Santambrogio. Meinongian Theories of Generality (Article)

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Meinongian Theories of GeneralityAuthor(s): Marco SantambrogioSource: Noûs, Vol. 24, No. 5 (Dec., 1990), pp. 647-673Published by: WileyStable URL: http://www.jstor.org/stable/2215808 .

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Meinongian Theoriesof GeneralityMARCO SANTAMBROGIO

UNIVERSITYF BOLOGNA,TALY

Facing the problem of making semantic sense of some complex ex-pression in ordinary language, one can sometimes adopt the "easy"way out claiming that the expression is not to be taken at face value.Then one feels free to appeal to some purportedly deeper level ofanalysis, where no urge is felt, for one reason or another, of assigningany one semantic value to it. E.g., one can claim that what appearsto be a complex but unitary expression is such only at the surfacelevel, whereas it is to be paraphrased away at the level of logicalform. Being entirely faithful to ordinary language, i.e., keeping theappeal to the surface/depth dichotomy to a minimum, is usuallymuch more difficult. Meinong, it seems to me, tried to adopt thelatter strategy, while Russell gave an outstanding example of theformer in his theory of definite descriptions. In this, however, asin so many other ways, he was simply following Frege.There are sentences containing definite descriptions for whichRussell's analysis obviously fails, namely those such as "The whaleis a mammal", "The horse is a four-legged animal", etc., whereno individual whale or horse is meant in particular. Russell, however,did not have to bother with them: in fact, Frege had already dealtwith them and the way he had done so is the paramount exampleof the strategy of paraphrasing away. As we all know, the sentence"The horse is a four-legged animal" is taken by Frege to mean"All horses (or, all normal specimen of horses) are four-legged".The expression "the horse", as a whole, has disappeared from logicalform and so has the need of making semantic sense of it and assigningit some entity or other. In fact, the idea of having "indefinite"entities play this role was ridiculed by Frege (see, e.g., "What isa Function?") just as much as he did in the case of "variable"NOUS 24 (1990) 647-673? 1990 by Nous Publications

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648 NOUSobjects ("indefinite" and "variable" or "arbitrary" objects actuallyamount to the same thing).It is not at all obvious, however, that the sentences "The horseis a four-legged animal" and "All horses are four-legged" areequivalent in meaning. For one thing, the latter seems to requirethat we somehow run through all the individual horses, in orderto see that it is true-an idea which is certainly absent from theformer and which raises a number of difficult problems of its own,due to the possible infinity of the objects we might have to runthrough. I have considered these matters at length elsewhere (seemy "Frege on variables and variable objects"). This is one of thereasons (the most compelling one, to my mind) why some amongFrege's contemporaries, notably Meinong, Twardowski and Erd-mann decided to remain faithful to ordinary language and continuedto think that there must be some entity corresponding to the ex-pression "the horse". After all, this was entirely in keeping withthe tradition in logic which, in its Platonic quarters at least, didacknowledge such universal entities as the horse(and what is the useof having such entities, if it is not to account for general, or univer-sal propositions?)It must be emphasized that Meinong's incomplete objects, asthe referents of definite descriptions in the "generic" use, are justthe "indefinite" or "variable" objects that Frege tried to ridicule,as this point has not received much attention in the literature.However, in order to illustrate the details of the doctrine of generalobjects as referents of such expressions as "the horse", I shall notdiscuss Meinong, despite the fact that he is the best known figurein this tradition. A much clearer and more compact statement ofthat doctrine is to be found, e.g., in Twardowski's book, On theContentand Object of Presentations.1

After sketching in the briefest outline Twardowski's version ofthat doctrine, I shall defend it and present the leading ideas of aformal semantics for general objects.TWARDOWSKI'S THEORY OF GENERAL OBJECTS.

That definite descriptions in the generic use refer to general objectsis stated by Twardowski in so many words: "The substantive inconnection with the definite article is the genuine name for the generalobject; in languages which have lost 'the definite article, its nameis the substantive without an addition" (Twardowski, 1977: 100-101).The main example he considers is the familiar one of "the triangle",going back to Aristotle. Now, what kind of entity is the triangle?It is a Platonic idea, it is "a group of constituents which are common




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MEINONG AND GENERALITY 649to several objects" and it is a whole that belongs together and sub-sumes individual objects (ibid.).2 By means of it one can conceivethat which is common to all objects of individual presentations oftriangles (i.e. all individual triangles) and thereby grasp all trianglesin a single mental act: "If one admits this, as one surely must,then one concedes also that the object of a general presentation [i.e.a general object] is different from the objects of individual presen-tations which are subsumed under it" (p. 99). Of any one amongthe latter one can affirm, e.g., that it has an area of, say, two squareinches, a right angle, and so on. But the general presentation ofthe triangle is neither the presentation of a right-angled triangle,nor that of a triangle with a certain colour, or area, or location.Similarly, Meinong stated at some point that the idea "fish" can-not intend the class of all fish, since it intends not even some fish,much less the totality of all fish; it intends a fish, a single fish, butnot any particular fish (see Grossmann, 1974: p. 42). Most impor-tant is the statement that such sentences as "The triangle has innerangles summing to 180 degrees" and "All triangles have inner anglessumming to 180 degrees" cannot be equivalent in meaning: "Thisfollows, among other things, from the fact that one can have a generalpresentation also in those cases where the number of objects of thecorresponding individual presentations . . . is infinitely large"(Twardowski, 1977: 98).Plainly, Twardowski (just like Meinong) is here echoing Locke'stheory of general and abstract ideas. The following passage is clearlymeant as a defence of Locke from one of Berkeley's attacks:

Nobody can intuitively conceive of a "general" triangle; a trianglewhich is neither right-angled, nor acute-angled, nor obtuse-angledand which has no colour and no determinate size; but there existsan indirect presentation of such a triangle as certainly as there existsindirect presentations of a white horse that is black, of a woodencannon made of steel, and the like. (Twardowski, 1977: 101)Now, just like its Lockean version, this theory underwent a numberof objections. Lesniewski, one of Twardowski's pupils, found at thebeginning of his philosophical career a simple argument that conclu-sively established, he thought, the absurdity of it. The followingprinciple, he argued, must hold of general objects: each one of themhas exactly those properties which are common to all individual objectsrepresented by it. It can be stated formally thus:(*) Q(the P) -. (x)(Px -1 Qx)-here "Q" and "P" are any pair of predicates and "the P" isthe name of the general P. This principle is not explicitly stated,




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650 NOUSto the best of my knowledge, by Twardowski (or Meinong), butit is not an implausible way of expressing the idea that a generalobject is what is common to all the subsumed individuals. Unfortunatelya simple argument shows that (*) leads to absurdities.3 Lesniewskiwas impressed by his discovery (which apparently prompted themistrust in informal philosophical arguments that was to be a per-manent feature of his thought). However, there is no need to beoverwhelmed by it-for one thing, it is not at all obvious that (*)is the only way of formally stating the intuitive principle-e.g. theremight exist a restricted but otherwise plausible version of it. Weshall come back to this.Among Twardowski's critics we also find Husserl. In the secondof his Logical Investigations, he acknowledges 'general objects' anddistinguishes them from ordinary individual objects; he also carefullydistinguishes theform 'The A' from the form 'All the A's' on logicalgrounds and is prepared to take the former-'The Red', forexample-as referring to some general object. However, he forcefullyclaims that Twardowski's theory runs into the same difficulties asLocke's absurd theory of the general triangle. The following passageis meant as a criticism to both of them:

Locke should, above all, have reminded himself that a triangle issomething which has triangularity, but that triangularityis not itselfsomething that has triangularity. The universal idea of triangle, asan idea of triangularity, is therefore the idea of what every triangleas such possesses, but it is not therefore the idea of a triangle. Ifone calls the general meaning a concept,he attributeitself the concept'scontent,every subject having this attribute the concept's bject, henone can put the point in the form: it is absurd to treat a concept'scontent as the same concept's object, or to includea concept's contentin its own conceptual extension* [Husserl's Footnote*: I should nottherefore think it correct to say with Meinong (Humestudien,, 5)that Locke confuses the content and the extension of the concept].(Husserl, 1970, II, $11, pp. 359-60, vol. 1)

(Husserl's terminology is clearly different from Twardowski's). Now,it is certainly possible to frame a theory of attributes along theselines, that is, to take e.g. the attribute of triangularity as an abstractobject, whose properties are different in kind from, though relatedto, those of individual triangles. Theories of attributes have beendeveloped in various forms and, although it is by no means a trivialtask to construct such a theory, nobody ever supposed that it isan intrinsically incoherent one-contrary to what happens withgeneral objects. But Husserl is simply wrong in confusing Twar-dowski's or Locke's general triangle with triangularity. We shalllater expand on this distinction. (He is also wrong in assuming that




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MEINONG AND GENERALITY 651the absurdity of Locke's general triangle has been proved conclusivelyby Berkeley).None of these criticisms is fatal to the theory we are interestedin. Similarly, there is no reason to be overwhelmed by Berkeley'sobjections to Locke, or by Frege's arguments against a closely relatedcircle of ideas or by David Lewis' sarcasm aimed at the universallygeneric pig of "the dark ages of logic" (see Lewis 1970: 52). I shallhere try to defend the doctrine of general objects, mainly by exploringthe philosophical foundations of a formal semantics for them.

FINE'S SEMANTICS.In modern logic, apart from Russell's The Principles of Mathematicsthere is only one attempt, to the best of my knowledge, at vindicatingthis theory of generality by giving it a formal semantics meetingmodern standards of rigour. It is given by Kit Fine, in Reasoningwith ArbitraryObjects, 1985. I shall briefly sketch it here and thenI shall explain why it seems to me that, useful as it is in other respects,it is not entirely appropriate as an explication of the Twardowski-Meinong theory. After that, I shall explore an alternative approach,which is more in their spirit.

First, Fine gives us a domain I of ordinary individuals supportinga standard model for first-order language L. Second, he supplementsthe domain I of individuals with a disjoint set A of arbitraryobjects-A-objects, for short. A-objects are equipped with a partialordering relation


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652 NOUSobjects which pre-Fregean logicians had been so fond of and whichwere afterwards superseded by the quantifier/bondage conceptionof the variable). The truth definition unambiguously determines thelogical behaviour of A-objects. Let F(a,, . . . ,ad be a formula inwhich those symbols for A-objects occur as shown within parentheses.The formula is true in a generic modelM* for arbitraryobjectsiff allformulae F[al/f(a,), . . . an/f(an)J, obtained by substituting thenames of A-objects with the names of their respective images alongeach one of the partial functions f in V, are true in the standardfirst-order model M, built on the domain I of ordinary individuals.The intuitive idea is that an A-object has precisely those propertiesthat all individuals in its range have-assuming that it is alreadyknown what it is for an individual to have a property.A full blown semantics can be given along these lines. It answersquite a few of the usual objections brought against Locke, in particularBerkeley's. In a nutshell, Berkeley noted that, if there existed suchan object as the general or arbitrary number, then it would haveto be either odd or even, since all individual numbers have the complexproperty of being either odd or even. But it cannot be odd, fornot all individual numbers are odd and it cannot be even for thevery same reason. It then follows that an arbitrary object can havea disjunctive property without having either of the disjuncts. It wasthought that this in itself was fatal to Locke. Fine however neatlyaccounts for this. Any formula of the form F(a)v -F(a)-a being anyA-object-is true, since we apply the clause for disjunction in theordinary truth definition only after projecting a onto the ordinaryindividuals in its range: no matter how we project it, the individualsthus obtained all satisfy any instance of the Excluded Middle. Itdoes not follow from this that either F(a) or -F(a) holds.In deriving his conclusion, Berkeley appeals to the principle ac-cording to which a general object satisfies exactly those propertieswhich are common to all individuals in its range. Fine calls thisthe Principle of Generic Attribution, but of course he does not assumeit in Lesniewski's form: a different form of it is incorporated intothe truth definition itself, stating that an A-object has a propertyiff all individuals in its range have it.Whatever its merits on other grounds, however-in particular,as a defense of Locke-it is debatable whether Fine's semantics canbe taken as an explication of the Twardowski-Meinongian theory.As Fine himself acknowledges,4 the fact that A-objects are constructed"from below", in terms of ordinary individuals, runs against oneof the leading ideas of both Twardowski and Meinong. Both of thembelieved that an individual is a complex (a collection, a bundle)of other entities-whether such primitive entities are properties, par-




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MEINONG AND GENERALITY 653ticularized properties or instances, or still other entities, we can leaveopen for the time being. But in Fine's semantics it is the other wayaround: in a sense, A-objects are complexes of individuals; moreover,sentences concerning ordinary individuals must already have beenevaluated before we can start evaluating those concerning A-objects.The dependence on ordinary individuals is also responsible forsome perplexing features of Fine's arbitrary objects. Consider firstthe clause 'Let x andy be two real numbers' introducing, accordingto Fine, two A-objects. This is already puzzling, for the clause seemsto refer to two independent objects having the same range. Sincethe properties of independent A-objects are entirely fixed by theproperties of the individuals in their respective ranges, we face achoice here: either we countenance indiscernible but distinct objectsor we deny that they are independent after all. Fine chooses thelatter: what is really introduced by that clause are not two indepen-dent arbitrary real numbers, but the arbitrary ordered pair of reals-xandy being its first and second component respectively, which areclearly distinct as A-objects. Now the problem is, if we always followthis strategy of positing arbitrary n-tuples instead of n independentA-objects, then as soon as we introduce two syntactically distinctnames for arbitrary objects, we immediately know that we have twodistinct objects. There will be little to discover about such objects,if their identity or their diversity are so easily ascertained. If, onthe other hand, we cannot always follow that strategy, then we needsome criterion to tell us when it is: but such a criterion is likelyto be what was needed in the first place to tell us when two arbi-trary objects are distinct. Be that as it may, let us go back to theclause 'Let x andy be arbitrary reals'. As it is ordinarily used, itdoes not exclude that x andy be the same (ordinary) number; butit does not exclude that they be distinct either. It then follows thatthe equality x =y ought to turn out to be neither true not false ac-cording to the truth definition. And yet, if x and y are, as Finemaintains, distinct, it is definitely false that they are identical andthe identity statement ought to turn out false.In fact one can even doubt that the equality has here its usualmeaning. For instance, there is nothing in Fine's definitons to preventa situation like this to occur in a model: two arbitrary objects, aand b are such as to make a = b true (for every in V projects themboth onto the same individual) and yet they are two distinct en-tities. Moreover, consider such formulae as x = i and x = b, i beingan individual and b an A-object. An A-object satisfying the formermust be distinct from i (as the domain of individuals is disjoint fromthe set of A-objects); and an A-object satisfying the latter can bedistinct from b, as in the case b is independent.




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654 NOUSIn connection with problems such as these, Fine has suggestedthat two relations of equality must be distinguished, one relating

ordinary individuals while the other relates A-objects. Thus, twoA-objects a and b can be distinct as A-objects without forcing a = bto be false (' =' being the relation defined on individuals). Evenif this distinction could solve all the problems mentioned abovewhich is not certain-I find this move perplexing. To posit two kindsof properties and relations, one for arbitrary objects and the otherfor ordinary individuals, is not in itself objectionable (indeed, it isin the Meinongian spirit). But how could there be two relationsof identity,given that identity is the (unique) relation holding betweenany one object and itself? Surely, there are different sorts of criteriaof identity: abstract entities, e.g., cannot be distinguished in thesame ways as material objects, and natural kinds are distinguishedin still others. But the identity relation itself does not thereby change.I have no doubt that all these puzzles can be answered. Butin any case the difference in philosophical perspective between Fine'ssemantics and Twardowski's and Meinong's theory of general objectsis such that it may be worth trying a different route.

A DIFFERENT PROPOSALLet us first of all clarify intuitively the notion of a general object,following the Meinong-Twardowski tradition. This traditionacknowledges that general objects can be "given" to us prior tothe individuals which they subsume. Furthermore, as Platonic ideas,they are intuitively arranged in an order relation, according to theirgreater or lesser generality: the horse is, as a general object, lessgeneral than the mammal, but more general than the white horse.Plato's "definitions" of the sophist in The Sophist (219 A ff.) arejust meant to explore some fragments of that relation, which weshall indicate by '?


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MEINONG AND GENERALITY 655tic operations map general objects into more specific ones. This hasnot been systematically studied by modern logic.5 We shall not gointo it; instead, we will take the order relation as given, withoutconsidering how; in other words, we will start with a domain ofgeneral objects, A, together with an order relation


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656 NOUSThis is then the first of the principles we shall take as characterizing,in purely structural terms, general objects:

(A) The P is P.Here 'P' is any unary predicate and 'the P' is the correspondingdefinite description in the generic reading. Unfortunately, as weshall see, (A) is too general as it is and needs some qualification.Meinong, incidentally, assumed it in its present, unrestricted form,according to which even the round square, e.g., is square and round.In order to formulate our second principle, let us consider theorder relation again. There is a whole class of properties which arehereditary in the sense that, whenever a general object has any oneof them, all the less general objects also have it. E.g. if the generaltriangle has inner angles summing to 180 degrees, then the sameholds of the general rectangular triangle, of the general isoscelestriangle, etc. This can be expressed as follows:(B) For every general objects a and b, such that a>> b, and everyformula F(x) not containing symbols for relations, if F(a) thenF(b).This principle is in need of qualification. For one thing, there areproperties that clearly do not satisfy it: one can, e.g., think of thecitrus without thinking of the lemon, the orange, the tangerine,etc.-one may not even be aware that tangerines exist. Somethingsimilar holds for belief and there is a sense in which one can saythat it is possible for the general triangle to be isosceles, whereasthis is clearly impossible for the general scalenon triangle. I conjecturethat the properties for which (B) fails are precisely the intensionalones. Incidentally, this may give us an independent criterion forintensionality. We shall assume that (B) holds for all the extensionalproperties.On the other hand, suppose that, for some given a, all objectsbi such that bi


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MEINONG AND GENERALITY 657ment 'The corvus s attached to its offspring'. We have two generalobjects here: the corpus and the offspring of the corpus, which arerelated to each other. Now, principle (C) invites us to consider allthe objects less general than those mentioned in the statement; butwe cannot consider those that are less general than the corpus in-dependentlyrom those that are less general than the offspring of thecorpus, or we might end up asserting that the corpuscorax loves theoffspring of the corvuscornix,which is false. That the corpus s attach-ed to its offspring means that the corpuscoraxis attached to the off-spring of the corpus corax, the corpus cornix to the offspring of thecorpuscornix, and so on. In Fine's terminology, what we have hereis a case of dependence. The way I propose to deal with dependenceis, however, different from Fine's.Fine has a special order relation, < (utterly unrelated with our


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658 NOUSvariable ranging over shifts. Then, given any n-tuple , its admissible refinementsare just the n-tuples of the form< S(a1), . ,S(an) > . Let I be the identical shift: I(a) = a, forevery a.This is then our final formulation of the second principle:(D) For all extensional F(xi, . . ., xJ, F[xi/ai, . . . x/naa] iffF[xi S(a, . I xn/S(an)], for every shift S, different from theidentical shift I.This is comparable with Fine's Principle of Generic Attribution,but it differs from it if only because it does not even mention in-dividuals. (D), like (A) above, sharply distinguishes general objectsfrom attributes, for there is no reason to think that it applies tothe latter, not even with respect to a restricted class of predicates.I have proved (in my "Generic and Intensional Objects" in Syn-these, 1987) that a full formal semantics can be given satisfying bothprinciples (A) and (D). The definition of reference and truth satisfiesall the usual Tarskian requirements. The denotation of a term suchas THETAx.F(x) is set as the join (in the lattice theoretic sense)of all general objects satisfying F(x), and it proves that this objectitself satisfies F(x), provided it is different from the minimum ob-ject in the lattice. The minimum must exist, since the lattice is assumedto be complete; such an object can be thought of as the overdefined,impossible or otherwise non exemplified general object, the roundsquare and the golden mountain. As I do not know how to separatethe analytic from the synthetic, I do not distinguish the round circle,which cannot exist because of its "inner" incoherence, from thegolden mountain, which might exist for all our logical theory is con-cerned, but whose existence is excluded on other grounds, e.g. byour physical or economic theories and by (external or global) in-compatibility with other possible general objects. Were a generalmethod found for distinguishing the golden mountain from the roundsquare, a whole class of distinct impossible objects can be posited,instead of the unique one-to be written as OA-which I presentlyconsider. Accordingly, principle (A) is satisfied in a restricted form:the F is F, provided that it is not (one of) the impossible object(s).That (D) is also satisfied is an immediate consequence of the factthat that semantics really amounts to a special case of Beth seman-tics for intuitionistic logic. To have an idea of why this is so, con-sider that it is easy to order the set of shifts on the general objects;the shifts themselves can be thought of as stages of knowledge andtherefore play the role of nodes in a Beth model. The mathematicaldetails are given in my "Generic and Intensional Objects", men-tioned above.




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MEINONG AND GENERALITY 659INDIVIDUALS

In the model we have been considering, no room is left for in-dividuals: the domain of discourse consists entirely of general objects.In the Meinong-Twardowskian tradition, in fact, one cannot takeindividuals as given: rather, they are "constructed" out of abstract"constituents" which have some kind of precedence for us. Suchconstituents do not exist as such; they exist "in" the individuals.Let us try then to introduce individuals in our semantics as par-ticular sets (or bundles) of general objects, and then explain what"'existence" means.As a first step in this direction, let us characterize those propertieswhich are satisfied by just one individual (traditional logic referredto them as species infimae). The task is not quite trivial, as we cannotyet refer to individuals in the definitions at this stage-althoughwe are informally guided by the intuitive idea of an individual. Thereis an indirect way of achieving the same result, however, throughgeneral objects; in other words, we can find a structural conditionon general objects, which can be described without mentioning in-dividuals, characterizing the properties satisfied by just oneindividual.

As I said, the lattice of general objects being complete, it hasa minimum, OA' to be thought of as the round square, or anyother impossible general object. Given two general objects a andb, suppose that there is no other object but OA that is less generalthan both, i.e. a b = OA-take as a, e.g., the square and, as b, theround (figure). Then we say that a and b are incompatible: here isno way of "putting them together" without producing aninconsistency.Let us now think of any definite description in the genericreading, "the man", say, and the general object which it refersto, the (general) man. There are many (individual) men, some short,some tall; no one can be both short and tall. Accordingly, theremust be two incompatible general objects, the short man and thetall man, both less general than the man. It is plausible to supposethat, whenever a predicate is satisfied by several individuals, thecorresponding general object can be made more specific in at leasttwo incompatibleways. It is not so with predicates which are satisfiedby just one individual, "x is presently king of Spain", say.(Throughout this informal discussion, "individual" is used in theintuitive sense, which we must explicate). Then of course the cor-responding general object-the present king of Spain, as a generalobject, which is different from the individual who is king of Spain-can still be made more specific in more than one way: the present




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660 NOUStall king of Spain and the present bald king of Spain, say. But sup-pose that any two such specifications, a and b, are incompatible;aFib = OA. Then either a = OA or b = OA-i.e., either a or b byitself was already impossible. At this point, the reader might wonder:let the present tall king of Spain be a and the present short kingof Spain be b; then presumably aFb = OA and yet it does not ap-pear that either a = OAor b = OA. However, recalling what wassaid above about the golden mountain, it will be seen that, in fact,either a = OA or b = OA: as a matter of fact, it is the presentshort king of Spain which is just as impossible (externally) as thegolden mountain; in neither of these objects is there any inner in-coherence but, on the background of some theory, physical or other-wise, they are incompatible with things which are known to exist(e.g., pictures showing king Juan Carlos being taller than average,assuming some theory as to their reliability).Let us now define a definitegeneral object as any general objecta such that for any b,c such that ba


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MEINONG AND GENERALITY 661it is reflexive only when it is defined. As a matter of fact it almostexactly amounts to Castafieda's notion of consubstantiation (seeCastafieda, 1974: 13).We can now introduce individuals. Of course, it would be aserious mistake to identify an individual with any one definite generalobject. The latter is the object of some presentation, to use Twar-dowski's phrase; but an individual can be presented in many dif-ferent ways. Let us then assume that the ways in which an individualcan be presented form a set; if we hold some version of the so calledbundle theory, we can actually say an individual is the set of itspresentations. More cautiously, we shall define a pseudo-individual(something that is in a one to one correspondence with an individual)as any maximal set of compatible general objects, not containingOA and containing at least one definite general object. We clearlywant to exclude OA since, although we can think of the roundsquare, there is no individual it can possibly present. As to the goldenmountain and Zeus' preferred unicorn, in this world they both col-lapse to OA (which does not prevent us from being able to thinkof them or even hallucinate them) and are therefore no part or presen-tation of any individual; but in other worlds, they can be differentfrom OA and then there will be (pseudo-)individuals to which theybelong. The requirements that a pseudo-individual contain at leastone definite object, follows from the fact that no matter how manygeneral objects we put together, we have no guarantee of capturinga unique individual (in the intuitive sense), unless uniqueness isalready built into at least one of them. E.g., no finite or even in-finite conjunction of such predicates as "being a unicorn", "beingwhite", "being mythological" and so on, is clearly sufficient to singleout a unique individual-similarly for the set of the correspondinggeneral objects. On the other hand, we do achieve uniqueness assoon as we have at least one predicate such as "being Zeus' pre-ferred unicorn" which has uniqueness built in, and to which adefinite general object corresponds.This accounts well, I feel, for Twardowski's claim that "Theobject of the general presentation is a part of the object of a subsumedpresentation, a part which stands in the relation of equality of certainparts of objects of other individual presentations" (Twardowski, 1977,p. 100). Pseudo-individuals bear a clear similarity (together withequally clear dissimilarities) with those bundles of consubstantiatedguises which are the ordinary material objects, according toCastafieda (Castafieda, 1974: 23 ff.) (but in general any pseudo-individual contains infinitely many non-definite objects).There are a few results about this semantics that are worth men-tioning. First, it is easy to prove that definite objects are exactly




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MEINONG AND GENERALITY 663that about which the statement says something true or false. But,second, the referent of an expression can also be taken as that whichmakesthe statement rue(or alse), or its contributiono truth.In both casesreference is relative to some statement or other: no expression hasreference in isolation. That there is a difference between the twosenses of reference, is clear in the case of expressions which arenot terms, for normally predicates, operators and the like havereference in the latter, not in the former sense. But it is with termsthat the distinction is interesting, if sometimes blurred.Let us consider the statement "Smith's murderer, in such andsuch awful circumstances is (must be) insane", in the attributivereading-I am here assuming the attributive/referential distinctionas introduced by Donnellan (see Donnellan, 1966). The statementis about Smith's murderer, whoever he/she is. That he/she is Smith'smurderer in such and such circumstances is what makes him/herthe referent of the description, in the sense of being what the state-ment is about. However, this is not all the definite description doesin that statement. If we ask, What makes that statement true? orequivalently, What makes the individual in question satisfy thepredicate 'is insane'? then again the answer is, That he/she is Smith'smurderer in such and such circumstances-assuming that the circum-stances are fully described, so as to make the foulness of the murderquite evident. Being such a murderer, having behaved so abnormally,is something we can cite as a reason, in order to show that we attri-bute insanity justifiably. This contribution of the definite descriptiondoes not consist just in its reference in the first of the two senses,for it is not the individual as such, as being that particular individual,that makes the statement true-in fact either we do not know orwe do not care who that individual in particular is. What we meanby uttering the statement in question attributively is, rather, thatqua Smith's murderer in such and such circumstances, Smith'smurderer is, and can be said to be, insane.7 Here the definite descrip-tion gives both what the statement is about, and what makes it,whatever it is, satisfy the predicate: it has reference in both senses.It is not so for every term. Consider the statement "Jones wasbrave". No doubt, it is about the individual called Jones; this isthe referent of "Jones" in the first sense. But if we ask "Whatis it that makes Jones satisfy the predicate 'x was brave'?", onecannot answer "It is Jones". What must be cited is something inJones, some fact about him or a trait of his character, which canbe taken as a justification (however partial) of the statement. Thisis not something the proper name can give us, for the proper namesimply refers in the first sense to an individual without giving anypresentation of it from a particular side. And it can only be a presen-




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664 NOUStation of an individual from this or that side, that can make ussee why it satisfies a predicate.To the other extreme, take "The whale is a mammal"; asTwardowski and Meinong observed, this is not about the totalityof whales; it is not about the whale, either, for no such object exists."The whale" here has no referent in the first sense; however, ithas reference in the second sense for, if we ask, "How can yousay this is a mammal?", it makes sense to answer "It is a whale ".What we mean by saying that the whale is a mammal is preciselythat any individual which is a whale, in so far as it is a whale, isa mammal (of course this entails that every individual whale is amammal, but not the other way around).The referent of a term, in the first sense, is an existing indi-vidual; in the second sense it is rather the way an individual can begiven or presented,a way that is either relevant or irrelevant to thetruth of the statements in which the term has reference. Generalobjects are, or correspond to, the ways individuals can be given;they can only be referents in the second sense of "reference". Inother words, they are not that aboutwhich we talk in ordinary circum-stances but, rather that throughwhich we refer to individuals. (Inci-dentally, "way of giving an individual" and "presentation" arejust the Fregean and Brentanian names of Aristotelian forms). Itis now apparent why no ontological inflation is involved in theMeinongian move of supplementing the universe of "objects" withthe general (Meinongianly: incomplete) ones. Furthermore, we nowsee how Meinong and Twardowski could consistently protest theirnominalism: general objects are non-existent, in that not for everyF(x), either F(a) or -F(a) holds (a being any general object). Laterwe shall see that the TertiumNon Datur does hold for individuals.The distinction between two senses of reference also accountsfor the attributive/referential distinction in the use of definite descrip-tions. In:(1) Smith's murderer is insane,in the referential reading, the subject term "Smith's murderer"refers, to an individual-it is immaterial, from our present pointof view, whether that individual is the one that uniquely satisfies,as a matter of fact, the description, or the one that is thought bythe speaker or the hearer (or both) to satisfy it uniquely. In theattributive reading, on the other hand, (1) ought to be taken asa shorthand8 for "Smith's murderer in such and such awful cir-cumstances is insane" and the definite description refers2 to somegeneral object: having so foully murdered Smith is a reason rele-vant to justifying the attribution of insanity. It is a general reason,




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MEINONG AND GENERALITY 665in the sense that anybody fulfilling that description and in so faras he fulfils it, is liable to be called insane; hence the appropriatenessof the clause, which is sometimes added in order to signal that theattributive reading is meant, "whoever he is".Being able to refer2 to presentations, we can also account forsuch expressions as qua, quatenus, as such, as far as, etc. for whichtraditional logic invented the theory of reduplicatio. Consider thefollowing configuration of strokes:

If we see it as, or under the description a token of the type 7', thenwe can assert that it is the result of concatenating these configurations:

| I I I andThat is, it can be obtained from them qua token of the type 7. Thesame does not hold of it qua token of the type 2 (that it can alsobe presented as a token of type 2, can be seen by rotating the pageby 90 degrees).9Now we are also in a position to see the intuitive reason explain-ing the failure of intersubstitutability, in the semantics outlined above,of two definite descriptions pointing to the same individual (i.e.belonging to the same pseudoindividual): definite descriptions, bothproper and improper, if taken to refer2 to general objects, are tobe understood as always prefixed by "as such" or other similarexpressions. Consider this example: Benjamin Franklin was boththe inventor of the bifocals and the general postmaster (in 1779);he was also a benefactor of mankind and a powerful man. Theremarkable properties are not on equal footing. In the followingsentences:(2) The inventor of the bifocals, as such, was a benefactor ofmankind,(3) The general postmaster, as such, was a powerful man,the definite descriptions are clearly not intersubstitutable: the generalpostmaster as such was not a benefactor of mankind, nor was theinventor of the bifocals a powerful man. These distinctions are lostif descriptions are taken to refer directly referr) to individuals withoutthe mediation of the presentations (i.e., general objects) which aretheir referents2.Let us now revert to the reconstruction of the notion of an in-dividual within our semantics. Being sets of general objects, pseudo-




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666 NOUSindividuals clearly do not belong to the domain of a model, as definedso far. Let us then supplement the domain with a set of new elements,one for each pseudo-individual that can be formed in the originaldomain. Let them be called individuals. Terms, as we have seen,can have reference either of type 1 or type 2, or both. Typically,proper names have only the former kind of reference, as they haveno descriptive content which can be used to justify an assertion;let them be assigned individuals as their referents,. Proper definitedescriptions in the referential use come close to performing the func-tion of proper names. Their descriptive contents are used in orderto fix the individuals they refer to, but they are not used in theprocess of justifying the assertions in which they occur; hence theyhave reference1, but no references. A proper definite descriptionin the attributive use, as I said above, has both kinds of reference,for its descriptive content both fixes the unique individual satisfyingit and gives a reason for it to satisfy the predicate in the assertionin which it is used. Accordingly, it will be assigned the uniquesingular object satisfying it as its referent2 and the unique individualin which the latter occurs as its referent,. Improper definite descrip-tions, such as "the whale" (unless the context makes it clear thatsome particular whale can be singled out as the only relevant onein the vicinity) will only be assigned a general object, as theirreference2.Now we must specify the truth conditions for sentences contain-ing terms that have reference,. Formally, let the language L be sup-plemented with a new style of individual constants, i, j, k, . . ..to be interpreted into the set of individuals. Let i' be the pseudo-individual corresponding to individual i. Here is our noninductivetruth definition for sentences containing the new individual constants.

Definition.Let F(ii, . . ., i) be any sentence with the individualconstants as shown. F(il, ... , i) is true iff there are general ob-jects a,, . , an such that akEik', for k < n +1, and such thatF(al, ..., a is true according to the truth definition for generalobjects.Let us now see what kind of truth we have thus defined. First ofall, it is easy to see that this is a bona ide truth definition, in thesense that, e.g., F&G is true just in case F is true and G is true,that if F is true then - F is not true, etc. Moreover, it can be proventhat for any F(x) in which the only terms occurring are individualconstants and x, and any individual constant i, either F(i) or -F(i)holds, and therefore F(i)v -F(i) holds. The same does not hold forgeneral objects. It can be proven, in other words, that all individualsexist and they are the only existing entities. (It will be remembered




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MEINONG AND GENERALITY 667that existence, in the present context, is not a property expressibleby an ordinary predicate: something exists if it is determinate inevery respect, that is, for every (sufficiently definite) question wemight care to ask about it, there is exactly one definite answer-inother words, for every prediate F(x), either F(i) or -F(i) holds).It is also easy to prove that, given any definite general object, thereis exactly one (pseudo)-individual to which it belongs; there is there-fore a close connection between definiteness (of a general object)and existence (of the unique individual to which it belongs). It canalso be proven quite easily that, if a and b are two coincident generalobjects, then they are both definite and belong to the same (existingpseudo-)individual.The definition above says that an individual has a property,F(x), just in case there is a general object in the corresponding pseudo-individual that satisfies F(x). As general objects are in fact presenta-tions of individuals, this means that a presentation of that individualcan be found which is such as to justify attributing the propertyF(x) to anything that can be similarly presented (trivially, if a generalobject a, satisfies F(x), then any individual containing a also satisfiesF(x), according to the definition). This in turn means that an individualhas a given property only if a general reason can be given for itshaving it; in other words, it is not the individual per se, so to speak,in virtue of being that very individual, that has a property, butonly in so far as it can be given as, or qua, such and such.This notion of truth I shall call mediate, in view of the fact thatit is closely reminiscent of a notion of mediation employed by Kant.It is meant to contrast with baretruth: if F(x) holds of individual iper se, without there being any general characterization of that in-dividual, however detailed, to warrant attributing F(x) to it (andto all the individuals that can be similarly characterized), then F(i)is barely true, for i has F(x) in its bare individuality. Indexicalsand proper names provide examples of bare truths (possibly, notthe only ones): "being individual i", "being here" and the like,seem to be properties applying to individuals per se, for I cannotthink of any general characterization of an individual warrantingits being this very individual.

A PARALLEL WITH THE THEORY OF GUISESThe semantics I have outlined was developed in the first place notin order to account for either Meinong's or Twardowski's doctrines,but in an effort to understand some of Kant's theories. It comesas no great surprise, therefore, that it bears a rather close similaritywith another Kantian construction, namely Castafieda's Theory of




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668 NO USGuises, as set forth in "Thinking and the Structure of the World"in Philosophia, 4 (1974). I shall here point first at some points ofcontact, and then at some of the discrepancies.First, the ontological picture emerging from the semantics ofgeneral objects is similar to that associated with the Theory of Guisesin that the substances in the world, the individual material objectswhich I call individuals, are conceived of as composed of infinitelymany components. I think of the latter as aspects or presentations,corresponding to all the descriptions (definite and indefinite) applyingto an individual. Such aspects are usually taken as somehow relatedto the senses of descriptions, rather than being their referents, butI have tried to show that they can in fact be "objectified" and referredto, even if ordinary assertions are not about them. All this is ratherclose to the Theory of Guises; the latter takes ordinary objects asbundles of infinitely many consubstantiated guises. As guises(Meinongianly) satisfy the principle "The F is F", they are in factthe concrete universals of pre-Fregean logic. Guises are referred toby such terms as "the F"-"the man next door", "the circle",etc.: in themselves, without considering matters of predication, theyseem to be utterly indistinguishable from what I call general objects.Reference to guises is primary, according to Castafieda; it isclearly reminiscent of the notion of references, which is fundamentalin the semantics for general objects, in the sense that the truth defini-tion is framed in terms of it. There is a difference, however, inthat guises seem to be that about which we ordinarily talk accordingto the Theory of Guises, whereas general objects can be referredto without being talked about(it will be remembered that two sensesof "reference" were distinguished above).In any theory aiming at constructing ordinary individuals outof "presentations", the need arises of distinguishing those presenta-tions that can only present exactly one individual from the rest.Intuitively, these correspond to the proper definite descriptions. Theyare, according to Castafieda, the existing guises, which can enterexactly one bundle of consubstantiated guises. Consubstantiationis the fundamental notion, in terms of which all this can be defined.Apart from terminological differenes (e.g., I prefer to follow commonusage and say that ordinary individuals, rather than presentations,exist; what correspond to existing guises in the semantics for generalobjects, are then the definitegeneral objects), this is just what I triedto achieve by means of the notion of coincidence, which is, as amatter of fact, the same notion as consubstantiation-the only differ-ence being that the latter is taken as primitive, whereas coincidenceis defined in lattice theoretical terms; one can then prove, ratherthan postulate, that it possesses the right structural properties. It




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MEINONG AND GENERALITY 669will be remembered that if two general objects a and b are coinci-dent, then they are both definite, and therefore belong to exactlyone (pseudo-)individual (the same for both); every (pseudo-)individualexists in the sense that it satisfies the Excluded Middle.Consubstantiation plays a crucial role in the Theory of Guises,far more central than that of coincidence in the semantics for generalobjects, as "empirical" predication is defined in terms of it. Althoughit is in fact possible to define some kind of predication in termsof coincidence, I have given a direct definition of truth of the standardkind. It is here, I think, that the gulf between the two approachesappears: whereas the ontology of the two theories is, apart fromminor differences,'0 the same, the kinds of predication they con-sider differ. First, as I am skeptical that the a priori and the em-pirical components of truth can be sharply separated, I have onlyone definition of truth and of predication instead of the several kindsconsidered in the Theory of Guises, none of which entirely overlapswith mine. (The fact that a separate clause is provided for sentencescontaining individual constants, in the semantics outlined above,does not mean that a different notion of truth or predication is ap-pealed to). That the whale is a mammal or, for that matter, thatthe whale is a whale, counts as true in the semantics for generalobjects just in the same sense as that the whale is a playful creature.This means, among other things, that the one kind of predicationwe have in the semantics for general objects entirely accounts forCastafieda's Meinongian predication. Second, the semantics forgeneral objects goes beyond the scope of the Theory of Guises, inthe sense that it accounts for the truth of such statements as "Thewhale is playful'", "The robin sings" etc., which are not easily dealtwith in the Theory of Guises: the kind of predication involved inthem evidently cannot be Meinongian predication, but neither canit be consubstantiation, as "the whale" is not an existing guise andconsubstantiation only holds between existing guises. Non existingguises can only enter in internal or Meinongian predication, con-flation and identity, none of which can possibly account for the truthof those statements. (If those statements are taken as analytic andif Meinongian predication is meant to account for all there is toanalyticity, then this fact does point to a serious limitation in theTheory of Guises; but I do not think either that such statementsare analytic or that Meinongian predication is just analytic predica-tion. Still, those statements are true and this has to be explainedsomehow).Given the wider scope of the semantics for general objects (inthe sense just illustrated) and having defined truth independentlyfrom the notion of coincidence ( = consubstantiation), some simplifica-




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670 NOUStions are possible; e.g., individuals can be defined as maximal setsof compatible objects, including the non-definite ones ( = non-existingguises, in Castafieda's terminology). In other words, The Circleappears as a constituent in any circular individual object-just asboth Meinong and Twardowski claimed.A detailed comparison with the Theory of Guises is renderedsomewhat difficult by the fact that it is formalized only in part.But, apart fom technicalities, I think I see a substantial agreementbetween the Theory of Guises and the semantics for general ob-jects, as far as the basic metaphysical perspective is concerned. Ithas to be stressed, though, that on the latter more properties canbe predicated truthfully of non definite general objects, than justthose holding of non existing guises, according to the former.

INTENTIONALITYThat sentences in which reference is made to general objects canhave a definite truth value, is enough to grant the latter the statusof objects; and yet, they do not exist. I have tried to show that notension is involved here. In fact, we are all familiar with somethingthat fits that description, namely whatever our mind conceives asan object. There are good reasons, I surmise, to take general ob-jects as being just the objects of thought, intentional objects.I am concerned here with verbs of propositional attitudes, suchas "seek", in the object-complement construction. It has at timesbeen suggested that intentional verbs are basically expressive of whatRussell called 'propositional attitudes' and that therefore the termoccurring as a complement of such verbs in most cases in naturallanguage is, for logical purposes, to be so paraphrased as to un-cover a sentential complement. Quine's treatment of 'hunt' and'want' in "Quantifiers and Propositional Attitudes" is paradigmaticin this respect. However, it is debatable whether any satisfactoryreduction exists of the object-complement construction to thesentential-complement one. In any case, I will only concern myselfin what follows with such sentences as "I seek a sloop" (in thesense that what I seek is mere relief from slooplessness) where "asloop" is taken as a genuine term.Let me first of all list some well known phenomenological dataabout intentional objects. First, intentional objects (just like thegeneral ones) are indeterminate:f I seek a sloop, what I want is asloop, but it does not have, e.g., any particular size or colour. Sec-ond, most intentional objects do not exist. Third, the substitutivityofidenticals fails as far as intentional objects are concerned. Fourth,if I am seeking a sloop (not a particular one, just relief from




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672 NOUSa form which is modified by the individual characteristicsof these individual presentations"(Twardowski, 1977, p. 101).3In the formula Q(theP) I. (x)(Px -_ Qx), take Px as being the property x = x, sothat "theP" is to be read as "the self-identical", Qx as the property of being equal to theself-identical: x = theP. By substitution we have theP = theP -. (x)(x= x -_ x = theP), from which it follows, by applying ModusPonens, hat (xXx = the P), asserting that thereis only one object in the universe. This elegant formulation of Lesniewski's argument isdue to Bacon, "The Untenability of Genera", Logiqueet Analyse, 65/66 (1974): 197-207.In this paper, Bacon does not consider, however, the possibility of restricting somehow theoriginal formula, e.g. requiring that "the P" is not to occur in Qx. Incidentally, with thisrestriction, the formula expresses a basic fact of the method of "adjoining indeterminates"in topos theory, for which see lemma 4.17 in John Bell, Toposes nd LocalSet Theory,Oxford:Blackwell, 1988.

4'In general, an arbitrary object with certain values is the Meinongian object withthe properties common to those values. The important differences between the two theoriesshould be noted though. First, my arbitrary objects are specified 'from below', in termsof the values they take; Meinongian objects are specified 'from above', in terms of the prop-erties they have. This makes a big difference both to the formulation and development ofthe respective theories" (Fine, 1985, p. 41).5This is not entirely fair to the theory of properties, as developed, e.g., in Bealer'sQualityndConcept, xford, ClarendonPress(1982), where a number of operationson propertiesare defined. Clearly, one can then define an ordering on properties just as it is customaryto do with formulae via Lindenbaum's algebra.6Some further assumptions have been made in my paper "Generic and IntensionalObjects", in Synthese, 3 (1987), such as distributivity of the lattice of general objects. Suchassumptions are needed mainly for technical reasons, although they also have a clear in-tuitive content.7Traditional logic deals with statements of the form "x is y, qua z" in the theory ofreduplicatio.What is "duplicated" here is the reference of the definite description.8Often, the description of the relevant circumstances can be left out, as the contextof the utterance makes it clear anyway; nevertheless, such a description is an unarticulatedconstituent,-to employ Perry's felicitous expression-of the content of the statement. It isin fact hard to imagine any context at all in which the statement (1) could properly be usedattributively, in which a description of the relevant circumstances does not figure either asan articulated or as an unarticulated constituent.91nhis paper "Intentionalityand Identityin Human Action and PhilosophicalMethod",in Nods 13 (1979): 235-260, Castafieda observes that the logical form of such statementsas 'X's A'ing is quaA'ing a B'ing" can be interpreted in three distinct ways: (a) 'quaA'ing'modifies, i.e. is part of, the subject; (b) 'qua A'ing' is part of the predicate, and (c) 'quaA'ing' is a modality modifying the sentence 'X's A'ing is a B'ing'. Clearly, our construalin the main text is along alternative (a).10E.g., it is a minor difference, in my view, that Castafieda does not have singularterms referringto concrete individuals, whereas I do. But it is noteworthythat singulartermsreferring to individuals in my frameworkdo not refer in the same sense as, e.g., THETA-terms referring to general objects. It will be remembered that two senses of referring havebeen distinguished in the main text; individuals can only be referred to in the sense of beingwhat is talkedabout.

BIBLIOGRAPHYBacon, John1974 "The Untenability of Genera", Logiqueet Analyse, 65/66; 197-207.Bealer, George1982 Qualityand Concept, Oxford: Clarendon Press).Bell, John1988 Toposesand Local Set Theories.An IntroductionOxford: Blackwell).




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MEINONG AND GENERALITY 673Castafieda, Hector-Neri1974 "Thinking and the Structure of the World.", Philosophia (1974): 3-40.1979 "Intensionality and Identity in Human Action and Philosophical Method", Noas

13: 235-260.Donnellan, Keith1966 "Reference and Definite Descriptions", The Philosophical eview, 75: 281-304.Fine, Kit1985 Reasoning with Arbitrary Objects (Oxford: Blackwell).Frege, Gottlob1970 "What is a Function?", in Philosophical Writings of Gottlob Frege, by P. Geach andM. Black (Oxford: Blackwell).1968 The Foundationsf Arithmetic,Engl. Trans. by J. Austin (Oxford: Blackwell).Grossmann, R.1974 Meinong(London and Boston: Routledge and Kegan Paul).Heyer, G.1985 "Generic Descriptions, Default Reasoning and Typicality", Theoreticalinguistics,12: 33-72.Husserl, Edmund1970 LogicalInvestigations, indlay's transl. (London and Boston: Routledge and KeganPaul).Kneale, W. and Kneale, M.1962 TheDevelopmentf Logic, (Oxford: Oxford University Press).Lewis, David1970 "General Semantics,", Synthese 2: 18-67.Luschei, E.1962 The Logical System of Lesniewski (Amsterdam: North Holland).Russell, Bertrand1903 The Principles of Mathematics, (Cambridge University Press).Santambrogio, Marco1987 "Generic and Intensional Objects", Synthese 3: 637-663.forth- "Frege on Variables and Variable objects", in K. Mulligan, ed., Essayson Ontology,coming Kluwer.Twardowski, Kasimir1977 On the Contentand Objectof Presentations, translated by R. Grossmann (The Hague:Martinus Nijhoff).

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Santambrogio. Meinongian Theories of Generality (Article)