Truth Makers Simons

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Philosophy and Phenomenological ResearchVol. XLIV, No. 3 , March 1984

Truth-MakersK E V I N M U L L I G A NUniversity of Ha m bu rg

P E T E R S I M O N SUniversity of Salzburg

B A R R Y S M I T HUniversity of Manchester

When I speak of a fact . . . Imean the kind of thing that makes apro po sitio n true o r false. (Russell,1972, P. 36.)

$1.Making T r u eDur ing the realist revival in the early years of this century, p hilosop hersof various persuasions were concerned to investigate the ontology oftruth. That is, whether or not they viewed truth as a correspondence,they were interested in the extent to which one needed to assume theexistence of entities serving some role in acco unting fo r the tru th of sen-tences. Certain of these entities, such as the Satze an sich of B olzano, theGedanken of Frege, or the propositions of Russell and Moore, wereconceived as the bearers of the properties of truth and falsehood. Somethinkers however, such as Russell, Wittgenstein in the Tractatus, andHusser l in the Logische ~nZersuchun~en,rgued that instead of, or inaddition to, truth-bearers, one must assume the existence of certainentities in virtue of which sentences and/or propositions are true. Vari-ous names were used for these entities, notably 'fact', 'Sachverhalt', and'state of affairs'.' In order n o t to prejudge the suitability of these wo rds

Ontologies of Sachuerhalte were defended also by Reinach (in his 191 I ) and Ingarden

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we shall initially employ a more neutral terminology, calling any enti-ties which are candidates for this role truth-makers.'The fall from favour of logical realism brought with it a correspon-ding decline of interest in the ontology of truth. The notions of corre-spondence and indeed of truth itself first of all came to appear obscureand 'metaphysical'. The n Tarski's w ork , while rehabilitating the idea oftruth, seemed to embody a rejection of a full-blooded co rr e~ po nd en ce .~In the wake of Tarski, philosophers and logicians have largely turnedtheir attentions away from the complex and bewildering difficulties ofthe relations between language and the real world, turning instead tothe investigation of mo re tracta ble set-theoretic surrogates. W ork alongthese lines has indeed expanded to the extent where it can deal with alarge variety of modal, temporal, counterfactual, intentional, deictic,and other sentence-types. However, while yielding certain insights intothe structures of language, such semantic investigations avoid the prob-lem of prov iding a n eluc idation of the basic truth-relation itself. In placeof substantive accounts of this relation, as proffered by the Tractatus orby chapter I1 of Principia mat he ma tic^,^ we are left with such bloodlesspseudo-elucidations as: a monadic predication 'Pa' is true iff a is amember of the set which is the extension of 'P'. Whatever their formaladvantages, approaches of this kind do nothing to explain how sen-tences ab ou t the real world are m ade tr ue o r false. For the extension of'P' is simply the set of objects such that, if we replace 'x' in 'Px' by anam e of the object in question , we get a true sentence. Set-theoretic elu-cidations of the basic truth-relation can, it would seem, bring us no fur-ther forward.Putnam (pp. 2 5 f f . ) has argued that Tarski's theory of truth, throughits very innocu ousne ss, its eschew al, of 'undesirable' notions, fails todetermine the concept it was intended to capture, since the formal char-acterisation still fits if w e re-interpret 'true' to m ean, for exam ple,'warrantedly assertible' an d adjust o ur interp retation of the logical con-stants accordingly. Putnam's conclusion (p. 4 ) is that if we want toaccount for truth, Tarski's w ork needs supplementing with a philosoph-

(1964165, chap. XI; cf. the discussion in Smith, 19 78 ). Meinong preferred to use theterm 'Objektive'.Cf. Husserl, LU VI, $39: "At each step . . . one must distinguish the true-makingstate of affairs from the s tate of a ffairs constitutive of the self-evidence itself."Aristotle's famous "To say of what is that it is not, or of what is not that it is, is false,while to say of wh at is that it is, o r of w ha t is not tha t it is no t, is true" (M et., 10 11 ~2 5f f . ) is, as Tarski himself is anxious to claim (19 44, p. 343 ), less than a full-blooded cor-respondence theory, but Aristotle is elsewhere (op. cit., 1027~22, C I ~ I ~ ~ L re-f .) pared to speak of truth reflecting 'combinations' of subject and attribute in reality. Cf. also the opening sections of Weyl, 1918.


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ically non-neutral correspondence theory. This paper is about such atheory. If we are right that the Tarskian account neglects precisely theatomic sentences, then its indeterminacy is not ~urprising.~f, as wesuggest, the nature of truth is underdetermined by theories like that ofTarski, then an adequate account of truth must include considerationswhich are other than purely semantic in the normally accepted sense.Our suggestion here - a suggestion which is formulated in a realistspirit- is that th e way t o such a theory lies throu gh direct examinationof the link between truth-bearers, the material of logic, and truth-mak-ers, that in the world in virtue of which sentences or propositions aretrue.

Th e glory of logical atomism w as tha t it showed tha t not every kindof sentence needs its own characteristic kind of truth-maker. Providedwe can account for the tr uth an d falsehood of atom ic sentences, we candispense with special truth-makers for, e.g., negative, conjunctive, dis-junctive, and identity sentences. As Wittgenstein pregnantly put it:M y fundame ntal idea is tha t the 'logical constants' d o not represent; that the logic of factsdoes no t allow of representation. (Tractatus, 4.0312)This insight is an indispensable prerequisite for modern recursiveaccounts of t rut h. It add s further weight to the idea tha t our attentionsshould be focussed on atomic sentences. We shall in fact concentrate onthose which predicate something of one or more spatio-temporalobjects. Whether this is a serious limitation is not something that weneed here decide, for sentences of this kind mu st a t all events be handledby a realist theory.

The neutral term 'truth-maker' enables us to separate the generalquestion of the need for truth-m akers from th e more particular questionas to what sort - or sorts- of entities truth-makers are. In the mainpart of the paper we shall consider the claims of one class of entity,which we call moments, to fill this role. Since moments, once commonin philosophical ontologies, have been relatively neglected in moderntimes, we shall both explain in some detail what they are, and suggestarguments for their existence independent of their possible role as

' It parallels, perhaps, th e indeterminacy of a theory of the natural num bers founded onthe five Peano a xioms . It is no t only th e natural numb ers as we normally conceive themwhich provide a model for such a theory, but also, for example, the negative integers,the even numbers, the natural numbers greater than a million, and many other pro-gressions. Even if we add recursive axioms for addition and multiplication to eliminatethe interpretations above, we cannot rule out non-standard models. We can narrowdow n to the natura l numb ers only if we take acco unt of their application, outside theformal theory, in counting.


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truth-makers. We shall then consider the light that is thrown by thisdiscussion of moments on better-known theories of truth-makers -and particularly upon the theory of the Tractatus.$2. MomentsA moment is an existentially dependent or non-self-sufficient object,tha t is, an object which is of such a na ture th at it cann ot exist alone, butrequires the existence of s om e other ob ject outside itself. This charac ter-isation needs sharpening, but it will be useful to provide some prelimi-nary examples of types of moments, and some indications of the hon-ourable pedigree of the concept in the philosophical tradition.

Consider, first of all, that sequence of objects described at the begin-ning of Robert Musil 's novel The Man without Qualities:

a depression ov er the Atlantic an area of high pressure over Russia, patch es of pedestrian bustle, the pace of Vienna, a skidding, an a brupt braking, a traffic accident, the carelessness of a pedestrian, the gesticulations of the lor ry driver, the greyness of his face, the promp t arrival of the am bulance, its shrill whistle, the cleanliness of its interior, the lifting of the ac cident victim in to the ambulance.

It might a t first seem strange t o ad mit expression s like 'a's carelessness'or 'b's cleanliness' as referring ex pression s at all. There is an ingrainedtendency amongst contemporary philosophers to regard such forma-tions as mere f a ~ o n s e parler, properly to be eliminated from any lan-guage suitable for the purposes of philosophical analysis in favour ofmore robust talk involving reference only to, for example, materialthings. Here, however, we wish t o revert to an older tradition which canreadily accommodate expressions of the type illustrated as designatingspatio- tem poral objects, albeit objects which exhibit the peculiarity tha tthey depend for their existence upon other object^.^ A skidding, forexample, ca nnot exist unless there is something that skids and a surfaceover which it skids. A smiling mo uth smiles only in a hum an face.

We use 'object' for all those entities which can be named, leaving open whether thereare other, non-objectual entities, such as the Sachuerhalte and Tatsachen of the earlyWittgenstein.

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The concept of moment makes its first appearance in the philosophi-cal literature in the Categories of Aristotle, chapter 2. Here Aristotleintroduces a fourf old distinction a m on g objects according as they are orare not said of a subject and according as they are or are no t in a sub-ject:'

Not in a Subject In a Subject[Substantial] [Accidental]

[Second Substances] [Non-substantialSaid of a Universals]Subject[Universal, man whiteness,General] knowledge

[First Substances] [Indiv idual Accidents]Not said ofa Subject this individu al this individu al[Particular, man, horse, mind, whiteness, knowledgeIndividual] body of gram ma rAn individual accident is, in our terms, one special kind of moment,being such that, to use Aristotle's words, 'it cannot exist separatelyfrom what it is in' (Cat. , 1 ~ 2 0 ) .This 'being in' is not the ordinarypart-whole relation; for the parts of a substance are themselves sub-stances (Me t . , 1 o z 8 ~ ~ -1 0 ) , a su bstan ce a re itshere the entities 'in'individual accidents. If we are prepar ed to follow Aristotle and manyScholastics in accepting that there are particulars standing to manynon-substantial predicates as individual substances stand to substantialpredicates, then we tap a rich source of moments. The particular indi-vidual redness of, say, a glass cube, which is numerically distinct fromthe individual redness even of a qualitatively exactly similar cube, is amoment, as is the snubbedness of Socrates' nose, and the particularindividual knowledge of Grfiek grammar possessed by Aristotle at somegiven time.

Whilst accidents o r particularised qualities are the kinds of m om entsmost commonly found in the tradition, it must be pointed out thatmany other objects meet o ur definition. On e group of examples no t for-eign to Aristotle are boundaries (the surface of Miss Anscombe's wed-' On the provenance of such diagrams, cf. Angelelli, 1967, p. 1 2 .


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ding ring, th e edge of a piece of pa per, the W inter Solstice). And furtherexamples are provided by all kinds of configurations and disturbanceswhich require a medium, such as a smile on Mary's face, a knot in apiece of string, sound waves, cyclones, etc., and more generally allevents, actions, processes, states, and conditions essentially involvingmaterial things: the collision of two billiard balls or Imperial State car-riages, the thru sts an d parries of duelling swordsm en, the explosion of agas, the remaining glum of Mary's face, John's having malaria, two bil-liard balls' being at rest relative to each other, and countless more.

We make no attempt here to carry out the task of dividing all theseexamples into mutually exclusive and exhaustive categories. It is impor-tant for ou r purposes only to realise that m ome nts may be parts of oth ermoments, that moments, like substances, may be divided into simpleand complex. This is most clearly shown for temporally extendedmoments. T he first wrinkling of John 's brow is a par t of his frown, thefirst dull throbbing a part of his headache, the final C major chord apart of a performance of Beethoven's Fifth. More controversially, per-haps, we would regard certain kinds of spatially extended moments asparts of others, as the redness of one half of a glass cube is part of theredness of the whole cube.'

Although we have cast ou r net wide, we kno w a priori tha t no t every-thing can be a moment: the world is not a moment, since if it were, itwo uld re quire so me thing o utside itself in ord er to exist, in which case itwould not be the world.9

Moments reappear in post-Scholastic philosophy as the modes ofDescartes, Locke, and H um e. For Descartes, a mode is that which is nota substance, whereBy substance we can mean n othin g other th an a thing existing in such a manner th at it hasneed of no other thing in o rder t o exist. (Principia philosophiae, I, LI)Wh ile transpo sed in to the idiom of ideas, Locke's definition is in accordwith that of Descartes:

* Cf. Husserl LU 111, $4; Smith a n x ~ u l l i ~ a n ,g 8 ra , $3 .According to Spinoza (Ethics, Part I) this is the only non-moment and similar viewscan be fou nd in Husserl. Camp bell, 1976 , p. 103, suggests that Spinoza's views may beupheld on the basis of modern physics. However, as Husserl indicates, there are vari-ous possible senses of 'dependent', which accordingly allow different notions ofmoment and substance to be defined (cf. Simons, 198 2). Individual organisms, con-ceived by Aristotle as substances, are mere modes for Spinoza and mere aggregates forLeibniz; since all three, we may suppose, were operating with different notions of sub-stance, these conceptions need not in fact be incompatible.


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Modes I shall call complex Ideas, which however compounded, contain not in them thesuppos ition of subsisting by themselves, but are considered as Dependencies o n, or Affec-tations of Substances; such are the Ideas signified by the Words Triangle, Grati-tude, Murther, etc. (Essay, Book 11, chap. XII, $4)Hum e, though he has less to say a bo ut modes than Locke, assumes tha tit is well-known what they are, and gives a dance and beauty as exam-ples (Treatise, Book I, Part 11, @I).It was, however, in the philosophy of the German-speaking worldthat the Aristotelian ontology, and particularly Aristotle's theory ofsubstance and accident, was most systematically preserved.'" Thus thedoctrine of moments was fundamental to many students of Brentano,having ready application in psychology. Carl Stumpf explicitly distin-guished among the contents of mental acts between dependent( 'partial') and independent cbntents (1873, p. 109),a d istinction refinedand generalised to all objects by his stud ent Husserl." In his earlyontology Meinon g too k it for granted tha t properties a nd relations areparticulars, not universals.'"In modern Anglo-Saxon philosophy commitment to entities of thiskind is rarer, a notable swimmer against the tide being Stout, with his'characters'. Support for the notion has been otherwise sporadic, andnever enthusiastic, often coming, again, from philosophers acquaintedwith the Scholastic notion of accident."

'" Cf. Smith and Mulligan, 1982, $$I-3. " See the third Logical Investigation and also Husserl, 1894, which represents a half-way

stage between the early Brentanist theory and Husserl's fully developed formal ontol-0 9 .

I Findlay, 196 3, pp. 129, 131; Grossmann, 1974, pp. 5, IOO f ." Th e following list is not comp lete, but it sho ws the tenacity of the idea, despite its lackof general acceptance:

J. Cook Wilson, 1926,II, p. 713, P. F. Strawson, 1 9 x 9 , ~ . 68; 1974, p . 131 (par ti -cularised qualities);D. C. Williams, 1953, K. Campbell, 1976, chapter 14 (tropes);P. T. Geach, 1961, pp. 77 -80 (individualised form s);G. Kiing, 1967, pp. 166 ff . (concrete properties) ;D.C. Long, 1968 (quality-instances);N. Wolterstorff, 1970, pp. 130 ff . (cases or aspects);R. Grossman, 1974, pp. 5 ff . (instances);A. Kenny, 1980, p. 35 f. (accidents).

It is interesting that none of these thinkers has recognised the possibilities oframification among moments; e.g., that there are moments of moments, moments ofparts, parts of moments, etc. Cf. Husserl, LU 111, $18 ff., Smith and Mulligan 1983.


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We have taken the term 'moment' from Husserl's masterful andpainstaking study of the notions of ontological dependence and inde-pendence and of associated problems in the theory of part and whole.14A moment is an object whose existence is dependent upon that ofanother object. This dependence is itself no contingent feature of themom ent, bu t something essential to it. An a deq uate theory of m omen tsmust therefore involve appeal to the notion of de re or ontologicalnecessity," in con tras t to bot h de dicto (logical) necessity and causalnecessity. The objects on which a moment depends may be called itsfundaments. N o w an object one of w hose par ts is essential to it (as, say,his brain is essential to a man) is in one sense dependent on that part,dependent as a matter of necessity. Here, however, the whole containsthe part it needs. Thus it is already, in relation to that part, self-sufficient, by contrast with other parts - organs other than the brain,for example-which can exist together in a whole of this kind only inso far as they are bo und up w ith (ar e mom ents of ) the brain. So we spec-ify that the fund am ents of a m om ent cann ot be wholly contained withinit as its proper or improper parts. This also excludes the undesirableconsequence of having everything figure as its own fundament, andhence, trivially, as a moment of itself. Moments may accordingly bedefined as follows: a is a moment iff a exists and a is de re necessarilysuch that either it does not exist or there exists at least one object b ,which is de re possibly such that it does not exist and which is not aproper o r improper par t of a. In such a case, b is a fund am ent of a , andwe say also tha t b founds a or a is founded o n b. If c is any object con-taining a funda me nt of a as proper o r improper part, bu t not containinga as proper or improper part, we say, following Husserl, that a isdependent on c. Moments are thus by definition dependent on theirfundaments. Objects which are not moments we call independentobjects or substances. There is nothing in this accoun t which precludesfundamenta from themselves being moments, nor the mutual founda-tion of t wo or more m omen ts on each other.16

l 4 The interpretation and defence'of Husserl's theory, the history of the concept sinceBrentano, and its applications in various disciplines, are all topics we have treatedelsewhere: cf. the essays in Smith, ed., 1982.

'I De re necessity will be und erstoo d here as a m atter of the necessary structure of objectsand object-configurations, not, as in many contemporary writings on essentialism andrelated notions, as a matter of relations between objects and concepts, or betweenobjects and descriptions under which they fall.These issues are discussed in Smith and Mulligan, 1982, $6, 1982a, and in Smith,1981.

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Clearly moments, like substances, come in kinds, including naturalkinds." And just as com mitm ent to individual substances o r thingsentails neither the acceptanc e nor the rejection of an ontology of univer-sals o r species which thes e exemplify, so we can distinguish a realist an da nominalist option with regard to kinds of mom ents. A stro ng realism,as in Aquinas and perhaps Aristotle, sees both substances and momentsas exemplifying universals. On the other hand, a thoroughgoing nomi-nalism, which is only one step- but i t is an im porta nt step- removedfrom reism, accepts only particular substances and moments, conceiv-ing the existence of our talk about moment-kinds as having its basissimply in relations of n atu ral resemblance a m ong exam ples of mom entsgiven in experience.

Further details about the kinds of moments and substances may bespared here. Suffice it to note that all the intuitive examples offeredabove clearly fit ou r specification, since in each case there exist objects,no t part of tho se in question, w hose existence is a prerequisite for tha tof the respective moments. In most of the examples it is clear that themom ents a re no t of th e right category t o be even possible parts of theirfundaments, which reinforces Aristotle's remark that accidents are intheir substances b ut n ot a s parts. At the sa me time his ' in' is frequentlyinappropriate; for instance a duel is 'in' neither of the duellers, not is it' in' the duelling pai r o r the aggregate of duellers.Is$3. Mom ents as Tru th-MakersThe idea tha t w ha t we call mom ents cou ld serve as truth-makers is per-haps u nusual, b ut it is not w itho ut precedent. If we return to Russell, w efind that am ong st the exam ples of facts he gives is the de ath of Socrates,"a certain physiological occurrence which happened in Athens longago" (loc. cit.). From this we infer tha t, fo r Russell, at least some statesand events are truth-ma kers. This indicates th at he is not conforming tothe ordina ry usage of 'fact', since w ha t is norm ally said to be a fac t isnot the death of Socrates but th at Socrates died.19 Socrates' death to ok" Husserl's characterisation of foundation and dependence in LU I11 makes indispens-

able use of kin ds, which w e have here tried to av oid: cf. Simons, 1982 and for an expo-sition more sympathetic to Husserl, Smith, 1981.When Leibniz objects to relational accidents as accidents "in two subjects, with one legin one, and the o ther in the othe r, which is contrary to the notio n of accidents" (Alex-ander, ed., p. 71), he too is misled by the connotations of 'in', which applies at best tothose non-relational accidents located within the space occupied by their fundaments.A better all-purpose preposition is the genitive 'of'.

I 9 See Vend ler, 1967, chapter 5, "Facts and E vents," w ho sh ows very clearly that: "If thecorrespondence theory requires a relation between empirical statements and observ-

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place in Athens, and was caused by his drinking hemlock. We do nothowever say that Socrates' death is true. By contrast, that Socrates diedis true, but that he died had no cause and did not take place anywhere,at any time. This discrepancy was pointed out by Ramsey, who drewthe conclusion th at facts are no t to be distinguished from true proposi-tions.'" H er e then, we shall distance ourselves from Russell's usage,but no t from his theory.Supp ort for Ramsey7s distinction and , surprisingly, for a view ofsome moments as truth-makers comes from other quarters. Davidson,no t kno w n as a friend of facts, says of a sentence like 'Am undsen flew tothe North Pole in 1926' th at "if [it] is true , then there is an event th atmakes it true" (1980, p. 117) and holds that "the same event may make'Jones apologized' and 'Jones said "I apologize"' true " (op . cit., p. 1 70) .The clue that moments may serve as truth-makers comes initiallyfrom linguistic considerations. Most terms which describe moments, orunder which moments fall, are in fact nouns formed by nominalisationof verbs and verb-phrases. These are morphologically varied: somehave sepa rate but related form s ('birth', 'flight', 'death'), som e are sim-ply gerunds ('overturning', 'shooting'), some are homeomorphic withthe corr espo ndin g verb ('hit', 'kiss', 'smile, 'jump', 'pul l7),and some areformed using particular morphemes for the purpose ( 'generosity7,'redness', 'preg nancy', 'child hood', 'collision7, etc.). Of these the mos tneutral and universally applicable is the gerundial form '- ing',which, w hen applied not t o a verb but to a nou n o r adjective comple-ment, attaches to the copula to give phrases of the form 'being (a)

'. Gerundial phrases are often equivalent to other morphologicalforms: there is no difference in o u r view ( or Aristotle's) between acube's being white and its whiteness, nor is there a difference betweenthe collision of two objects and their colliding. All of these forms are,however, radically distinct from nominalisations constructed by meansof the con junction 'that', a fact no t always appreciated in the analyticliterature on propositions, states of affairs, facts, etc.Thus, following Russell's suggestion, we shall here consider thetheory obtained from the view that what makes it true that Socratesdied is Socrates' death, what makes it true that Amundsen flew to thepole is his flight, w ha t makes it true t ha t M ar y is smiling is her (present)smile, and so on. Or, in other words, that for many simple sentences

able entities in the world, then facts are not qualified for this latter role" (p. 145 f.).Vendler is one of the few philosophers to have seriously studied nominalisations.Another is Husserl (in the appendix on syntactic forms and stuffs to the Formal andTranscendental Logic). Cf. also Strawson, 1974, especially pp. 130 ff.

to Ramsey, 1978, p. 44. Cf. Prior, 1971, p. 5. Ramsey's arguments are anticipated byReinach in his 1911: see especially $8 f. of the translation.

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about spatio-temporal objects the truth-makers for these sentences arethe moments picked out by gerundials and other nominalised expres-sions closely related to the main verbs of the sentences in question. Inplace of Tarski-biconditionals of the form:'This cube is white' is true iff this cube is white,we thereby obtain - at least in simple cases - sentences of the form:

If 'This cube is white' is true, then it is true in virtue of the beingwh ite (the whiten ess) of this cube, a nd if n o such whiteness exists,then 'This cube is white' is false.

Because the whiteness in questio n here is a particular dep endent on thecube, and not a universal whiteness shared by all cubes, its existencedoes nothing to ma ke sentences abo ut other things' being white eithertrue or false.

If all atom ic sentence s con tain a m ain verb, an d all nom inalisationsdenote moments, then it would follow, in fact, that all truth-makers aremoments , that w hat makes it t rue that a is F is a's being F, what m akesit true tha t a R's b is a's R-ing b, and so on. This simplest possible ver-sion of the the ory is inade quate as it stands, however. No t only because,as we shall see, there are certain types of n ot o bviously non-atom ic sen-tences, for example existence and identity sentences, recalcitrant to theanalysis, but also, and more importantly, because the theory whichclaims that by nominalising a sentence we have thereby designated therelevant truth-maker can hardly count as a substantial elucidation ofmaking true. It seems - like Tarski's theory - to turn on a linguistictrick.

In fact the device of nominalisation gives us only the kernel of atheory. That this kernel requires considerable expansion may be gath-ered from certain intuitive considerations relating to the status ofmom ents as entities in the wo rld existing independently of o ur sentence-using acts. For we w an t to say, surely, tha t if a m om ent a makes the sen-tence p true, and b is any moment containing a as part, then b makes ptrue as well. That John's head ached between I p.m. and I : IO p.m. ismade true not just by that ten-minute segment of his headache, but byany part of it containing this segment. So p may have a minimal truth-maker without having a unique one."' Further, a sentence may be" We may call this minimal truth-maker the truth-maker for the sentence, thereby mak-

ing a non-Russellian use of definite descriptions. Th us S ham y, 1980, has shown howdefinite descriptions may pick out maxima rather than unique objects. 'The coffee inthis room', for example, picks out the total quantity of coffee in the room. Thatdescriptions may pick o ut also minima is shown no t only by the example mooted in the

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made true by n o single truth- ma ker but only by several jointly, o r againonly by several separately. Thus w e k no w tha t viral hepatitis comes intwo sorts: acute infectious or A-hepatitis, and homologous serum orB-hepatitis. If the hapless Cyril has both A- and B-hepatitis simulta-neously, then that he has viral hepatitis is made true both the bymom ent o r mom ents which m ake i t t rue that he has A-hepati tis, an d bythe-m ome nt or m ome nts m aking it true that he h as B-hepatitis, thougheither would have sufficed alone. So the sentence 'Cyril ha s viral hepati-tis' ha s in such circumstanc es a t least tw o truth-makers. In general thereis no guarantee that the logical simplicity of a sentence guarantees theuniqueness o r the on tological simplicity (atomicity) of its actual or pos-sible t ru th- ma ker(s) .

The re is, of course, a tem ptat ion t o argue tha t 'Cyril has viral hepati-tis' is not logically simple but implicitly disjunctive, its logical formbeing not adequately mirrored in its grammatical form, which is that ofa logically simple sentence. But we believe that the given sentence isindeed logically simple: it contains no logical constants and no expres-sion, 'viral hepatitis' included, which is introduced into the language bydefinition as equivalent to an expression containing a logical constant.

In taking this view we are consciously departing from a dogma thathas characterised much of analytic philosophy since its inception: thedogma of logical form. This has many manifestations. One versionappears in The Principles of Mathematics where Russell, whilst on theone hand regarding all complexity as mind independent, neverthelessholds th at this sam e complexity is capable of logical analysis (1903,p.46 6) . This idea of a perfect parallelism of logical and o ntological com-plexity is the misery of logical a tomism , leading Russell to a m etaphys-ics of sense-data an d Wittgenstein to sup raexperie ntial simples." Here,in contrast, we uphold the independence of ontological from logicalcomplexity: ontologically com plex objects (tho se having proper pa rts)are not for that reason also in some way logically complex, any morethan there is reason to suppose that to every logically complex (true)sentence there corresponds an ontologically complex entity whichmakes it true.

A second and more elusive-version of the dogma enjoys wider sup-port. It includes the Russell-Wittgenstein position as a special case, butis no t confined to logical atomists . Rough ly speaking, it says that if asentence has or could have more than one truth-maker, then it is logi-

text but also by, e.g., 'the place where the accident happened', which picks out thesmallest spatial extent circumcluding the accident.

" The difference between Russell and Wittgenstein consists principally in the fact thatWittgenstein has stronger criteria for simplicity and independence: cf. Simons, 1981.



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cally complex. If the sentence app ear s nevertheless to be simple in form ,this complexity is hidden and is to be uncovered by a process of analy-sis.

One possible argument for this view may be put in terms of truth-makers thus: since disjunctive and existential sentences may have morethan one truth-maker, and conjunctive and universal sentences must,except in degenerate cases, have m ore th an on e, sentences which may o rmus t have more th an on e truth-m ake r a re implicitly disjunctive o r exis-tential, o r conjunctive o r universal. As it stand s this argum ent is palpa-bly invalid, being of the form 'All A are B, therefore all B are A'; butthere are other reasons why the position has been found attractive.'?Here, however, we shall confine ourselves to registering our dissentfrom the view. Although 'Cyril has viral hepatitis' may be logicallyequivalent to (i.e., have th e sam e truth-conditions as) 'Cyril has A -hepa-titis or Cyril has B-hepatitis' , this is not something that can be estab-lished by any lexical, grammatical, or logical analysis of the meaning ofthe sentence, but at most by empirical research. This research does notuncover a hidden ambiguity in the term 'hepatitis'; we simply discoverthat the term is determinable.

Since we are realists in respect to mom ents, an d regard the ir investi-gation as a substantial, often as an empirical matter, we hold it to beperfectly normal for us to know that a sentence is true, and yet notkno w completely what ma kes it true. Thu s the characterisation of t hattheory whereby the meaning of a sentence is given by its truth-condi-tions as 'realist ' (Du m me tt, chap. 13) is for us ironical. A knowled ge oftruth-conditions takes us at most one step towards reality: one can,surely, envisage understanding a sentence (kn ow ing its meaning), whilstat the same time having on ly partial knowledge of the n atur e of its pos-sible truth -m ake rs. Thos e wh o used the term 'hepatitis' before the dis-covery of its varieties did not fail to understand the term; they weresimply (partly) ignorant ab ou t hepatitis. Tha t the investigation of w hat" On e attractio n, which dies hard , is tha t of exhibiting all the entailments of a sentence

as resulting from the substitution of synonyms and from the application of the infer-ence rules for the logical constants (i.e., of exhibiting all entailments as analytic in theFregean sense). A sentence p' analyses p , let us say, when p' arises from p in thismanner. T he tw o sentences are then logically equivalent, and the purely logical conse-quences of p' (those obtained th roug h the rules for logical constants alone) properlyinclude those of p. So p has some consequences which cannot be derived from it bypurely logical means, but can from p ' . Since p' more closely resembles the desiredideal, it is comm on t o conceive it as exhibiting a 'hidden' logical form of p. If the idealis discredited how ever (cf. the attem pt in Smith, 1981), then this conception too losesits attraction. The ideal amou nts t o the disputed claim, which we reject, that all neces-sity is analytic.

TRUTH -MAKERS 299


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make s a particular sentence true is thus fun dame ntally an empirical, no ta philosophical on e, is no t belied by the fact tha t for m any sentences wecan pick out the relevant truth-makers by nominalisation. There is, inthe general case, n o cheap and easy way to determine the truth-makerseven of simple descriptive sentences via linguistic transformations.

Are all truth -m ake rs mo me nts? For three kinds of sentences this maybe questioned. The first are predications which are, as Aristotle wouldsay, in the category of substance: predications like 'John is a man','Tibbles is a cat', and so on, telling us what a thing is. Since these aretrue atomic sentences, but logically contingent, we should expect themto have truth-makers. In virtue of the special status of such sentences,might it not be the things themselves, Jo hn an d Tibbles, which play therole of making true, or are there certain moments of John and Tibbleswhich are essential to them as men or cats which serve to make thegiven sentences true ? On e reason for thinking the latter is that, if Joh nmake s the sentence 'John is a man ' true, then he also mak es 'John is ananimal ' t rue, which means that these two sentences, having the sametruth-maker, have the same truth-conditions, and are logically equiva-lent. Only if logical equivalence and synonymy are the same, however,is this objection really telling. We conceive it as in principle possiblethat one and the same truth-maker may make true sentences with dif-ferent meanings: this ha ppe ns an yway if w e take non-atom ic sentencesinto account, an d no arguments occur to us which suggest that this can-not ha ppen for atom ic sentences as well. A mo re imp ortant point is thatif John makes i t true bo th th at John is a man and th at John is an animal,and Tibbles l ikewise makes i t true both that Tibbles is a cat and thatTibbles is an animal, th en there is no n on-circular way of accounting viatruth-makers for the fact that both are animals but that one is a manand the other a cat. Such an account could be provided if there aremoments characteristic of humanity and of felinity which are bothcharacteristic of animality.

A second g rou p of pro blem sentences are singular existentials such as'John exists'. These are certainly logically contingent, and perhapsatomic, an d so they ou ght intuitively to have truth-makers, but then thequestion arises wh at these are. W e baulk, f or reasons familiar from thetradition, at providing John with a special moment of existence. Theresort to the sentence '3a.a = John', widely held to be equivalent to 'Johnexists' , is no step forward, since we are left with the question what, ifanything, makes the sentence 'John = John' true, and such sentencesbelong to o ur third prob lem group . A natural way o ut is, again, to electJo hn himself tru th-m ake r of the given sentence, which wo uld once m ore

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lead us to a view according to which a t least some truth-makers are n otmoments. Indeed, a reist who recognised the need for truth-makerswould have no option but that of taking things to do the job in everycase. One the other hand, someone who was committed to momentswould in any event have the problem of providing an account of sen-tences expressing their existence, and again the relevant moment itselfwould seem t o be the most o bvious candidate truth-maker.14The third kind of problem sentences are identities. One possible lineis that these too are made true by the objects in question, for instancethat 'Hesperus = Phos phoru s' is made tru e by Venus. This has the con-sequence that the identity is equivalent to 'Venus exists' as this sentencehas been conceived above. A different solution is required for the viewof those logicians an d metaphysicians w ho thin k th at a n identity of theform 'a = a' may be true even though there exists no object designatedby the term 'a'. O ne alternative here is to em brace com mitm ent to non-existent objects which may be taken as truth-makers for the given sen-tences even in those circumstances where 'a exists' is false. Proponentsof such a view will need to em brace a ne w entity, such as a mom ent ofexistence, as truth-m aker for tru e sentences of th e for m 'a exists'.'I Theview is, we believe, wo rth pursuing, th oug h we d o not follow it up here.But there is another view which holds that in some cases 'a' may notdesignate, yet 'a = a' be true. He re we ca nnot imagine wh at m ight serveas truth-maker. And indeed this suggests the most plausible solution:there is none. T he ground s for believing th at 'a = a' is true even when 'a'is emp ty are th at the sentence is a logical tru th, i.e., t ha t identity is a log-ical constant. This account is therefore in harmony with the logicall4 To regard a as truth-maker for 'a exists' is of course to cut against the grain of the

established Fregean view t ha t all meaningful existential assertions are assertions a bo utconcepts (Gru ndlag en, $53 ). At the sam e time however a reading of Kant in the lightof our conception must cast doubt upon the common assumption that, with his doc-trine that 'existence is not a predicate', he had merely anticipated Frege. If God's exis-tence is rejected, Kant writes, "we reject the thing itself with all its predicates; and noquestion of contradiction can arise" (A ~9 jI B 6 2 3 , ur italics).

For Kant singular existence statements are meaningful (since synthetic), whereFrege's official line (cf., e.g., his ''ijber den Begriff der Za hl. Au seinandersetzung mitKerry") is tha t they a re meaningless. Even w here Frege bends over backwards to givethem a m eaning (in the "Dialog m it Punjer iiber Existenz") they come out either asnecessarily true or as disguised metalinguistic statements.

'I Meinon g significantly calls that w hich makes th e difference between a n object's exist-ing and its no t existing a 'moda l m ome nt' (cf. his 1915, pp . 266 ff.; Findlay, 1963,chap. 4 ) . There are other such moments, among them one marking the factuality orsubsistence (Bestehen) of an objective o r state of affairs. The doctrine of modalmomen ts was refined and considerably extended by Ingarden in his 1964165, especiallyvol. I.


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26

atomist principle tha t no special objects correspond t o the logical con-stants. As in th e case of s ingular existentials, th e special sta tus of iden-tity sentences is reflected in their special position in regard to truth-maker^.'^

Whether or not i t is correct that things as well as moments can betruth-makers, the possibility emphasises one merit of the present theoryover rival correspondence theories of truth which invoke a special cat-egory of non-objectual entity - facts, states of affairs, or whatever -simply to serve as truth-makers. For if we are convinced for other rea-sons that th ings and mom ents exist, a nd if-as we shall argu e below-we can be said unproblematically to be acquainted with them, forexamp le perceptually, then th e resultant theory of truth -ma kers is bothmore economical and stronger than rival theories whose truth-makersare less firmly tied into our ontology and epistemology.

The relation of m aking tru e is to be distinguished both from th at ofdesignation an d from tha t between an object an d a predicate o r conceptunder which the object falls. Truth-makers cannot, on our theory, bethe designata of the sentences they make true, even if we confine our-selves to atomic sentences. This is, of course, no news to those whobelieve (as we do ) tha t sentences d o no t designate at all . But for thosewho incline to the contrary it only needs pointing out that sentenceswith more than one t ruth-maker would on their account have to betreated either as ambiguous or as multiple-designating. Both alterna-tives are implausible. We argued against the first above. As to the sec-on d, we a re not against plural o r multiple designation as such- quite

N ot all the alternatives canvassed here are compa tible with one ano ther; the followingis an inconsistent tetrad:

( I ) ' a = a' is true but has no truth-makers.(2) If 'E!a'is true, then a makes it true.(3 ) '3x .+x' is ma de true by wha tever makes any instance '+a' true.(4 ) 'E!a'and ' 3 x . x = a' are logically equivalent.

Various means of resolving this inconsistency suggest themselves. That closest to clas-sical logic would reject ( I ) and make a the truth-maker for ' a = a'; it must then regard' a = a' as meaningless or false if a does n ot exist. Th e solution closest to free logic is toreject (3 ) and replace it by:

(3') ' 3 x . +x ' is ma de true by whateve r pairs a, b are such that a makes'E!altrue and b makes '+a' true.If we intioduce a nonstandard particular quantifier v for which there holds theequivalent of ( 3 ) with 'v' replacing ' 3 ' , then 3x.+x' and ' ~ x . E ! x+x' are logicallyequivalent. Such a quantifier already exists in the work of Leiniewski (cf. Simons,1981a).


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the contraryz7- but there is no distinction amongst multiple designat-ing or plural terms which corresponds t o tha t between several objects'jointly (i.e., conjunctively) making a sentence true, and their severally(i.e., disjunctively) making a sentence true.

A furthe r difficulty faced by any view t o the effect that (tru e) ato m icsentences designate their truth- m ake rs is that, if w e are right ab ou t sin-gular existential sentences being made true by their subjects, then both'a' a nd 'a exists ' have the sam e designatum, so one has the problem ofexplaining their syntatic and semantic diversity. Since the nominalisa-tions considered above can appear as rightfully in designating phrasesas any other com mo n nou ns, truth-m akers can be designated. But this isnot t o say th at they are designated by the sentences they ma ke true. It issti l l more obvious that truth-makers do not fall under sentences asobjects fall under predica tes. T he se ma ntic relations of designating, fall-ing under a nd m aking true are all distinct. W ha t makes 'John's headaches' true - a moment of John - is something that falls under thepredicate 'is a hea dac he' an d is designated by 'John's (pre sen t) hea d-ache'. But from the fact that sentences, terms, and predicates have dif-ferent syntactic and semantic roles, i t does not follow that there arethree kinds of entity stand ing over against them. N or how ever does thefact tha t truth-m ake rs are designated by terms a nd fall under predicatesimply that any of these syntactic and semantic roles collapse into oneanother.

Since truth-makers can be designated, they can be quantified over.From 'John's singing exist^','^ we can infer '3a .a is a singing an d Joh ndoes a' or, more idiomatically, 'John is singing', and conversely. Thatmany normal sentences about events are equivalent to existential sen-tences was asserted already b y,Ra ms ey (1978, p. 4 3), an d the same viewhas also been tak en by Davidson (1980, p. 118 ). It is certainly true th at'Amundsen flew to the No rth Pole' does not, where 'Amundsen's flightto the Nor th Pole too k place' does, imply tha t only one flight tookplace. Both Ramsey and Davidson conclude from this that sentenceslike the former are existential sentences in which events are quantifiedover. But this is an instance of the dogma of logical form at work. Thesentence is undoubtedly logically equivalent to such an existential gen-eralisation, but that tells us only that they have the same truth-condi-tions. Despite this, and despite their having the same event as truth-

'' Simons, 1982a, b.Like Ramsey, we say that events exist, where it would be more idiomatic to say thatthey occur or hap pen . Similarly we use 'exist' for states of affairs, instead of the mor eusual 'obtain' or 'hold'.

18


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maker, the tw o are of quite different form . The Ram sey-Davidson viewmay spring in pa rt from an ec ho of the false view th at truth-m akers a redesignated by their sentences. Realising that uniqueness is not guaran-teed, they move f rom designation to the next best thing, quantification.No doubt events make quantificational sentences true, but they makeother, non-quantificational sentences true as well, including sentencesequivalent to the quantificational ones.z9$4. Moments as Objects of PerceptionM ost philosophers will acknowledge the credentials of a t least some ofthe objects we have called mom ents. H owe ver, many of the sentences ofthe types we have considered require, on our theory, truth-makerswhose existence is controversial, such as particularised qualities. So ifmom ents a re to play the role we suggest, it is incum bent on us to give ageneral defence of their existence, controv ersial cases included, which isas far as possible independent of their putative status as truth-makers.This is the m ore i mp orta nt since we have dissociated ourselves from theRamsey-Davidson argument via logical form, which is treated by manyas a principal reason for believing in events and their ilk.A num ber of argum ents can be offered by friends of moments a gainstt h e ~ c e p t i c . ~ "e shall concentrate here on just one such, which turnson the fact th at m ome nts, like things, m ay be the objects of mental acts,in particular of acts of perception. If it is conceded that there are epi-sodic mental acts such as seeings, hearings o r smellings which have astheir objects such things as Mary or a table, then, the argument goes,acts of sim ilar kinds m ust be recognised which take a s their objects suchmoments as the roughness of the table, Mary's smile, John's gait orR u p e r t ' s h ~ w l i n g . ~ 'he philosopher staring hard at a picture of twol9 Ad hominem, Davidson's ow n psycho-physical identity theory allows one single event

to make true two non-synonymous sentences, one in physical, one in mental vocabu-lary. Davidson, 198 0, pp. 214 ff .

j0 A reistic ontolog y, in w hich th ere are o nly independent things standing in relations oftotal and partial resemblance, will be unable to account satisfactorily for the naturalaftinities even between these things, let alone between entities such as smiles, gaits,howls, strokes, aches, etc. The friend of moments can however point to the similaritiesbetween moments to flesh out the account, whilst however avoiding commitment touniversals (cf. Simons, 1 983 fo r a sketch of an ontology of things and m oments whichremains squarely within the ambit of nominalism). This is one reason for being welldisposed toward moments. O ther arguments turn o n the fact that only a commitmentto moments can enable us to render intelligible the constraints on division of materialobjects into smaller pieces, and that the existence of formal as well as material rela-tions between objects makes sense only on the assumption tha t there are mom ents. Cf.Smith and Mulligan, 1982, 1982a." This argument derives from Husserl. See, e.g., LU VI, $$48-50.

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swordsmen en face may be tempted to think that only independentobjects are depicted- the two swordsmen, their swords. But whoeverobserves swordsmen in the real world sees not only them and theirsw ords but also their partic ular lunges, parries a nd m uch else. These arealso depicted in fencing manuals, an d it is perception of them, n ot sim-ply of the swordsmen, which forms the basis for our judgments of aswordsman's competence. Similarly what his mother hears is Rupert 'showling, and it is this, or perhaps a particular pitch this howling sud-denly takes on, which causes her to get up to feed him. This last pointmakes clear that, counting events as moments, we accept that momentscan stand in causal relations to one another. Rupert 's howling causesSusan's hearing him howl, and this (given the prevalent neural condi-t ions underlying maternal concern) causes her to get up. The episodicperceivings are themselves moments standing in causal relations toother events.

This argume nt has the a dvan tage tha t i t can claim to be neutral withrespect to particular theories of perception. The proponent of momentsclaims merely that whatever connection a theory of perception makesbetween perceptions and their objects, this connection holds whetherthe object is a thing or a moment or a combination of the two. Thisincludes theories which award a central role to a causal connectionbetween object an d perceptual ac t. Th us any acc ount of the role of sen-sations in perceiving things will, w e claim, hav e a parallel in th e percep-tion of moments. Profile and perspective problems will present them-selves in precisely the same way for perceivings of things and moments.( D o I see the sw ords m an or just the profile presented to m e? D o I see hiseasy parry o r only the phase no t obscured by his interposed should er?)Further, the problems posed by the interplay between cognition orback ground knowledge an d perception, an d by the intentionality (opac-ity) of perception are- quite reasonably - assumed to arise for boththings and moments. Thus the proponent of moments does not claimtha t we invariably perceive m om ents as the sorts of moments they are,only that what we perceive in such cases are mom ents. So meo ne seeinga flash of lightning sees a moment: a discharge dependent on thecharged air and water-molecules in which it takes place. But he maywell n ot k no w t ha t it is such a discharge, a nd there is, surely, a sense inwhich he does no t see i t s f~ndaments .~ ''' Depen dence w as originally defined by th e psychologist Stumpf ( 1 8 7 3 , chap. 5 ) in terms

of the impossibility of separate perception. Th at is (roughly) a is dep end ent upon b iff acannot be perceived separately from 6. It was definitions of this sort which served asthe starting point for Husserl's work on a more general, ontological theory of depen-dence relations and Husserl clearly believed that his work represented a natural


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Many philosophers are prepared to accept truth-bearers as abstractentities, and would argue that this obviates the need for truth-makers,since predications about truth-makers can, they contend, be traded infor predications ab ou t truth-bearers, with little or n o trouble. It is a dis-tinguishing feature of the perceivability-argument for moments that itthwarts a move of this kind. For the moments we have given as exam-ples can, but their associated abstract truth-bearers cannot, be objectsof perceptual acts.33

The ma in objection t o mom ents has always been tha t any job they docan be done by independen t objects, together with ( on a weak opt ion)the senses of predicate expressions and the relation of falling under, or(o n a stro ng op tion ) universals an d the relation of exemplifying. Butwhoever wishes to reject moments must of course give an account ofthose cases where we seem to see an d hear them, cases we rep ort usingdefinite descriptions such as 'the smile that just appeared on Rupert'sface'. This means that he must claim that in such circumstances we seenot just indep enden t things per se, but also things as falling under cer-tain concepts o r as exemplifying certain universals. On some accounts(Bergm ann, Grossm an) it is even claimed th at w e see the universal in thething. But the friend of moments finds this counterintuitive. When wesee Rupert's smile, we see something just as spatio-temporal as Ruperthimself, and not something as absurd as a spatio-temporal entity thatsome how con tains a concep t o r a universal. The friend of m omen ts maysimply take the everyday descriptions at face value, which means thathis account has a head-start in terms of naturalness.

Confronted with prima facie examples of perceivings of moments,such as John's hearing the angry edge to M ary's voice, o r Tom's seeingthe kick that Dick gives Harry, or Susan's seeing Rupert's smile, theopponent of moments may react in a number of different ways. Oneploy is to claim that the noun-phrases apparently designating momentsmay be replaced salva veritate by expressions designating only indepen-

extrap olati on of th at of Stumpf. It would thu s be surprising if it were possible to findclear-cut examples of moments in Husserl's sense which are perceivable separatelyfrom their fundaments. Can we see a shadow or a silhouette in separation from itsobject, or is it not rather the case that in seeing a shadow we see also the object itself(albeit from a certain perspective)? When we perceive the warmth flowing from asource of radiant heat do we thereby perceive also the source (again, from a certainperspective)?

'' On Locke's theory of perception we never perceive substances (substrata) but onlytheir accidents (Essay,Book 11, chap. XXIII). A less extreme and inherently more plau-sible position is that whenever we perceive a substance we do so by virtue of perceivingone or mo re of its moments. Cf. Kenny, 1980, p. 35. If this is right, then the percep tionof moments, far from being peripheral, is a key issue in cognitive theory.



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dent things; 'Susan sees Rupert's smile' by 'Susan sees the smilingRupert', for example. For m om ents of mom ents, as in our first example,or relational moments, as in our second, the replacements will have tobe more complicated. 'John hears Mary's angrily edged voice' will notdo, as a voice is itself a moment, so it must be something like 'Johnhears the angrily-speaking M ary ', or, m ore implausibly still, 'John hearsthe wi th-an-angri ly-edged-voice-speaking Mary ' , the hyphenatedphrase being treated as an unanalysed predicate. For the relationalexample we either need t w o perceptual acts: 'Tom sees the kicking Dickand the kicked Harry', or, since we have ostensibly only one act here:'Tom sees the two-person complex consisting of the kicking Dick andthe kicked Harry'.

Leaving aside all worries as to the precise nature of the relationbetween Rup ert himself and the smiling Rup ert,34 an d q uestions as towhether there are such things as person-complexes, such attempts arethwarted by opacity problems. For Susan can of course see the smilingRupert without seeing his smile, John can hear Mary, and, we shouldadd, her angry voice, while m issing its angry edge, and T om can see thetw o men an d miss the kick. In saying this we are deliberately using theperceptual verb 'see' transparently. It might be thought that a wayround the recognition of a separate category of moments would be todistinguish between this tran spare nt sense, and an op aqu e or phenome-nological sense, e.g., by subscripting the verb with 't' and 'p' respec-tively. But however we try to capture 'Susan sees, Rupert's smile', e.g.,with 'Susan sees, the smiling Rup ert', o r 'Susan sees, the smiling Ru per tand sees, someone smiling', we always miss the mark. For instance,Susan may see, the smiling Rupert when in fact he is frowning- shemistakes his expression- o r she may see, someone w ho is smiling, andmistake him for Rupert.Similar problems beset attempts to use paraphrases involving propo-sitional complements: 'Susan sees tha t Ru per t is smiling' (she m ay seethe smile, but fail to recognise its bearer), or complements using 'as':'Susan sees Rupert as smiling' (so she might, but he may be frow ning ).

To rescue his position, the opponent of moments may resort to as e r i e s o f de re p e r c e p t u a l p r e d i c a t e s , ' s e e s - t o - b e - s m i l i n g ' ,'hears-to-be-angrily-speaking', etc., which allow that, e.g., Susan maysee-to-be-smiling (R up er t), w ith ou t recognising t ha t it is he, i.e., by tak-

'4 The most likely answer to this problem is that they are (if Rupert smiles) identical.(W hat if he does no t?) But Bretano would seem t o regard Ruper t as a proper part ofsmiling Rupert. In his terminology, Rupert is a substance, smiling Rupert an accident.Cf. Brentano, 1933, pp. 107 ff., 119 ff. , 151 ff.; Chisholm, 1978.


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ing the terms for the fundaments outside the scope of the intentionalverb and putting them in extensional position^.^^ But this ploy cannotcope w i g situations like the following. To m wrongly thinks that Dick'skicking of H ar ry co nstitutes an atta ck o n him, whe re it is in fact simplytheir somewhat unusual way of greeting each other. The moment theo-

-rist can accept th at T o m sees, Dick's kick, a nd since this is his greeting,Tom sees, Dick's greeting of Harry. But the opponent cannot capturethis true material equivalence since he has the true 'Tom sees-to-kick(Dick, Harry)', where all the argument places are extensional, but his'Tom sees-to-greet (Dick , H ar ry )' is false, since T om does no t recognisethe kick for the greeting it is. There is no way for the oppo nent to copewith this, short of creating a new extensional position for a term desig-nating som ething (i.e., som e m om en t) which is both a kick a nd a greet-ing, and this is to concede defeat.j6

It may be that reserves of ingenuity may turn up new ploys to keepmoments at bay, but we dare to predict that they will be no more suc-cessful than these. Alternative attempts to cope with the cases we havementioned in ways that d o no t involve commitment t o mom ents will,we suggest, either fall short of adequacy or be ontologically and epis-temological ly more complex and more impla~sible.~ '$5. Truth-Making and the TractatusWe h ave a rgued tha t it is possible to establish a case for the existence ofmom ents, an d for the role of m oments as truth-makers, a t least for cer-tain large and important classes of sentences. In the present section wewish to supplement these arguments with a brief discussion of what isstill almost certainly the mo st sophisticated account of truth -m aking tohave appeared to date, the isomorphism theory of the Tractatus.

'I Cf. Quine, 1976, chap. 17; Chisholm, 1981, chap. 9.' 6 While the Ramsey-Davidson account of event-sentences can in large part be replaced

by a logic of predicate-modifiers - cf. Clark, 1970; Parsons, 1972 - this does notdispose of events, as Horgan (1978) thinks: no amount of predicate modification canaccount for our perception of events.

" Even stronger arguments for the existence of moments may be formulated on the basisof their role as objects of memory and other acts. For here, the (normal- cf. n. 32)co-presence in perception of the moment with its fundament is quite commonly con-founded by the selectivity of memory. John may for many years remember, for exam-ple, the intonation of a particular utterance Mary once directed at him, while forget-ting both M ary herself and indeed the utterance in question. Mary's smile may remindhim (de re) of th at of his nurse, w hose smile captivated him at a tender age, though hehas long since forgotten the nurse herself.

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The structure of the objects which make a sentence true is not, wehave argued, som ething tha t ca n be read off fro m the sentence itself bypurely logical means. The determination of this structure may be atleast as difficult and empirical a matter as the determination of thetruth-value of the sentence in question. For Wittgenstein, by contrast,the determination of the structure of truth-makers is a task not ofontology and of the various material disciplines, but of logic, for which'nothing is accidental'. He could not, therefore, have included truth-makers among the objects found in everyday experience and treated ofby the different sciences. He embraced instead a special category ofnon-o bjectual entities, w hich h e called Sachverh alte, to d o the job ofmaking true. Yet there is much th at we ca n learn fro m his theory of theSachverhalt. W e have indeed already taken to hear t the doctrine whichunderlies this theory th at it is a m istake t o postula te special truth-mak-ers corresponding to logically compound sentences. And we shall haveoccasion in $6 below to reflect upon Wittgenstein's own ingeniousdevelopment of this doctrine- in his theory of the Tatsache.

Th e theory of Sachverhalte m ay be sum ma rised briefly as follows: thesimple objects which, in Wittgenstein's eyes, make up the substance ofthe world, are configurated together in various ways. An elementarysentence is true iff the simple objects designated by its constituent sim-ple names are configurated together in a Sachverhalt wh ose constituentscorrespond one-to-one with the constituents of the sentence, theconfiguration of the objects being mirrored in the structure of the sen-tence. Sentence an d Sachverhalt a re then said to h ave the sam e logische(mathematische) Mannigfaltigkeit (4.04).

Wittgenstein tells us little as to the nature of the objects which areconfigurated together into Sachverhalte; but he does supply certainhints, as for example a t 2.0131, where we are told thatA speck in the visual field need not be red, but it must have some colour . . . A tonemust have some pitch, the object of the sense of touch must have some hardness, etc.Con sider, then, a sen tence like: 'This spe ck [here before m e now] is red'.This sentence is made true, it would seem, by a Sachverhalt which is acombination of two objects, the speck itself and its colour. One inter-pretation of Sachverhalte sees them as involving both spatio-temporalparticulars a nd un iversal properties an d relations (colour, pitch, h ard-ness, lies between, and the like).38Again, it is not qlear ho w particularsand universals may both be constituents of a single entity. A morepromising interpretation may be constructed on the basis of some of

Stenius, 1964, e.g., p. 63, and the relevant writings of G. Bergmann and E. Allaire.

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Wittgenstein's ow n remarks on the forms a nd natures of simple objectsat the beginning of 2. It is, Wittgenstein tells us, not accidental to anobject that it can occur in those Sachverhalte in which it does occur.Every one of its possibilities of occurrence in states of affairs must bepart of the nature of the object itself, must be written into the objectfrom the very start (2.012, 2.0121, 2.0123). Its possibility of occurringin states of affairs Wittgenstein calls the form of an object (2.0141).Distinct objects may exhibit distinct forms, may be located, so to speak,in distinct spaces of possible states of affairs (2.013),~~ome objectsare such that, in virtue of their form , they call for others as a matte r ofnecessity; a tone must have some pitch, objects of the sense of touchmust have some degree of hardness, an d so on. Some objects are, tha t isto say, founded on oth er objects in the sense of ou r discussion above.40It is, we suggest, because analytic-philosophical interpreters of theTractatus have standardly lacked a theory of lateral foundation rela-tions, relations which may bind together individual objects, that theyhave been con strained t o resort t o views of the kind which see Sachver-halte as involving both individuals and universal properties. It is opento us here, however, to develop a view of Sachverhalte as involvingindividuals alone, linked together by relations of foundation. 'Thisspeck is red' might be made true, on such a view, by a two-object Sach-verhalt comprising the speck and an individual moment of rednesslinked by a relation of mutual foundation. A sentence like 'Atom astrikes [at some given instant of time] ato m b' might be true by a three-object Sachverhalt comprising a, b, and that event or individualmom ent c which is their momenta ry impac t, linked by relations of one-sided foundation: between c and a, and between c and b. Here theimpact moment is distinct in its ontological form from the independentobjects with which it is configurated, but it is no less particular thanthese object^.^' A realist semantics of a non-trivial sort, to be estab-lished on the basis of an investiga tion of the range of possible forms an dkinds of (dependent and independent) objects, seems therefore not,

39 There are two possible readings of Wittgenstein's talk of 'possible states of affairs' inthe Tractatus. On the first, Meinongian reading, we can say that there.are possiblestates of affairs in addition to the actual states of affairs; on the second, more soberreading, we say that there are only actual states of affairs, though it is possible thatothers might have been actual. Here and in what follows we adopt the second reading.Terms apparently d enoting possible states of affairs ough t 'therefore to be treated inevery case as syncategorematic.

40 More precisely, what we have here is generic foundation in the sense of $4 of Simons,1982.

4' For further details cf. Simons, 1981.


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after all, to be so completely at variance with a semantics of the kindpresented in the T ractatus. We a re driven back to one im porta nt differ-ence, th at W ittgenstein believed tha n a n ade quate semantic theory m ustembrace com mitm ent to absolutely simple objects, w here we are willingto content ourselves with the question of relative simplicity, for exam-ple of the simplicity that is determined by the elementary sentences ofthe various material science^.^" An investigation of the natures ofdependent and independent objects treated of by these sciences thenreveals itself as an investigation of objects in the light of their possibleconfigurations into Sachverhalte, and a taxonomy of objects in oursense is seen to give rise to an exactly correspo ndin g taxon om y of dif-ferent kinds of Sachverhalt- something like the zoology of facts men-tioned by Russell in his lectures on logical atomism (1972, p. 72 f.).43As an interpretation of the Tractatus, however, even of a Tractatusmodified by the admission of the possibility of our grasping the naturesof (relat ively) s imple objects an d of (relat ively) s imple object-configurations, an account of this kind is still so far inadequate. For ithas not been made clear what these s implest kinds of object-configurations are, merely that, in order to exist at all, they mustinvolve objects which m anifest a d istinction in form som ething like thedistinction defended above between moments and independent objects.Wittgenstein himself, a s already noted , was ever keen to em phasise tha tSachverhalte are entities of a peculiar kind, entirely distinct fromobjects. And this view has acquired the status of orthodoxy amongstcontemporary philosophers, despite the fact that Wittgenstein himselfoffered no more than loose, metaphorical indications of the differencein question. But how is a Sachverhalt such as, for example, that whichinvolves the three ob jects a, b, an d r, to be distinguished fro m the corre-

On absolute and relative simplicity cf. Husserl, LU 111 $I and Experience and judg-ment, $928 f .

41 T o determine which are the simplest kinds of objects constituting the subject-matter ofa given material discipline is to determine also the kinds of Sachuerhalte which maketrue, a s a Wittgensteinian might conceive things, the elementary sentences of th at dis-cipline. Wittgenstein himself embraced something like this project with respect to thediscipline of psychology in his unjustly neglected "Some Remarks on Logical Form" of1929. It is one conseque nce of o ur argum ents t ha t Wittgenstein's idea of a directlydepicting language, or of a family of such languages, may prove to be capable of beingresurrected. Since, as we stressed above, there is lacking any isom orphism between thelogically simple sentences of natural languages and their truth-makers, a directlydepicting language would need to employ mechanisms which do not closely resemblelinguistic devices with which we are familiar; it may perhaps approximate to the pic-ture-languages employed in organic chemistry. Cf. Smith, 1981, Smith an d M ulligan,1982, $6, 1983.


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sponding complex object (a's-standing-in-the-relation-r-to-b)? Wittgen-stein seems to have been con tent t o regard this distinction as not fur therexplicable, emb racing mysticism of a kind w hich ma y have done m uchharm to the enterprise of a correspondence theory of tru th. C an we d obetter? O ne course wo uld be t o develop a view of Sachverhalte as beingdistinguished from the corresponding complexes in involving, or inbeing in some sense dependent upon, the sentences or sentence-usingacts through which they are disclosed: for example, and most naively,by treating Sachverhalte as ordered pairs consisting of the relevantcomplex object a nd so me app rop riat e sentence. Such a move is howevertantamount to sacrificing the conception of Sachverhalte as entities inthe world existing independently of mind a nd language. T o treat Sach-verhalte in this way, o r as logical fictions of any kind , is to aba nd on theproject of a realist semantics.Here we wish to leave open the question whether a more acceptableaccount of the distinction between Sachverhalt and complex could bedeveloped.44 t is one implication of ou r argum ents above th at some, atleast, of the considerations which have been held to motivate the dis-tinction are lacking in force. But are there other reasons why the logicaldifference between na me an d (elem entary) sentence should be held t o bereflected in a corresponding ontological difference between objects andsomehow non-objectual and intrinsically unnameable Sachverhalte? O ris the assumption of special categories of entities to do the job of mak-ing true one m ore reflection of the runnin g together of logic an d ontol-ogy so characteristic of analytic philosophy ?$6. Some Principles of Truth-MakingWe shall sketch one possible beginning of a formal theory of the rela-tion of making true. Such a theory is, we shall assume, constrained bythe requirements w e have placed o n a realist semantics, an d by the prin-ciple of the heterogeneity of logic and ontology that forestalls any tooready imputation of logical structure to the objects - both dependentand independent- of the material Th us we assume tha t the(ontological) relations holding among truth-makers - most impor-tantly the relations of part and whole - are distinct from the logical44 Such an accou nt is attempted in Mulligan, 1983; contrast Simons 1983a.Thus work on the formal properties of the truth-relation such as that of van Fraasen

(in Anderson an d Belnap, $z o .j ), whilst having a numb er of method ological similari-ties to the account presented here, falls short of our requirements in being committedto different logical categories of truth-maker for different logical categories of sen-tence.

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relations holding among propositions or sentences. The fragments out-lined here are otherwise intended to be consistent not only with theviews outlined above, but also with a range of possible variants..

For the relation of truth-making we use the sign ' I = ' , which can beread 'makes true that' . Individual truth-makers - whether moments,things, or other, more conlplex entities - we shall represent by lettersa, b, c ; sentences (or any other candidate bearers of truth) by letters p,q, r. '+' in all tha t follows will signify a connective at least as stron g asthe entailment of Anderson and Belnap.

The first principle of tru th-m aking mu st be tha t wha t is made true istrue, i.e.

But is the converse of ( I ) also valid; i.e., is it true that

We have argued that ( 2 ) ca n be a ffirmed even of simple descriptive sen-tences only in certain circumstances. A simple sentence like 'Cyril hashepatitis' may be true although there is no single object that makes ittrue: from the point of view of its truth-makers the sentence maybehave as a non-degenerate conjunction. Similarly in regard to, say,'Jack likes Jill an d Jill likes Joe' o r 'There have been fo rty U.S. Presi-dents to 1981' it is surely counterintuitive to assume th at there are anysingle composite objects making these sentences true, a Jack's likin g Jilland a Jill's lik ing Jo e mereologically fused together, or a mereologicalfusion of all and only U.S. Presidents from Washington to Reagan (inwhich G rover C leveland som ehow gets counted twice). Rather w eshould accept tha t the given sentences are ma de tru e by not one bu t sev-eral truth-m akers jointly or, a s we like to pu t it, by a m anifold or plural-ity of truth-makers. Such a manifold is not a new, conjunctive objectsuch as a set. Ther e are n o conjunctive objects, any mo re than there aredisjunctive, negative, o r implicative objects. A manifold is noth ing oth erthan the objects i t comprehends (and thus a m anifold comprehending asingle object is simply that object itself).

This suggests a me ans of dealing form ally with conjunctive sentencesand related forms by introducing terms for m anifolds corresponding innatural languages to singular and plural definite referring expressionslike 'Jack an d Jill', 'the m en in this room', 'Jason a nd the Argonauts',and so on. Here 'r','A', etc., will be used to stand in for non-emptylists of such expressions. ' a E I?' will signify that the individual a is oneof I?, that some term designating a occurs on the list I?.4646 We spare the details of manifold theory here. It can be compared to a theory of sets

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true tha t i t is not o do rou s); but even such a m ove will be inadequate todeal with o the r classes of negative sentence s like 'Ba'al doe s no t exist'.Here there is quite l i terally no thing which can do the job of makingtrue, and whilst some might be tempted to appeal to the world as awhole t o d o this job, i t seems more adeq uate to regard sentences of th egiven kind as true not in virtue of any truth-maker of their own, butsimply in virtue of the fact that the corresponding positive sentenceshave no t ruth-make r.

Th e otherwise attractive principle

must therefore be rejected in its full generality. Manageable principleshaving nice truth-functional properties can however be defended if werestrict o ur attention to those propositions satisfying ( 6 ) .The strongerprinciple ( 2 ) picks out the propositions in this class which are atomic,but only in the sense that they can be m ade true by some one individual:it does not even come near to delineating the class of logically atomicpropositions, since there are logically compound sentences satisfying( 2 ) ,and logically atomic sentences for which ( 2 ) is false.

Clearly any whole containing a truth-maker of some proposition pwhich is atomic in the sense of (2 ) itself makes p true, i.e.,where 's'signifies the relation of prope r o r improper pa rt t o whole.48The principle em bodied in ( 7) may be extended t o positive propositionsin general by defining a relation C of mereological containmentbetween manifolds. Intuitively we wish 'r C A' t o express the proposi-tion that the matter of r is contain ed in the m atte r of A, such th at if 'r 'and 'A' are singleton-lists then 'L ' is just 'G'. The definition

will not serve, since A may carve up the matter of r in such a way thatthere are individuals in A which com prehe nd n o single individuals in r.On the other hand the definition

appears acceptable.We accordingly assert:

48 On the question whether p has a minimal truth-maker see Smith, 1982.

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which implies a principle of thinning:(11) r I = p . + V A . r , A I = p .

T w o further intuitive a xiom s are

And (10) and ( I3) in tu rn imply(14 ) r I = p . A p + q : + r I = q

whence, in particular,r ~ = p . + r = p ~ q ,so that

the converse of w hich we affirm as an, ax iom :

and by (14) and (12) we have also(18) r I = p A q : * r I = p . A r I = q .

Quantified sentences may be manag ed in a similar way as follows:

which brings us back once more, within the province of truth-func-tional logic, to th e problem of dealing wit h c om pou nd sentences involv-ing negation.It was in the face of this problem that Wittgenstein developed histheory of Tatsachen (facts). Wittgenstein introduces the term 'fact' asmeaning 'the existence and non-existence of states of affairs.' The exis-tence of states of affairs he calls a positive fact, their non-existence anegative fact (2.06).'" Intuitively the idea seems to be that we can pro-duce a more adequate theory of truth-makers, a theory which can cope49 (13) may be too stro ng: it implies that, w here p -z q, we can conclude that any truth-

maker for p contains some truth-maker for q. Consider, however, an entailment suchas: that there exists a funeral entails tha t there exists a death. He re a truth-m aker of theantecedent, i.e., any co mp lex event which is a funeral, need no t (a nd typically doesnot) contain a death as one of its parts. Funeral and death are connected, rather, pre-cisely by a (lateral) relation of one-sided fo und atio n.

I" Cf. also 2.062, z.11, z.zo~, .1and compare the discussion in Dietrich, $2.

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( i i i ) ' for 'A ' of the form ~ k . ,ot bo th 'B' designates a fact an d'C' does not designate a fact.

Thus 'A' designates a fact iff '-A also designates a fact. (ForL U p A" des ignates a fact', o r equivalently'-A is a fact', we mayalso writ e '+A'.)

There is clearly a certain tension between this ontology of positiveand negative facts and the 'fundamental idea' of logical atomismexpressed by Wittgenstein in the passage cited in $I above. Yet itwould contradict Wittgenstein's pronouncements at I and 1.1 perhapsto o char itably to dismiss his talk of facts, of 'th e existence an d non-exis-tence of states of affairs', as a mere f a ~ o n e parley. N ot only Wittgen-stein, but indeed almost all other philosophers who have investigatedthe relation of making true, have felt compelled in the face of the prob-lems raised by negative propositions to adopt an ontology of truth-makers as special, non-objectual entities having a complexity which isessentially logical. We remain convinced nevertheless that it is possibleto develop a theory of the truth-relation which appeals only to objectsfirmly tied into our ordinary and scientific experience. For it is in suchexperience, and not in the abstract models of logical semantics, thatthere lie the origins of our knowledge of truth and f a l s e h ~ o d . ~ 'BIBLIOGRAPHYAnderson, A.R. a nd Belnap, N. D. (1975) Entailment, vol. I, Princeton:

Princeton University Press.Angelelli, I. (1967) Studies on Gottlo b Frege a n d Traditional Philoso-

phy, Dordrecht: Reidel.Alexander, H. G., ed. (1956) The Leibniz-Clarke Correspondence,

Manchester: Manchester University Press.Anscombe, G. E. M . an d Geach, P. T. (1961) Three Philosophers,

Oxford: Blackwell.Brentano, F. (1924 ) Psychologie vom empirischen Standpunkt, 2nd ed.,

Leipzig: Meiner; English translation as Psychology from anEmpirical Standpoint, London: Routledge, 1973.(193 3) Kategorienlehre, Leipzig: M eine r; English trans latio n asThe Theory of Categories, The Hague: Nijhoff, 1981.

Campbell, K. (1976) Metaphysics. Alz Introduction, Encino: Dicken-son.

I' Our thanks go to Roderick Chisholm, Kit Fine, Wolfgang Kiinne, Richard Routleyand to other participants in the 1981 Wittgenstein Symposium in Kirchberg, wherethese ideas were first aired.

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Chisholm, R. M. (1978) "Brentano's Conception of Substance andAccident," G raz er Phiios ophisc he Studien, 5, 197-210.- (1981) The First Person, Brighton: Harvester.

Clark, R. (1970) "Concerning the Logic of Predicate Modifiers," Nozis,4, 311-35.Davidson, D. (198 0) Essays on Actions a n d Events, Ox for d: Claren-don.

Dietrich, R.-A. (1974) Sprache und Wirklichkeit in Wittgelzsteins Trac-tatus, Tubingen: Niemeyer.

Dum mett, M . A. E. (197 3) Frege. Philosophy of Language, Lon don:Duckworth.

Findlay, J. N . (1 963 ) Meinong's Theory of O bjects an d Values, 2nd ed.,Oxford: Clarendon.Frege, G. (196 9) Nachgelassene Schriften, ed. H . Herm es, et al., Ha m -burg: Meiner, 1969.

Grossmann, R. (1974) Meinong, London: Routledge.Horgan, T. (1978) "The Case against Events," Philosophical Review,

87, 28-47.Husserl, E. (1894) "Psychologische Studien zur elementaren Logik,"Philosophische Monatshefte, 30, 159-91, reprinted in E. Hus-serl, Aufsatze und Rezensionen ( 1 8 9 0 - I ~ I O ) ,The Hague:Nijhoff, 1979, 92-123; English translation by D. Willard, ThePersonalist, 58, 1977, 295-320.(LU = 1goo101) Logische Untersuchungen, 1st ed., Halle:

Niemeyer, 2nd ed., 1913121; English translation (based o n 2nded.) as Logical Investigations, Lond on: Routledge, 1970.(1929) Formale und transzendentale Logik, Halle: Niemeyer,English translation 'as Formal and Transcendental Logic, TheHague: Nijhoff, 1969.(1939) Erfahrung und Urteil. Untersuchungen zur Genealogieder Logik, Prague: Academia; English translation as Experi-ence an d Judgment, Lond on: Routledge, 1973.

Ingarden, R. (1964165) De r Streit um die Existenz der Welt, 2 vols., the2nd in 2 parts, Tiibingen: Niemeyer.

Kenny, A. J. P. (1980) Aquinas, Oxford: Oxford University Press.Kung, G. (1967) Ontology and the Logistic Analysis of Language,

Dordrecht: Reidel.Long, D. C. (1968) "Particulars and their Qualities" as reprinted in M.J. Loux, ed., Universals a n d Particulars, No tre Dame: N otre

Dame University Press, 1976, 310-30.


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Meinong , A . (1915) i jber Mijgl ichkei t und Wahrscheinl ichkei t ,Leipzig: Barth (reprinted as vol. VI of Meinong-Gesamtaus-gabe) .

Mulligan, K. (1983) "Wie die Sachen sich zueinander verhalten insideand outside the Tractatus, " Rivista d i Filosofia (special issue o nWittgenstein, forthcom ing) .

Parsons, T. (1972) "Some Problems concerning the Logic of PredicateModifiers," in D. Davidson and G. Ha rm an, eds., Semantics ofNa tura l Languages, D ordrech t: Reidel, I27-4 I .

Prior, A. N. (1971) Objects of Thought, ed. P. T. Geach and A. J . P.Kenny, Oxford: Clarendon.

Putnam, H. (1978) Meaning and the Moral Sciences, London: Rout-ledge.Quine, W. V. 0. (1976) The Ways of Paradox and other Essays, rev.ed., Cambridge, Massachusetts: Harvard University Press.

Ramsey, F. P. (1978 ) Foun dations, e d. D. H. Mellor, London: Rout-ledge.

Reinach, A. (19 I I ) "Zur Theorie des negativen Urteils," in A. Pfander,ed., Miinchener Philosophische Abhandlungen, Leipzig: Barth,196-254; English translation in Smith, ed., 1982, 3 I 5-78.

Russell, B. A. W. (1903) The Principles of Mathematics, Cambridge:Cambridge University Press, 2nd ed., London: Allen andUnwin, 1937.(1972) Russell's Logical Atomism, ed. D. F. Pears, London:

Fontana.Sharvy, R. (1980) "A More General Theory of Definite Descriptions,"

Philosophical Review, 89, 607-24.Simons, P. M. (1981) "Logical and Ontological Independence in the

Tractatus," in Ethics: Foun dations, Problems, a n d Applica-tions, Proceedings of the 5th International Wittgenstein Sym-posium, Vienna: Holder-Pichler-Tempsky, Dordrecht: Reidel,464-67. (1981a) "A N ote o n LeSniewski and Free Logic," Logiqu e et Analyse, 24, 41 5-20 . (1981b) "Unsaturated ness," Gra zer Philosophische Studien,

14, 73-96. (1982) "The Formalisation of Husserl's Theory of Wholes and Parts," in Smith, ed., I 13-59. (1982 a) "Num ber and M anifolds," in Smith, ed., 160-98. (19 82b ) "Plural Reference and Set Theo ry," in Smith, ed.,

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