionem per modum illum quo recipitur materialiter secundum virtutem conjunctam organo. Sed hoc nomen cognitio non significat aliquem modum participandi in principali sua significatione. Unde dicendum est, quod omnia illa nomina quae imponuntur ad significandum perfectionem aliquam absolute, proprie dicuntur de deo, et per prius sunt in ipso quantum ad rem significatam, licet non quantum ad modum significandi, ut sapientia, bonitas, essentia et omnia hujusmodi; et haec sunt de quibus dicit Anselmus, quod simpliciter et omnino melius est esse quam non esse. Illa autem quae imponuntur ad significandum perfectionem aliquam exemplatam a deo, ita quod includant in sua significatione imperfectum modum participandi, nullo modo dicuntur de deo proprie; sed tamen ratione illius perfectionis possunt dici de deo metaphorice, sicut sentire, videre et hujusmodi. Et similiter est de omnibus aliis formis corporalibus, ut lapis, leo et hujusmodi: omnia enim imponuntur ad significandum formas corporales secundum modum determinatum participandi esse vel vivere vel aliquam divinarum perfectionum.» 1SN d. 22, q. 1, a. 2 co 23 «Ad primum igitur dicendum, quod cum in nomine duo sint, modus significandi, et res ipsa significata, semper secundum alterum potest removeri a Deo vel secundum utrumque; sed non potest dici de Deo nisi secundum alterum tantum. Et quia ad veritatem et proprietatem affirmationis requiritur quod totum affirmetur, ad proprietatem autem negationis sufficit si alterum tantum desit, ideo dicit Dionysius, quod negationes sunt absolute verae, sed affirmationes non nisi secundum quid: quia quantum ad significatum tantum, et non quantum ad modum significandi.» 1SN d. 22, q. 1, a. 2, ad 1-um

249

precisely the recognition of this paradox that helps us gain some insight into the incomprehensible divine unity reflected in created multiplicity24.

24 So, from this point of view, I do not find the contrast between “Neoplatonic henology”, as opposed to “Thomistic ontology” so sharp as some Thomistic scholars, most notably Gilson, would. But this would deserve a separate study. The issue receives intriguing discussion in TAYLOR, R. C.: Aquinas, the Plotiniana Arabica, and the Metaphysics of Being and Actuality, «Journal of the History of Ideas», (1998), pp. 217-239.

250

Man = Body + Soul: Aquinas’s Arithmetic of Human Nature

1. Introduction

For philosophers who find both a dualistic and a purely materialistic account of the human soul unacceptable, the Aristotelian-Thomistic conception of the soul as the substantial form of the living body may appear to be an intriguing alternative. However, even if one is not afraid of the prospect of committing oneself to an apparently “obsolete” metaphysics, developing such a commitment may not look to be a wise move after all, since upon closer inspection the doctrine may seem to be frustratingly obscure, if not directly self-contradictory.

In what follows I first present what may seem to be a fundamental problem with Aquinas’s conception. Second, I will provide the solution that emerges from some crucial distinctions made by Aquinas in this context. The subsequent analysis of these distinctions will show how they fit into the larger context of Aquinas’s general metaphysical, mereological and logical considerations, providing further clues as to how these considerations fit together in Aquinas’s thought. In the concluding section of the paper I will argue that with the proper understanding of these conceptual connections, despite possible appearances to the contrary, Aquinas’s conception does indeed offer a viable alternative to the modern dilemma of dualism vs. materialism.

2. The problem

In his recent book, Aquinas on Mind, Anthony Kenny calls our attention to the problem as follows:

“If we identify the human soul with Aristotelian substantial form, it is natural to identify the human body with prime matter. But body and soul are not at all the same pair of items as matter and form. This is a point on which Aquinas himself insists: the human soul is related to the human body not as form to matter, but as form to subject (S 1-2,50,1). A human being is not something that has a body; it is a body, a living body of a particular kind. The dead body of a human being is not a human body any longer — or indeed any other kind of body, but rather, as it decomposes, an amalgam of many bodies. Human bodies, like any other material objects, are composed of matter and form; and it is the form of the human body, not the form of the matter of the human body, that is the human soul”1

Despite the fact that one might object to the way in which Kenny poses the problem—unfortunately, the rather sloppily presented contrast between matter and subject is not quite supported by the passage he refers to, and Aquinas himself would not contrast the two in the way in which Kenny intends this contrast2—, there is a genuine problem here.

For Aquinas does indeed say both that a human being is a human body, namely, a rational, sensitive, living body, and that a human being consists of a soul and a body. But these two

1 Kenny, 1995, 28. 2 For Aquinas the contrast between (prime) matter and subject in the strict sense is the contrast between that which is informed by a substantial form and that which is informed by an accidental form. See c. 1. of his De Principiis Naturae. However, apparently, Kenny rather intends to distinguish here between what in another place Aquinas calls subiectum informe and subiectum formatum; cf. text quoted in n. 6. But this is not the issue in the text referred to by Kenny.

251

claims are apparently incompatible. For according to the latter claim the body is an integral part3 of the whole human being consisting of body and soul. But then the whole human being cannot be this body, for no integral part can be the same as the whole of which it is only a part.

Furthermore, if the human soul is the substantial form of the human body, then, since what a substantial form informs is the Aristotelian prime matter, according to Aquinas, it seems that the human body has to be prime matter.4 However, the human body cannot be prime matter, since prime matter in itself cannot exist in actuality, whereas the human body obviously does exist in actuality. 5

To be sure, at this point one might easily retort that the human body does exist in actuality precisely because it is actually informed by the soul. So the human body is prime matter actually informed by the soul. 6

However, this quick riposte will not do. For if we were to identify the human body with the matter that the soul informs in the context of the claim that a human being is composed of body and soul, then we would also have to admit that the human body in this composition is that component which persists through a substantial change, such as death, since prime matter in the composition of a material substance is precisely that part which is the permanent subject of a substantial change, when it loses one substantial form and takes on another.7 But the human body

3 Cf. in Meta lb. 5, lc. 21, n. 1099. For detailed discussion of the notions of integral part and whole, as opposed to other kinds of parts and wholes distinguished by medieval philosophers, see D. P. Henry, 1991; for a discussion of Aquinas’s views in particular see especially pp. 218-328. However, in general, for the purposes of the present discussion the concept of integral part can be defined as follows: a is an integral part of A if and only if a ≠ A and there is some b such that a + b = A. For example, a slice of a cake is an integral part of it, since the slice is not the cake, yet there is something, namely, the rest of the cake, such that the slice and the rest together are the cake. (Here, if someone has worries concerning the possible situation in which the slice is actually cut out, and thus the separated part and the rest do not make up the original cake, we can take ‘the rest’ to include not only the remaining quantitative part, but also its continuity with the slice. Cf. what St. Thomas says about the issue in Meta lb. 5. lc. 21. esp. nn. 1104-1108.) Likewise, the tone C is an integral part of the chord C major, for the tone is not the chord, yet there is something, namely, the tones E and G together, such that the tone C and the tones E and G together are the chord C major, that is, C + E + G = C major. As these examples show, the ‘+’ symbol in the above definition is used as a collective nominal conjunction, which is in fact the general logical notion that has the familiar arithmetical operation only as its special case, as restricted to numerals. However, in general, if ‘a’ and ‘b’ are any two names, then ‘a + b’ is another name, the name of the integral whole having a and b as its integral parts, and the truth of ‘P(a + b)’ does not imply either ‘Pa’ or ‘Pb’. For example, while two and three are five, neither two nor three are five, and even if Plato and Socrates are men, neither of them is men, although, of course, each of them is a man, etc. 4 “ … dicimus quod essentia animae rationalis immediate unitur corpori sicut forma materiae, et figura cerae, ut in 2 De Anima dicitur. Sciendum ergo, quod convenientia potest attendi dupliciter: aut secundum proprietates naturae; et sic anima et corpus multum distant: aut secundum proportionem potentiae ad actum; et sic anima et corpus maxime conveniunt. Et ista convenientia exigitur ad hoc ut aliquid uniatur alteri immediate ut forma; alias nec accidens subjecto nec aliqua forma materiae uniretur; cum accidens et subjectum etiam sint in diversis generibus, et materia sit potentia, et forma sit actus.” 2SN d. 1, q. 2, a. 4, ad 3-um 5 “Sed dicebat quod corpus humanum ipsum esse corporis habet per animam.- Sed contra, Philosophus dicit in II De Anima, quod anima est actus corporis physici organici. Hoc igitur quod comparatur ad animam ut materia ad actum, est iam corpus physicum organicum: quod non potest esse nisi per aliquam formam, qua constituatur in genere corporis. Habet igitur corpus humanum suum esse praeter esse animae.” QDA a. 1, obj. 15. 6 “Ad decimumquintum dicendum quod in definitionibus formarum aliquando ponitur subiectum ut informe, sicut cum dicitur: motus est actus existentis in potentia. Aliquando autem ponitur subiectum formatum, sicut cum dicitur: motus est actus mobilis, lumen est actus lucidi. Et hoc modo dicitur anima actus corporis organici physici, quia anima facit ipsum esse corpus organicum, sicut lumen facit aliquid esse lucidum.” QDA a. 1, ad 15-um. 7 Cf. De Princ. c. 1.

252

does not persist through death, for when it ceases to be informed by the soul it ceases to be, since the dead body of the human being is not a human body, except equivocally, according to Aquinas. So the human body cannot be prime matter, which is the immediate and persistent subject of the substantial form of the body.

On the other hand, given Aquinas’s theory of the unity of substantial forms, it seems that it cannot be anything else either. For according to this theory, a substantial form cannot have anything else as its subject but prime matter, since otherwise it would have to inform something that would already exist in actuality. But this is impossible, for something that exists in actuality already has its own substantial form, so it cannot take on any other form as its substantial form.8

In fact, Aquinas’s doctrine of the unity of substantial forms involves even further strange consequences in this regard. For according to this doctrine, the form on account of which a man is a body, his corporeity, is the same as that on account of which he is an animal, his animality, and this, in turn, is the same as that on account of which he is a human, his humanity. But Aquinas also argues that a man’s humanity or quiddity is what he calls the “form of the whole” [forma totius], as opposed to the “form of the part” [forma partis], which he identifies as the soul, and that the form of the whole differs from the form of the part because the form of the whole contains both matter and form.9 So the form of the whole, the quiddity of man, contains the soul as its part, so it obviously cannot be the same as the soul. But if it is not the same as the soul, and yet it is a form of the human being, and it is clearly not an accidental form, then it seems that we have at least two substantial forms here, one of which is a part of the other, and which, besides the form of the part, also contains matter! At this point, perhaps, our confusion has reached its peak, so it is about time we set about clarifying the basic concepts involved in these considerations.

3. The solution

The question, then, is this: exactly how are we to understand Aquinas’s claim that a human being essentially consists of body and soul, given his other claim that the soul is the one and only substantial form of the body?

To answer this question first we have to consider Aquinas’s distinction, which he takes over from Avicenna, between several senses of the term ‘body’.10 In his De Ente et Essentia he writes as follows:

“The name ‘body’ can be taken in several senses. For a body (1), insofar as it is in the genus of substance, is said to be a body (1) because it has such a nature that three dimensions can be designated in it; but the three designated dimensions themselves are the body (2) which is in the genus of quantity. But it happens that something that has some perfection also has a further perfection, as is obvious in the case of man, who has a sensitive nature, and beyond that also an intellective one. Likewise, to the perfection of having such a form that in the thing three dimensions can be designated another perfection can be added, such as life, or something like that. The name ‘body’ (3), therefore, can signify something which has a form from which there follows the designability of three dimensions with precision, namely, so that from that form no further perfection would follow, but if something is added, then it is beyond the signification of

8 Cf. QDA a. 9. In corp.; ST1 q. 76, aa. 6, 7; 2SN d. 1, q. 2, a. 4; SCG lb. 2, c. 71; etc. 9 4SN d. 44, q. 1, a. 1, ad 2-um; SCG 4, 81; QDL 2, q. 2, a. 2; in Meta lb. 7, lc. 9. 10 Cf. 1SN d. 25, q. 1, a. 1, ad 2-um; SCG lb. 4, c. 81.

253

‘body’ (3) in this sense. And in this sense the body (3) will be an integral and material part of an animal, for in this way the soul will be beyond the signification of the name ‘body’ (3), and it will be superadded to the body itself, so that the animal will be constituted from these two, namely, from the soul and the body (3), as its parts. But the name ‘body’ (1) can also be taken so that it should signify some thing which has a form on account of which three dimensions can be designated in it, whatever that form may be, whether it may give rise to some further perfection or not. And in this sense ‘body’ (1) will be a genus of ‘animal’, for an animal contains nothing which is not contained implicitly in a body (1). For the soul is not a form other than that on account of which in that thing three dimensions can be designated; and so when it was said that a body (1) is that which has such a form that three dimensions can be designated in it, it was understood so that whatever that form might be, whether animality or stoneness, or whatever else. And thus the form of animal is implicitly contained in the form of body (1), insofar as body (1) is its genus.”11

To understand this passage correctly, we have to recall that according to Aquinas concrete common names signify the forms or natures of things, however, they do not refer to, or, using the medieval technical term, supposit for (supponit pro), these forms in virtue of their signification, but rather to the things themselves that have these forms in actuality. What we can use to refer to a form itself is the abstract name corresponding to the concrete name.12 But then, if it turns out that we use a name in different senses, that is, with various significations, this means that the same name in its different senses signifies different forms in the same thing, and thus, in the corresponding different senses, the corresponding abstract term will refer to those different forms. For example, if someone is a bachelor both in the sense of holding a bachelor’s degree and in the sense of being unmarried, then his bachelorhood in the first sense is certainly not the same as his bachelorhood in the second sense, which is clearly shown by the fact that if he gets married he loses the latter, but not the former. In fact, this example also shows that the forms signified [formae significatae] by concrete terms and referred to by their abstract counterparts do not even have to be forms in the strict metaphysical sense of being some determinations of some real, whether substantial or accidental, act of being of their supposita.13 For, obviously, the forms signified by the term ‘bachelor’ in both senses are some beings of reason: in the first sense the form signified is a relation of reason connecting the bachelor in question to some academic institution and its regulations, while in the second sense it is the privation of a relation of reason connecting him to his spouse, insofar as these relations are recognized by the relevant members of society.14

In the same way, while the term ‘body’, insofar as it is the genus of all bodies, signifies the substantial form of all bodies, referred to by the term ‘corporeity’ in the first sense, the same term in the sense in which it is in the genus of quantity signifies an accidental form of the same bodies, namely, their corporeity in the second sense, that is, their dimensions extending them in space.15 But it is neither the first, nor the second sense of the term ‘body’ distinguished by

11 EE c. 2. In the translation I marked each occurrence of the term ‘body’, indicating in each particular case in which of the three senses distinguished here the term is being used. 12 To be sure, there are concrete terms which refer to the forms they signify, but they do so not on account of their signification, but on account of the simplicity of the thing they signify. Cf. 3SN d. 11, q. 1, a. 4; 1SN d. 33, q. 1, a. 2, ad 2. For further details on Aquinas’s semantic theory, see Klima, 1996. 13 As St. Thomas wrote: “...dicendum est quod illud a quo aliquid denominatur non oportet quod sit semper forma secundum rei naturam, sed sufficit quod significetur per modum formae, grammatice loquendo. Denominatur enim homo ab actione et ab indumento, et ab aliis huiusmodi, quae realiter non sunt formae.” QDP, q. 7, a. 10, ad 8. 14 Concerning the semantic role and ontological status of beings of reason in Aquinas, see Klima, 1993. 15 “Et dicitur corpus mathematicum, corpus consideratum secundum dimensiones quantitativas tantum, et hoc est corpus in genere quantitatis …” 2SN d. 30, q. 2, a. 2.

254

Aquinas that is relevant to the claim that a human being, or indeed, any living being, is composed of body and soul. For the sense of the term ‘body’ relevant here, as Aquinas characterizes it, is clearly the sense in which a lifeless body, say a stone, is said to be a body, with the strict implication of lacking life. But since no living body can be a body in this sense, the corporeity of a living body in this sense is obviously not the substantial form of a living body. So while the forms signified by the term ‘body’ in the first and the third senses distinguished by Aquinas coincide in lifeless bodies, since in these bodies the term in both of these senses signifies their substantial form, the negative implication of the third sense of the same term, which it does not have in the first sense, prevents it from signifying the substantial form of living beings in this sense; therefore, in this sense it cannot refer to the whole living being, but only to a part of it.

So with this distinction at hand we can give an acceptable answer to the question of how Aquinas can claim both that a human being is a body and that he or she has a body, as his or her integral part. For a human being is a body in the first sense, while it has a body in the third of the three senses distinguished here, and thus no inconsistency is involved in these two claims.

However, this solution still does not answer the further doubts raised above. For it is still not clear how the corporeity signified in a human being by the term ‘body’ in its first sense is related to the corporeity signified in the same human being by the same term in its third sense, and how these are related to the soul of the same human being.

Before going into the details of this issue, however, we should recall the simple truth that there is more than one way to slice a cake. That is to say, the division of any integral whole into its integral parts will always depend on how we distinguish the parts in the whole.

Nevertheless, we must also keep in mind that the apparent arbitrariness involved in distinguishing the parts of something according to our criteria does not make these parts “unreal”. For example, if we take the hapless Socrates and distinguish his left and right or upper and lower parts, in this process we get parts no less real than by distinguishing his members or organs, the only difference being that while in the former cases we distinguished his parts on the basis of their spatial orientation, in the latter we distinguished them on the basis of their function. To be sure, we may find some divisions to be more natural than others, in that they better “cut at the joints” of some whole. But that has rather to do with the relative unity of the parts in constituting the absolute unity of the whole, or vice versa, than with the reality or non-reality of the parts.16 As St. Thomas reminds us:

“… nothing prevents some things from being many in some respect and being one in another. Indeed, all sorts of things that are many are one in some respect, as Dionysius says in the last chapter of On Divine Names. But we have to be aware of the difference that some things are many absolutely, and one in some respect, while the case is the reverse with others. Now something is said to be one in the same way as it is said to be a being. But a being absolutely speaking is a substance, while a being in some respect is an accident, or even [only] a being of reason. So whatever is one in substance, is one absolutely speaking, yet many in some respect. For example, a whole in the genus of substance, composed of its several integral or essential parts, is one absolutely speaking, for the whole is a being and a substance absolutely speaking, while the parts are beings and substances in the whole. Those things, however, which are diverse in substance, and one by accident, are diverse absolutely speaking, and one in some respect, as many humans are one people, or many stones are one heap; and this is the unity of

16 Cf. here what Aristotle and Thomas say about the different kinds of unity in Meta lb. 5. lc. 7 and 8.

255

composition or order. Likewise, many individuals that are one in genus or species are many absolutely speaking, and one with respect to something, for to be one in genus or species is to be one with respect to reason. [For example,] in the genus of natural things, some whole is composed from matter and form, as man from body and soul, who is one natural being, although he has a multitude of parts […]”17

So, although it is up to us to assign our criteria of distinguishing the integral parts making up some integral whole, which is, again, marked off by us as being the whole constituted by those parts, there will nevertheless be some absolute standard according to which the mereological constitution of the whole is not dependent on us, namely, the ontological status of the parts so distinguished and of the whole thus marked off. That is to say, even if we are absolutely free to regard a heap of stones as one, and an individual stone as a part of this one, nevertheless it is obvious that the unity of the individual stones is not of the same kind as the unity of the heap. For the heap is not a being in the same sense as the stones are, since precisely in that sense in which a stone is one being the heap is not one being, but rather it is several beings. Again, we are absolutely free to regard one half of one of these stones as one part of this one stone and the other half as the other part of the same stone, yet, it is clear that the unity of each of its halves is not the same as the unity of the stone, for in the sense in which one half of it is one being, the stone is not one being, but two beings, whereas in the sense in which the stone is one being, its halves are not even beings at all. For the stone is actually a being in its own right, while neither of its halves is actually a being in its own right; it only can be a being in its own right if the stone is actually cut into those two halves. But as the stone is actually undivided, it is one substance actually, while its two halves are two substances only potentially.18 And since only that thing is one entity in the absolute, unqualified sense which is a being in the absolute, unqualified sense, and only what is actually a substance is a being in the absolute, unqualified sense, only the stone is actually one in the absolute, unqualified sense. And so, despite the fact that we could distinguish in the stone two halves, and we can say that it is made up of those two halves, this will not make the stone into two beings or two entities.

Furthermore, when we divide a stone into two parts, we can do so in a number of different ways, since obviously such a division need not result in two equal halves:

= =

So clearly, if we divide it into two halves, or into one third and two thirds, or one quarter and three quarters, we are able to mark out these parts even before actually dividing it, on the basis of how much of the quantity of the whole we conceive of as belonging to the one part, and how much as belonging to the other. But then, in a similar manner, we can distinguish in the same thing not only parts of its quantity on this basis, but also any sorts of other parts, on the basis of how much of whatever we conceive in the thing we conceive as belonging to the one part and how much as belonging to the other.

Now, what does all this mean concerning the composition of man from body and soul? First of all, it is clear that the term ‘body’ in the first sense, in which it is the genus of all bodies, since it

17 ST1-2 q. 17, a. 4. 18 Cf. e.g. in Meta lb. 5, lc. 21, n. 1102; in Meta lb. 7, lc. 16, nn. 1632-1633.

256

is predicable of a whole human being and not only of some part of him or her, signifies the unique substantial form of any human being, and so what it signifies in human beings, their corporeity, coincides with their rational soul.19 In this sense, therefore, we do not distinguish the body from the soul as a part from another part, but as the whole from one of its parts.20 But this part of this whole, namely, the soul, is not distinguished from the other parts on the basis of dividing the quantity of this whole. Rather, the distinction is made on the basis of the different perfections, indicating the different modes of existence that we conceive in this whole, namely, the spatio-temporal, material mode of existence which this body has in common with all bodies, as opposed to the mode of existence which enables this body to perform several sorts of vital functions, that is, life, which it has in common with all living beings. But once we have distinguished these two modes of existence, namely, material, spatio-temporal existence on the one hand, and life on the other, we can obviously use different names, or the same names in different senses, to signify the substantial forms on account of which a thing has one of these modes of existence, or the other, or both in its own unique act of substantial being. So if we distinguish corporeity as that substantial form on account of which whatever has it exists in a material, spatio-temporal manner, whether the thing in question is alive or not, then the corporeity thus distinguished will clearly coincide in all living bodies with their soul, conceived as that substantial form on account of which whatever has this form is alive, whether it is a body or not. Therefore, in this non-exclusive sense, both the corporeity thus conceived and the soul thus conceived are nothing but the form of the whole, that is, the essence or quiddity of a living body. But if we conceive of corporeity as that on account of which whatever has it exists in a spatio-temporal manner, but is not alive, the corporeity thus conceived cannot coincide with the substantial form of a living body, so this conception of corporeity can mark out only some part of the essence of a living body. Also, if we conceive of the soul as that on account of which whatever has it is alive but is not a body, the concept of soul thus conceived can mark out only some part of a living body, in which both material existence and life are united in its single act of substantial existence, its spatio-temporal, material life.

Of course, spatio-temporality and life in themselves are not incompatible, which is shown by the manifest existence of living bodies. However, they do not entail each other either, as is shown by the manifest existence of lifeless bodies as well as by the at least conceivable existence of living immaterial substances. Therefore, it should come as no surprise that we can form both the non-exclusive and the exclusive concepts of those substantial forms on account of which any substance has either life or spatio-temporality or both. Accordingly, the concepts of ‘body’ and ‘soul’ in the relevant non-exclusive and exclusive senses can indeed be properly characterized by the following entailments and denials of entailments, just as St. Thomas suggested:

x is a body1 → x is spatio-temporal

~ (x is a body1→ x is not alive)

x is a body2 → x is spatio-temporal & x is not alive

y is a soul1 → (x has y → x is alive)

19 Cf.: “Non enim anima est alia forma ab illa, per quam in re illa poterant designari tres dimensiones; et ideo, cum dicebatur quod corpus est quod habet talem formam, ex qua possunt designari tres dimensiones in eo, intelligebatur: quaecumque forma esset, sive animalitas sive lapideitas sive quaecumque alia.” EE c. 2. 20 Cf. text quoted in n. 6.

257

~ (y is a soul1 → (x has y → x is not spatio-temporal))

y is a soul2 → (x has y → x is alive & x is not spatio-temporal)

Therefore, the essence of a living body, which can be referred to as a corporeity, in the first, non-exclusive sense, has to consist of a corporeity in the second, exclusive sense, and of a soul also in the second, exclusive sense, as its integral parts:

7. corporeity1 (of a living body1) = corporeity2 (of the same living body1) + soul2 (of the same living body1)

By contrast, the corporeity of a non-living body will be the same essence in both senses:

corporeity1 (of a non-living body1) = corporeity2 (of the same non-living body1),

But then a living body1 will have to consist of a body2, and a soul2:

9. living body1 = soul2 (of the same living body1) + body2 (of the same living body1)

In fact, this is precisely how Cajetan interprets St. Thomas’s above-quoted remarks in his commentary on the De Ente et Essentia:

“As of now, it seems to me that it must be said that man is composed from soul and body, and is a third thing not only as composed from two things, but also as from two parts which are a whole in reality. I take body not in so far as it is the genus, but in so far as it signifies a part, and take soul in its exclusive meaning, as defined in II de Anima. Thus viewed, body means a composite of matter and a corporeal perfection taken exclusively. Soul means the perfection of life exclusively.

I prove my thesis thus. Body differs really from soul, and not as a whole differs from a part; therefore it differs as a part from a part. The added point is proved: the whole includes, at least confusedly, the part, but the body viewed in this way excludes the soul. Thus the body is included in the definition of the soul as a subject supporting the soul, as St. Thomas says there. The first proposition is evident in itself and conceded by all. The consequence draws its force from an ade-quate division. For if the soul and the body differ really, the body must differ really from the soul as a whole from the part or as a part from a part. Man, therefore, is composed from body and soul as from parts that are really distinct, which was our thesis.”21

4. Man = Body2 + Soul2

So far, so good, one might say, but can all this “word-magic” solve the genuine philosophical problem of body and mind? For even if by using these “rubber-band” concepts of body and soul one may save the consistency of what Aquinas says in various contexts, making them comprise more in one context and less in another, body and soul are still claimed to be really distinct parts of a human being in the above-described exclusive senses of these terms. But then, if the body and the soul are really distinct entities, with one belonging to the spatio-temporal physical world and the other belonging to some alleged spiritual realm, then we immediately seem to face here the problem of “mysterious” interaction vs. causal closure, all too familiar from the woes of Cartesian dualism.

To this, we have first to reply that since a philosophical problem is some conceptual conflict, or rather a bundle of conceptual conflicts within a broad conceptual framework, there is no such thing as “the genuine philosophical problem” of anything apart from the conceptual framework

21 Cajetan, 1964, pp. 119-121.

258

that gives rise to it. So, if we find that despite superficial appearances to the contrary St. Thomas’s conception of body and soul is sufficiently different from the concepts figuring in the modern problem of body and mind, we may well find that in his conceptual framework the familiar problem, or rather the familiar bundle of problems, need not and does not arise at all. Indeed, what lies at the bottom of all the familiar problems is the assumption that body and soul are two distinct entities of radically different natures, having entirely distinct causal powers rooted in these distinct natures, on account of which they are accessible by us for observation in radically different ways.

If we understand it properly, however, we can easily realize that the real distinction of body and soul in the Thomistic-Aristotelian framework means nothing like this. In the first place, that body and soul, in the exclusive senses of these terms, are distinct parts of the same entity does not mean that they are distinct entities in the sense in which subsistent entities are distinct from one another. As St. Thomas often repeats, unum convertitur cum ente: there is one entity, absolutely speaking, whenever there is a being having one act of existence, even if the being in question is composed of several parts. But body and soul, as distinguished in the exclusive senses of these terms, have the same unique act of substantial existence, namely, the life of a living body; therefore, body and soul are one being, one entity, absolutely speaking, not two entities. Since causal powers and the corresponding actions belong to the beings which perform those actions by means of those powers, if the body and the soul are one being, then no question of their inter-action can arise on the basis of their distinct causal powers rooted in their radically distinct natures. For this question can properly be raised only concerning distinct beings each having a substantial act of being of its own, founding their distinct causal powers and the corresponding actions.22

However, at this point it may seem that by laying so much emphasis on their substantial unity this position does not leave any room for the real distinction of body and soul, or indeed, for a non-materialistic conception of the soul. For if soul and body are one entity, namely, a living body, having all their powers and actions in common in the whole they constitute, then their distinction is apparently a merely conceptual one: the concepts of body and soul provide us merely with different aspects for considering the same, essentially material entity.

But this objection is based on a radical misunderstanding of what it means for essential parts of the same entity to be distinct from one another, and yet to constitute the same one entity. For even if, for example, Socrates is an ensouled body, a unitary substance with one act of substantial being, his essential parts, his body and soul in the exclusive senses of these terms, are strictly distinct parts in the unitary whole insofar as the one part is that which accounts for one distinct sort of perfections of the whole Socrates, namely, spatio-temporality and whatever that entails; whereas the other part is that which accounts for another sort of perfections, namely, human life, and whatever that entails. But since these are obviously distinct perfections, whose distinction is given regardless of the intellect’s consideration, the parts of the whole accounting for these perfections, each for its own sort, have to be parts that are really distinct, again, regardless of the intellect’s consideration.

Nevertheless, while we maintain their real distinction in this way, we also have to realize that body and soul can be distinct only as distinct parts of the same substantially one whole. Indeed, 22 “Nihil autem potest per se operari, nisi quod per se subsistit. Non enim est operari nisi entis in actu, unde eo modo aliquid operatur, quo est. Propter quod non dicimus quod calor calefacit, sed calidum.” ST1 q. 75, a. 2.

259

they cannot possibly be distinct in the same way as the whole they constitute is distinct from other wholes of the same kind. For the whole they constitute is a complete substance, which therefore is a complete being in the primary, unqualified sense of the term ‘being’, having its own unique substantial act of existence. But then, no part of this one whole can have the same act of being in the same way, for otherwise they would not be parts in the whole, but whole beings in the same unqualified sense of the term as the original whole. Therefore, the essential parts of the whole, since they are essential, share the same act of being as the whole; nevertheless, since they are parts, they can have this existence only in the sense in which a part in a whole can. As St. Thomas says:

[…] existence [esse] is said to be the act of a being [ens] insofar as being, that is, that by which something is denominated a being in the nature of things. And being in this sense is attributed only to the things themselves which are contained in the ten categories, whence 'being' [ens] predicated on account of such [an act of] existence [esse] is divided by the ten categories. But this [act of] existence [esse] is attributed to something in two senses. In one sense as to that which [quod] properly and truly has being, or exists. And thus it is attributed only to a per se subsisting substance; whence that which truly exists is said to be a substance in bk. 1. of the Physics. All those [things], however, which do not subsist per se, but in others and with others, whether they are accidents or substantial forms or any sorts of parts, do not have existence [esse] so that they themselves would truly exist, but existence [esse] is attributed to them in another sense, namely, as to something by which [quo] something exists; as whiteness is said to exist, not that it itself would subsist in itself, but because it is by [this whiteness] that something has it that it is white. […]23

What this means, then, is that in line with St. Thomas’s general conception of the analogy of being, the whole and its essential parts, while they are denominated beings on account of the same substantial act of existence, they are not denominated beings in the same sense. For the whole substance is denominated a being in the primary, unqualified sense of being, in the sense in which only a complete, self-subsistent entity can be called a being, existing on its own. The essential parts of this being, namely, its matter and substantial form, however, can be called beings only in some derivative sense of the term. For the form can be called a being only in a secondary sense, because, insofar as it is a form, it can be said to exist only in a secondary sense. And this is so because for a form to exist in this secondary sense is nothing but for it to inform that which exists in the primary sense, namely, the primary substance. But this is just another way of saying that for the form to exist is nothing but for the thing to exist, or to have existence, in respect of the form, which makes it clear that the sense in which existence is attributed to the form is obtained by adding some qualification to the sense in which existence is attributed to the substance which is said to exist in the primary, unqualified sense. Obviously, similar considerations apply to the body, in the exclusive sense of the term, insofar as it is the other essential part of a living being.

But then, if we recognize the analogical character of the predication of the notion of being with respect to the whole and with respect to its essential parts, it should come as no surprise that body and soul in the exclusive senses of these terms are said to be one being, in the primary sense of the term, yet they can be said to be two beings in the derivative sense in which distinct parts of a whole can be said to be beings. But since having power and action can attach properly only to a being in the primary sense, the problem of interaction between body and soul still cannot arise, for both the actions and the corresponding powers will still belong only to the

23 QDL 9. q. 2, a. 2, in corp.

260

unified whole, and not to either of the parts. This has to be the case, at least, unless there is some action which can properly be said to belong only to one of them, in which case that part will also have to be regarded as a being not only in the sense in a which a part is a being, but also in the sense in which the whole is.

But this is precisely the point Aquinas makes with respect to the unique case of the human soul in his proof for its immortality:

“We have to say that the human soul is entirely incorruptible. For a clear understanding of which we should consider that what per se belongs to something cannot be removed from it, just as from a man it cannot be removed that he is an animal, nor from a number that it is either even or odd. It is clear, however, that being per se belongs to form, for everything has being in virtue of its proper form; whence being can in no way be separated from form. Therefore, things composed of matter and form are corrupted by losing the form to which being per se belongs. But the form itself cannot be corrupted per se, but it is corrupted per accidens, insofar as the composite thing that exists by the form loses its being, provided the form is such that it is not a thing that has being, but it is only that by which the composite thing has being. If, therefore, there is a form which is a thing that has being, then it is necessary for that form to be incorruptible. For being is not separated from something that has being, except by its form getting separated from it; therefore, if that which has being is the form itself, then it is impossible that being should be separated from it. It is manifest, however, that the principle by which a man understands is a form that has being in itself, and [that it does not have this being] only as that by which something [else] exists. For understanding, as the Philosopher proves in bk. 3. of the De Anima is not an act performed by some bodily organ.”24

Now, clearly, if understanding is the act of the intellective soul alone (which is a claim to be established by a separate argument, but that need not concern us here),25 then this means that the soul has some action and the corresponding power, which only a subsistent being has. But then, if the soul is a subsistent entity, this means that it is a being not only in the derivative sense in which a substantial form is a being, but also in the unqualified sense in which a subsistent entity is a being.

As we could see in the foregoing considerations, body and soul are one being in the absolute, unqualified sense, not two beings united in some mysterious interaction with one another. Nevertheless, despite the fact that this one being, the whole human being, is a material substance, if Aquinas’s claim that understanding is the act of the soul alone is true, then the form of this being has some act of its own which denominates the whole only through this part to which alone it can belong.26 But then, since this form has an activity of its own, it is a form which has the being of the whole not only in the sense in which any other form insofar as a form has being, but also in the same sense in which the whole has it. Therefore, it could be destroyed also only in

24 QDA a. 14, co. 25 Since in this context we are only concerned with what it means to say that the soul is both a form and a subsistent substance, and not with proving its truth, we should only consider under what conditions it would be true. To be sure, I also think Aquinas’s argument for the claim that understanding is the act of the intellect alone can indeed be shown to work, but the proof of this claim is a different issue, to be dealt with in another paper. 26 And this is why we can truly say that a man understands, and not only that a human soul understands, despite the fact that the act of understanding is an act inherent only in the soul, and not in the body-soul composite. Cf.: “… et operationes partium attribuuntur toti per partes. Dicimus enim quod homo videt per oculum, et palpat per manum, aliter quam calidum calefacit per calorem, quia calor nullo modo calefacit, proprie loquendo. Potest igitur dici quod anima intelligit, sicut oculus videt, sed magis proprie dicitur quod homo intelligat per animam.” ST1 q. 75, a. 2, ad 2-um. Cf. also De Unitate Intellectus, c. 3, n. 69. For a discussion of Aquinas’s general rule concerning the proper denomination of a whole by some property of its part see Klima, 1984.

261

the sense in which the whole is destroyed, namely, by losing its substantial form, but since it is a form, that is precisely the sense in which it cannot be destroyed. Hence, it is incorruptible. But then, if we really understand how these claims fit together, we can clearly see that Saint Thomas’s conception does indeed manage to steer its way safely between the Scylla of dualism and the Charybdis of materialism.

262

References

Aquinas’s works are referred to by their standard abbreviations.

Cajetan, T. 1964, Commentary on Being and Essence, tr. L. H. Kendzierski and F. C. Wade, S. J., Marquette University Press: Milwaukee, Wis., pp. 119-121.

Henry, D. P. 1991, Medieval Mereology, Bochumer Studien zur Philosophie, Band 16, B. R. Gruener, Amsterdam-Philadelphia

Kenny, A. 1995, Aquinas on Mind, New York: Routledge, p. 28.

Klima, G. 1984, “Libellus pro Sapiente: A Criticism of Allan Bäck’s Argument against St. Thomas Aquinas’s Theory of the Incarnation”, The New Scholasticism, 58, pp. 207-219.

Klima, G. 1993, “The Changing Role of Entia rationis in Medieval Philosophy: A Comparative Study with a Reconstruction”, Synthese, 96; No. 1, pp. 25-59.

Klima, G. 1996, “The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being”, Medieval Philosophy and Theology, 5, pp. 87-141.

263

Thomas of Sutton on the Nature of the Intellective Soul and the Thomistic Theory of Being

Thomas of Sutton

Thomas of Sutton was one of the earliest, and by all measures one of the most astute defenders of St. Thomas Aquinas’ characteristic theological and philosophical doctrines. As usual with medieval thinkers, we have little information regarding Sutton’s life1. The earliest reliable report on his life’s events is that he was ordained deacon at Blithe by Walter Giffard, the Archbishop of York, on September 20, 1274. After receiving the diaconate, Sutton entered the Dominican order, and became a friar at the Oxford convent around 1282. He had probably been a fellow of Merton College before he entered the order. It was also before 1282 that Sutton wrote his short treatises laying out his Thomistic conception of the unicity of substantial form: Contra Pluralitatem Formarum and De Productione Formae Substantialis. In Oxford he was closely associated with two other Dominicans, William Hothum and Richard Knapwell, who were also heavily involved in the defense of Thomistic positions. One source also mentions that Sutton studied in Paris, where he may have had first-hand experience of the immense influence of Henry of Ghent.2 But the center of his activity was Oxford, where he incepted as a master sometime between 1291 and 1300, and lectured till his death in about 1315.

This paper examines Sutton’s reply to contemporary challenges of the Thomistic position concerning the nature of the intellective soul, in particular, Aquinas’ famously controversial doctrine of the unicity of substantial form.3 Sutton’s arguments quite clearly indicate that acceptance or rejection of the Thomistic position ultimately depends on sharing or rejecting certain fundamental principles of St. Thomas’s theory of being. The paper intends to articulate these principles with clarity and precision, by contrasting them with the primary target of Sutton’s criticism, the radically different theory of Henry of Ghent.

The theory of being and the nature of the intellective soul

To see the connection between St. Thomas’s doctrine concerning the nature of the intellective soul and his theory of being, consider the following argument by Siger of Brabant:

“Praeterea, alia est ratio essendi formae materialis et compositi seu formae per se subsistentis. Ratio enim essendi formae materialis est secundum quam est aliquid aliud, ut ratio compositionis est secundum quam habet esse compositum, et ratio figurae secundum quam habet esse figuratum; unde ratio essendi formae materialis est quod sit unita alii. Ratio autem essendi compositi vel formae liberatae a materia est quod sit ens per se et separate, non unum ens cum

1 The little that can be known about Sutton is neatly summarized, with ample references, in F. J. Roensch, Early Thomistic School, Dubuque, Iowa 1964, 44-50. 2 Cf. Roensch, p. 73, n. 194. 3 For a summary account of Sutton’s psychology, see D. Sharp, Thomas of Sutton O.P., His Place in Scholasticism and an Account of His Psychology, in: Revue Néoscolastique de philosophie, Louvain, 36(1934), 332-354 and 37(1934), 88-104, 219-233.

264

alio. Ex hoc sic arguitur. Cum cessat ratio essendi alicuius, ipsum corrumpitur et non est; sed cum separatur forma materialis a materia, cessat eius ratio essendi, ut ex praedictis apparet; nulla igitur forma cuius separatio a materia non est sua corruptio est materialis. Sed separatio animae intellectivae a corpore et materia non est eius corruptio. Ergo non habet esse unitum ad materiam. Et declaratur ratio in exemplo. Cum ligna, lapides et lateres in domo cessant esse composita a forma compositionis eorum, cessat esse compositio; et cum secundum figuram cessat aliquid figuratum esse, cessat esse figura. Et similiter est de forma substantiali ad illud cuius est forma, quod, cum secundum eam cessat esse materia, cessat esse formae materialis, licet notius sit in accidentali forma quam substantiali. Et sunt istae rationes essendi, qua aliquid habet esse unite ad materiam et qua aliquid habet rationem subsistentis per se et separate, oppositae adeo quod eidem inesse non possunt. Unde anima intellectiva non potest habere rationem per se subsistentis et, cum hoc, unum facere cum materia et corpore in essendo4.”

As is clear from this passage, the fundamental reason why according to Siger it is impossible to hold St. Thomas’s doctrine, namely, that the intellective soul is both subsistent (on account of the immateriality of the intellect) and inherent (on account of the soul’s being the form of the body), is the radical incompatibility of these two modes of being. But then, as the argument makes clear, the whole issue of the tenability of the Thomistic conception of the nature of the intellective soul boils down to this ultimate question: are these modes of being really so incompatible that they cannot simultaneously characterize the act of being of the intellective soul?

Obviously, the question cannot be answered without clarifying what we should understand by these modes of being, which requires careful reflection on how we should construe the concept of being and its relation to the concepts of form and essence in general. As we shall see, recognizing this need is precisely the basic, underlying insight that drives Thomas of Sutton’s arguments in the debates concerning the nature of the intellective soul.

Sutton on the unicity of substantial form

In his Quaestiones Ordinariae, Sutton makes it quite clear that he does not regard the Averroistic position a threat anymore. Indeed, as he puts it, by his time nobody was so stupid as to side with the Commentator on the issue of the separate existence and the consequent unity of the intellect:

“Non est enim modo aliquis ita fatuus, quod adhaereat opinioni commentatoris, et si esset aliquis, posset faciliter convinci per rationes praecedentium doctorum5.”

However, given the immateriality of the intellective soul, it still demands clarification how it can also be the form of the body in the way the sensitive soul is, indeed, how it can be the very same form as the sensitive soul in one and the same human being. As Sutton puts it:

“Sed quia sensitiva et intellectiva videntur habere oppositas condiciones, sensitiva enim est actus corporis, intellectus non est actus corporis, sensitiva est materialis, intellectus est immaterialis, sicut dicunt auctores, ideo aliquantulum insistendum est, ut videamus, quomodo sit possibile tantam oppositionem esse in una simplici substantia6.”

One obvious way out of the apparent inconsistency resulting from attributing these opposite conditions to one and the same form would seem to be to distinguish the intellective soul from

4 Siger of Brabant, Quaestiones in tertium de anima, Louvain 1972, 79-80, ll.43-66. 5 Thomas of Sutton, Quaestiones ordinariae, München 1977. Henceforth: QORD. QORD, q. 18, p. 503. 6 QORD, q. 19. p. 532.

265

the sensitive and vegetative souls as well as from the form of corporeity (while the latter may be regarded either as three distinct forms, or one and the same material form extending the body and performing the vegetative and sensitive functions of an animal). But Sutton argues that this position, the thesis of the plurality of substantial forms, directly entails the Averroistic position, and is thus contrary to faith:

“Si quis igitur poneret substantiam intellectivam esse aliam a sensitiva et vegetativa, necessario incideret in errorem commentatoris Averroes, qui posuit intellectum esse substantiam separatam, et per consequens oporteret ponere unum intellectum omnium hominum, quia in substantiis separatis non possunt esse plures in eadem specie, cum non possint differre, nisi per differentias formales diversificant<es> speciem. Quia igitur illud manifeste repugnat fidei, ideo necesse est ponere quod intellectiva sit eadem substantia cum sensitiva. Solet tamen poni quod intellectiva et sensitiva sunt diversae formae; etiam in diebus nostris fuit communis opinio in Anglia. Sed qui sic posuerunt, non perceperunt errores, qui ex hoc sequuntur contra fidem, et pro tanto excusabiles sunt7.”

That is to say, according to Sutton, positing the intellective soul as an immaterial form distinct from the material substantial form(s) of the body, directly entails the Averroistic thesis of the unity of the intellect in all humans, even though several of his contemporaries failed to recognize this consequence of their position. However, this entailment is valid only if one holds, as Sutton clearly does, that plurification of individuals in the same species is possible only in matter. But then, one can certainly avoid this conclusion on the basis of a different theory of individuation. This was precisely the route taken by Henry of Ghent, criticized in particular by Sutton in this question. However, Sutton goes on to argue that such “evasions”, in terms of alternative theories of individuation, necessarily fail, and so anyone endorsing the plurality thesis is bound to fall back again into the Averroistic error.

Henry of Ghent on existence, essence, and individuation

To be sure, Henry’s “evasions” rest on certain radically different interpretations of the conceptual connections between the notions of individuation, unity, form, essence, and existence, which fundamentally distinguish his intuitions from Thomistic intuitions. Henry deals at some length with the issue of individuation in his second Quodlibet8. There he argues, on the basis of Avicenna’s famous remarks in bk. 5 of his Metaphysics, that any created form or essence, whether material or immaterial, considered in itself is indifferent to plurality or singularity, whence it has to be possible for any creaturely essence to be multiplied in several supposita:

“Quod autem non ex se sed solum ab alio agente singulare est in supposito subsistens, quia ex se nulli appropriatur et est essentia tantum, quantum est ex se, indifferenter natum est esse singulare, subsistendo in unico supposito, vel universale, subsistendo in pluribus9. Quod etiam bene dicit Avicenna et determinat in Vo Metaphysicae suae. Ex quo sequitur apertissime quod

7 Ibid. 8 Henry of Ghent, Quodlibet II, Leuven 1983. Henceforth: HQDL 2. In general, Henry’s Quodlibeta are going to be referred to by this abbreviation followed by the number of the quodlibet in question. Page numbers refer to the pagination of the edition of Henry’s Opera Omnia published in the Ancient and Medieval Philosophy series (Series 2) of the De-Wulf Mansion Centre. HQDL 2, q. 8, pp. 35-57. Cf. also HQDL 5, q. 8, which provides a somewhat different account, criticized by Scotus in Ord. II, d. 3, part 1, q. 2. But I am here concerned with the account that is the target of Sutton’s criticism in connection with the individuation of spiritual substances. 9 Cf. principle (1) below.

266

necesse est ut non sit essentia creaturae, in quantum creatura est, quin possit, quantum est ex se, in plura individua multiplicari, quantumcumque sit abstracta a materia10.”

Clearly, if Henry’s conception of individuation is right, and it is possible even for purely immaterial creaturely essences to multiply in several individuals, then Sutton’s charge that the plurality thesis implies the Averroistic thesis of the unity of the intellect is unjustified. Indeed, Henry is careful to point out even in this article, which otherwise does not directly deal with the individuation of the intellective soul, that on his conception of individuation, even though matter in the actual natural order does serve to individuate human souls, this is in no way absolutely necessary, which is all that is needed to invalidate Sutton’s charge:

“… animae rationales [...] individuantur per corpora quibus creando infunduntur, et infundendo creantur. Nec omnino crearentur, nisi corporibus dispositis quibus infunderentur, ut dictum est supra secundum Avicennam11. Dico secundum communem cursum divinae ordinationis, licet Deus per se ipsas possit individuas creare, quae modo sic per corpora esse incipiunt, ut non cum ipsis esse desinunt. Unde, cum fides teneat quod animae rationales sunt substantiae spirituales per se substare potentes, et quod sunt plures numero secundum hominum pluralitatem, et quod Deus potest eas creare sine corporibus per se subsistentes antequam corporibus uniantur (quod omnino fieri non posset, nisi essentia talis creaturae huiusmodi multiplicationem secundum numerum absque corpore pateretur), nulli fidelium debet provenire in dubium, quin sub eadem specie plura possunt esse individua in substantia spirituali solis substantialibus distincta, etiam absque omni quantitate et materia12.”

So, according to Henry’s conception, even though God actually uses bodies to individuate the intellective souls within the same species according to His ordination of the common course of nature, it would still be possible for Him to do so supernaturally, without the assistance of bodies. The general reason for this possibility is explained by Henry in somewhat more detail as follows:

“Nulla enim re alia addita essentiae rei, ipsamet fit suppositum subsistens in existentia actuali, hac sola intentione adiecta qua ipsa habet esse effectus Dei, et hoc in natura et essentia, ipsam de non esse in esse producendo. Quod quidem esse omnis creatura participat ex hoc quod ipsa in sua essentia est Dei factura, non quod ipsi essentiae, quasi praecedenti, Deus imprimat esse quo denominetur existens, sicut, praeexistente pariete, aliquis imprimit ei albedinem, sive creando sive non, qua denominatur albus. Hoc enim falsum est et omnino haereticum: Deus enim totum quod aliquid est in creatura, ab initio de nihilo fecit13.”

So, according to Henry, a created essence, which considered in itself is indifferent to plurality and singularity, is individuated precisely by its acquiring a singular act of existence, which is nothing but the created thing’s being created. Therefore, the cause of individuation of any creature is primarily God, who in a creative act produces the essence in a singular act of existence. This is why God can create two angels of the same species, merely on account of producing the existence of the one as distinct from that of the other:

“[…] dicendum est, descendendo ad nostram quaestionem, quod duo angeli in solis substantialibus existentes, posito etiam quod nullum accidens reale differens re ab eorum essentia in se habeant, neque scilicet potentiam neque habitum neque aliquid huiusmodi, sunt individualiter distincti hoc solo quod subsistunt in effectu. Ubi extra communitatem essentiae in ambobus subsistere unius non est subsistere alterius, cum unus eorum subsistere posset sine

10 HQDL 2, q. 8, pp. 38-39. 11 Cf. HQDL 2, p. 15, p. 43. 12 Ibid. pp. 52-53. 13 Ibid. pp. 49-50.

267

altero. Et sic per hoc ab invicem differunt, quod iste non est ille, duplicata scilicet natura speciei sive essentiae angelicae in eis per rationem subsistendi sive existendi in actu aliam in uno et aliam in altero, quae est praeter intellectum essentiae communis in utroque. […] Ut sic sit per aliud et aliud, quod uterque illorum dicatur esse angelus simpliciter et quod dicatur esse iste vel ille, quia intentio essentiae simpliciter, qua uterque dicitur angelus, est alia ab intentione subsistentiae huius et illius, qua dicuntur iste angelus et ille. Patet ergo quomodo per intentiones subsistentiae duorum angelorum fit essentiae communis individuatio in eis. Sed quia coniunctio istorum duorum, scilicet essentiae et subsistentiae in uno et in altero, non potest esse ex se ipsis — quia ex se non habent quod subsistunt in effectu, ut dictum est —, sed oportet quod fiat in eis per aliam causam, facientem utrumque eorum esse alterum per essentiam existentem in actu, et hunc non esse illum et e converso — ut sit totum causatum quod est in utroque —, ideo causa individuationis eorum prima et efficiens dicendus est Deus, qui dat utrique eorum subsistentiam in effectu et seorsum.14”

So, the primary cause of the individuation of a created nature is God’s creative act producing a singular creature of that nature, whose act of being is nothing but its being created by God, and it is the singularity of this act which determines the otherwise common nature of the creature in question to be had by this singular entity as opposed to that, in which the same nature would be realized in a numerically distinct act of existence. Therefore, to the objection that an essence which is indistinct in itself cannot be understood to be multiplied unless there is something distinguishing its instances, Henry answers that, indeed, there is something distinguishing these instances, namely, the distinct acts of existence which realize the same essence in numerically distinct individuals:

“Dicendum igitur ad argumentum quod unam et eandem essentiam ex se omnino simplicem, nullo addito, nec re nec intentione, differenti ab ea, distingui et multiplicari per plura individua est omnino inintelligibile et secundum rem impossibile. Sic enim quaecumque essentia in se considerata nullam potest omnino intelligi habere distinctionem, multiplicationem aut diversitatem. Sic enim considerata intelligitur ut neque in unico individuo existens neque ut in pluribus, neque ut universalis neque ut particularis, sed ut cui ambo nata sunt accidere. Si ergo huiusmodi essentia debeat distingui per plura individua numero, oportet quod hoc sit per aliquid additum distinguens, diversitate sua diversificans essentiam et multiplicans hinc inde.15”

However, according to Henry, the act of existence which sets apart one individual of a created nature from another cannot be regarded as a distinct thing added to the nature in question, rather it has to be something merely intentionally distinct from the essence to which it is added:

“Sed tale additum potest intelligi diversum ab essentia ipsa vel re, vel intentione tantum. Additione diversi primo modo non contingit essentiam separatam immaterialem numero distingui, quia neque per diversum additum substantiale neque accidentale. Non per substantiale, quia illud non posset esse nisi materia aut forma, < quod quidem non potest fieri, > quia per positionem haec essentia est immaterialis et specifica, sub qua non est ulterior forma substantialis et cui non est materia subiecta. Neque per accidentale diversum hinc inde, quia neque per diversum specie neque per diversum numero. Non per diversum specie, quia ad eandem essentiam substantialem specie necessario sequuntur, quantum est ex ratione speciei, eadem accidentia specie: eidem enim in quantum idem semper natum est accidere idem. Nec numero solo, quia accidens potius numeratur et individuatur per suum subiectum quam e converso. Universaliter ergo verum est quod per nulla accidentia realia, neque specie neque numero diversa, fit individuatio eiusdem essentiae sive formae in specie, quoniam omnis substantia in se recipiens accidentia oportet

14 Ibid. pp. 50-51. 15 Ibid. p. 54. Note in this passage Henry’s explicit statement of principles (1) and (2) listed below. The significance of this fact is that Sutton is going to attack Henry’s conception precisely on the basis of these two principles, while rejecting Henry’s (3) as nonsensical.

268

quod in se prius subsistat (et ita: quod sit individuata), quam subiectum alterius fiat, quia secundum Philosophum «substantia prior est accidente definitione, cognitione et tempore», et ideo substantia individuata potius est causa individuationis cuiuscumque accidentis quam e converso. Et sic nullo modo potest intelligi multiplicatio essentiae immaterialis per additionem diversi secundum rem. Oportet ergo quod sit additione diversi secundum intentionem solum. Et hoc est possibile, immo necessarium, ut supra est expositum16.”

Henry explains in more detail how he conceives of the intentional distinction between essence and existence in creatures in question 9 of his first Quodlibet. Although the notion of intentional distinction is difficult to capture (indeed, according to Sutton it is downright inconsistent)17, Henry’s idea here seems to be that we have to assume this type of distinction whenever one and the same absolute thing is also inherently related to something else, whence the same absolute thing, on account of its own nature, also has to be conceived in terms of a relational concept or intention. Therefore, since all created essences exist only insofar as they are created and kept in existence by God (whence in their actual existence they are inherently related to God), and, in virtue of the previous argument, their existence cannot be another thing added to them, a created essence and its existence (that is, its being created by God) also have to be regarded as intentionally distinct, although they are one and the same thing when the essence is produced in actual existence:

“Non enim debet imaginari creaturae essentia sicut aer indifferens ad obscuritatem et luminositatem, sed sicut radius quidam in se natus subsistere, a sole productus non necessitate naturae sed libera voluntate. Unde, si sol libera voluntate posset radium per se subsistentem producere, radius ille, quantum est de se et natura sua, indifferens esset ad esse et non esse, et quantum esset de se, esset non ens quoddam. Quantum autem est ex parte solis, posset esse in se recipere et reciperet cum fieret in effectu a sole, et esset ille radius factus et stans in se, lumen quoddam secundum suam essentiam, et similitudo lucis solaris, participans per hoc ipsa luce solis. Et ita esset ille radius quaedam participatio lucis solaris per suam essentiam et in sua essentia, non per aliquid additum suae essentiae receptum in ipsa, re differens ab ipsa, sicut lumen receptum in aere differt ab ipso. Et sicut est de isto radio lucis et luce solis, quod participat luce solis in eo quod est, in sua essentia existens, quaedam eius similitudo, sic est de creatura et Deo, quod ipsa participat esse Dei in eo quod est in sua essentia quaedam divini esse similitudo, sicut imago sigilli, si esset in se subsistens extra ceram, in sua essentia esset quaedam similitudo sigilli, non per aliquid additum ei. Et sic in quacumque creatura esse non est aliquid re aliud ab ipsa essentia, additum ei ut sit. Immo ipsa sua essentia, qua est id quod est quaelibet creatura, habet esse in quantum ipsa est effectus et similitudo divini esse, ut dictum est 18.”

On the basis of these passages, Henry’s conception criticized by Sutton can be summarized in the following theses.

A form or essence of any creature, considered in itself, is indifferent to existence and non-existence and to unity or multiplicity19.

16 Ibid. pp. 54-55. 17 Cf. QORD q. 26. esp. pp. 724-725. 18 HQDL 1, q. 9. 19 It must be added here that, according to Henry, just the opposite is true in the case of divine essence: “Nulla ergo essentia creaturae, ratione ea qua essentia est, habet rationem suppositi aut actualiter subsistentis. Ita quod nulla earum, quantum est ex se, de se sit singularitas quaedam, nullaque earum, sicut neque effective, sic nec formaliter est suum esse sive sua existentia, sed hoc est privilegium solius essentiae divinae quod ipsa ex se formaliter sit singularitas quaedam et idem in eo sunt essentia et existentia.”, HQDL 2, q. 8, p. 39. Importantly, this principle seems to be shared by Sutton, as part of the “common stock” of principles deriving from Avicenna.

269

Nevertheless, such a form is multipliable in actual existence only if there is something to distinguish one of its instances from another20.

What distinguishes one creature from another in the same species is its singular act of existence, the singularity of which is determined by the singularity of a creative act of God

Thus, this act of existence is inherently relational: for a creature to be in actual existence is for it to be created by God.

Thus, the act of existence in question is merely intentionally distinct from the actually existing singular essence, in the same way as a relation is merely intentionally distinct from its foundation.21

With these principles at hand, Henry is obviously able to evade Sutton’s charge, while maintaining the plurality thesis along with all its benefits in accounting for the opposite conditions of the immaterial intellective soul and the material forms of bodies.

Sutton’s criticism of Henry’s conception

Sutton clearly sees that he can handle Henry’s above-described “evasion” only by a direct attack on Henry’s conception of existence and individuation. In particular, he rejects (3) as nonsensical, on the basis of an argument which directly points to the most fundamental difference between their conceptions of existence:

“Advertendum est igitur quod esse non multiplicatur nisi per multiplicationem essentiae, et hoc potest sic videri: essentia quae est ipsum esse, non potest multiplicari, sed est una sola, scilicet deus ipse, ut alibi dictum est. Nec esse potest includi in essentia alicuius causati, quia essentia de cuius ratione est esse, non potest intelligi non esse, et per consequens non potest produci a non-esse in esse. Ad hoc igitur quod esse multiplicetur, oportet essentias multiplicari, quae recipiant esse et limitent esse, quod participant; esse enim subsistens non receptum in aliquo est illimitatum et unum tantum. Oportet igitur dicere quod, sicut forma multiplicatur per hoc quod recipitur in diversis materiis, ita esse actuale multiplicatur per hoc quod recipitur in diversis essentiis. Unde in multiplicatione decem praedicamentorum hoc est manifestum, quia per hoc quod ens, quod significat essentiam, multiplicatur per se et non per aliquid additum in essentias decem praedicamentorum, esse actuale receptum in essentiis illis et limitatum per illas multiplicatur in decem praedicamentis. Universaliter enim multiplicatio limitantium est causa multiplicationis eius quod limitatur, quia illimitatum in quantum huiusmodi est unum, sed per hoc quod participatur a diversis, contrahitur et multiplicatur in illis22.”

The most significant remark in this passage is the closing universal claim, which seems to provide the most general reason for Sutton’s rejection of Henry’s conception: the cause of the multiplication of something that can undergo limitation is the multiplication of those that limit it, for that which is unlimited, as such, is one. In fact, this claim seems to contradict already

20 Again, this principle is also shared by Sutton. Indeed, he presents for it a brief argument in QORD q. 27, p. 749. But then he goes on to use this same principle to prove the opposite conclusion, namely, that it is impossible for angels to be multiplied in the same species, for it is only designated matter that can be the distinctive constituent required for numerical distinctness within the same species, but angels cannot have matter, whence they cannot be thus distinguished. Of course, the question is whether Sutton manages to establish that it is only designated matter that can play this distinctive role.. 21 For a more detailed analysis of Henry’s conception of intentional distinction in his theory of relation see M. G. Henninger, Relations: medieval theories, 1250-1325, Oxford-New York 1989, 40-57. 22 QORD q. 27, pp. 753-754. (ll. 272-290)

270

Henry’s principle (1), for that which can undergo limitation, and hence multiplication, should be indifferent to number, and so it should not, as such, be one. But if we carefully consider Suttons’s argument, we can see that this is not the case. For the indifference to existence and number is a property of a form or nature in accordance with its absolute consideration: this is precisely the reason why the same nature, which can be regarded as the same on account of its lack of distinction in the mind’s consideration, can be realized in several individuals.23 But Sutton’s point (with which, as we could see, Henry also agreed) is that the same nature cannot be realized in actual being in several individuals, unless there is something that distinguishes its several instances in these individuals. The reason for this, of course, is the convertibility of being and unity: the indifference of nature to existence is its indifference to unity, which applies to it only in its absolute consideration, but its realization in actual being is the positing of a unit of that nature in actual being. Therefore, if on account of a lack of distinction in its actual being a nature cannot be multiply realized, then it can only be realized in one entity, which is the case with the absolutely simple and indivisible divine nature.24 So, a nature can be realized in several instances only if there is something setting these instances apart in their actual existence.

What distinguished these individual instances of a single nature for Henry were precisely the singular acts of existence of the singular supposita of the same nature. It is to this claim that Sutton objects by pointing out that considerations of the sort just mentioned also apply to existence itself:25 if it is realized without any distinction, then it can be realized only in one singular, unlimited act of existence, which is nothing but the divine essence, that is, God himself. Therefore, all other acts of existence can be realized as distinct from this singular, unlimited act of existence only by imposing upon them some limitation that distinguishes them from the unlimited divine existence as well as from each other. The limitations imposed upon the resulting limited acts of existence are nothing but the essences of creatures, which differ from each other on account of their contrary, specific differences. But without these limitations the only possible realization of actual existence is just the unlimited act of divine being: ipsum esse subsistens.

23 Perhaps, we should note here that despite possible modern worries to the contrary, the sameness of a nature in its several instances is no more mysterious than the sameness of a book in its several copies. Clearly, it would be preposterous for an author to claim to have written thousands of books and articles on the sole basis that they were printed in thousands of copies. 24 Cf. “…impossibile est intelligere quod sint plures albedines separatae; sed si esset albedo separata ab omni subiecto et recipiente, esset una tantum; ita impossibile est quod sit ipsum esse subsistens nisi unum tantum. Omne igitur quod est post primum ens, cum non sit suum esse, habet esse in aliquo receptum, per quod ipsum esse contrahitur; et sic in quolibet creato aliud est natura rei quae participat esse, et aliud ipsum esse participatum.” S. Thom. Qu. Disp. De Spirit. Creaturis q. 1.; “Deus enim per suam essentiam est ipsum esse subsistens: nec est possibile esse duo huiusmodi, sicut nec possibile foret esse duas ideas homini separatas, aut duas albedines per se substantes. Unde quidquid aliud ab eo est, necesse est quod sit tanquam participans esse, quod non potest esse aequale ei, quod est essentialiter ipsum esse.” S. Thom. Qu. Disp. De Malo, q. 16, a. 3.; “Non enim potest intelligi quod aliqua forma separata sit nisi una unius speciei, sicut si esset albedo separata, non posset esse nisi una tantum; haec enim albedo non differt ab illa nisi per hoc, quod est huius vel illius.” ST1 q. 75, a. 7. 25 Of course, this point immediately gives rise to the difficulty of how existence itself can be regarded as indifferent to existence. But, again, the answer should be clear if we keep in mind that indifference to existence and unity and number pertains to any form or nature only according to its absolute consideration and not in its actual realization. So even though no actual act of existence is indifferent to existence, because it cannot be but an act of existence, yet, if it is a created act, then it can be non-actual when it is not actually created by God, whence existence according to its absolute consideration is indifferent to actuality, and so also to unity and number. Cf. quote at n. 50 below. (QORD q. 26, pp. 731-732.)

271

Indeed, when Sutton directly takes issue with Henry’s conception concerning the individuation of the soul, he argues on the same basis:

“Propter hoc adhuc aliam ponunt fictionem26. Dicunt quod animae in eadem specie distinguuntur non per suas essentias, sed per suum esse. Sed istud inter alia minus valet. Esse enim inter omnia est communissimum, quantum est de se, in tantum quod, nisi contrahatur per essentiam alicuius generis, non pertinet ad aliquod genus. Et propter hoc esse non limitatum per aliquam essentiam est ipse deus, qui non est in aliquo genere. Esse igitur animae per hoc contrahitur ad speciem animae, quod est receptum in essentia animae. Unde esse animae distinguitur ab aliis esse per hoc, quod essentia animae distinguitur ab aliis essentiis. Non ergo distinguuntur animae per esse suum, sed potius e converso esse animarum distinguitur per distinctionem ipsarum animarum. Ergo oportet dare aliquid aliud, per quod animae distinguantur. Istud confirmatur per hoc, quod dicit auctor De causis propositione 16, quod intelligentiae sunt finitae superius, quia habent esse receptum in essentia et sic limitatum, sed inferius sunt infinitae, quia essentiae earum non recipiuntur in aliquo. Ipse vocat superius in eis esse, quod de se est communissimum, inferius in eis vocat essentiam, quia ipsa de se est determinati generis et etiam speciei. Ergo eodem modo oportet in omnibus intelligere quod esse non distinguitur, nisi per hoc quod essentia distinguitur, quia eadem ratio est in uno et in alio. Omnis enim creatura habet esse limitatum per essentiam27. Et videte: Si esse animae non limitaretur per essentiam animae, sed anima distingueretur ab aliis per suum esse, sequeretur quod anima esset ipse deus, quia illud esse haberet omnem perfectionem essendi ex hoc ipso quod non limitaretur per aliud, et tunc essentia animae esset suum esse subsistens, et sic esset deus, quod est nefas dicere28.”

So, for Sutton, it cannot be singular acts of existence that distinguish individual instances of the same form, for the role of forms is to distinguish acts of existence by limiting them in the first place, on account of their own per se differences29. But since the formal contrariety of specific differences can only yield specific distinction, any two singular creatures that differ by such formal differences will have to differ specifically in order to differ numerically. Therefore, Sutton concludes, the only way creatures can differ numerically within the same species is by differing, not with respect to such formal differences, but with respect to some other differences, namely, the per se opposite locations of the various parts of dimensive quantity, which directly follows upon matter. This is the fundamental reason why, according to Sutton, only material creatures can be numerically distinct within the same species30.

26 Cf. HQDL 2 q. 8. 27 Cf. ST1 q. 4 a. l ad3 28 QORD q. 18, pp. 506-507. 29 Cf. “… quia esse consequitur formam, multiplicatio ipsius esse est consequens multiplicationem formae et non causans multiplicationem formae.” QORD q. 27, p. 754. 30 Cf. ibid. pp. 749-751. Cf. also “Ad septimum dicendum est quod non est simile de quantitate et de esse substantiali, quia quantitas dimensiva ex se ipsa habet distinctionem partium eiusdem rationis propter diversitatem situs, qui est de ratione sua. Et ideo talis quantitas est causa multiplicationis individuorum eiusdem rationis in substantiis materialibus, sicut esse substantiale non habet de se distinctionem partium. Et propter hoc oportet quod non sit causa multiplicationis individuorum in una specie, sed multiplicatur in substantiis materialibus eiusdem speciei ex multiplicatione formae, et forma multiplicatur ex multiplicatione materiae in qua recipitur, materia autem multiplicatur ex multiplicatione quantitatis dimensivae, quantitas vero dimensiva propter diversum situm de se multiplicatur. Et ita tota radix multiplicationis substantiarum individualium est quantitas dimensiva; et quia quantitas dimensiva non est in angelis, ideo necesse est quod ibi non sit multiplicatio angelorum in una specie.” Ibid. pp. 762-763.

272

The Thomistic theory of being and individuation vs. Henry’s theory

As we could see, Sutton’s criticism of Henry’s conception of the individuation of created essences, and hence of human souls, was based in particular on his rejection of Henry’s principle (3). Sutton’s reason for this rejection, in turn, is based on his acceptance of the common principles (1) and (2), with the addition of the following Thomistic principles concerning the relationship between form/essence and existence:

(I) Existence is the actuality of form/essence, whereas form/essence is a determination/limitation of existence, provided they are distinct; otherwise they are the same, absolutely unlimited act of divine existence.

(II) Any singular act of existence is primarily distinguished from another by the limitation its form/essence imposes upon it. (That is to say, there can be two distinct acts of existence only if (a) they are the acts of two distinct (types of) forms, or (b) they are the acts of two distinct instances of the same form. But in case (b) the distinct instances of the same form are clearly not distinct on account of their difference in form—just like two copies of the same book are not distinct on account of the difference in their content, which is why it is enough to read one copy in order to read the book—, but on account of something else that individuates them, and so their acts of existence are distinct secondarily, on account of whatever individuates these instances.)

As we could see, with these principles at his disposal Sutton can argue further to show that since the only act of existence that is unlimited by some form/essence is divine existence, any created act of existence has to be primarily distinguished from divine existence and from any other created act of existence by its form/essence.

But then, the only further principle he needs against Henry’s conception of individuation is the following:

(III) Distinction in form always yields a specific distinction

Sutton brings up this last principle early on in his argument against Henry’s “evasions” to show that if human souls were not individuated by bodies, then they would have to differ formally, which, in virtue of (III), would yield the absurd conclusion that individual humans differ specifically from each other:

“Quod primum impossibile sequatur, potest videri sic: si animae distinguantur non per corpora, sed per se ipsas, cum ipsae sint formae, distinctio earum erit formalis, non materialis. Universaliter autem omnis diversitas formalis diversificat speciem. Omnes igitur animae humanae erunt diversae secundum speciem ab invicem31.”

In the subsequent paragraphs Sutton goes on to argue further against a possible objection to this principle, but in fact its validity can also be shown on the basis of (1) shared by Henry. For if there is a difference in form between two individuals, then, in virtue of (1), each of the individuals in question is just one (bearer) of the several possible instances of its form. But the several possible individuals which would share the same form (which is not numerically the same, but only according to its absolute consideration) would have to belong to the same species, whereas those that would share the other form would have to belong to another species;

31 QORD q. 18. p. 504.

273

therefore, the two initial individuals that differed in form had to differ specifically, and not only numerically. Q. e. d.

However, if any created act of existence is distinguished from another by its form, while a distinction in form has to yield specific difference, then Sutton is justified in claiming both that no individuals of the same species can be said to be primarily distinguished by their acts of existence, and that whatever primarily distinguishes distinct individuals of the same species has to be something other than their forms.

In several places, while criticizing not only Henry’s, but also Scotus’s, and Richard of Middleton’s views on individuation,32 Sutton deploys a barrage of arguments to show that the distinctive principle accounting for the individuation of the same substantial form in several instances can only be matter primarily distinguished by the per se opposite positions of its parts.33 Indeed, he goes so far as to argue on this basis that it is impossible even for God to create several immaterial individuals in the same species; in particular, it would be impossible for God to create several separate human souls (which, of course, would have to be immaterial individuals of the same species).34 But then, further, if he is right in this claim, then he was also right in reducing the plurality thesis to the undesirable Averroistic conclusion.

However, instead of following the further ramifications of Sutton’s arguments, I would rather return to digging down to their roots, summarizing what I take to be Sutton’s most fundamental insights into St. Thomas’s theory of being, and pointing out their role in his defense of the Thomistic position concerning the nature of the intellective soul.

Sutton vs. Henry on the participation of being

On the basis of the foregoing considerations, I think we can establish that the difference between Henry’s and Sutton’s respective conceptions of the nature of the intellective soul can be reduced to their fundamentally different conceptions of the participation of being. Indeed, Sutton himself is quite aware of this fundamental difference as well as its consequences, as he makes it quite clear in the following passage:

“Unde aliqui doctores35 bene ostendunt ratione necessaria quod esse differt ab essentia angeli realiter ex hoc, quod essentia angeli habet esse participatum. Patet enim per ea quae dicta sunt, quod essentia non sic participat esse, quod habeat esse limitatum per differentiam contrahentem esse ad constituendum essentiam, de cuius intellectu sit esse, ut ideo dicatur participare esse, id est partem eius capere, quia est de essentia eius quae est limitata, sicut species participat genus. Sed oportet quod habens essentiam sic participet esse, quia capit non totam perfectionem essendi, sed partem, in quantum esse limitatur per essentiam in qua suscipitur; quae essentia est

32 Esp. QORD q. 27, pp. 757-760. Note that in these arguments Sutton cannot assume (1), which is directly contradicted by positing a formal principle of individuation that cannot be indifferent to multiplication, since it is by definition not multipliable. 33 Cf. Thomas of Sutton, Quodlibeta, München 1969. Henceforth: QDL. QDL 1 q. 21, QDL 3, qq. 21-22, QDL 4, q. 16; QORD q. 18, QORD q. 27. 34 For this point, see esp. QORD q. 27, ad 9-um, and ad 10-um, where he writes: “… animae non possunt causari diversae nisi in diversis corporibus animarum, quia diversitas animarum non est de se intelligibilis in una specie, sed solum ex diversitate corporum. Quod autem non est intelligibile, per nullum agens fieri potest.” p. 764. 35 Giles of Rome, De esse et essentia, Frankfurt/M. Minerva 1968, q. 9, q. 11; cf. Thomas of Sutton, Tract. de esse et essentia, in: W. Seńko, Trzy studia nad spuścizną i poglądami Tomasza Suttona dotyczącymi problemu istoty i istinenia, in: Studia Mediewistyczne, 11(1970), 111-280, esp. c.2, 239.

274

limitata ad genus determinatum et ad speciem. Et sic limitatur esse per essentiam, sicut forma equi limitatur per hoc, quod recipitur in materia tamquam in susceptivo participante. Isto enim modo actus participatur a potentia, et isto modo participatum realiter differt a participante et non est de intellectu ipsius. Unde patet quod male dicunt, qui ponunt36 essentiam participare esse sic, quod essentia causata capit a deo se ipsam includentem esse, quod esse est pars respectu esse divini, et quod non capit aliud a se secundum rem, sed quod est inter capiens et captum relatio rationis tantum, sed quod inter capiens et deum a quo capit est relatio realis. Istud dictum est erroneum, quia sequuntur multa inconvenientia, ut dictum est, si ponatur quod essentia sic participet esse, quod esse sit de suo intellectu; sequitur scilicet quod nihil sit causatum in rerum natura et quod omnia sint aeterna37.”

The contrast between these conceptions is brought out by Sutton in a particularly vivid manner in his Tractatus de esse et essentia, where he uses the analogy of the sun and its light, also used by Henry in his own description of his conception38:

“… quidam ex adverso supradictis vitiis contradicentes dicunt, quod esse nullam rem absolutam ponit in essentia vel supra essentiam sed realiter est idem cum ea nisi quia addit respectum quondam ad creatorem, prout ipsa essentia est in effectu. Ad cuius evidentiam distinguit duplex esse, scilicet esse essentiae et esse actualis existentiae. Esse quidem essentiae non est aliud quam ipsa essentia habens ideam in Deo, et tale esse est illud, quod significat definitio, quia definitio indicat quid est esse rei. Esse vero actualis existentiae est illud idem esse, nisi quia addit respectum dependentiae ad productorem rei, prout res in actu effecta est, ut ex hoc essentia creaturae dicatur esse, in quantum est creata sive prout est effectus creatoris et non per aliquam rem sibi additam. Et secundum hoc dicitur, quod quaelibet creatura participat esse, in quantum est similitudo in effectu expressa a Deo: sicut si sol produceret radium voluntate, ipse radius sic productus esset similitudo solis absque additione alterius rei, sic etiam creatura, ut dicunt, voluntarie a Deo producta dicitur participare esse divinum, non propter additionem alicuius dicentis aliam rem ab ipsa essentia. Non ergo est imaginandum, quod ipsa essentia participet esse, quasi sit aliquid substratum ipsi esse, ita quod esse sit aliquid informans et perficiens essentiam creaturae, sicut forma perficit materiam sibi substratam, talis enim imaginatio falsa est; sic ergo concludit, quod esse sit idem quod essentia addens solum praedictum respectum39.”

By contrast, in describing his own Thomistic position, Sutton uses the analogy of sunshine received in and colored (i.e., filtered, dimmed, and thus diminished) by transparent bodies (such as the stained glass windows of cathedrals):

“Ut tamen praedicta considerentur et nostra intentio clarius elucescat, imaginandum est, quod divinum esse se habeat ad modum cuiusdam lucis solaris diffusae per totum diaphanum aeris et ipsa et natura creata se habent ad modum diaphani corporis. Dices autem, quod illa lux est splendida per essentiam suam, corpus vero diaphanum in tantum splendet sive lucet, in quantum lumen participat a dicta luce, non enim lumen habet radicem in diaphano. Imaginemur ulterius, quod dicta lux solaris sua virtute producat corpus diaphanum, quod producendo semper ei assistat et suo lumine perfundat; et corpus sic productum in tantum actu subsistat, in quantum lumen participat. Constat autem, quod corpus, <cum est a luce>40, producitur seu lumen

36 HQDL 10 q. 7; HQDL 11 q. 3. 37 QORD q. 26, p. 730. Cf. also “…falsa est imaginatio, qua aliqui imaginantur quod per creationem esse imprimatur essentiae, sicut per generationem forma imprimitur materiae. Sed vera imaginatio est quod tam essentia quam esse producantur per creationem; essentia scilicet determinati generis participans esse ab esse separato, quia alio modo esse multiplicari non potest nisi per diversa participantia. Unde ponere essentiam non differre ab esse, est ponere tantum unum ens quod est esse separatum, ita quod nihil aliud habeat esse.” QDL 3, q. 8, pp. 396-397. 38 Cf. text quoted at n. 18. 39 TEE c. 2, 239, ll. 6-25. 40 My conjectural emendation for the text’s nonsensical “dum ist a luce”. Another possibility would be to read here “cum ista luce producitur”, provided “lux” can be taken to refer not to the lux producens but rather to the lumen

275

participat a luce producente ex natura suae diaphaneitatis. Quod magis appareret, si diceremus ipsum lumen se incorporari ad modum coloris, qui dicitur esse quaedam lux incorporata in corpore terminato. Dicemus tunc lumen in diaphano causari, et ex principiis essentialibus eius, in quantum aptum natum est lumen perfundi, et in natura sua hoc unum sibi incorporetur, cum secundum dictam suppositionem ipso lumine actu subsistat; positum est enim ipsum corpus secundum se totum sic a luce produci, quod eius lumine participato subsistit. Sed quia, ut dictum est, corpus non potest sibi esse causa lucendi, cum lumen a se non habeat, ideo dicemus lumen in diaphano causari principaliter a sole lumen diffundente41.”

As can be seen, Sutton here sharply contrasts two fundamentally different (although quite difficult to distinguish) conceptions as to how being can be said to be participated. According to Henry of Ghent’s “Augustinian” theory, participating in existence is nothing but being just a “fragmentary” act of existence meted out directly by the divine will to the capacity of a creature, which is determined by the creature’s idea in the mind of God. Accordingly, the realization of these ideas is nothing but their participation in divine being, which, in turn, is just the act of their being created, an inherently relational act, merely intentionally distinct from the individual instances of the nature it realizes.

An important consequence of this conception is that the real identity along with the mere intentional distinction between an essence and its actual existence does not entail that this essence/existence has to be the unlimited act of divine existence/essence. An act of created existence is a directly and per se delimited act, insofar as it is a singular realization of a per se limited essence, different from any other essence on account of their per se opposite differences.

On this basis we can say that according to this conception, the determination of the concept of being as it can be applied to more and more specific participated acts of existence moves “from outside in”: it is starting with a comprehensive, “catch-all concept” of being, which comprehends in its scope even the infinity of divine being, and which gets restricted, specified and individualized according to the essential order of things determined by their archetypes, the divine ideas.42 So, this conception conceives of the determination of the concept of being in terms of what can be called an “extensional restriction” of a general concept by means of its “intensional specification”, just like adding more and more specific differences to a generic concept restricts the extension of the resulting more and more specific concepts by specifying their content, their intension.

By contrast, according to Sutton’s Thomistic theory, the participation of being is to be conceived in terms of the “intensional diminution” of a concept by the addition of diminishing qualifications, and its consequent “extensional amplification”. For example, the common term “white” without any qualification is applicable only to something that is wholly white. However, adding the qualification “in its one half” intensionally diminishes its conditions of applicability43,

participatum. 41 TEE c. 3, 244, ll. 11-30. 42 Cf. HQDL 5, q. 2, q. 6; 7, q. 2. 43 In this case, the “delimiting” in question concerns just one “dimension” of whiteness, namely, the extent of a surface it covers. But whiteness can be diminished also in respect of such other features as e.g. intensity, or clarity, which would yield other diminutions of the conditions of the applicability of its concept, thus yielding several broader concepts, which would cover not only things that are white with a 100% albedo (the measure of reflectivity in modern physics), but also things that reflect only a lesser percentage of white light, and not equally all wavelengths (which, at a certain degree would yield not something white with a certain tint, but a different color altogether).

276

and thus, as a result, extends the applicability of the term and the corresponding concept even to such things that are not wholly white. In the same way, “being” without any qualification or determination can be applied only to that which is wholly and absolutely being, that is, God, ipsum esse subsistens44. However, the qualification “of such and such nature” diminishes the conditions of its strict applicability, and thus extends it even to things that are not wholly beings, but only in respect of some specific nature, which is not its being itself. So, upon this conception, the determination of the concept of being as it is applicable to more and more diminished, participated acts of existence is moving “from inside out”: it starts with a very restricted concept, which, however, on account of its various “intensionally diminishing” qualifications, gains an extended, less restricted applicability45.

Most importantly, this conception immediately yields a conclusion opposite to Henry’s, namely, that if an essence is really identical with its act of existence, then that act of existence can only be the single, unlimited act of divine existence, whence it cannot be any sort of limited, participated, creaturely act of existence.46 The reason for this should be clear if we consider that if an act of existence is identified with the essence it actualizes, then the act of existence/essence in question has to be unlimited, since nothing delimits itself.47 Indeed, according to Sutton, as will be obvious from the subsequent quotations, this consequence has to be regarded as analogous with adding the qualification ‘with respect to whiteness’ to the predicate ‘white’. Clearly, this qualification is non-diminishing precisely because of the identity of what is signified by the absolute predicate and what is referred to in the qualification (whence whatever can be said to be ‘white with respect to whiteness’ must be said to be ‘white’ without qualification and vice versa).48 So, the kind of limitation Sutton has in mind is only possible if there is a real distinction

44 To be sure, one must add here that this absolutely primary concept of being which is applicable only to God is not primary quoad nos, but it certainly is primary secundum se. For more on this epistemological issue see the closing section of G. Klima, Aquinas on One and Many, forthcoming in: Documenti e Studi sulla Tradizione Filosofica Medievale (Società Internazionale per lo Studio del Medioevo Latino). 45 For more on this issue, see G. Klima, The Semantic Principles Underlying Saint Thomas Aquinas’s Metaphysics of Being, in: Medieval Philosophy and Theology, 5(1996) 87-141. 46 Cf. QDL I, q. 6, p. 50; and the passages quoted in nn. 22 and 28. 47 Cf. “Praeterea: omne, quod participat aliquid, est aliud ab eo, quod participatur. Quod etiam ipsum nomen participationis ostendit. Nam id participatur proprie, quod diminutive in aliquo alio ab eo suscipitur. Si autem dicatur, quod essentia idem est realiter quod esse, impropriissime diceretur, quod essentia participet esse, nihil enim seipsum participat. Sed nihil est, quod ita proprie dicatur, sicut quod essentia participet esse, immo illa creatura participans esse est ita propria et per se, sicut ista essentia divina est suum esse. Nam sicut esse per essentialia proprie convenit Deo, ita esse per participationem per se convenit creaturae. Sicut ergo in Deo una et eadem res est esse et essentia, quia ibi non est participans et participatum, ita <in> creatura, in qua est participatio, alia res est participans a participato; alioquin ratio participationis in creaturis locum non haberet, quod est contra naturam eius.” TEE c. 3, 248. (ll. 4-16) 48 More precisely, assuming that x’s essence is x’s existence, the consequence in question is the following: “x exists with respect to its essence; therefore, x exists without any limitation [i.e., x IS/EXISTS, period]”. In this conception, this consequence has to be regarded as analogous to the following: “x is white with respect to its whiteness; therefore, x is white without qualification [i.e. x is white, period]”. Cf. “Ad quartum dicendum quod omnis creatura est finita simpliciter, inquantum esse eius non est absolutum subsistens, sed limitatur ad naturam aliquam cui advenit. Sed nihil prohibet aliquam creaturam esse secundum quid infinitam. Creaturae autem materiales habent infinitatem ex parte materiae, sed finitatem ex parte formae, quae limitatur per materiam in qua recipitur. Substantiae autem immateriales creatae sunt finitae secundum suum esse, sed infinitae secundum quod eorum formae non sunt receptae in alio. Sicut si diceremus albedinem separatam existentem esse infinitam quantum ad rationem albedinis, quia non contrahitur ad aliquod subiectum; esse tamen eius esset finitum, quia determinatur ad aliquam naturam specialem.” ST1 q. 50, a. 2, ad 4-um.

277

between a created act of existence and the essence delimiting it, and so no wonder he promptly reduces Henry’s identification of essence and existence in creatures to the absurdity that a created essence in that case would not be created, which, on the other hand, does not seem to follow at all on Henry’s conception of participation.

But Sutton is steadfast in holding on to his own Thomistic conception, and it is with this conception at hand that he handles several, apparently obvious objections coming from the other side. In particular, he uses this conception of participation to defuse an objection utilizing one of his own premises for the real distinction of essence and existence in creatures. According to the objection, if Sutton is right in claiming that the identification of existence with essence would yield the conclusion that it cannot be understood to be non-existent, and thus it cannot be created, then the same should apply to any act of existence that Sutton posits to be distinct from its created essence, for obviously no act of existence can be understood to be non-existence, just as no man can be understood to be a non-man, etc.:

“Sed de hoc oritur dubitatio. Si enim essentia non posset intelligi non existens, si includeret esse, et ita non posset habere causam sui esse, eadem ratione videtur sequi quod essentia non habeat causam sui esse, si esse ponatur differre realiter ab essentia, quia illud esse non potest intelligi non esse, sicut homo non potest intelligi non-homo nec aliquid potest intelligi sub suo opposito. Esse ergo si realiter differt ab essentia, adhuc illud esse non habebit causam et per consequens essentia non erit producta in esse a non-esse, sed erit aeterna etiam secundum suam actualem existentiam. Et ita sequuntur eadem inconvenientia, posito quod esse differat ab essentia realiter, quae sequuntur ponentes quod esse non differt realiter ab essentia, ut videtur49.”

Sutton answers this objection by making it clear that according to his conception, the participation of being is the limitation of an act of being by a really distinct, finite essence, in pretty much the same way as a part of a surface is a limitation of its color:

“Ad hanc vero dubitationem tollendam advertendum est quod, quamvis aliquid non-contractum non possit intelligi cum suo opposito, ipsum tamen contractum per aliquid diminuens potest intelligi cum suo opposito; verbi gratia, album per se sumptum non potest intelligi non-album, album tamen secundum dentes potest intelligi non-album simpliciter vel non-album secundum faciem. Vel melius exemplum est de forma, quae naturaliter est separata a materia, scilicet forma angeli non limitata per materiam; non enim potest intelligi non-separata. Anima tamen separata, quae est contracta per materiam, potest intelligi non-separata, quia non per naturam suam est separata, sed propter improportionem corporis; et ideo separata pro uno tempore potest intelligi non-separata pro alio tempore. Nunc autem si esse sit in essentia rei, illud esse non erit contractum neque per differentiam neque per aliquod susceptivum, ut visum est. Et ideo esse tale non potest intelligi non esse, et per consequens nec talis essentia potest intelligi non esse. Sed si ponamus quod esse sit contractum per essentiam in qua recipitur, tamquam diminutum per essentiam a qua participatur, potest illud esse intelligi non esse pro aliqua duratione, sicut et essentia in qua recipitur. Tale enim esse non existit nisi per accidens. Sed quia esse per se convenit rei subsistenti, ideo sicut illud, cuius est esse, potest intelligi non esse ante suam productionem et post suam desitionem, ita illud esse, quod est actualitas eius, potest intelligi non esse ante productionem illius cuius est et post suam desitionem. Et propterea non sequuntur illa inconvenientia, ponendo quod esse realiter differt ab essentia, quae sequuntur ponendo quod esse non differt ab essentia50.”

On the basis of this passage, the analogy should be obvious: just as that which is totally white cannot be understood to be non-white in respect of any of its parts, so too that which is totally

49 QORD q. 26, p. 731. 50 QORD q. 26, pp. 731-732.

278

being cannot be understood to be non-being in any respect at all; but just as that which is only partially white can be understood to be non-white in respect of another part, so too that which is only partially being, because it is a being limited by a finite essence, can be understood to be a non-being in some other respect (where, of course, the same applies to the limited act of existence as to the thing that has this limited existence). For example, that which is limited by its nature to exist for a certain time can be understood not to exist at another time, and that which is limited to exist under certain conditions (at the very least under the condition of being kept in existence by God) can be thought not to exist under different conditions. In the same way, a form which is limited to exist under the condition of informing a body for a certain time but has the natural capacity to go on existing after getting separated from the body after that time can be thought to exist separately from the body, even though it actually exists informing a body; so even if it is actually material in its present condition, it can be thought to be immaterial at another time, in a different condition.

Sutton’s Thomistic theory of being and the nature of the intellective soul

In the end, therefore, Sutton thinks of the human soul as providing a peculiar kind of determination, or limitation of the act of being which actualizes it. It is precisely this peculiar kind of limitation that establishes the human soul as a “borderline case” between the realms of absolute materiality and absolute immateriality without any contradiction, despite the per se opposition between these primary differences of the category of substance. On this basis, Sutton is able to present the case of the Thomistic conception of the intellective soul as being free from any inconsistency, despite the fact that it entails the attribution of the opposite conditions of materiality and immateriality to one and the same entity. The point, however, is that these attributions do not pertain to the soul in the same respect and without any qualification, precisely because of the soul’s “borderline status” between pure materiality and pure immateriality:

“Sciendum est igitur quod anima humana sic condita est, ut ipsa secundum suam naturam sit in confinio materialium et immaterialium. Unde in Libro de causis dicitur quod ipsa anima est in horizonte aeternitatis et temporis, propter hoc quod ipsa est omnium substantiarum intellectualium infima, et per consequens, cum substantiae intellectuales sint aeviternae, ipsa est infima omnium aeviternorum. Ipsa etiam per comparationem ad formas materiales, quae sunt corruptibiles, in tempore est suprema: Et sic est in horizonte corruptibilium et incorruptibilium, sive in confinio aeternitatis participatae et temporis. Et propter hoc oportet quod anima humana, sic in medio constituta, sapiat naturam tam formarum materialium quam immaterialium51.”

In general, Sutton’s Thomistic conception of the participation of being clearly provides him with a more flexible conceptual apparatus than Henry’s “Augustinian” conception. In any case, it is not surprising that the Thomistic conception is particularly apt for treating the ontological status of the intellective soul as a borderline case between pure materiality and pure immateriality. For 51 QORD q. 19, pp. 532-534. (ll. 180-190, 207-229) Cf.: “propter hoc anima constituta est in confinio substantiarum separatarum quae sunt incorporales et formarum materialium: quae sunt corporales: est enim infima formarum incorruptibilium et suprema formarum corruptibilium: et propter hoc est partim separata a materia, et partim in materia. Secundum intellectum namque et voluntatem separata et incorruptibilis est: et quantum ad hoc pertinet ad genus substantiarum separatarum: sed secundum alias potentias est actus materiae, et secundum illas est corruptibilis: et sic pertinet ad genus formarum materialium quae sunt corruptibiles. Quod patet ex hoc quod per potentias illas, scilicet sensitivam et vegetativam, continet perfectionem quae reperitur in formis brutorum, sed eminentius.” Thomas of Sutton, De Pluralitate Formarum, in: S. Thomae Aquinatis Opera Omnia, Stuttgard-Bad Cannstatt 1980, c. 1, in fine

279

on this conception it does not yield any inconsistency that the act of existence of the soul is material and inherent on account of the soul’s actually informing a human body, and yet, the same act of existence is also subsistent in a different respect, namely on account of being the existence of a substance that has an immaterial power and a corresponding operation of its own, and thus this act of existence is also immaterial after it ceases to be the act of existence of the body.

On the other hand, such a borderline case is certainly more troublesome on the other conception, which would specify various acts of being in the same way as the essences with which they are identical in re, namely, by means of opposite differences. In this conceptual setting, materiality and immateriality, being the directly opposite differences of two radically different and distinct realms of being, constitute such a sharp division between these two realms that no single and undivided entity can possibly find a place between them, on pain of inconsistency. But if the Thomistic conception is correct, then the human soul is constituted right there, in a however paradoxical, but in no way inconsistent existential situation.

280

Natural Necessity and Eucharistic Theology in the late 13th century

Introduction

The title of this presentation, I’m afraid, is a little bit misleading. For this presentation will not, as it cannot, cover the broad topic indicated in the title. Rather, it will concern itself only with some preliminary ideas leading the way to a larger project, which, however, should eventually bear an even broader title. As a matter of fact, here I will consider at some length only two authors from the beginning of the period indicated in the title, namely, Aquinas and Siger of Brabant. (Or perhaps three authors, provided the anonymous author of the Physics-commentary I’ll consider is not Siger.) Nevertheless, I think a careful contrast of their views on the issues raised by the conflict between Aristotelian natural necessity and the theology of the Holy Eucharist will bring into focus certain basic conceptual differences within the larger conceptual unity of the period. Indeed, such conceptual differences are especially worth considering if we try to detect those original “hairline cracks” in the 13th-century “cathedral of thought” which later on grew into the ever wider “cracks” and “fissures” that eventually allowed it to be brought down by the series of social and ideological “quakes” of the turbulent late-medieval and early modern period. Obviously, such issues cannot be dealt with in the framework of such a brief presentation, nor am I at this point sufficiently prepared to deal with them. However, in line with the workshop character of this meeting, toward the end of this talk I will risk some working hypotheses concerning these broader issues, to ask for corrections, qualifications, and pointers for my further research in this area.

The conflict

The conflict between Eucharistic theology and the Aristotelian notion of what is necessary in virtue of a thing’s nature is brought to the fore most perspicuously by the following two short passages from Aquinas:

“Praeterea, de eodem praedicatur definitio et definitum. Sed ens per se est definitio vel descriptio substantiae. Si ergo in sacramento altaris accidentia sunt per se non in subiecto, sequitur quod sint substantiae; quod est absurdum.” QDL 9, q. 3, obj. 2

“Praeterea, quicumque separat definitionem a definito, ponit duo contradictoria esse simul vera: quia hoc ipsum quod est homo, est animal rationale mortale; et ita si ponatur esse homo et non esse animal rationale mortale, ponitur esse homo et non esse. Sed definitio accidentis est quod inest substantiae; unde etiam in definitione singulorum accidentium oportet quod ponatur substantia. Ergo cum deus non possit facere contradictoria simul esse vera, neque facere poterit quod accidens sit sine substantia.” 4SN, d. 12, q. 1, a. 1a, obj. 2

In order that we can fully appreciate the strength of these arguments as well as the replies Aquinas provides to them, we should dwell a little bit on some of their assumptions not quite spelled out in the arguments themselves.

The first, commonly endorsed presupposition is that God cannot make contradictories true. As is well-known, this was understood not to impose any limitation on divine omnipotence, in the sense of not placing any lack of power in God. The nicest illustration of this doctrine I have found in a booklet by Armandus de Bellovisu, one of Aquinas’s immediate disciples, entitled

281

Explicationes Terminorum Theologicorum, Philosophicorum et Logicorum.1 Armandus’s example is that just as the fact that a teacher cannot teach a donkey theology does not involve any defect in his teaching abilities, but rather a defect in the donkey’s ability to receive knowledge, so the fact that God cannot make contradictories true does not involve any defect in his creative power, but rather a defect in the contradictories’ ability to receive being.

The second, also universally accepted assumption is that the quidditative definition of a thing signifies the thing’s nature.

The third common assumption is that denying of a thing something that is involved in the thing’s quidditative definition results in a contradiction. Clearly, this assumption, along with the previous one, entails that when we talk about natural necessity in this context, what is meant is not some weaker-than-logical, causal necessity (in the sense in which natural necessity is commonly contrasted with logical necessity in modern philosophy). What is naturally necessary in the sense relevant here, that is, in the sense that it is necessary on the basis of what is involved in the thing’s nature, is necessary in such a manner that its opposite would be logically contradictory, and hence, in virtue of the first assumption, impossible to realize even by divine power.

The fourth assumption is that “something which is in a subject” [quod est in subjecto], or some equivalent formulation [such as ens in alio], is the quidditative definition of an accident, or at least a description having the force of a quidditative definition, based on what Aristotle says at the beginning of his Categories.

Now these assumptions obviously entail that the claim that an accident exists without a subject is contradictory, and hence that it cannot be made true even by divine power. But this conclusion would mean that the miracle of the Holy Eucharist would be impossible; therefore, one of these assumptions has to be discarded. However, none of these assumptions is easily dismissible. Eliminating the first would go directly against the first principle, the principle of non-contradiction. Rejecting the second would be contrary to what is meant by a quidditative definition. Denial of the third would again be contrary to what it means to have something involved in the thing’s quidditative definition. And finally, rejecting the fourth would seem to undermine the very point of the Aristotelian distinction between substance and accident.

Aquinas’s solution

Yet, Aquinas’s reply takes aim at this last assumption. In his reply to the objection of the Quodlibeta he first points out that the usual way of quoting the definition of accident is in conflict with Avicenna’s conclusion, according to which the existence of a thing cannot figure in its definition. Then, on the basis of this observation, he moves on to show what should be regarded as the correct interpretation of the definition of substance, and, correspondingly, that of accident. Finally, he points out that with this understanding of the definition of accident there is no contradiction involved in the claim that an accident miraculously exists without a subject:

1 Armandus de Bellovisu: Explicationes Terminorum Theologicorum, Philosophicorum et Logicorum, Wittebergae, 1623, p. 28: “… et illud quod non potest facere dicitur impossibile, non propter defectum divinae potentiae, sed propter defectum rei factibilis quae non est capax. Sicut magister in theologia de potentia absoluta potest docere theologiam, sed quod non possit docere asinum non est defectus potentiae in magistro, sed est defectus asini, qui non est capax doctrinae.”

282

“Ad secundum dicendum, quod secundum Avicennam in sua Metaph., esse non potest poni in definitione alicuius generis et speciei, quia omnia particularia uniuntur in definitione generis vel speciei, cum tamen genus vel species non sit secundum unum esse in omnibus. Et ideo haec non est vera definitio substantiae: substantia est quod per se est; vel: accidens est quod est in alio. Sed est circumlocutio verae descriptionis, quae talis intelligitur: substantia est res cuius naturae debetur esse non in alio; accidens vero est res, cuius naturae debetur esse in alio. Unde patet quod, quamvis accidens miraculose sit non in subiecto, non tamen pertinet ad definitionem substantiae; non enim per hoc eius naturae debetur esse non in alio; nec egreditur definitionem accidentis, quia adhuc natura eius remanet talis ut ei debeatur esse in alio.” QDL 9, q. 3, ad 2-um

The same point is made in somewhat more detail in the reply to the objection in the commentary on the Sentences.

“Ad secundum dicendum, quod sicut probat Avicenna in sua Metaph., per se existere non est definitio substantiae: quia per hoc non demonstratur quidditas ejus, sed ejus esse; et sua quidditas non est suum esse; alias non posset esse genus: quia esse non potest esse commune per modum generis, cum singula contenta in genere differant secundum esse; sed definitio, vel quasi definitio, substantiae est res habens quidditatem, cui acquiritur esse, vel debetur, ut non in alio; et similiter esse in subjecto non est definitio accidentis, sed e contrario res cui debetur esse in alio; et hoc nunquam separatur ab aliquo accidente, nec separari potest: quia illi rei quae est accidens, secundum rationem suae quidditatis semper debetur esse in alio. Sed potest esse quod illud quod debetur alicui secundum rationem suae quidditatis, ei virtute divina agente non conveniat; et sic patet quod facere accidens esse sine substantia, non est separare definitionem a definito; et si aliquando hoc dicatur definitio accidentis, praedicto modo intelligenda est definitio dicta: quia aliquando ab auctoribus definitiones ponuntur causa brevitatis non secundum debitum ordinem, sed tanguntur illa ex quibus potest accipi definitio.” 4SN, d. 12, q. 1, a. 1a, ad 2-um

Again, there are a number of points in these two passages that must not escape our attention if we want to understand properly the significance of Aquinas’s solution.

First of all, St. Thomas does not reject here any of the philosophical assumptions listed above exclusively on the basis of the conflict between the claim they entail and an unquestionable theological conclusion. Rather, this conclusion only signals for him that there must be something wrong with at least one of these assumptions, whence it has to be revised in the light of further careful, philosophical analysis. (This is a point I dwelled on at some length in my paper presented in Erfurt, comparing in detail the respective methodologies involved in Aquinas’s and the Latin Averroists’ handling of such conflicts.)

The philosophical analysis in question is provided by Avicenna, a pagan philosopher, and an outstanding Aristotelian authority. (To be sure, it has to be added here that Siger in his commentary on the Metaphysics, when he considers Avicenna’s relevant arguments, quite flatly states that the authority of Avicenna should not be given credence here, since his position is based on error.)2 The details of the Avicennean argument indicated by Thomas are difficult to interpret, but the gist of the idea seems to be quite clear. Suppose that what the term ‘substance’ signifies, the quiddity of substance, is the same as what the term ‘being’ signifies in all substances. Then the term ‘substance’ would be common to all substances in the same way as the term ‘being’ is. However, since ‘being’ cannot be a genus, in that case ‘substance’ would not be a genus either, which is false. Hence, if all the other premises are true, then we have to reject the

2 “Ad auctoritatem Avicennae dicitur quod non est ei credendum quoniam erravit.” Siger de Brabant: Quaestiones in Metaphysicam, (ed. A. Maurer), Louvain-la-Neuve: Éditions de l’Institute Supérieur de philosophie, 1983, Introductio, q. 7, p.35.

283

initial assumption, namely, that what the term ‘substance’ signifies, the quiddity of substance, is the same as what the term ‘being’ signifies in all substances.

The only questionable premise, namely, that ‘being’ is not a genus, is briefly justified by the following consideration. A generic term signifies something that is common to all individuals that fall under it. But the term ‘being’ signifies not what is common to all individuals that fall under it, but it signifies precisely that on account of which they differ from one another, namely, their being. Therefore, the term ‘being’ cannot be common to all these individuals in the way a genus is.

Well, perhaps, one might have qualms about this argument to the effect that according to Aquinas a genus does not signify one common thing any more than the term ‘being’ does, and so the alleged difference — namely, that while the genus signifies something common to all its inferiors, the term ‘being’ signifies something that distinguishes these inferiors — cannot serve to establish the distinctness of what they signify. But perhaps we can quickly allay such worries by pointing out that even though what the genus signifies is not one common thing, but rather the individualized natures of the things that fall under it, nevertheless, these things, insofar as they fall under the genus do not differ from one another on account of these individualized natures. On the contrary, the individualized natures signified in the individuals by the genus are precisely the reason why all these individuals fall under the same genus. On the other hand, given the convertibility of one and being, these individuals are individuals distinct from one another precisely on account of the fact that they have distinct acts of being, and these distinct acts are precisely what is signified in them by the term ens.

In any case, whether or not the argument as presented here is conclusive sub specie aeternitatis, its conclusion certainly allows a more sophisticated analysis of the usual formula of the definition or quasi-definition of accident. For if what the definition of an entity signifies is one thing, and what the term ens signifies in the same entity is another, then a formula containing ens in place of the generic term of a definition cannot be regarded as a definition signifying the quiddity of this entity. Consequently, it is wrong to construe the quasi-definitions of substance and accident, namely, ens per se and ens in alio, respectively, as consisting of the quasi-generic term ens, and the quasi-differences per se and in alio. But it is only this understanding of these formulae which would allow the objections to the doctrine of the holy Eucharist to proceed, for it is only this understanding of these formulae which would entail that an accident without a subject would have to be an entity which lacks something from its quiddity, namely, an inherent act of being (esse inhaerens), the act of being in a subject.

So the point of Aquinas’s rejection of our fourth assumption above is that the usual formula, or any equivalent formulation, cannot be taken as a quidditative definition of accident, provided it is interpreted as signifying the act of being of accidents, and specifying what kind of act it is. His reason for this rejection is not the conflict with a theological doctrine that would otherwise emerge, but the general Avicennean consideration concerning quidditative definitions, according to which such definitions cannot signify (by their quasi-generic term) and specify (by their quasi-difference) the kind of act of being that the entity to which such a definition applies is supposed to have.

But this solution is obviously incomplete until one tells what, then, the correct definition of accident is, or rather, what the proper understanding of the usual formula should be. What Aquinas provides here as an answer is in perfect agreement with the requirement that a

284

quidditative definition should signify the quiddity of the thing defined (that is to say, of the thing to which the definition applies). He says that ens in alio should be interpreted as signifying a thing which by its nature demands an act of being in something else. Obviously, in this reply everything hinges on how we understand the phrase res cui debetur esse in alio, which, taking into consideration its context as well, I translated in my previous sentence as ‘a thing which by its nature demands an act of being in something else’. The crucial question here, therefore, is how we should understand the possibility that a thing can lack something demanded by its nature, as opposed to the impossibility and self-contradiction that a thing could lack something from its nature.

As is usually the case with difficult metaphysical questions, a relatively well-understood, mundane example can be helpful here in clarifying the relevant conceptual relationships. One such example is provided by what Aquinas says about how the nature of heavy bodies demands that they should be down, that is, near the center of the universe, which, nevertheless, does not mean that it would entail a contradiction for a heavy body to be up, that is, removed from the center. As he writes:

“Nihil enim prohibet aliquid non habere in sua natura causam alicuius, quod tamen habet illud ex alia causa: sicut grave non habet ex sua natura quod sit sursum, tamen grave esse sursum, non includit contradictionem; sed grave esse sursum secundum suam naturam contradictionem includeret.” De Unitate Intellectus , c. 5

So, for a heavy body to be up is not incompatible with its nature. What would be incompatible in this way would be for the heavy body to lack from its nature the disposition to be down, when nothing forces it to be up. Clearly, when something that is involved in the nature of the thing is merely dispositional, then there is no contradiction involved in the fact that a powerful external agent can overcome this natural disposition, and can force the thing in question to be in a way in which it would not be, were it not for the contrary action of this agent:

“Quod autem aliquid deficiat a sua naturali et debita dispositione, non potest provenire nisi ex aliqua causa trahente rem extra suam dispositionem, non enim grave movetur sursum nisi ab aliquo impellente, nec agens deficit in sua actione nisi propter aliquod impedimentum.” ST1 q. 49, a. 1.

So a powerful agent can overcome what is dictated by the thing’s natural disposition in that it may force the thing to have an actual property which without the influence of the agent it would not have. However, if the disposition itself is involved in the thing’s nature so that eliminating that disposition would destroy the thing’s nature, then this disposition is inseparable from the thing, even by an infinite power; for the separation in the sense that the thing would still exist while its nature is destroyed would involve the contradiction that the thing should both exist and not exist, since the destruction of the thing’s nature is nothing but the destruction of the thing itself.

Now applying these considerations to the case of the accidents maintained by divine power without their subjects, we can explicate St. Thomas’s solution in the following manner. When the substance of the bread is converted into the body of Christ, and thereby it ceases to be the subject of its accidents, the accidents can be maintained in their existence by divine power in pretty much the same way as heavy bodies can be kept in place by a force pulling them upwards even when they lose their support, as for example the roof of a house could be kept up in the air by a helicopter even if the walls that supported the roof were destroyed by an earthquake. Clearly, such a situation would not entail any contradiction whatsoever. The roof would not

285

cease to be a heavy body, and thus it would still preserve its natural disposition to fall when it is unsupported, even if it actually does not fall, because of the force keeping it from following what is demanded by this disposition. Indeed, that it did not lose this disposition is clearly demonstrated by the fact that it still needs the force to keep it from falling: had it lost this disposition, it would not need the force to keep it from falling, for to have this disposition is precisely to behave in the way demanded by the disposition, provided that nothing interferes, and thus not to have it is not to behave in the way demanded by the disposition, even when nothing interferes.

But the same goes for the accidents without their subject in the miracle. Given the fact that they are accidents, they have a nature that involves a disposition demanding that they should exist in a subject. Therefore, anything that would take away that disposition would destroy that nature, and thus the accident itself, whence to posit an accident in being without that natural disposition would be to posit contradictories. However, this does not mean that the accident cannot be preserved in its being, leaving that natural disposition intact and yet without the actual realization of what that disposition demands, given the fact that the actual demand of that disposition can be overcome by a greater power.

There are, therefore, two crucial points in Aquinas’s solution. The first is a negative point, stating that the usual definitional formula is not to be understood as defining what kind of entities accidents are in terms of specifying what sort of act of being such kind of entities must actually have. The other is an affirmative point, which states that the customary formula should be understood as defining accidents by specifying their nature in terms of a disposition which demands a certain kind of being. To have that disposition involved in the nature of thing, however, means only that if nothing interferes with the natural operation of the thing, then the thing will have what is demanded by that disposition, namely, an inherent act of being. But this is not incompatible with the case when there is a powerful agent that does interfere with the natural operation of the thing and provides it with a non-inherent act of being.

The position of the Anonymous Physics-commentary

Now if we turn to the relevant passage from the anonymous Physics-commentary, we find the exact opposite position:

“Ad tertium dicendum, quod deus potest omne, quod habet rationem possibilis simpliciter. Est autem possibile de aliquo solum quod non est contrarium suae rationi. Cum ergo non esse in subiecto sit contrarium rationi accidentis, non habet rationem possibilis, sed impossibilis contradictionem implicantis, cum ratio accidentis secundum Philosophum sit non tantum, ut aptum natum sit esse in subiecto, sed ut sit in subiecto.”3

The author here obviously rejects both what I identified as the negative and what I identified as the affirmative points of St. Thomas’s solution. On the one hand, he denies that what belongs in the nature of an accident would be simply an aptitude, a disposition to have an inherent act of being. On the other hand, he asserts that to be in a subject belongs to the ratio of accident, which amounts to the claim that what is signified by the definition of accident specifies precisely the kind of esse an accident has to have, namely, an act of inherent being, esse in subiecto.

3 Ein Kommentar zur Physik des Aristoteles aus der Pariser Artistenfakultat um 1273, ed. A. Zimmermann, Berlin: De Gruyter, 1968, p. 25.

286

This denial of Aquinas’s solution would then lead us back to the original problem, namely, the apparent impossibility of the miracle. The next sentence, however, does concede some sort of inexplicable possibility for the miracle, to be held by faith alone.

Nec apparet aliqua, quae aliquando sunt in subiecto, aliquando exsistere sine subiecto lumine rationis naturalis, licet per miraculum credendum sit hoc posse fieri.4

Nevertheless, the author simply does not tell us whether there is a resolution of the contradiction resulting from his position, and if so, what that resolution would be, or whether perhaps we should hold the possibility of the miracle by faith despite the (alleged) fact that it involves an irresoluble contradiction.

The next step in the author’s argument is to deny the principle that serves as the basis for upholding the possibility of the miracle, once it is assumed that for an accident to exist without a subject does not involve a contradiction, namely the principle that whatever a superior agent can produce with the cooperation of an inferior agent, it can produce also without this cooperation:

Substantia enim est causa materialis accidentis, et hoc modo deus non <est> causa accidentis Non oportet autem, si deus potest facere aliquem effectum mediante eius causa, causa aliqua, quae est illius forma vel materia, quod possit illum effectum facere per se. Tunc enim contingeret, quod exsistentia solius dei exsisterent omnia entia in propriis eorum naturis et secundum eorum proprias rationes. Non oportet etiam, quod illud, quod potest causa primaria efficiens mediante secundaria efficiente, quod illud possit sine secundaria, eo quod effectus non fit sine causa ad effectum illum determinata potius quam ad oppositum. Primaria autem sic per secundarias determinatur.5

Siger of Brabant’s Position

In the authentic commentary of Siger of Brabant on the Liber de Causis we find the same rejection:

“Unde sophistice quidam arguunt credentes naturali ratione ostendere et demonstrare quod causa prima possit facere quod accidens existat sine subiecto illius accidentis, propter hoc quod causa prima est causa omnium causarum mediarum accidentis inter ipsam et accidens, et ideo sola facere possit quod existat accidens, quamquam accidenti nulla existat aliarum causarum accidentis; et cum substantia sit aliqua causa accidentis, poterit facere ut sine substantia subsistat accidens. Ratio, ut manifeste apparet, deficit secundum ea quae prius dicta sunt. Ut tamen sane intelligatur, sciendum est quod primariam causam posse facere accidens existere sine subiecto illius accidentis confitemur. Hoc tamen est non propter istam rationem: est enim oratio conclusa peior seipsa non conclusa.”6

But in this text Siger does not go as far as to claim the contradictoriness of the assumption that an accident should exist without a subject. All he denies here is the principle concerning the hierarchy of agents. Accordingly, he does not deal here with the issue of whether the definition of accidents involves the type of being they should have, and whether on account of this it would be contradictory for an accident to exist without a subject, as the author of the Physics-commentary explicitly states.

4 Ibid. 5 Ibid. 6 Les Quaestiones super Librum de Causis de Siger de Brabant, ed. Marsala, A., Publications Universitaires: Louvain, Béatrice-Nauwelaerts: Paris, 1972, p. 41.

287

However, we do have some evidence that this would quite fairly characterize Siger’s view on the matter. In his commentary on the Metaphysics, after vehemently denying the thesis of the real distinction between essence and existence in the creatures as stemming from an error of Avicenna’s,7 he insists in his reply to one of Aquinas’s arguments for the real distinction that esse need not multiply in beings because of something added to it, but rather it is multiplied on account of its ratio essendi, the diversity of which in different kinds of beings is entailed by Aristotle’s claim that ens cannot be a genus.8 However, in the question directly addressing this latter issue, he explicitly concludes that the reason why ens cannot be a genus is that the ratio essendi of accidents, being a non-absolute ratio, cannot be the same as the ratio essendi of substances, which is an absolute ratio.9 In a different context — most notably in the context of the question whether the intellect can be both subsistent and inherent — he also insists that these rationes essendi are so incompatible, that they cannot belong to the same thing.10 But also in the context where he directly addresses the question of what sort of quiddity accidents have, he explicitly asserts: “accidens non habet rationem essendi nisi in habitudine ad substantiam, et ideo definiri non potest sine substantia”.11 Now the implication of this, along with Siger’s previous identification of essence with existence, is clearly that the same thing, while remaining the same thing, cannot have one ratio essendi after the other, and thus, an accident, having the ratio essendi of an inherent being, cannot, while remaining what it was, an accident, have later on the ratio essendi of a subsistent being, on pain of contradiction.

7 Siger de Brabant: Quaestiones in Metaphysicam, (ed. A. Maurer), Louvain-la-Neuve: Éditions de l’Institute Supérieur de philosophie, 1983, Introductio, q. 7, p. 34, ll. 30-40. 8 “Ad aliud, quod similiter fuit medium Thomae (ScG, II, 52), dicitur quod esse per se subsistens, quod est maxime proprie esse et actualissimum, illud est unum tantum, scilicet Esse Primum. Esse tamen posterius et causatuum, quod accedit ad naturam potentiae, non est unum sed plura, secundum quod sunt plura entia causata. Et tu arguis quod esse illud, secundum quod esse est, non est multiplicatum; ergo multiplicatur per aliquid cuius est esse illud. Et dicendum quod bene argueres si esse in omnibus entibus causatis esset unius rationis: tunc enim non multiplicaretur nisi per aliquid additum sibi. Nunc autem non est unius rationis in omnibus entibus. Et ideo ex sola multiplicatione rationis essendi multiplicatur esse in entibus. Nec potest ratio essendi multiplicari per aliquam rationem sibi additam, quia non est aliqua ratio sibi addita. Omnis enim ratio est essendi ratio. Ex hoc enim probat Aristoteles IIIo hujus quod ens non potest esse genus.” Ibid. pp. 36-37. 9 “Dico ad hoc quod ens non significat aliquam rationem unam contractam ad substantiam et ad accidentia, sed significat rationem diversam in substantia et accidentibus. Quod probatur sic. Omnis enim ratio quam significat aliquod nomen vel est ratio absolute dicta, vel est ratio dicta per ordinem ad aliud, quia nulla potest esse his communis. Si igitur ens significet aliquam rationem unam in substantia et accidentibus, vel illa erit ratio absolute dicta vel erit ratio dicta per habitudinem ad aliud. Si primo modo, tunc ens non praedicabitur de accidente, cum accidentis non sit ratio essendi absolute dicta. Si secundo modo, tunc ens non praedicabitur de substantia, cum substantiae non sit ratio essendi dicta per habitudinem ad aliud. Relinquitur igitur quod ens non significet aliquam rationem unam in substantia et accidentibus.” Ibid. lb 33, q. 12, p. 101. 10 “Praeterea, alia est ratio essendi formae materialis et compositi seu formae per se subsistentis. Ratio enim essendi formae materialis est secundum quam est aliquid aliud, ut ratio compositionis est secundum quam habet esse compositum, et ratio figurae secundum quam habet esse figuratum unde ratio essendi formae materialis est quod sit unita alii. Ratio autem essendi compositi vel formae liberatae a materia est quod sit ens per se et separate, non unum ens cum alio. ... Et sunt istae rationes essendi, qua aliquid habet esse unite ad materiam et qua aliquid habet rationem subsistentis per se et separate, oppositae adeo ut eidem inesse non possunt. Unde anima intellectiva non potest habere rationem per se subsistentis et, cum hoc, unum facere cum materia et corpore in essendo." Siger of Brabant: De Anima Intellectiva, in: Bazán, B.: Siger de Brabant, Louvain-Paris, 1972, pp. 79-80. Cf. also St. Thomas's De Unitate Intellectus nn. 37-38. 11 Siger de Brabant: Quaestiones in Metaphysicam, (ed. A. Maurer), Louvain-la-Neuve: Éditions de l’Institute Supérieur de philosophie, 1983, lb. 7, q. 10, p. 341.

288

Conclusion

But even without going into the further details of Siger’s position, I think the foregoing considerations allow us to draw some general conclusions, which give rise to a number of interesting questions in the broader context of this inquiry.

First of all, as from the analysis of Aquinas’s solution and from the anonymous Physics-commentary’s rejection of this type of solution it became clear, the way an author handles the problem generated by the requirement of positing the miraculous non-inherent existence of accidents is primarily dependent on his conception of what the Aristotelian description of accidents signifies. To be sure, the issue here is clearly not a matter of mere semantics. For the question is not whether by a clever reinterpretation of our terms we can turn an originally contradictory claim into a non-contradictory one. The question rather is whether in keeping with the original intention of the Aristotelian description one is forced to conclude that attributing non-inherent existence to accidents is contradictory or not.

But then this naturally leads to the further question whether the original Aristotelian intention should be interpreted as defining accidents in terms of specifying the kind of act of being these entities have, or rather as defining them in terms of their nature, which, being the kind of nature it is, demands inherent existence. And it is at this point that the question will directly attach to the general problem of the real distinction between essence and existence. For given that a quidditative definition signifies the essence of the thing defined, the question in fact is whether the significatum of the definition in this thing will be the same as, or distinct from, what the term ‘ens’ or ‘esse’ signifies in the same thing, and thus whether the definition directly provides a specification of the kind of esse the thing has, or rather only a specification of the thing’s nature, which then would further determine the kind of esse it requires.

Furthermore, through these considerations the issue is also closely related to the question of the analogy vs. univocity of being. In any case, from Siger’s discussion in the Metaphysics-commentary it seems to be quite clear that he regards the difference between the rationes essendi of substance and accident as the ultimate foundation of the claim that the notion of being is analogous, whence it cannot be a genus.12

By contrast, if one were to allow that the esse of an accident is an act of being in the same sense as the act of being of a substance is, regardless of whether the accident actually inheres or not, then the contradiction would not even pose a threat, for then the miracle would simply consist in “detaching”, as it were, the relation of actual inherence from the accident in question, while maintaining its unchanged being in its unchanged nature (which actually may be the same thing), since this unchanged nature accounts only for the aptitude to have this relation or mode of inherence “attached” to it, if no greater power “detaches” it.

Now this seems to be Scotus’s approach to the matter.13 As we could see, in the Metaphysics-commentary Siger established the accidents’ absolute dependence on substance on the basis of rejecting what he took to be Avicenna’s error in interpreting Aristotle. On the other hand, it was

12 Cf. text in n. 8. 13 In any case, this is the conception of the inherence of accidents he advances in his Metaphysics-commentary. Joannis Duns Scoti Opera Omnia, t. 7, Quaestiones subtilissimae super libros Metaphysicorum Aristotelis, Parisiis, apud Ludovicum Vivès, 1893, lb. 7, q, 1, pp. 350-355.

289

precisely Avicenna’s “essentialism” that allowed Thomas to interpret this dependence in terms of an aptitude to inhere rather than in terms of actual inherence. But Aquinas’s solution is also radically dependent on his thesis of the real distinction and on his doctrine of the analogy of being, both of which are rejected by Scotus.

So an interesting historical-hermeneutical question stemming from these considerations is the following: exactly how could this new type of solution emerge? What conceptual changes took place between Thomas’s and Scotus’s time that allowed such a radical reinterpretation of the fundamental Aristotelian distinction between substance and accident?

I think it is clear that we can learn a great deal concerning how Scotus’s approach emerged from a further careful study of these issues in the works of such “intermediary” figures as for example Giles of Rome or Henry of Ghent, both of whom seem to have moved in the direction of identifying accidents with their act of being, while treating their inherence as an attached modus, which can easily be “detached” by divine power.

But the further, really intriguing lessons we may learn from such investigations concern the broader issues I indicated at the beginning of this talk. For what is really interesting in the apparently ever greater “autonomy” that accidents seem to have gained in the discussions of the theologians of the late 13th and early 14th centuries is that the semantics of the discourse concerning these easily “detachable” accidents is very much like the semantics of the discourse concerning simple substances. But this, it would appear, might provide a perfectly good motivation for attempts to simplify the semantics of discourse concerning all mundane entities along these lines, thereby directly pointing the way toward the great “semantic schism” of the later middle ages, caused by the emergence of 14th-century nominalism.

290

Table of Contents

LOGIC AND METAPHYSICS, MEDIEVAL AND MODERN ...................................3 Approaching Natural Language via Mediaeval Logic.....................................................4

Old Directions in Free Logic: Existence and Reference in Medieval Logic ................22

Latin as a formal language: Outlines of a Buridanian Semantics..................................42

Contemporary “Essentialism” vs. Aristotelian Essentialism.........................................69

Aquinas’ Theory of the Copula .....................................................................................85

ONTOLOGICAL ALTERNATIVES VS. ALTERNATIVE SEMANTICS IN MEDIEVAL PHILOSOPHY..........................................................................................99

Ontological Alternatives vs Alternative Semantics In Mediaeval Philosophy............100

The Changing Role of Entia rationis in Mediaeval Semantics and Ontology: A Comparative Study with a Reconstruction ..................................................................120

Ockham’s Semantics and Ontology of the Categories ................................................144

Buridan’s Logic and the Ontology of Modes ..............................................................162

‘DEBEO TIBI EQUUM’: A Reconstruction of the Theoretical Framework of Buridan’s Treatment of the Sophisma .........................................................................177

THOMISTIC SEMANTICS AND METAPHYSICS.................................................189 The Semantic Principles Underlying Saint Thomas Aquinas's Metaphysics of Being190

Aquinas on One and Many ..........................................................................................235

Man = Body + Soul: Aquinas’s Arithmetic of Human Nature....................................250

Thomas of Sutton on the Nature of the Intellective Soul and the Thomistic Theory of Being............................................................................................................................263

Natural Necessity and Eucharistic Theology in the late 13th century.........................280