Metaphysics and Truthmakers 9783110326918, 9783110326581

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Jean-Maurice Monnoyer (Ed.) Metaphysics and Truthmakers

Philosophische Analyse Philosophical Analysis Herausgegeben von / Edited by Herbert Hochberg • Rafael Hüntelmann • Christian Kanzian Richard Schantz • Erwin Tegtmeier Band 18 / Volume 18

Jean-Maurice Monnoyer (Ed.)

Metaphysics and Truthmakers

ontos verlag Frankfurt I Paris I Ebikon I Lancaster I New Brunswick

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Contents Jean-Maurice MONNOYER “Vingt ans après”

7

Kevin MULLIGAN, Peter SIMONS & Barry SMITH Truth-Makers (1984)

9

Kevin MULLIGAN Two Dogmas of Truthmaking

51

Peter SIMONS Truth in virtue of Meaning

67

Barry SMITH & Jonathan SIMON Truthmaker Explanations

79

David ARMSTRONG Truthmakers for Negative Truths and for truths of mere possibility

99

Philipp KELLER A World of Truthmakers

105

David ARMSTRONG Reply to Keller

157

François CLEMENTZ Relational Truthmakers

163

Herbert HOCHBERG “Is True” and “Makes true”, Two predicates without properties

199

Frederic NEF Senex erit puer. Truthmakers for tensed sentences

221

Jonathan LOWE Truthmaking as Essential Dependance

237

Pascal ENGEL Identity Makers

261

Stefano CAPUTO Truth-Making : what it is not and what it could be

275

Stephen MUMFORD A new Solution to the Problem of Negative Truths

313

Peter SIMONS The Price of Positivity : Mumford and Negatives

331

Vingt ans après JEAN-MAURICE MONNOYER Université de Provence This volume is a collection of papers read at the Conference « Truths and Truthmakers : Vingt ans après » which was held at the University of Aix-en-Provence (Aix-Marseille 1) from December 9th to December 11th 2004. « Vingt ans après » : the phrase was clearly intended as a wink at the title of a famous book by the French novelist Alexandre Dumas, where his three Musqueteers get reunited « twenty years after ». Our idea, from the start, was to provide both a companion to David Armstrong’s recently published book Truth and Truthmakers (Cambridge University Press, 2004) and a collective volume in celebration of the twentieth anniversary of Kevin Mulligan, Peter Simons & Barry Smith’s seminal article « Truth-Makers » (1984). Indeed, the latter is widely regarded as having brought the very concept of a truthmaker back to the forefront, although the concept in question could hardly have escaped the attention of philosophers, at least since the golden days of Medieval philosophy. I am particulary grateful to E. Sosa for allowing me to include « Truth-makers », which is reprinted by permission of the publishers for the first time since it originally appeared in Philosophy and Phenomenological Research (44,1984, 287-321). It certainly looked as an exciting, and altogether illuminating, project to ask each of the three co-authors to revisit the topic of thruthmaking vingt-ans après – though not an easy task, to be sure, as the issue had become more and more complex and since its main import somehow evolved in the meantime. K. Mulligan, P. Simons and B. Smith have been writing extensively on this subject ever since, though never in single volume. It will be seen that, whereas there are is now some amount of disagreement in important respects, there is still much that is agreed on the main issues at stake. Clearly, the debate about truthmakers is not merely terminological. While still emphazing the failure of a purely semantic account of truth, the discussion has now taken an evident metaphysical turn, bearing not only on the existence, but also on the very nature of those entities that truthmakers are held to be (along with other entities, such as meanings or essences). Of course, an enormous debt is also owed to Professor D. Armstrong, who, at the Aix Conference (and in this volume as well), accepted to lend himself to a vivid and open-minded discussion of his own views – notably, his endorsement of so-called « Truthmaker Maximalism ». As it stands, the volume is

8 on line with our original project. It contains a reply by Armstrong to his youngest objector among the participants, Philipp Keller, as well as P. Simons’ comments on a paper by S. Mumford on the vexed issue (also discussed by Armstrong) of whether negative truths require negative facts as their truthmakers. It also includes papers by other participants in the debate which took place in Aix, such as S. Caputo, F. Clementz, P. Engel an F. Nef, who helped to broaden the scope of the discussion. It came as a happy surprise that, absent any preliminary agreement on a pre-established ordre du jour (beyond the general topic of truthmaking), so much convergence on the focus resulted in the end. Thanks are specially due to H. Hochberg and E.J. Lowe, who, though they could not attend the Conference, also accepted to contribute to this volume – and whose papers clearly bear witness of the perennial fecundity of analytical metaphysics. The Aix Conference was held with the help of CEPERC (CRS 6059) and his director, Pierre Livet. It was organized within the framework of the Séminaire de métaphysique and, more broadly, of the Institut d’Histoire de Philosophie. I am extremely grateful to Alonso Tordesillas, director of the IHP (EA 3276), for his help and financial support. Absa D’Agaro and Christine Carcassonne also deserve special thanks for their invaluable secretarial assistance. Finally, I would like to thank Pr. Hüntelman for his encouragement and advice : without his help, this book would clearly never have existed.

Truth-Makers* KEVIN MULLIGAN University of Hamburg PETER SIMONS University of Salzburg BARRY SMITH University of Manchester

When I speak of a fact . . . I mean the kind of thing that makes a proposition true or false. (Russell, 1972, p. 36.)

§ 1. Making True During the realist revival in the early years of this century, philosophers of various persuasions were concerned to investigate the ontology of truth. That is, whether or not they viewed truth as a correspondence, they were interested in the extent to which one needed to assume the existence of entities serving some role in accounting for the truth of sentences. Certain of these entities, such as the Sätze an sich of Bolzano, the Gedanken of Frege, or the propositions of Russell and Moore, were conceived as the bearers of the properties of truth and falsehood. Some thinkers however, such as Russell, Wittgenstein in the Tractatus, and Husserl in the Logische Untersuchungen, argued that instead of, or in addition to, truth-bearers, one must assume the existence of certain entities in virtue of which sentences and/or propositions are true. Various names were used for these entities, notably ‘fact’, ‘Sachverhalt’, and ‘state of affairs’.1 In order not to prejudge the suitability of these words we shall initially employ a more

*

First published in Philosophy and Phenomenological Research, 44 (1984), 287-321. Ontologies of Sachverhalte were defended also by Reinach (in his 1911) and Ingarden (1964/65, chap. XI; cf. The discussion in Smith, 1978). Meinong preferred to use the term ‘Objective’. 1

10 neutral terminology, calling any entities which are candidates for this role truth-makers.2 The fall from favour of logical realism brought with it a corresponding decline of interest in the ontology of truth. The notions of correspondence and indeed of truth itself first of all came to appear obscure and ‘metaphysical’. Then Tarski’s work, while rehabilitating the idea of truth, seemed to embody a rejection of a full-blooded correspondence.3 In the wake of Tarski, philosophers and logicians have largely turned their attentions away from the complex and bewildering difficulties of the relations between language and the real world, turning instead to the investigation of more tractable set-theoretic surrogates. Work along these lines has indeed expanded to the extent where it can deal with a large variety of modal, temporal, counterfactual, intentional, deictic, and other sentence-types. However, while yielding certain insights into the structures of language, such semantic investigations avoid the problem of providing an elucidation of the basic truth-relation itself. In place of substantive accounts of this relation, as proffered by the Tractatus or by chapter II of Principia Mathematica,4 we are left with such bloodless pseudo-elucidations as: a monadic predication ‘Pa’ is true iff a is a member of the set which is the extension of ‘P’. Whatever their formal advantages, approaches of this kind do nothing to explain how sentences about the real world are made true or false. For the extension of ‘P’ is simply the set of objects such that, if we replace ‘x’ in ‘Px’ by a name of the object in question, we get a true sentence. Set-theoretic elucidations of the basic truth-relation can, it would seem, bring us no further forward. Putnam (pp. 25 ff.) has argued that Tarski’s theory of truth, through its very innocuousness, its eschewal of ‘undesirable’ notions, fails to determine the concept it was intended to capture, since the formal characterisation still fits if we re-interpret ‘true’ to mean, for example, ‘warrantedly assertable’ and adjust our interpretation of the logical 2

Cf. Husserl, LU VI, § 39: “At each step ... one must distinguish the true-making state of affairs from the state of affairs constitutive of the self-evidence itself.” 3 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 what is that it is, or of what is not that it is not, is true” (Met., 1011b32 ff.) is, as Tarski himself is anxious to claim (1944, p. 343), less than full-blooded correspondence theory, but Aristotle is elsewhere (op. Cit., 1027b22, 1051b32 ff.) prepared to speak of truth reflecting ‘combinations’ of subject and attribute in reality. 4 Cf. Also the opening sections of Weyl, 1918.

11 constants accordingly. Putnam’s conclusion (p. 4) is that if we want to account for truth, Tarski’s work needs supplementing with a philosophically non-neutral correspondence theory. This paper is about such a theory. If we are right that the Tarskian account neglects precisely the atomic sentences, then its indeterminacy is not surprising.5 If, as we suggest, the nature of truth is underdetermined by theories like that of Tarski, then an adequate account of truth must include considerations which are other than purely semantic in the normally accepted sense. Our suggestion here – a suggestion which is formulated in a realist spirit – is that the way to such a theory lies through direct examination of the link between truth-bearers, the material of logic, and truth-makers, that in the world in virtue of which sentences or propositions are true. The glory of logical atomism was that it showed that not every kind of sentence needs its own characteristic kind of truth-maker. Provided we can account for the truth and falsehood of atomic sentences, we can dispense with special truth-makers for, e.g., negative, conjunctive, disjunctive, and identity sentences. As Wittgenstein pregnantly put it: My fundamental idea is that the ‘logical constants’ do not represent; that the logic of facts does not allow of representation. (Tractatus, 4.0312)

This insight is an indispensable prerequisite for modern recursive accounts of truth. It adds further weight to the idea that our attentions should be focused on atomic sentences. We shall in fact concentrate on those which predicate something of one or more spatio-temporal objects. Whether this is a serious limitation is not something that we need here decide, for sentences of this kind must at all events be handled by a realist theory. The neutral term ‘truth-maker’ enables us to separate the general question of the need for truth-makers from the more particular question as to what sort – or sorts – of entities truth-makers are. In the main part of the paper 5

It parallels, perhaps, the indeterminacy of a theory of the natural numbers founded on the five Peano axioms. It is not only the natural numbers as we normally conceive them which 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 progressions. Even if we add recursive axioms for addition and multiplication to eliminate the interpretations above, we cannot rule out non-standard models. We can narrow down to the natural numbers only if we take account of their application, outside the formal theory, in counting.

12 we shall consider the claims of one class of entity, which we call moments, to fill this role. Since moments, once common in philosophical ontologies, have been relatively neglected in modern times, we shall both explain in some detail what they are, and suggest arguments for their existence independent of their possible role as truth-makers. We shall then consider the light that is thrown by this discussion of moments on better-known theories of truth-makers – and particularly upon the theory of the Tractatus. § 2. Moments A moment is an existentially dependent or non-self-sufficient object, that is, an object which is of such a nature that it cannot exist alone, but requires the existence of some other object outside itself. This characterisation needs sharpening, but it will be useful to provide some preliminary examples of types of moments, and some indications of the honourable pedigree of the concept in the philosophical tradition. Consider, first of all, that sequence of objects described at the beginning of Robert Musil’s novel The Man without Qualities: A depression over the Atlantic an area of high pressure over Russia, patches of pedestrian bustle, the pace of Vienna, a skidding, an abrupt braking, a traffic accident, the carelessness of a pedestrian, the gesticulations of the lorry driver, the greyness of his face, the prompt arrival of the ambulance,

13 its shrill whistle, the cleanliness of its interior, the lifting of the accident victim into the ambulance. It might at first seem strange to admit expressions like ‘a’s carelessness’ or ‘b’s cleanliness’ as referring expressions at all. There is an ingrained tendency amongst contemporary philosophers to regard such formations as mere façons de parler, properly to be eliminated from any language suitable for the purposes of philosophical analysis in favour of more robust talk involving reference only to, for example, material things. Here, however, we wish to revert to an older tradition which can readily accommodate expressions of the type illustrated as designating spatiotemporal objects, albeit objects which exhibit the peculiarity that they depend for their existence upon other objects.6 A skidding, for example, cannot exist unless there is something that skids and a surface over which it skids. A smiling mouth smiles only in a human face. The concept of moment makes its first appearance in the philosophical literature in the Categories of Aristotle, Chapter 2. Here Aristotle introduces a fourfold distinction among objects according as they are or are not said of a subject and according as they are or are not in a subject:7 Not in a subject (Substantial)

Said of a subject (Universal, General)

Not said of a subject (Particular, Individual) 6

In a subject (Accidental)

[Non-substantial [Second Substances] Universals] man

whiteness, knowledge

[First Substances]

[Individual Accidents]

this individual man

this individual whiteness,

We use ‘object’ for all those entities which can be named, leaving open whether there are other, non-objectual entities, such as the Sachverhalte and Tatsachen of the early Wittgenstein. 7 On the provenance of such diagrams, cf. Angelelli, 1967, p. 12.

14 horse, mind, body

this individual knowledge of grammar

An individual accident is, in our terms, one special kind of moment, being such that, to use Aristotle’s words, ‘it cannot exist separately from what it is in’ (Cat., 1a20). This ‘being in’ is not the ordinary part-whole relation; for the parts of a substance are themselves substances (Met., 1028b9-10), where the entities ‘in’ a substance are its individual accidents. If we are prepared to follow Aristotle and many Scholastics in accepting that there are particulars standing to many non-substantial predicates as individual substances stand to substantial predicates, then we tap a rich source of moments. The particular individual redness of, say, a glass cube, which is numerically distinct from the individual redness even of a qualitatively exactly similar cube, is a moment, as is the snubbedness of Socrates’ nose, and the particular individual knowledge of Greek grammar possessed by Aristotle at some given time. Whilst accidents or particularised qualities are the kinds of moments most commonly found in the tradition, it must be pointed out that many other objects meet our definition. One group of examples not foreign to Aristotle are boundaries (the surface of Miss Anscombe’s wedding ring, the edge of a piece of paper, the Winter Solstice). And further examples are provided by all kinds of configurations and disturbances which require a medium, such as a smile on Mary’s face, a knot in a piece of string, sound waves, cyclones, etc., and more generally all events, actions, processes, states, and conditions essentially involving material things: the collision of two billiard balls or Imperial State carriages, the thrusts and parries of dueling swordsmen, the explosion of a gas, the remaining glum of Mary’s face, John’s having malaria, two billiard balls’ being at rest relative to each other, and countless more. We make no attempt here to carry out the task of dividing all these examples into mutually exclusive and exhaustive categories. It is important for our purposes only to realise that moments may be parts of other moments, that moments, like substances, may be divided into simple and complex. This is most clearly shown for temporally extended moments. The first wrinkling of John’s brow is a part of his frown, the first dull throbbing a part of his headache, the final C major chord a part of a

15 performance of Beethoven’s Fifth. More controversially, perhaps, we would regard certain kinds of spatially extended moments as parts of others, as the redness of one half of a glass cube is part of the redness of the whole cube.8 Although we have cast our net wide, we know a priori that not everything can be a moment: the world is not a moment, since if it were, it would require some thing outside itself in order to exist, in which case it would not be the world.9 Moments reappear in post-Scholastic philosophy as the modes of Descartes, Locke, and Hume. For Descartes, a mode is that which is not a substance, where By substance we can mean nothing other than a thing existing in such a manner that I has need of no other thing in order to exist. (Principia philosophiae, I, LI) While transposed into the idiom of ideas, Locke’s definition is in accord with that of Descartes: Modes I shall call complex Ideas, which however compounded, contain not in them the supposition of subsisting by themselves, but are considered as Dependencies on, or Affectations of Substances; such are the Ideas signified by the Words Triangle, Gratitude, Murther, etc. (Essay, Book II, chap. XII, § 4)

Hume, though he has less to say about modes than Locke, assumes that it is well-known what they are, and gives a dance and beauty as examples (Treatise, Book I, Part II, § VI).

8

Cf. Husserl LU III, § 4; Smith and Mulligan, 1982a, § 3. According to Spinoza (Ethics, Part I) this is the only non-moment and similar views can be found in Husserl. Campbell, 1976, p. 103, suggests that Spinoza’s views may be upheld on the basis of modern physics. However, as Husserl indicates, there are various possible senses of ‘dependent’, which accordingly allow different notions of moment and substance to be defined (cf. Simons, 1982). Individual organisms, conceived by Aristotle as substances, are mere modes for Spinoza and mere aggregates for Leibniz; since all three, we may suppose, were operating with different notions of substance, these conceptions need not in fact be incompatible. 9

16 It was, however, in the philosophy of the German-speaking world that the Aristotelian ontology, and particularly Aristotle’s theory of substance and accident, was most systematically preserved.10 Thus the doctrine of moments was fundamental to many students of Brentano, having ready application is psychology. Carl Stumpf explicitly distinguished among the contents of mental acts between dependent (‘partial’) and independent contents (1873, p. 109), a distinction refined and generalised to all objects by his student Husserl.11 In his early ontology Meinong took it for granted that properties and relations are particulars, not universals.12 In modern Anglo-|Saxon philosophy commitment to entities of this kind is rarer, a notable swimmer against the tide being Stout, with his ‘characters’. Support for the notion has been otherwise sporadic, and never enthusiastic, often coming, again, from philosophers acquainted with the Scholastic notion of accident.13 We have taken the term ‘moment’ from Husserl’s masterful and painstaking study of the notions of ontological dependence and independence and of associated problems in the theory of part and whole.14 A moment is an object whose existence is dependent upon that of another 10

Cf. Smith and Mulligan, 1982, § § 1-3. See the third Logical Investigation and also Husserl, 1894, which represents a handway stage between the early Brentanist theory and Husserl’s fully developed formal ontology. 12 Findlay, 1963, pp. 129, 131; Grossmann, 1974, pp. 5, 100 f. 13 The following list is not complete, but it shows the tenacity of the idea, despite its lack of general acceptance. J. Cook Wilson, 1926, II, p. 713, P.F. Strawson, 1959, p. 168; 1974, p. 131 (particularised qualities); D.C. Williams, 1953, K. Campbell, 1976, chapter 14 (tropes); P.T. Geach, 1961, pp. 77-80 (individualised forms); G. Küng, 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 of ramification among moments; e.g., that there are moments of moments, moments of parts, parts of moments, etc. Cf. Husserl, LU III, § 18 ff., Smith and Mulligan 1983. 14 The interpretation and defense of Husserl’s theory, the history of the concept since Brentano, and its applications in various disciplines, are all topics we have treated elsewhere: cf. The essays in Smith, ed., 1982. 11

17 object. This dependence is itself no contingent feature of the moment, but something essential to it. An adequate theory of moments must therefore involve appeal to the notion of de re or ontological necessity,15 in contrast to both de dicto (logical) necessity and causal necessity. The objects on which a moment depends may be called its fundaments. Now an object one of whose parts 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 contains the 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 in so far as they are bound up with (are moments of) the brain. So we specify that the fundaments of a moment cannot be wholly contained within it as its proper or improper parts. This also excludes the undesirable consequence of having everything figure as its own fundament, and hence, trivially, as a moment o f itself. Moments may accordingly be defined as follows: a is a moment iff a exists and a is de re necessarily such 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 a proper or improper part of a. In such a case, b is a fundament of a, and we say also that b founds a or a is founded on be. If c is any object containing a fundament of a as proper or improper part, but not containing a as proper or improper part, we say, following Husserl, that a is dependent on c. Moments are thus by definition dependent on their fundaments. Objects which are not moments we call independent objects or substances. There is nothing in this account which precludes fundamenta from themselves being moments, nor the mutual foundation of two or more moments on each other.16 Clearly moments, like substances, come in kinds, including natural kinds.17 And just as commitment to individual substances or things entails neither the acceptance nor the rejection of an ontology of universals or species which these exemplify, so we can distinguish a realist and a nominalist 15

De re necessity will be understood here as a matter of the necessary structure of objects and object-configurations, not, as in many contemporary writings on essentialism and related notions, as a matter of relations between objects and concepts, or between objects and descriptions under which they fall. 16 These issues are discussed in Smith and Mulligan, 1982, § 6, 1982a, and in Smith, 1981. 17 Husserl’s characterisation of foundation and dependence in LU III makes indispensable use of kinds, which we have here tried to avoid: cf. Simons, 1982 and for an exposition more sympathetic to Husserl, Smith, 1981.

18 option with regard to kinds of moments. A strong realism, as in Aquinas and perhaps Aristotle, sees both substances and moments as exemplifying universals. On the other hand, a thoroughgoing nominalism, which is only one step – but it is an important step – removed from reism, accepts only particular substances and moments, conceiving the existence of our talk about moment-kinds as having its basis simply in relations of natural resemblance among examples of moments given in experience. Further details about the kinds of moments and substances may be spared here. Suffice it to note that all the intuitive examples offered above clearly fit our specification, since in each case there exist objects, not part of those in question, whose existence is a prerequisite for that of the respective moments. In most of the examples it is clear that the moments are not of the right category to be even possible parts of their fundaments, which reinforces Aristotle’s remark that accidents are in their substances but not as parts. At the same time his ‘in’ is frequently inappropriate; for instance a duel is ‘in’ neither of the duelers, not is it ‘in’ the dueling pair or the aggregate of duelers.18 § 3. Moments as Truth-Makers The idea that what we call moments could serve as truth-makers is perhaps unusual, but it is not without precedent. If we return to Russell, we find that amongst the examples of facts he gives is the death of Socrates, “a certain physiological occurrence which happened in Athens long ago” (loc. Cit.). From this we infer that, for Russell, at least some states and events are truth-makers. This indicates that he is not conforming to the ordinary usage of ‘fact’, since what is normally said to be a fact is not the death of Socrates but that Socrates died.19 Socrates’ death took place in Athens, and 18

When Leibniz objects to relational accidents as accidents “in two subjects, with one leg in one, and the other in the other, which is contrary to the notion of accidents” (Alexander, ed., p. 71), he too is misled by the connotations of ‘in’, which applies at best to those non-relational accidents located within the space occupied by their fundaments. A better all-purpose preposition is the genitive ‘of’. 19 See Vendler, 1967, chapter 5, “Facts and Events,” who shows very clearly that: “If the correspondence theory requires a relation between empirical statements and observable entities in the world, then facts are not qualified for this latter role” (pp. 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 and Transcendental Logic). Cf. Also Strawson, 1974, especially pp. 130 ff.

19 was caused by his drinking hemlock. We do not however say that Socrates’ death is 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 drew the conclusion that facts are not to be distinguished from true propositions.20 Here then, we shall distance ourselves from Russell’s usage, but not from his theory. Support for Ramsey’s distinction and, surprisingly, for a view of some moments as truth-makers comes from other quarters. Davidson, not known as a friend of facts, says of a sentence like ‘Amundsen flew to the North Pole in 1926’ that “if [it] is true, then there is an event that makes it true” (1980), p. 117) and holds that “the same event may make ‘Jones apologized’ and ‘Jones said “I apologize”’ true” (op. cit., p. 170). The clue that moments may serve as truth-makers comes initially from linguistic considerations. Most terms which describe moments, or under which moments fall, are in fact nouns formed by nominalisation of verbs and verb-phrases. These are morphologically varied: some have separate but related forms (‘birth’, ‘flight’, ‘death’), some are simply gerunds (‘overturning’, ‘shooting’), some are homeomorphic with the corresponding verb (‘hit’, ‘kiss’, ‘smile’, ‘jump’, ‘pull’), and some are formed using particular morphemes for the purpose (‘generosity’, ‘redness’, ‘pregnancy’, ‘childhood’, etc.). Of these the most neutral and universally applicable is the gerundial form ‘ – – ing’, which, when applied not to a verb but to a noun or adjective complement, attaches to the copula to give phrases of the form ‘being (a) – – ’. Gerundial phrases are often equivalent to other morphological forms: there is no difference in our view (or Aristotle’s) between a cube’s being white and its whiteness, nor is there a difference between the collision of two objects and their colliding. All of these forms are, however, radically distinct from nominalisations constructed by means of the conjunction ‘that’, a fact not always appreciated in the analytic literature on propositions, states of affairs, facts, etc. Thus, following Russell’s suggestion, we shall here consider the theory obtained from the view that what makes it true that Socrates died is Socrates’ death, what makes it true that Amundsen flew to the pole is his flight, what makes it true that Mary is smiling is her (present) smile, and so 20

Ramsey, 1978, p. 44. Cf. Prior, 1971, p. 5. Ramsey’s arguments are anticipated by Reinach in his 1911: see especially § 8 f. of the translation.

20 on. Or, in other words, that for many simple sentences about spatiotemporal objects the truth-makers for these sentences are the moments picked out by gerundials and other nominalised expressions closely related to the main verbs of the sentences in question. In place of Tarskibiconditionals 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 being white (the whiteness) of this cube, and if no such whiteness exists, then ‘This cube is white’ is false.

Because the whiteness in question here is a particular dependent on the cube, and not a universal whiteness shared by all white things, its existence does nothing to make sentences about other things being white either true or false. If all atomic sentences contain a main verb, and all nominalisations denote moments, then it would follow, in fact, that all truth-makers are moments, that what makes it true that a is F is a’s being F, what makes it true that a R’s b is a’s R-ing b, and so on. This simplest possible version of the theory is inadequate as it stands, however. Not only because, as we shall see, there are certain types of not obviously non-atomic sentences, for example existence and identity sentences, recalcitrant to the analysis, but also, and more importantly, because the theory which claims that by nominalising a sentence we have thereby designated the relevant truth-maker can hardly count as a substantial elucidation of making true. It seems – like Tarski’s theory – to turn on a linguistic trick. In fact the device of nominalisation gives us only the kernel of a theory. That this kernel requires considerable expansion may be gathered from certain intuitive considerations relating to the status of moments as entities in the world existing independently of our sentence-using acts. For we want to say, surely, that if a moment a makes the sentence p true, and b is any moment containing a as part, then b makes p true as well. That John’s head ached between 1 p.m. and 1:10 p.m. is made true not just by that tenminute segment of his headache, but by any part of it containing this segment. So p may have a minimal truth-maker without having a unique

21 one.21 Further, a sentence may be made true by no single truth-maker but only by several jointly, or again only by several separately. Thus we know that viral hepatitis comes in two sorts: acute infectious or A-hepatitis, and homologous serum or B-hepatitis. If the hapless Cyril has both A- and Bhepatitis simultaneously, then that he has viral hepatitis is made true both by the moment or moments which make it true that he has A-hepatitis, and by the moment or moments making it true that he has B-hepatitis, though either would have sufficed alone. So the sentence ‘Cyril has viral hepatitis’ has in such circumstances at least two truth-makers. In general there is no guarantee that the logical simplicity of a sentence guarantees the uniqueness or the ontological simplicity (atomicity) of its actual or possible truth-maker(s). There is, of course, a temptation to argue that ‘Cyril has viral hepatitis’ is not logically simple but implicitly disjunctive, its logical form being not adequately mirrored in its grammatical form, which is that of a logically simple sentence. But we believe that the given sentence is indeed logically simple: it contains no logical constants and no expression, ‘viral hepatitis’ included, which is introduced into the language by definition as equivalent to an expression containing a logical constant. In taking this view we are consciously departing from a dogma that has characterised mush of analytic philosophy since its inception: the dogma of logical form. This has many manifestations. One version appears in The Principles of Mathematics where Russell, whilst on the one hand regarding all complexity as mind independent, nevertheless holds that this same complexity is capable of logical analysis (1903, p. 466). This idea of a perfect parallelism of logical and ontological complexity is the misery of logical atomism, leading Russell to a metaphysics of sense-data and Wittgenstein to supraexperiential simples.22 Here, in contrast, we uphold the independence of ontological from logical complexity: ontologically 21

We may call this minimal truth-maker the truth-maker for the sentence, thereby making a non-Russellian use of definite descriptions. Thus Sharvy, 1980, has shown how definite descriptions may pick out maxima rather than unique objects. ‘The coffee in this room’, for example, picks out the total quantity of coffee in the room. That descriptions may pick out also minima is shown not only by the example mooted in the text but also by, e.g., ‘the place where the accident happened’, which picks out the smallest spatial extent circumcluding the accident. 22 The difference between Russell and Wittgenstein consists principally in the fact that Wittgenstein has stronger criteria for simplicity and independence: cf. Simons, 1981.

22 complex objects (those having proper parts) are not for that reason also in some way logically complex, any more than there is reason to suppose that to every logically complex (true) sentence there corresponds an ontologically complex entity which makes it true. A second and more elusive version of the dogma enjoys wider support. It includes the Russell-Wittgenstein position as a special case, but is not confined to logical atomists. Roughly speaking, it says that if a sentence has or could have more than one truth-maker, then it is logically complex. If the sentence appears nevertheless to be simple in form, this complexity is hidden and is to be uncovered by a process of analysis. One possible argument for this view may be put in terms of truth-makers thus: since disjunctive and existential sentences may have more than one truth-maker, and conjunctive and universal sentences must, except in degenerate cases, have more than one, sentences which may or must have more than one truth-maker are implicitly disjunctive or existential, or conjunctive or universal. As it stands this argument is palpably invalid, being of the form ‘All A are B, therefore all B are A’; but there are other reasons why the position has been found attractive.23 Here, however, we shall confine ourselves to registering our dissent from the view. Although ‘Cyril has viral hepatitis’ may be logically equivalent to (i.e., have the same truth-conditions as) ‘Cyril has A-hepatitis or Cyril has B-hepatitis’, this is not something that can be established by any lexical, grammatical, or logical analysis of the meaning of the sentence, but at most by empirical research. This research does not uncover a hidden ambiguity in the term ‘hepatitis’; we simply discover that the term is determinable.

23

One attraction, which dies hard, is that of exhibiting all the entailments of a sentence as resulting from the substitution of synonyms and from the application of the inference rules for the logical constants (i.e., of exhibiting all entailments as analytic in the Fregean sense). A sentence p´ analyses p, let us say, when p´ arises from p in this manner. The two sentences are then logically equivalent, and the purely logical consequences of p´ (those obtained through the rules for logical constants alone) properly include those of p. So p has some consequences which cannot be derived from it by purely logical means, but can from p´. Since p’ more closely resembles the desired ideal, it is common to conceive it as exhibiting a ‘hidden’ logical form of p. If the ideal is discredited however (cf. the attempt in Smith, 1981), then this conception too loses its attraction. The ideal amounts to the disputed claim, which we reject, that necessity is analytic.

23 Since we are realists in respect to moments, and regard their investigation as a substantial, often as an empirical matter, we hold it to be perfectly normal for us to know that a sentence is true, and yet not know completely what makes it true. Thus the characterisation of that theory whereby the meaning of a sentence is given by its truth-conditions as ‘realist’ (Dummett, chap. 13) is for us ironical. A knowledge of truth-conditions takes us at most one step towards reality: one can, surely, envisage understanding a sentence (knowing its meaning), whilst at the same time having only partial knowledge of the nature of its possible truth-makers. Those who used the term ‘hepatitis’ before the discovery of its varieties did not fail to understand the term; they were simply (partly) ignorant about hepatitis. That the investigation of what makes a particular sentence true is thus fundamentally an empirical, not a philosophical one, is not belied by the fact that for many sentences we can pick out the relevant truth-makers by nominalisation. There is, in the general case, no cheap and easy way to determine the truth-makers even of simple descriptive sentences via linguistic transformations. Are all truth-makers moments? For three kinds of sentences this may be questioned. The first are predications which are, as Aristotle would say, 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 are true atomic sentences, but logically contingent, we should expect them to have truthmakers. In virtue of the special status of such sentences, might it not be the things themselves, John and Tibbles, which play the role of making true, or are there certain moments of John and Tibbles which are essential to them as men or cats which serve to make the given sentences true? One reason for thinking the latter is that, if John makes the sentence ‘John is a man’ true, then he also makes ‘John is an animal’ true, which means that these two sentences, having the same truth-maker, have the same truthconditions, and are logically equivalent. Only if logical equivalence and synonymy are the same, however, is this objection really telling. We conceive it as in principle possible that one and the same truth-maker may make true sentences with different meanings: this happens anyway if we take non-atomic sentences into account, and no arguments occur to us which suggest that this cannot happen for atomic sentences as well. A more important point is that if John makes it true both that John is a man and that John is an animal, and Tibbles likewise makes it true both that Tibbles is a cat and that Tibbles is an animal, then there is no non-circular

24 way of accounting via truth-makers for the fact that both are animals but that one is a man and the other a cat. Such an account could be provided if there are moments characteristic of humanity and of felinity which are both characteristic of animality. A second group of problem sentences are singular existentials such as ‘John exists’. These are certainly logically contingent, and perhaps atomic, and so they ought intuitively to have truth-makers, but then the question arises what these are. We baulk, for reasons familiar from the tradition, at providing John with a special moment of existence. The resort to the sentence ‘a . a=John’, widely held to be equivalent to ‘John’ exists, is no step forward, since we are left with the question what, if anything, makes the sentence ‘John = John’ true, and such sentences belong to our third problem group. A natural way out is, again, to elect John himself truthmaker of the given sentence, which would once more lead us to a view according to which at least some truth-makers are not moments. Indeed, a reist who recognised the need for truth-makers would have no option but that of taking things to do the job in every case. One the other hand, someone who has committed to moments would in any event have the problem of providing an account of sentences expressing their existence, and again the relevant moment itself would seem to be the most obvious candidate truth-maker.24 The third kind of problem sentences are identities. One possible line is that these too are made true by the objects in question, for instance that ‘Hesperus = Phosphorous’ is made true by Venus. This has the consequence that the identity is equivalent to ‘Venus exists’ as this sentence has been conceived above. A different solution is required for the 24

To regard a as truth-maker for ‘a exists’ is of course to cut against the grain of the established Fregean view that all meaningful existential assertions are assertions about concepts (Grundlagen, § 53). At the same time however a reading of Kant in the light of our conception must cast doubt upon the common assumption that, with his doctrine that ‘existence is not a predicate’, he had merely anticipated Frege. If God’s existence is rejected, Kant writes, “we reject the thing itself with all its predicates; and no question of contradiction can arise” (A595/B623, our italics). For Kant singular existence statements are meaningful (since synthetic), where Frege’s official line (cf., e.g., his “Über den Begriff der Zahl. Auseinandersetzung mit Kerry”) is that they are meaningless. Even where Frege bends over backwards to give them a meaning (in the “Dialog mit Punjer über Existenz”) they come out either as necessarily true or a disguised metalinguistic statements.

25 view of those logicians and metaphysicians who think that an identity of the form ‘a = a’ may be true even though there exists no object designated by the term ‘a’. One alternative here is to embrace commitment to nonexistent objects which may be taken as truth-makers for the given sentences even in those circumstances where ‘a exists’ is false. Proponents of such a view will need to embrace a new entity, such as a moment of existence, as truth-maker for true sentences of the form ‘a exists’.25 The view is, we believe, worth pursuing, though we do not follow it up here. But there is another view which holds that in some cases ‘a’ may not designate, yet ‘a = a’ be true. Here we cannot imagine what might serve as truth-maker. An indeed this suggests the most plausible solution: there is none. The grounds for believing that ‘a = a’ be true. Here we cannot imagine what might serve as truth-maker. And indeed this suggests the most plausible solution: there is none. The grounds for believing that ‘a = a’ is true even when ‘a’ is empty are that the sentence is a logical truth, i.e., that identity is a logical constant. This account is therefore in harmony with the logical atomist principle that no special objects correspond tot he logical constants. As in the case of singular existentials, the special status of identity sentences is reflected in their special position in regard to truthmakers.26

25

Meinong significantly calls that which makes the difference between an object’s existing and its not existing a ‘modal moment’ (cf. his 1915, pp. 266 ff.; Findlay, 1963, chap. 4). There are other such moments, among them one marking the factuality or subsistence (Bestehen) of an objective or state of affairs. The doctrine of modal moments was refined and considerably extended by Ingarden in his 1964/65, especially vol. I. 26 Not all the alternatives canvassed here are compatible with one another; the following is an inconsistent tetrad: (1) ‘a = a’ is true but has no truth-makers. (2) If ‘Ela’ is true, then a makes it true. (3) ‘∃x.Φx’ is made true by whatever makes any instance ‘Φa’ true. (4) ‘E!a’ and ‘∃x.x = a’ are logically equivalent. Various means of resolving this inconsistency suggest themselves. That closest to classical logic would reject (1) and make a the truth-maker for ‘a = a’; it must then

26 Whether or not it is correct that thins as well as moments can be truthmakers, the possibility emphasises one merit of the present theory over rival correspondence theories of truth which invoke a special category of non-objectual entity – facts, states of affairs, or whatever – simply to serve as truth-makers. For if we are convinced for other reasons that things and moments exist, and if – as we shall argue below – we can be said unproblematically to be acquainted with them, for example perceptually, then the resultant theory of truth-makers is both more economical and stronger than rival theories whose truth-makers are less firmly tied into our ontology and epistemology. The relation of making true is to be distinguished both from that of designation and from that between an object and a predicate or concept under which the object falls. Truth-makers cannot, on our theory, be the designata of the sentences they make true, even if we confine ourselves to atomic sentences. This is, of course, no news to those who believe (as we do) that sentences do not designate at all. But for those who incline to the contrary it only needs pointing out that sentence with more than one truthmaker would on their account have to be treated either as ambiguous or as multiply-designating. Both alternatives are implausible. We argued against the first above. As to the second, we are not against plural or multiple designation as such – quite the contrary27 – but there is no distinction amongst multiple designating or plural terms which corresponds to that between several objects’ jointly (i.e., conjunctively) making a sentence true, and their severally (i.e., disjunctively) making a sentence true. A further difficulty faced by any view to the effect that (true) atomic sentences designate their truth-makers is that, if we are right about singular existential sentences being made true by their subjects, then both ‘a and ‘a exists’ have the same designatum, so one has the problem of explaining regard ‘a = a’ as meaningless or false if a does not exist. The solution closest to free logic is to reject 3 and replace it by: (3*) ‘∃x.Φx’ is made true by whatever pairs a, b are such that a makes ‘E!a’ true and b makes ‘Φa’ true. If we introduce a non-standard particular quantifies for which there holds the equivalent of (3) with ‘Σ’ replacing ‘∃’, then ‘∃x.Fx’ and ‘Σx.E!x∧Φx’ are logically equivalent. Such a quantifier already exists in the work of Lesniewski (cf. Simons, 1981a). 27 Simons, 1982a, b.

27 their syntactic and semantic diversity. Since the nominalisations considered above can appear as rightfully in designating phrases as any other common nouns, truth-makers can be designated. But this is not to say that they are designated by the sentences they make true. It is still more obvious that truth-makers do not fall under sentences as objects fall under predicates. The semantic relations of designating, falling under and making true are all distinct. What makes ‘John’s headaches true – a moment of John – is something that falls under the predicate ‘is a headache’ and is designated by ‘John’s (present) headache’. But from the fact that sentences, terms, and predicates have different syntactic and semantic roles, it does not follow that there are three kinds of entity standing over against them. Nor however does the fact that truth-makers are designated by terms and fall under predicates imply that any of these syntactic and semantic roles collapse into one another. Since truth-makers can be designated, they can be quantified over. From ‘John’s singing exists’,28 we can infer ‘a.a is a singing and John does a’ or, more idiomatically, ‘John is singing’, and conversely. That many normal sentences about events are equivalent to existential sentences was asserted already by Ramsey (1978, p. 43), and the same view has also been taken by Davidson (1980, p. 118). It is certainly true that ‘Amundsen flew to the North Pole’ does not, where ‘Amundsen’s flight to the North Pole took place’ does, imply that only one flight took place. Both Ramsey and Davidson conclude from this that sentences like the former are existential sentences in which events are quantified over. But this is an instance of the dogma of logical form at work. The sentence is undoubtedly logically equivalent to such an existential generalisation, but that tells us only that they have the same truth-conditions. Despite this, and despite their having the same event as truth-maker, the two are of quite different form. The Ramsey-Davidson view may spring in part from an echo of the false view that truth-makers are designated by their sentences. Realising that uniqueness is not guaranteed, they move from designation to the next best thing, quantification. No doubt events make quantificational sentences

28

Like Ramsey, we say that events exist, where it would be more idiomatic to say that they occur or happen. Similarly we use ‘exist’ for states of affairs, instead of the more usual ‘obtain’ or ‘hold’.

28 true, but they make other, non-quantificational sentences true as well, including sentences equivalent to the quantificational ones.29 § 4. Moments as Objects of Perception Most philosophers will acknowledge the credentials of at least some of the objects we have called moments. However, many of the sentences of the types we have considered require, on our theory, truth-makers whose existence is controversial, such as particularised qualities. So if moments are to play the role we suggest, it is incumbent on us to give a general defence of their existence, controversial cases included, which is as far as possible independent of their putative status as truth-makers. This is the more important since we have dissociated ourselves from the RamseyDavidson argument via logical form, which is treated by many as a principal reason for believing in events and their ilk. A number of arguments can be offered by friends of moments against the sceptic.30 We shall concentrate here on just one such, which turns on the fact that moments, like things, may be the objects of mental acts, in particular of acts of perception. If it is conceded that there are episodic mental acts such as seeings, hearings or smellings which have as their objects such things as Mary or a table, then, the argument goes, acts of similar kinds must be recognised which take as their objects such moments as the roughness of the table, Mary’s smile, John’s gait or Rupert’s howling31 The philosopher staring hard at a picture of two swordsmen en 29

Ad hominem, Davidson’s own psycho-physical identity theory allows one single event to make true two non-synonymous sentences, one in physical, one in mental vocabulary. Davidson, 1980, pp. 214 ff. 30 A reistic ontology, in which there are only independent things standing in relations of total and partial resemblance, will be unable to account satisfactorily for the natural affinities 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 similarities between moments to flesh out the account, whilst however avoiding commitment to universals (cf. Simons, 1983 for a sketch of an ontology of things and moments which remains squarely within the ambit of nominalism). This is one reason for being well disposed toward moments. Other arguments turn on the fact that only a commitment to moments can enable us to render intelligible the constraints on division of material objects into smaller pieces, and that the existence of formal as well as material relations between objects makes sense only on the assumption that there are moments. Cf. Smith and Mulligan, 1982, 1982a. 31 This argument derives from Husserl. See, e.g., LU VI, § § 48-50.

29 face may be tempted to think that only independent objects are depicted – the two swordsmen, their swords. But whoever observes swordsmen in the real world sees not only them and their swords but also their particular lunges, parries and much else. These are also depicted in fencing manuals, and it is perception of them, not simply of the swordsmen, which forms the basis for our judgments of a swordsman’s competence. Similarly what his mother hears is Rupert’s howling, and it is this, or perhaps a particular pitch this howling suddenly takes on, which causes her to get up to feed him. This last point makes clear that, counting events as moments, we accept that moments can stand in causal relations to one another. Rupert’s howling causes Susan’s hearing him howl, and this (given the prevalent neural conditions underlying maternal concern) causes her to get up. The episodic perceivings are themselves moments standing in causal relations to other events. This argument has the advantage that it can claim to be neutral with respect to particular theories of perception. The proponent of moments claims merely that whatever connection a theory of perception makes between perceptions and their objects, this connection holds whether the object is a think or a moment or a combination of the two. This includes theories which award a central role to a causal connection between object and perceptual act. Thus any account of the role of sensations in perceiving things will, we claim, h ave a parallel in the perception of moments. Profile and perspective problems will present themselves in precisely the same way for perceivings of things and moments. (Do I see the swordsman or just the profile presented to me? Do I see his easy parry or only the phase not obscured by his interposed shoulder?) Further, the problems posed by the interplay between cognition or background knowledge and perception, and by the intentionality (opacity) of perception are – quite reasonably – assumed to arise for both things and moments. Thus the proponent of moments as the sorts of moments they are, only that what we perceive in such cases are moments. Someone seeing a flash of lightning sees a moment: a discharge dependent on the charged air and water-molecules in which it takes place. But he may well not know that it is such a discharge, and there is, surely, a sense in which he does not see its fundaments.32

32

Dependence was originally defined by the psychologist Stumpf (1873, chap. 5) in terms of the impossibility of separate perception. That is (roughly) a is dependent upon b iff a cannot be perceived separately from b. It was definitions of this sort which

30 Many philosophers are prepared to accept truth-bearers as abstract entities, and would argue that this obviates the need for truth-makers, since predications about truth-makers can, they contend, be traded in for predications about truth-bearers, with little or no trouble. It is a distinguishing feature of the perceivability-argument for moments that it thwarts a move of this kind. For the moments we have given as examples can, but their associated abstract truth-bearers cannot, be objects of perceptual acts.33 The main objection to moments has always been that any job they do can be done by independent objects, together with (on a weak option) the senses of predicate expressions and the relation of falling under, or (on a strong option) universals and the relation of exemplifying. But whoever wishes to reject moments must of course give an account of those cases where we seem to see and hear them, cases we report using definite descriptions such as ‘the smile that just appeared on Rupert’s face’. This means that he must claim that in such circumstances we see not just independent things per se, but also things as falling under certain concepts or as exemplifying certain universals. On some accounts (Bergmann, Grossman) it is even claimed that we see the universal in the thing. But the friend of moments finds this counterintuitive. When we see Rupert’s smile, we see something just as spatio-temporal as Rupert himself, and not something as absurd as a spatio-temporal entity that somehow contains a concept or a universal. The friend of moments may simply take the everyday descriptions at face value, which means that his account has a head-start in terms of naturalness. served as the starting point for Husserl’s work on a more general, ontological theory of dependence relations and Husserl clearly believed that his work represented a natural extrapolation of that of Stumpf. It would thus be surprising if it were possible to find clear-cut examples of moments in Husserl’s sense which are perceivable separately from their fundaments. Can we see a shadow or a silhouette in separation from its object, 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 a source of radiant heat do we thereby perceive also the source (again, from a certain perspective)? 33 On Locke’s theory of perception we never perceive substances (substrata) but only their accidents (Essay, Book II, chap. XXIII). A less extreme and inherently more plausible position is that whenever we perceive a substance we do so by virtue of perceiving one or more of its moments. Cf. Kenny, 1980, p. 35. If this is right, then the perception of moments, far from being peripheral, is a key issue in cognitive theory.

31 Confronted with prima facie examples of perceivings of moments, such as John’s hearing the angry edge to Mary’s voice, or Tom’s seeing the kick that Dick gives Harry, or Susan’s seeing Rupert’s smile, the opponent of moments may react in a number of different ways. One ploy is to claim that the noun-phrases apparently designating moments may be replaced salva veritate by expressions designating only independent things; ‘Susan sees Rupert’s smile’ by ‘Susan sees the smiling Rupert’, for example. For moments of moments, as in our first example, or relational moments, as in our second, the replacements will have to be more complicated. ‘John hears Mary’s angrily edged voice’ will not do, as a voice is itself a moment, so it must be something like ‘John hears the angrily-speaking Mary’, or, more implausibly still, ‘John hears the with-an-angrily-edgedvoice-speaking Mary’, the hyphenated phrase being treated as an unanalysed predicate. For the relational example we need two perceptual acts: ‘Tom sees the kicking Dick and the kicked Harry’, or, since we have ostensibly only one act here: ‘Tom sees the two-person complex consisting of the kicking Dick and the kicked Harry’. Leaving aside all worries as to the precise nature of the relation between Rupert himself and the smiling Rupert,34 and questions as to whether there are such things a person-complexes, such attempts are thwarted by opacity problems. For Susan can of course see the smiling Rupert without seeing his smile, John can hear Mary, and, we should add, her angry voice, while missing its angry edge, and Tom can see the two men and miss the kick. In saying this we are deliberately using the perceptual verb ‘see’ transparently. It might be thought that a way round the recognition of a separate category of moments would be to distinguish between this transparent sense, and an opaque or phenomenological sense, e.g., by subscripting the verb with ‘t’ and ‘p’ respectively. But however we try to capture ‘Susan sees Rupert’s smile’, e.g., with ‘Susan sees p the smiling Rupert’, or ‘Susan sees t the smiling Rupert and sees p someone smiling’, we always miss the mark. For instance, Susan may see p the smiling Rupert when in fact he is frowning – she mistakes his expression – or she may see t someone who is smiling, and mistake him for Rupert.

34

The most likely answer to this problem is that they are (if Rupert smiles) identical. (What if he does not?) But Brentano would seem to regard Rupert as a proper part of smiling Rupert. In his terminology, Rupert is a substance, smiling Rupert an accident. Cf. Brentano, 1933, pp. 107 ff., 119 ff., 151 ff.; Chisholm, 1978.

32 Similar problems beset attempts to use paraphrases involving propositional complements : ‘Susan sees that Rupert is smiling’ (she may see the smile, but fail to recognize its bearer), or complements using ‘as’: ‘Susan sees Rupert as smiling’ (so she might, but he may be frowning). To rescue his position, the opponent of moments may resort to a series of de re perceptual predicates, ‘sees-to-be-smiling’, ‘hears-to-be-angrilyspeaking’, etc., which allow that, e.g., Susan may see-to-be-smiling (Rupert), without recognizing that it is he, i.e., by taking the terms for the fundaments outside the scope of the intentional verb and putting them in extensional positions.35 But this ploy cannot cope with situations like the following. Tom wrongly thinks that Dick’s kicking of harry constitutes an attack on him, where it is in fact simply their somewhat unusual way of greeting each other. The moment theorist can accept that Tom sees t Dick’s kick, and since this is his greeting, Tom sees t Dick’s greeting of Harry. But the opponent cannot capture this 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, Harry)’ is false, since Tom does not recognize the kick for the greeting it is. There is no way for the opponent to cope with this, short of creating a new extensional position for a term designating something (i.e., some moment) which is both a kick and a greeting, and this is to concede defeat.36 It may be that reserves of ingenuity may turn up new ploys to keep moments at bay, but we dare to predict that they will be no more successful than these. Alternative attempts to cope with the cases we have mentioned in ways that do not involve commitment to moments will, we suggest, either fall short of adequacy or be ontologically and epistemologically more complex and more implausible.37

35

Cf. Quine, 1976, chap. 17; Chisholm, 1981, chap. 9. 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 not dispose of events, as Horgan (1978) thinks: no amount of predicate modification can account for our perception of events. 37 Even stronger arguments for the existence of moments may be formulated on the basis of 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 confounded by the selectivity of memory. John may for many years remember, for example, the intonation of a particular utterance Mary once directed at him, while 36

33 § 5. Truth-Making and the Tractatus We have argued that it is possible to establish a cast for the existence of moments, and for the role of moments as truth-makers, at least for certain large and important classes of sentences. In the present section we wish to supplement these arguments with a brief discussion of what is still almost certainly the most sophisticated account of truth-making to have appeared to date, the isomorphism theory of the Tractatus. The structure of the objects which make a sentence true is not, we have argued, something that can be read off from the sentence itself by purely logical means. The determination of this structure may be at least as difficult and empirical a matter as the determination of the truth-value of the sentence in question. For Wittgenstein, by contrast, the determination of the structure of truth-makers is a task not of ontology 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 of by the different sciences. He embraced instead a special category of non-objectual entities, which he called Sachverhalte, to do the job of making true. Yet there is much that we can learn from his theory of the Sachverhalt. We have indeed already taken to heart the doctrine which underlies this theory that it is a mistake to postulate special truth-makers corresponding to logically compound sentences. And we shall have occasion in § 6 below to reflect upon Wittgenstein’s own ingenious development of this doctrine – in his theory of the Tatsache. The theory of Sachverhalte may be summarized briefly as follows: the simple objects which, in Wittgenstein’s eyes, make up the substance of the world, are configurated together in various ways. An elementary sentence is true iff the simple objects designated by its constituent simple names are configurated together in a Sachverhalt whose constituents correspond oneto-one with the constituents of the sentence, the configuration of the objects being mirrored in the structure of the sentence. Sentence and Sachverhalt are then said to have the same logische (mathematische) Mannigfaltigkeit (4.04). forgetting both Mary herself and indeed the utterance in question. Mary’s smile may remind him (de re) of that of his nurse, whose smile captivated him at a tender age, though he has long since forgotten the nurse herself.

34 Wittgenstein tells us little as to the nature of the objects which are configurated together into Sachverhalte; but he does supply certain hints, as for example at 2.0131, where we are told that A speck in the visual field need not be red, but it must have some colour ... A tone must have some pitch, the object of the sense of touch must have some hardness, etc.

Consider, then, a sentence like: ‘This speck [here before me now] is red’. This sentence is made true, it would seem, by a Sachverhalt which is a combination of two objects, the speck itself and its colour. One interpretation of Sachverhalte sees them as involving both spatio-temporal particulars and universal properties and relations (colour, pitch, hardness, lies between, and the like).38 Again, it is not clear how particulars and universals may both be constituents of a single entity. A more promising interpretation may be constructed on the basis of some of Wittgenstein’s own remarks on the forms and natures of simple objects at the beginning of 2. It is, Wittgenstein tells us, not accidental to an object that it can occur in those Sachverhalte in which it does occur. Every one of its possibilities of occurrence in states of affairs must be part of the nature of the object itself, must be written into the object from the very start (2.012, 2.0121, 2.0123). Its possibility of occurring in 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 affair (2.013).39 Som objects are such that, in virtue of their form, they call for others as a matter of necessity; a tone must have some pitch, objects of the sense of touch must have some degree of hardness, and so on. Some objects are, that is to say, founded on other objects in the sense of our discussion above.40 38

Stenius, 1964, 1964, e.g., p. 63, and the relevant writings of G. Bergmann and E. Allaire. 39 There are two possible readings of Wittgenstein’s talk of ‘possible states of affairs’ in the Tractatus. On the first, Meinongian reading, we can say that there are possible states of affairs in addition to the actual states of affairs; on the second, more sober reading, we say that there are only actual states of affairs, though it is possible that other might have been actual. Here and in what follows we adopt the second reading. Terms apparently denoting possible states of affairs ought therefore to be treated in every case as syncategorematic. 40 More precisely, what we have here is generic foundation in the sense of § 4 of Simons, 1982.

35 It is, we suggest, because analytic-philosophical interpreters of the Tractatus have standardly lacked a theory of lateral foundation relations, relations which may bind together individual objects, that they have been constrained to resort to views of the kind which see Sachverhalte as involving both individuals and universal properties. It is open to us here, however, to develop a view of Sachverhalte as involving individuals alone, linked together by relations of foundation. ‘This speck is red’ might be made true, on such a view, by a two-object Sachverhalt comprising the speck and an individual moment of redness, linked by a relation of mutual foundation. A sentence like ‘Atom a strikes [at some given instant of time] atom b’ might be made true by a three-object Sachverhalt comprising a, b, and that event or individual moment c which is their momentary impact, linked by relations of one-sided foundation : between c and a, and between c and b. Here the impact moment is distinct in its ontological form from the independent objects with which it is configurated, but it is no less particular than these objects.41 A realist semantics of a non-trivial sort, to be established on the basis of an investigation of the range of possible forms and kinds of (dependent and independent) objects, seems therefore not, after all, to be so completely at variance with a semantics of the kind presented in the Tractatus. We are driven back to one important difference, that Wittgenstein believed that an adequate semantic theory must embrace commitment to absolutely simple objects, where we are willing to content ourselves with the question of relative simplicity, for example of the simplicity that is determined by the elementary sentences of the various material sciences.42 An investigation of the natures of dependent and independent objects treated of by these sciences then reveals itself as an investigation of objects in the light of their possible configurations into Sachverhalte, and a taxonomy of objects in our sense is seen go give rise to an exactly corresponding taxonomy of different kinds of Sachverhalt – something like the zoology of facts mentioned by Russell in his lectures on logical atomism (1972, p. 72 f.).43

41

For further details cf. Simons, 1981. On absolute and relative simplicity cf. Husserl, LU III§ I and Experience and Judgment, § § 28f. 43 To determine which are the simplest kinds of objects constituting the subject-matter of a given material discipline is to determine also the kinds of Sachverhalte which make true, as a Wittgensteinian might conceive things, the elementary sentences of that discipline. Wittgenstein himself embraced something like this project with respect 42

36 As an interpretation of the Tractatus, however, even of a Tractatus modified by the admission of the possibility of our grasping the natures of (relatively) simple objects and of (relatively) simple object-configurations, an account of this kind is still so far inadequate. For it has not been made clear what these simplest kinds of object-configurations are, merely that, in order to exist at all, they must involve objects which manifest a distinction in form something like the distinction defended above between moments and independent objects. Wittgenstein himself, as already noted, was ever keen to emphasize that Sachverhalte are entities of a peculiar kind, entirely distinct from object. And this view has acquired the status of orthodoxy amongst contemporary philosophers, despite the fact that Wittgenstein himself offered no more than loose, metaphorical indications of the difference in question. But how is a Sachverhalt such as, for example, that which involves the three objects a, b, and r, to be distinguished from the corresponding complex object (a’s-standing-in-the-relation-r-to-b)? Wittgenstein seems to have been content to regard this distinction as not further explicable, embracing mysticism of a kind which may have done much harm to the enterprise of a correspondence theory of truth. Can we do better? One course would be to develop a view of Sachverhalte as being distinguished from the corresponding complexes in involving, or in being in some send dependent upon, the sentences or sentence-using acts through which they are disclosed: for example, and most naively, by treating Sachverhalte as ordered pairs consisting of the relevant complex object and some appropriate sentence. Such a move is however tantamount to sacrificing the conception of Sachverhalte as entities in the world existing independently of mind and language. To treat Sachverhalte in this way, or a logical fiction of any kind, is to abandon the project of a realist semantics. Here we wish to leave open the question whether a more acceptable account of the distinction between Sachverhalt and complex could be to the discipline of psychology in his unjustly neglected “Some Remarks on Logical Form” of 1929. It is one consequence of our arguments that Wittgenstein’s idea of a directly depicting language, or of a family of such languages, may prove to be capable of being resurrected. Since, as we stressed above, there is lacking any isomorphism between the logically simple sentences of natural languages and their truth-makers, a directly depicting language would need to employ mechanisms which do not closely resemble linguistic devices with which ware familiar; it may perhaps approximate to the picture-languages employed in organic chemistry. Cf. Smith, 1981, Smith and Mulligan, 1982, § 6, 1983.

37 developed.44 It is one implication of our arguments above that some, at least, of the considerations which have been held to motivate the distinction are lacking in force. But are there other reasons why the logical difference between name and (elementary) sentence should be held to be reflected in a corresponding ontological difference between objects and somehow non-objectual and intrinsically unnameable Sachverhalte? Or is the assumption of special categories of entities to do the job of making true one more reflection of the running together of logic and ontology so characteristic of analytic philosophy? § 6. Some Principles of Truth-Making We shall sketch one possible beginning of a formal theory of the relation of making true. Such a theory is, we shall assume, constrained by the requirements we have placed on a realist semantics, and by the principle of the heterogeneity of logic and ontology that forestalls any too ready imputation of logical structure to the objects – both dependent and independent – of the material world.45 Thus we assume that the (ontological) relations holding among truth-makers – most importantly the relations of part and whole – are distinct from the logical relations holding among propositions or sentences. The fragments outlined here are otherwise intended to be consistent not only with the views outlined above, but also with a range of possible variants. For the relation of truth-making we use the sign ‘|=’, which can be read ‘makes true that’. Individual truth-makers – whether moments, things, or other, more complex entities – we shall represent by letters a, b, c; sentences (or any other candidate bearers of truth) by letters p, q, r. ‘ ’ in all that follows will signify a connective at least as strong as the entailment of Anderson and Belnap. The first principle of truth-making must be that what is made true is true, i.e.

44

Such an account 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 and Belnap, § 20.3), whilst having a number of methodological similarities to the account presented here, falls short of our requirements in being committed to different logical categories of truth-maker for different logical categories of sentence.

45

38 (1) a |= p. → p. But is the converse of (I) also valid ; i.e., is it true that (2) p → ∃ a.a |= p ? We have argued that (2) can be affirmed even of simple descriptive sentences only in certain circumstances. A simple sentence like ‘Cyril has hepatitis’ may be true although there is no single object that makes it true: from the point of view of its truth-makers the sentence may behave as a non-degenerate conjunction. Similarly in regard to, say, ‘Jack likes Jill and Jill likes Joe’ or ‘There have been forty U.S. Presidents to 1981’ it is surely counterintuitive to assume that there are any single composite objects making these sentences true, a Jack’s liking Jill and a Jill’s liking Joe mereologically fused together, or a mereological fusion of all and only U.S. Presidents from Washington to Reagan (in which Grover Cleveland somehow gets counted twice). Rather we should accept that the given sentences are made true by not one but several truth-makers jointly or, as we like to put it, by a manifold or plurality of truth-makers. Such a manifold is not a new, conjunctive object such as a set. There are no conjunctive objects, any more than there are disjunctive, negative, or implicative objects. A manifold is nothing other than the objects it comprehends (and thus a manifold comprehending a single object is simply that object itself). This suggests a means of dealing formally with conjunctive sentences and related forms by introducing terms for manifolds corresponding in natural languages to singular and plural definite referring expressions like ‘Jack and Jill’, ‘the men in this room’, ‘Jason and the Argonauts’, and so on. Here Γ, ∆, etc., will be used to stand in for non-empty lists of such expressions. ‘a ∈ Γ’ will signify that the individual a is one of Γ, that some term designating a occurs on the list Γ.46 We can now generalise (1) to the following axiom: (3) Γ |= p. →p. 46

We spare the details of manifold theory here. It can be compared to a theory of sets truncated at the first type, without a null set and with no type difference between individuals and unit sets. Cf. Simons, 1982b.

39 And its converse (4) p → ∃Γ.Γ |= p is seen to be acceptable for all simple descriptive sentences and for their conjunctive compounds. Disjunctive sentences raise no special problems for the theory, since a disjunctive sentence is true only to the extent that one or other of its disjuncts is true – which implies that even a disjunctive sentence like ‘This rabbit is male or this rabbit is female’, which exhausts the usual possibilities, is made true not by nothing at all, but by whatever is the relevant actually existing condition of the rabbit. Difficult problems are however posed by compound sentences involving negation. Can it be said that all negative sentences about spatio-temporal objects are, like positive sentences, made true by some relevant object or manifold of objects, i.e., that (5) ¬p → ∃Γ.Γ |= ¬p ? A duality of this kind can be maintained, it would seem, only for certain kinds of sentences.47 ‘This snow is not warm’, for example, may reasonably be conceived as being made true by the individual moment of coldness actually inhering in the snow; ‘This salt is not sweet’ by the individual moment of taste inhering in the salt: the respective moments of the coldness and taste are such that they exclude those moments whose existence is denied in the given sentences. What, however, of a sentence like ‘This liquid is odorless’? Here there need be nothing in the liquid which excludes its being odorous: it may simply lack any odor. We may be tempted in regard to this and similar examples to appeal to things themselves, rather than to moments in the things, as that which does 47

And we must reject also any definition of the relation of making true in terms of an existence predicate and entailment connective taken as primitive, for example of the form: Γ|= p : = p .E! Γ |= p. This principle certainly holds from left to right: it expresses the fact that ‘|=‘ is in one sense a link between the domain of ontology and the domain of logic. But from right to left the principle fails, as can be seen, for example, by considering disjunctive values of p.

40 the job of making true (to say that the liquid itself makes it true that it is not odorous); but even such a move will be inadequate to deal with other classes of negative sentences like ‘Ba’al does not exist’. Here there is quite literally no thing which can do the job of making true, and whilst some might be tempted to appeal to the world as a whole to do this job, it seems more adequate to regard sentences of the given kind as true not in virtue of any truth-maker of their own, but simply in virtue of the fact that the corresponding positive sentences have no truth-maker. The otherwise attractive principle (6) p ↔ ∃Γ. Γ |= p must therefore be rejected in its full generality. Manageable principles having nice truth-functional properties can however be defended if we restrict our attention to those propositions satisfying (6). The stronger principle (2) picks out the propositions in this class which are atomic, but only in the sense that they can be made true by some one individual: it does not even come near to delineating the class of logically atomic propositions, 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 p which is atomic in the sense of (2) itself makes p true, i.e., (7) "∀b: a |= p∧ a ≤ a b.→b |= p, where ‘≤’ signifies the relation of proper or improper part to whole.48 The principle embodied in (7) may be extended to positive propositions in general by defining a relation of mereological containment between manifolds. Intuitively we wish ‘⊆’ to express the proposition that the matter of is contained in the matter of, such that if ‘Γ’ and ‘∆’ are singleton-lists then ‘⊆’ is just ‘≤’. The definition (8) Γ⊆ ∆: = ∀a ∈ Γ. ∃b ∈ ∆.a ≤ b

48

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

41 will not serve, since may carve up the matter of in such a way that there are individuals in which comprehend no single individuals in . On the other hand the definition (9) Γ⊆ ∆: = ∀a ∈ Γ.∀c (c ≤ a →∃b ∈ ∆. ∃d.d ≤ c ∧ d ≤b) appears acceptable. We accordingly assert: (10) Γ|= p. → ∀∆. Γ ⊆ ∆→∆ |=p, which implies a principle of thinning: (11) Γ|=p. → ∀∆.Γ, ∆|=p. Two further intuitive axioms are: (12) Γ|=p. ∧∆ |=q: →Γ, ∆ |= p∧ q (13) Γ|=p. ∧ p→q: → ∃∆. ∆ ⊆ Γ∧ ∆|=q.49 And (10) and (13) in turn imply (14) Γ|=p. ∧ p →q: →Γ|=q whence, in particular, (15) Γ|=p.→ Γ|=p ∨ q, so that (16) Γ|=p.∨Γ|=q: →Γ|=p ∨ q, 49

(13) may be too strong: it implies that, where pq, we can conclude that any truthmaker for p contains some truth-maker for q. Consider, however, an entailment such as: that there exists a funeral entails that there exists a death. Here a truth-maker of the antecedent, i.e., any complex event which is a funeral, need not (an typically does not) contain a death as one of its parts. Funeral and death are connected, rather precisely by a (lateral) relation of one-sided foundation.

42 the converse of which we affirm as an axiom: (17) Γ|=p ∨ q: → Γ |=p.∨ Γ|=q, and by (14) and (12) we have also (18) Γ|=p ∧ q: →Γ|=p. ∧ Γ|=q. Quantified sentences may be managed in a similar way as follows: (19) Γ|= ∃a.p : ↔∃a.Γ|=p (20) Γ|= ∀a.p :∀a.Γ|=p, which brings us back once more, within the province of truth-functional logic, to the problem of dealing with compound sentences involving negation. It was in the face of this problem that Wittgenstein developed his theory of Tatsachen (facts). Wittgenstein introduces the term ‘fact’ as meaning ‘the existence and non-existence of states of affairs.’ The existence of states of affairs he calls a positive fact, their non-existence a negative fact (2.06).50 Intuitively the idea seems to be that we can produce a more adequate theory of truth-makers, a theory which can cope equally with all truthfunctional compounds (including – though these were perhaps not uppermost in Wittgenstein’s mind – the most intractable cases of sentences asserting or denying the existence of complexes), if truth-makers are conceived not, as in the simple Sachverhalt-theory, as configurations of objects, but rather as new entities, formed from Sachverhalte by application of special functors, the existence of...and the non-existence of..., in a way which allows the construction of compound facts whose structure would mirror exactly the structure of logically compound propositions. We can produce a formal approximation to what Wittgenstein might have had in mind if we introduce variables ‘s’, ‘t’, ‘u’ to stand in for names of actual and possible Sachverhalte (or of other candidate elementary truthmakers), writing

50

Cf. Also 2.062, 2.11, 2.201, 4.1 and compare the discussion in Dietrich, § 2.

43

as an abbreviation for ‘the existence of s’ and

as an abbreviation of ‘the non-existence of s’51 To enable us to build up recursively a vocabulary of expressions capable of designating compound facts we shall introduce

as an abbreviation for ‘the exclusion of the non-existence of t by the existence of s’. If we now define BF, the manifold of basic candidate factexpressions, consisting of all expressions of the forms ,

,

then the totality F of candidate fact-expressions may be defined as the closure of BF under successive applications of the functors ,

,

.

It is clear that both F and BF are in a certain sense too large: they contain expressions which do not designate facts (which do not designate anything at all). An expression ‘A’ in BF designates a fact iff (i) for ‘A’ of the form ‘

‘, s exists,

(ii) for ‘A’ of the form ‘ does not designate),

‘, s does not exist (or, equivalently, ‘s’

(iii) for ‘A’ of the form ‘

‘, not both ‘s’ and ‘t’ designate facts.

An expression ‘A’ in F but not in BF designates a fact iff 51

51. See n. 28 above.

44 (i) for ‘A’ of the form ‘ (ii) for ‘A’ of the form ‘B (iii) for ‘A’ of the form ‘C ‘C’ does not designate a fact.

‘, ‘B’ designates a fact, ‘, ‘B’ does not designate a fact, ‘, not both ‘B’ designates a fact and

’ also designates a fact. (For Thus ‘A’ designates a fact iff ‘ ‘“ ” designates a fact’, or equivalently, ‘A is a fact’, we may also write ‘ ’.) There is clearly a certain tension between this ontology of positive and negative facts and the ‘fundamental idea’ of logical atomism expressed by Wittgenstein in the passage cited in § 1 above. Yet it would contradict Wittgenstein’s pronouncements at 1 and 1.1 perhaps too charitably to dismiss his talk of facts, of ‘the existence and none-existence of states of affairs’, as a mere façon de parler. Not only Wittgenstein, but indeed almost all other philosophers who have investigated the relation of making true, have felt compelled in the fact of the problems raised by negative propositions to adopt an ontology of truth-makers as special, non-objectual entities having a complexity which is essentially logical. We remain convinced nevertheless that it is possible to develop a theory of the truthrelation which appeals only to objects firmly tied into our ordinary and scientific experience. For it is in such experience, and not in the abstract models of logical semantics, that there lie the origins of knowledge of truth and falsehood.52 BIBLIOGRAPHY Anderson, A. R. and Belnap, N. D. (1975) Entailment, vol. I, Princeton:Princeton University Press. Angelelli, I. (1967) Studies on Gottlob Frege and Traditional Philosophy, Dordrecht: Reidel. 52

Our thanks go to Roderick Chisholm, Kit Fine, Wolfgang Künne, Richard Routley and to other participants in the 1981 Wittgenstein Symposium in Kirchberg, where these ideas were first aired.

45 Alexander, H. G., ed. (1956) The Leibniz-Clarke Correspondence, Manchester, Manchester University Press. Anscombe, G. E. M. and Geach, P. T. (1961) Three Philosophers, Oxford: Blackwell. Brentano, F. (1924) Psychologie vom empirischen Standpukkt, 2nd ed., Leipzig: Meiner; English translation as Psychology from an Empirical Standpoint, London, Routledge, 1973. ————— (1933) Kategorienlehre, Leipzig: Meiner; English translation as The Theory of Categories, The Hague: Nijhoff, 1981. Campbell, K. (1976) Metaphysics. An Introduction, Encino: Dickenson. Chisholm, R. M. (1978) “Brentano’s Conception of Substance and Accident,” Grazer Philosophische Studien, 5, 197-210. ————— (1981) The First Person, Brighton: Harvester. Clark, R. (1970) “Concerning the Logic of Predicate Modifiers,” Noûs, 4, 311-35. Davidson, D. (1980) Essays on Actions and Events, Oxford: Clarendon. Dietrich, R.-A. (1974) Sprache und Wirklichkeit in Wittgensteins Tractatus, Tübingen: Niemeyer. Dummett, M. A. E. (1973) (1973) Frege. Philosophy of Language, London: Duckworth. Findlay, J. N. (1963) Meinong’s Theory of Objects and Values, 2nd ed., Oxford: Clarendon. Frege, G. (1969) Nachgelassene Schriften, ed. H. Hermes, et al., Hamburg: Meiner, 1969. Grossmann, R. (1974) Meinong, London: Routledge. Horgan, T. (1978) “The Case against Events,” Philosophical Review, 87, 28-47.

46 Husserl, E. (1894) “Psychologische Studien zur elementaren Logik,” Philosophische Monatschefte, 30, 159-91, reprinted in E. Husserl, Aufsätze und Rezensionen (1890-1910), The Hague: Nijhoff, 1979, 92-123; English translation by D. Willard, The Personalist, 58, 1977, 295-320. ————— (LU = 1900/01) Logische Untersuchungen, first edition, Halle: Niemeyer, second edition., 1913/21; English translation (based on second edition) As Logical Investigations, London: Routledge, 1970. ————— (1929) Formale und transzendentale Logik, Halle: Niemeyer, English translation as Formal and Transcendental Logic, The Hague: Nijhoff, 1969. ————— (1939) Erfahrung und Urteil. Untersuchungen zur Genealogie der Logik, prague: Academia; English translation as Experience and Judgment, London: Routledge, 1973. Ingarden, R. (1964/65) Der Streit um die Existenz der Welt, 2 vols., the 2nd in 2 parts, Tübingen: Niemeyer. Kenny, A. J. P. (1980) Aquinas, Oxford: Oxford University Press. Küng, 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 and Particulars, Notre Dame: Notre Dame University Press, 1976, 310-30. Meinong, A. (1915) Über Möglichkeit und Wahrscheinlichkeit, Leipzig: Barth (reprinted as vol. VI of Meinong-Gesamtausgabe). Mulligan, K. (1985) “Wie die Sachen sich zueinander verhalten inside and outside the Tractatus”, Teoria 5, 145-174. Parsons, T. (1972) “Some Problems concerning the Logic of Predicate Modifiers,” in D. Davidson and G. Harman, eds., Semantics of Natural Languages, Dordrecht: Reidel, 127-41.

47 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: Routledge. Quine, W. V. O. (1976) The Ways of Paradox and other Essays, rev. ed., Cambridge, Massachusetts: Harvard University Press. Ramsey, F. P. (1978) Foundations, ed. D.H. Mellor, London: Routledge. Reinach, A. (1911) “Zur Theorie des negativen Urteils,” in A. Pfänder, ed., Münchener Philosophische Abhandlungen, Leipzig: Barth, 196-254; English translation in Smith, ed., 1982, 315-78. Russell, B. A. W. (1903) The Principles of Mathematics, Cambridge: Cambridge University Press, 2nd ed., London: Allen and Unwin, 1937. ————— (1972) Russell’s Logical Atomism, ed. D.F. Pears, London: Fontana. Sharvey, 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: Foundations, problems, and Applications, Proceedings of the 5th International Wittgenstein Symposium, Vienna: Hölder-Pichler-Tempsky, Dordrecht: Reidel, 464-67. ————— (1981a) “A Note of Lesniewski and Free Logic,” Logique et Analyse, 24, 415-20. ————— (1981b) “Unsaturatedness,” Grazer Philosophische Studien, 14, 73-96. ————— (1982) “The Formalisation of Husserl’s Theory of Wholes and Parts,” in Smith, ed., 113-59. ————— (1982a) “Number and Manifolds,” in Smith, ed., 160-98. ————— (1982b) “Plural Reference and Set Theory,” in Smith, ed., 199-256.

48 ————— (1983) “A Lesniewskian Language for the Nominalistic Theory of Substance and Accident,” Topoi, 2, 99-109. ————— (1985) “The Old Problem of Complex of Fact,” Teoria, 5, 205-226. Smith, B. (1978) “Essay in Formal Ontology,” Grazer Philosophische Studien 6, 39-62. ————— (1981) “Logic, Form, and Matter,” Proceedings of the Aristotelian Society Suppl. Vol. 55, 47-63. ————— (1982) “Some Formal Moments of Truth,” in Language and Ontology, Proceedings of the 6th International Wittgenstein Symposium, Vienna: Hölder-Pichler-Tempsky, Dordrecht: Reidel, 186-90. ————— ed. (1982) Parts and Moments. Studies in Logic and Formal Ontology, Munich: Philosophia. Smith, B. and Mulligan, K. 1982 “Pieces of a Theory,” in Smith, ed., 15 110. ————— (1983) “Framework for Formal Ontology,” Topoi, 2, 73-86. Stenius, E. (1964) Wittgenstein’s Tractatus, Oxford: Blackwell. Stout, F. G. (1923) “Are the Characteristics of Particular Things Universal or Particular?”, Proceedings of the Aristotelian Society Supp. Vol. 3, 95-113. Strawson, P. F. (1959) Individuals. An Essay in Descriptive Metaphysics, London: Methuen. ————— (1974) Subject and Predicate in Logic and Grammar, London: Methuen. Stumpf. C. (1873) Über den psychologischen Raumvorstellung, Leipzig: Hirzel.

Ursprung

der

49 Tarski, A. (1944) “The Semantic Conception of Truth and the Foundations of Semantics,” Philosophy and Phenomenological Research, 4, 341 75. Weyl, H. (1918) Das Kontinuum, Leipzig: Veit. Williams, D. C. (1953) “The Elements of Being,” Review of Metaphysics, 6, 1-18, 172-92. Wilson, J. Cook (1926) Statement and Inference. With other Philosophical Papers, 2 vols., Oxford: Clarendon. Wolterstorff, N. (1970) On Universals, Chicago: University of Chicago Press.

Two Dogmas of Truthmaking KEVIN MULLIGAN Université de Genève

§1

Two Dogmas

The literature on truthmaking is now almost a hundred years old. Throughout this period many friends of truthmaking have accepted two claims: D1 D2

There are truths which have no truthmakers Truth-makers are ontologically or metaphysically fundamental.

In some cases they have explicitly endorsed these claims, in other cases they are implicitly committed to them. The two claims are dogmas and, as is the way with dogmas, are by no means independent. In §2 I put forward an alternative to the two dogmas and argue that it is to be preferred. My alternative to D1 is a version of truth-maker maximalism, TMM

Every true truth-bearer has a truth-maker1,

which is strengthened in two ways. First, I identify truth-bearers with propositions and truth-makers with obtaining states of affairs: TMMPS

Every proposition that p which is true is made true by the obtaining state of affairs that p

Secondly, I take TMMPS to flow from the nature of truth and of propositions:

1

Truthmaker maximalism was endorsed by one of the first friends of truthmakers, the realist phenomenologist Alexander Pfänder (1921) – for details, see Mulligan 2006. It has recently been defended by the Australian realist David Armstrong (2004). Some of the points dealt with in what follows are dealt with more fully in Mulligan 2006a, 2006b.

52 TME

In virtue of the essence of propositions and of truth, every proposition that p which is true is made true by the obtaining of the state of affairs that p

My alternative to D2 is the claim that the truth-makers isolated by (TME) are never ontologically fundamental. I must therefore explain what it is to be ontologically or metaphysically fundamental, provide some candidates for the role of what is ontologically fundamental, and elucidate the nature of truthmaking. What is the relation between (D1) and (D2) ? Philosophers who reject truth-maker maximalism, who accept that there are truths without truth-makers, accept D1. Why ? One powerful motivation is that there are truths which, if they had truthmakers, would have ontologically baroque truthmakers. But, it is thought, truthmakers must be ontologically romanesque (D2). The view that atomic facts (and perhaps sums thereof) are good candidates for the role of truthmakers but that non-atomic facts could not play this role is motivated by the conviction that negative or disjunctive facts, for example, cannot be part of the furniture of the world. The laughter that greeted Russell’s early endorsement of negative facts was surely an expression of this conviction. Even atomic facts have been thought to be insufficiently fundamental to provide truthmakers. One alternative is the view that bearer-specific properties or tropes, particularly if these are identified with individual states and processes and taken to depend for their existence on their bearers, are to be preferred to atomic facts for the purposes of truthmaker theory. Another alternative has it that “sparse” properties, which “clothe” space-time points, provide us with the only truth-makers we need. Yet another, even sparser alternative says that, for example, the truth that Sam is sad is made true by sad Sam. If truthmaker maximalism is false, that is, if (D1) is true, then truthmakers will not figure in a general account of truth, as opposed to accounts of some types of truth. They could only figure in such a general account if the truth of truth-bearers which do not have truthmakers could be shown to be completely determined by the truth of truth-bearers which do have truthmakers. No plausible account of this type seems to be forthcoming. It is

53 therefore something of a mystery why friends of truthmaking who reject truthmaker maximalism regularly claim that a theory of truthmakers is part of a theory of truth, for example, part of a theory of truth as correspondence. If it is true that the main motivation for endorsing (D1) is (D2), then we need to consider what it means to say that something is or is not more ontologically or metaphysically fundamental than something else; what it means to say that something is ontologically fundamental; and identify some plausible candidates for (a) the role of what is ontologically fundamental and (b) the role of what is ontologically non-fundamental. The candidates for the latter role that I shall consider are propositions and obtaining states of affairs or facts. As already noted, some have thought that atomic facts are ontologically basic. I shall give some reasons for thinking that no facts are ontologically basic. If there are facts and propositions, then it is very plausible to think that facts make propositions true. Once we see that the categories of facts and propositions are categories of what is ontologically secondary, then one of the main obstacles to accepting facts and propositions disappears. Consider (1) (2) (3) (4) (5) (6)

Sam is sad The proposition that Sam is sad is true The state of affairs that Sam is sad obtains If Sam is sad and the proposition that Sam is sad is true, then the proposition that Sam is sad is true because Sam is sad If Sam is sad and the state of affairs that Sam is sad obtains, then the state of affairs that Sam is sad obtains because Sam is sad If the proposition that Sam is sad is true and the state of affairs that Sam is sad obtains, then the proposition that Sam is sad is true because the state of affairs that Sam is sad obtains

The “because” ’s in (4) and (5) tell us that (1) is more fundamental than (2) and more fundamental than (3). One might accept both (4) and (5) because one thinks that propositions just are states of affairs. Then (6) would have to be rejected, for all instances of

54 (7)

p because p

are false. But there are good reasons for thinking that propositions are not just states of affairs. Propositions consist exclusively of concepts but every state of affairs contains at least one property. Properties, whether thought of as bearer-specific (“tropes”) or as multiply-exemplifiable, are not concepts. We understand concepts, not properties. We perceive properties, not concepts. (What are often called “Russellian propositions”, then, belong with what I here call “states of affairs”). It is sometimes claimed that propositions are more “fine-grained” than states of affairs because, for example, the proposition that Tully is bald and the proposition that Cicero is bald are distinct propositions, whereas the state of affairs that Tully is bald and the state of affairs that Cicero is bald are one and the same state of affairs. But to say that propositions are more fine-grained than states of affairs may suggest that they are made of the same materials. They are not. Even if one accepts that propositions are not states of affairs, one might reject (5). Why ? Perhaps because one is impressed by the idea that (1) represents or is “about” the state of affairs that Sam is sad. Perhaps also because one thinks both this and that either the state of affairs that Sam is sad obtains or that the state of affairs that Sam is not sad obtains. And then by appealing to the principle that what something represents is more fundamental than representations of it one arrives at the conclusion that (5) is false. But this line of thought goes wrong at the very beginning. (1) is about Sam. Neither (1) nor any proper part of (1) represents a state of affairs. It is plausible to think that (3) may figure in a specification of the correctness condition for judgements or assertions that (1): (8) (9)

If x judges correctly that (1), then (3) If x judges correctly that (1), then x judges correctly that (1) because (3)

But it does not follow that judgements or assertions that (1) involve any representation of states of affairs. (1) is more fundamental than (2) and more fundamental than (3). (1) mentions only Sam. (2) mentions a proposition, (3) a state of affairs. The onto-

55 logical commitment of (1) is more modest than the ontological commitments of (2) and of (3). What, then, are the best candidates for the role of what is ontologically fundamental ? Space-time and substances, that is, enduring three-dimensional particulars, is one answer. Space-time, processes and states, is another answer. If there are both substances and processes and states, then processes and states are not ontologically fundamental but are closer to rock-bottom than anything except substances. These answers are acceptable to a concretist nominalist. An anti-nominalist might combine the claim that there are substances or processes with the claim that there are kinds, kinds of processes or kinds of substances. Substances or processes and kinds, he might claim, are ontologically fundamental. If substances, processes, states and kinds are ontologically fundamental or ontologically more fundamental than facts, properties and relations, then (a) nothing on the list of what is fundamental is identical with anything on the list of what is not fundamental and (b) nothing on the first list is such that it can be constructed out of what is on the second list. Let me consider only a representative handful of the many objections and apparent counter-examples to (a). Some friends of bearer-specific properties and relations identify these with processes. But processes have temporal parts, no properties have temporal parts. If there are two-legged processes such as collisions, these processes are not bearer-specific relations. First, because collisions have temporal parts, unlike relations. Secondly, because binary relations have order-properties, unlike two-legged processes. Many if not all properties and relations are determinates or determinables of other properties and relations. Processes and states are neither determinables nor determinates. Finally, if there are kinds and properties, no kind is a property. Properties are predicable, unlike kinds. Kinds have instances, for example, processes or substances. Properties are exemplified. Instantiation is always an internal relation, exemplification may be an external relation. Many philosophers have thought that substances and processes can be constructed out of objects and properties. But if we are impressed by the arguments in favour of concretist nominalism, the thesis that everything other than space-time is wholly in time or wholly in space, we should resist

56 this view. Concretist nominalism, of course, typically fails to distinguish between what is ontologically fundamental and what is not fundamental. But if we make this distinction then a plausible version of concretist nominalism is that everything that is ontologically fundamental is wholly in time or wholly in space and so not repeatable2. If kinds are to figure in a list of what is ontologically fundamental, then it has to be shown that kinds cannot be constructed out of objects and properties or facts. Armstrong (1997 : 67-8) hypothesizes that kinds supervene on facts (what he calls “states of affairs”), where these are taken to involve nothing but thin particulars, properties and relations. One problem with Armstrong’s proposal is that whereas the claim that a relation supervenes on its terms and even the claim that properties, relations and facts supervene on properties, relations or facts are intelligible, it is by no means obvious what it means to say that a kind supervenes on facts. One may plausibly think that a substance-kind or a process-kind supervenes on a particular substance or process, that if the latter exist, so must the former3. But that is not quite the claim Armstrong has in mind. If a substance were just a fact, then it would follow that the kind to which the substance/fact belongs supervenes on the substance/fact. But on the concretist nominalist view of what is ontologically fundamental a substance is wholly spatial. It is therefore no fact, since the properties and relations making up facts are not wholly spatial. I therefore hypothesize that the exemplification of essential properties is secondary with respect to the instantiation of kinds or types. That is to say, for example, (10) If Sam exemplifies the property of being a man and if Sam instantiates the kind Man, then he exemplifies the property because he instantiates the kind. One reason for accepting (10) is the falsity of (11) If Sam instantiates the kind Man and Sam is a man, then Sam instantiates the kind Man because Sam is a man. 2

For the view that universals are repeatable and yet exist wholly in space and time, see Johansson, forthcoming. 3 Cf. Fine 1994-1995, p. 288.

57 and the truth of (12) If Sam exemplifies the property of being a man and Sam is a man, then Sam exemplifies the property because he is a man Even if it were possible to defuse all the objections to the claim that substances or processes are more basic than propositions, states of affairs, facts and their ilk, the claim remains vague in the absence of an account of the ways in which ontologically basic entities are connected with ontologically secondary entities. An answer to this question will take us to the heart of truthmaker theory, since such a theory has to say what it means to say that something makes something else true.

§2

Truth and Truthmaking

One of the more glaring gaps in discussions of truth-making is the lack of attempts to elucidate the very notion of “making”4. Such an elucidation should provide answers to at least the following questions. Is the “make” in “make true” elliptic for “because” ? Does an account of truthmaking essentially involve an appeal to explanation or grounding ? If so, what particular “because” is involved ? Is truthmaking a relation ? If so, what sort of relation ? What is the connexion between the relation and explanation ? If truthmaking is a relation, what is the connexion between the relation and the functor of necessitation which is appealed to in order to “capture” the relation ? No friend of truthmaking thinks that the “make” in “make true” is the causal “make” employed in, for example, “Sam made Erna cry”. Yet analogues of all the questions just raised can, of course, be asked about the causal “make”. There are good reason for thinking that there are causal relations between substances and processes as well as between processes and states. For example, Caused (The explosion, Sam’s heart attack). 4

But cf. Johansson 2004.

58 There are also causal explanations, Sam had a heart attack because the explosion took place And there is perhaps a functor of causal necessitation. And so the question arises what the connections are between causal necessitation, the causal relation and causal explanations. Friends of truthmaking often claim that truthmaking is “really”, “at bottom”, a relation, in particular, an internal relation. The truth of the matter, it seems to me, is that one type of truthmaking is a relation and another type is not a relation. More exactly, the truthmaking appealed to by one theory of truthmaking is no relation and the truthmaking appealed to by another type of theory is indeed a relation. Consider (13) If the proposition that Sam is sad is true and the state of affairs that Sam is sad obtains, then the obtaining state of affairs that Sam is sad makes the proposition that Sam is sad true. I suggest that (13) is merely elliptic for (14) If the proposition that Sam is sad is true and the state of affairs that Sam is sad obtains, then the proposition that Sam is sad is true because the state of affairs that Sam is sad obtains In order to evaluate this suggestion it is necessary to say something about the type of “because” employed. The “because” in (14) is not any causal “because”. How might it be characterised in positive terms ? It is the essential or conceptual “because”. But what does this mean ? It will be helpful to consider another example of this “because”. Consider (15) (16) (17) (18)

the number of F’s = the number of G’s there is a one-one correlation between the F’s and the G’s (15) iff (16) If (15) and (16), then (16) because (15)

59 A philosopher who endorses (18) should, I suggest, accept that (18) itself holds in virtue of the nature or essence of numbers. To say this is to say that the claim formulated with the help of the essential “because”, (18), is itself to be explained in terms of a claim about the instantiation of essences or natures, a claim which employs the “because” of essence. The “because” of essence may occur without the essential “because”, as in (19) If x endures/occurs/obtains/is alive/enjoys intentional existence/ist-zum-Tode…, then x endures/occurs/obtains/is alive/enjoys intentional existence/ist-zum-Tode…becauseessence of the essence of x. But the essential “because” requires the “because” of essence5. Let us now see how the distinction between the essential “because” and the “because” of essence figure in a theory of truthmaking which endorses truthmaker maximalism and rejects the claim that truthmaking, as the theory conceives of it, is a relation. Consider (20) If the proposition that Sam is sad is true, then the proposition that Sam is sad is true because the state of affairs that Sam is sad obtains If the “because” here is the essential “because”, then (20) holds in virtue of the essence of something. The most plausible candidates are the essences of truth and of propositions. The generalisation of (20) so understood is then just TME

In virtue of the essence of propositions and of truth, every proposition that p which is true is made true by the obtaining of the state of affairs that p

There is both a priori and a posteriori knowledge of the essences, natures or types of objects. (TME) is a trivial, a priori truth. It has seemed to many to be false or non-trivial only because of the mistaken assumption that ob5

For an account of the “because” of essence different from that employed here, cf. Fine 1994. Is the essential “because” which is employed in (4)-(6) above grounded in a “because” of essence ? I discuss this question in Mulligan 2006a.

60 taining states of affairs, if there are such things, must be ontologically fundamental. Might there not, after all, be a relation of truthmaking ? The foregoing suggests that, if there is such a thing, then the “make” in “makes true” must not be elliptic for any sort of “because”. Let us consider, first, the more general question whether there is any sort of relational, non-causal making in the large family of instances of “x makes y F” – making valuable (“valifying”), wrong-making, making probable (“probabilising”), making possible, making necessary, making obligatory and so on6. It has been argued that events make propositions probable and that “probabilise” really expresses a relation7. But a candidate closer to present concerns is provided by fact-making8. Consider (21) (22) (23) (24)

Sam makes the state of affairs that Sam exists obtain Sam’s sadness makes the state of affairs that Sam is sad obtain Sam’s jump makes the state of affairs that Sam jumps obtain Sam’s jump over the fence makes the state of affairs that Sam jumps over the fence obtain

Now (21) is not elliptic for (25) The state of affairs that Sam exists obtains because Sam exists And (21) is true whether Sam is a substance or a process. Of course, one who thinks that Sam’s sadness and Sam’s jump are properties, unitproperties or multiply-exemplifiable properties, will say that “make” in 6

Cf. Perzanowsky 1991, 1994. Kneale says "probable" is "elliptic" for the "relation" of "probabilification". Similarly, Nicod writes about the Johnson-Keynes theory that "the perception of this principle that probability is a relation, not a quality, of propositions removes from probability everything that seemed elusive and provisional" (Kneale 1949 : 10-11; Nicod 1924 : 20, cf. 19). One critic of Kneale's view relies on arguments which resemble those brought against the very idea of truthmaking, cf. Toulmin 1958 : 72ff..

7

8

That there are fact-makers is not exactly a common claim. Cf. Vallicella’s (2000) exploration of “existence-makers” for states of affairs, Smith 1999, §16, Plourde 2004.

61 (22)-(24) is elliptic for “because”9. But if, as I argued above, Sam’s sadness is a wholly particular, wholly temporal state and his jump a wholly particular and wholly temporal process, and if states and processes are not properties or relations, the way is open to claim that “make” in (22)-(24) has a relation as its semantic value. Then there are cases where making a state of affairs obtain, making a fact exist, are really relations. Some cases. But clearly fact-maker maximalism, (26) If the state of affairs that p obtains, something makes the state of affairs that p obtains is false, if fact-making is a relation. Nothing makes the state of affairs that there are neither witches nor genders obtain although this state of affairs certainly obtains. Nevertheless, where some ontologically fundamental entity makes a state of affairs that p obtain, it will also make the proposition that p true. And in each case the making is a relation. This claim contrasts with a weaker and a stronger claim. The weaker claim concedes that there are makers which are objects but denies that “makes obtain” expresses a relation. On this view, making is not a relation but relation-like. The stronger claim is that “makes obtain” expresses a relation and that “obtains” is a derelativisation of “makes obtain”. Parallel claims are the claim already mentioned to the effect that “is probable” is a derelativisation of “makes probable” and the claim that “true” is a derelativisation of “makes true”. My impression is that the claim that there is a relation of making can only be defended if one accepts the stronger claim. We have identified two distinct truthmaker connexions. There is the tie expressed by the essential “because”, which is in turn rooted in a “because” 9

Armstrong (1997 115-6) argues that the truth that a instantiates universal F is made true by what he calls the state of affairs of a’s being F and that truthmaking is a relation. He argues that this is the way to counter the possibility of a Bradleyan regress. I follow Husserl in thinking that formal relations, such as parthood and exemplification, unlike material relations and properties, such as the relation of love and the property of sadness, put a stop to any regress. If Sam exemplifies the property of sadness, nothing connects Sam, the property of sadness and the relation of exemplification.

62 of essence. And there is the relation of truthmaking (or relation-like truthmaking) which relates ontologically fundamental entities to true propositions in virtue of making states of affairs obtain. (TME) makes use of the tie but not of any relation of making. A philosopher who denies that there are obtaining states of affairs or rejects the very idea of fact-making, may, then, simply say that some, but not all, true propositions stand in the truthmaking relation to ontologically basic entities. And this is indeed what many friends of truthmaking do say. (TME), I argued, is an a priori triviality. Many friends of truthmaking have thought that truthmaker theory is one way to do ontology, and in particular, one way to do a posteriori, realist ontology or metaphysics, that is to say, one way to find out what is ontologically fundamental. If there really is a relation of truthmaking, it is easy to see that some such relations will only be discoverable a posteriori. It is enough to accept two very plausible principles about relational truthmaking: (27) If x makes y true than anything containing x as a part makes y true (28) If x makes y true then any z which is such that x makes z exist makes y true. Then many instances of these principles will furnish truthmakers which cannot be read off from their truth-bearers. As far as I can see, someone who rejects (27) or (28) does so because he is attached to the idea that whatever makes a truth-bearer true must be represented by the truth-bearer. One traditional way of understanding both (TMPPS) and (TME) is also attached to this idea and says that propositions represent states of affairs which, if they obtain, make the proposition true. But above I have given some reasons for rejecting the claim that propositions or other truth-bearers represent states of affairs. Whether or not one accepts that there is a truthmaking relation, there is much to be said for (TME). The attractions of truthmaker essentialism are evident ; it tells us that truth and truthmaking are interdependent and shows what this means. It is perhaps, together with Armstrong’s recent account, one of the only two accounts of truthmaking which can claim to be a part of a philosophical account of truth. I have argued that one main obstacle to taking seriously obtaining states of affairs as truthmakers is the false view

63 that obtaining states of affairs are ontologically fundamental. But there are, of course, two further obstacles. If (TME) is to be accepted, then it has to be shown that there are propositions and that they are truth-bearers, and also that there are obtaining states of affairs. The arguments in favour of the view that there are propositions and that they are the primary truthbearers have persuaded many philosophers and I shall here simply assume that such arguments are sound10. Arguments in favour of the indispensability of obtaining states of affairs or facts, which are generally also arguments in favour of states of affairs understood as Armstrong understands them, fall into two main categories. In the first category we find arguments to the effect that certain truths can only be true if there are facts. One example is the claim that true causal explanations require us to assume facts. Another example is Armstrong’s argument that the truth that an object exemplifies a certain property can only be made true by what he calls a state of affairs11. A similar argument can be made using the account of states of affairs given here: the proposition that a exemplifies the property F is made true by the obtaining state of affairs that a exemplifies the property F. But such an argument cuts much less ice than Armstrong’s argument. In Armstrong’s formulation, “makes true” expresses a relation of which the first term is a particular, a state of affairs. In my formulation, it expresses no relation. Indeed it would be in the spirit of the present view to claim that, (29) If Sam exemplifies the property of sadness and the state of affairs that Sam is sad obtains, then the state of affairs that Sam is sad obtains because Sam exemplifies the property of sadness. In other words, property exemplification is more fundamental than facthood. In the second category of arguments for the indispensability of facts there is the claim that knowledge must be knowledge of facts, that if there is knowledge-that, then there are facts. This claim belongs to a large family of claims which all have the following structure: given the existence of certain psychological states and acts, it follows that different types of formal 10 11

See Kuenne 2003 ch. 5. See note 7 above.

64 terms and predicates are neither semantically valueless nor semantically superfluous. One such claim is the argument from the activity of colligation to the conclusion that the formal category, number, is not empty. Another, that the formal predicate “is valuable” is not empty because there is affective knowledge of value. Another concerns the most basic formal category, that of objecthood. To be an object is to be the object of a singular term or of acts of referring or perception. “Is an object” is a derelativisation of “is an object of”. What is true of “is an object” is not true of “is a thing /substance/entity”. We know that there are objects because we know that there are perceptions and non-empty singular terms. Elsewhere I have sketched an account of knowledge which has as a consequence that knowledge is of obtaining states of affairs12. This account and the analogous claims just mentioned are compatible with the view that such formal objects as propositions, classes and states of affairs as well as formal properties such as number, being true and obtaining and formal relations such as exemplification and membership are not ontologically fundamental. Since I believe that there are facts or obtaining states of affairs and that none of these is ontologically fundamental, I suggest that the role of a theory of relational making is best taken care of within the theory of factmaking. This theory requires much honest toil. Essentialist truthmaker maximalism is not quite an example of theft but it certainly requires less toil than the theory of fact-making13.

REFERENCES Armstrong, D. 1997 A World of States of Affairs, Cambridge University Press 2004 Truth and Truthmakers, Cambridge University Press Fine, K. 1994-5 "Ontological Dependence", Proceedings of the Aristotelian Society, 95, 269-90. ——1994 "Essence and Modality", Philosophical Perspectives, (ed. J. Tomberlin), 8, 1-16.

12

See Mulligan 2006a. Thanks to Kit Fine, Ghislain Guigon, Herb Hochberg, Ingvar Johansson and Fraser MacBride for discussions and criticisms. 13

65 Johansson, I. 2004 “Truthmaking: A Cognition-Independent Internal Relation with Heterogeneous Relata”, Experience and Analysis. Papers of the 27th International Wittgenstein Symposium, Austrian Ludwig Wittgenstein Society, Kirchberg am Wechsel, 154-156. —— “Roman Ingarden and the Problem of Universals”, Proceedings of the 2004 Montreal conference, Logic, Ontology, Aesthetics. The Golden Age of Polish Philosophy, forthcoming. Kneale, W. 1949 Probability and Induction, Oxford, Clarendon Press Künne, W. 2003 Conceptions of Truth, Oxford, Clarendon Press Mulligan, K 2006 "Wahrheit und Wahrmachen in 1921", forthcoming in a volume edited by G. Imaguire & C. Schneider ——2006a “Facts, Formal Objects and Ontology, Modes of Existence. Papers in Ontology and Philosophical Logic, Proceedings of the May 2005 Bergamo Conference, eds. Andrea Bottani & Richard Davies, forthcoming. ——2006b “Ascent, Propositions and other Formal Objects”, Proceedings of the May 2004 Padova conference on Propositions, forthcoming. Nicod, J. 1924 Le Problème logique de l'induction, Paris, Félix Alcan Perzanowsky, J. 1991 "Modalities, Ontological", Handbook of Metaphysics and Ontology, Vol. II, eds. H. Burkhardt & B. Smith, Munich: Philosophia Verlag, 560-562. ——1994 "Reasons and Causes", Logical and Causal Reasoning, eds. J. Faye, U. Scheffler, M. Urchs, Berlin: Akademie Verlag, 169-189. Pfänder, A. 1921 Logik, Jahrbuch für Philosophie und phänomenologische Forschung, Vol. IV, zweite durchgesehe Auflage 1929, Halle, Niemeyer. Plourde, J. 2004 Nécessité, possibilité et impossibilité dans le Tractatus logicophilosophicus. Essai d’une reconstruction de la théorie wittgensteinienne des modalités, Geneva PhD. Smith, B. 1999 "Truthmaker realism", Australasian Journal of Philosophy, 77 (3), 274-291. Toulmin, S. 1958 The Uses of Argument, Cambridge University Press. Vallicella, W. F. 2000 “Three Conceptions of States of Affairs”, Nous, 34:2, 237-259.

Truth in virtue of meaning PETER SIMONS University of Leeds

Abstract In this paper I examine and guardedly defend the traditional empiricist claim that analytic truths are true in virtue of the meanings of the terms they contain. However, in view of the elusiveness of the notion of meaning, this is glossed as the view that analytic truths are those for which assent is enforced by linguistic practice in a community. electron • noun Physics a stable negatively charged subatomic particle with a mass 1,836 times less than that of the proton, found in all atoms and acting as the primary carrier of electricity in solids. Compact Oxford English Dictionary

Truthmaking and analyticity This paper is an investigation of some limits of the correct application of the concept of truthmaking. For every true statement or proposition, we may ask the question why it is true. A correct and substantive answer to this question which is itself another statement (proposition), can be considered to give a sufficient reason for the truth of the original proposition. Where the answer is correct and substantive and consists of a proposition of the form ‘p is true because such and such exist(s)’, then we are in the presence of these reasons which give us truthmakers. The object or objects in question, which simply by existing ensure the truth of the proposition p, may rightly be called the truthmakers for p. A nontrivial account of truthmaking holds that some truths have truthmakers. Some theories of truthmaking, such as that of David Armstrong,1 hold that every truth has a truthmaker. I do not so hold, as I have detailed elsewhere, and shall not reiterate here.2 Truthmaking is especially apt in accounting for the truth of 1

Armstrong 2004. Armstrong’s position is now standardly called truthmaker maximalism. 2 Simons 2000, 2005.

68 contingent propositions. In our 1984 paper,3 we deliberately restricted attention to contingent truths, leaving the issue of non-contingent or necessary truths aside. The question then arises, why, or in virtue of what, necessary truths are true. For a truthmaker maximalist such as Armstrong, this is answered by adverting to the entity or entities which, by existing, render the truth in question true. In Armstrong’s case the entities are the meanings themselves that comprise the proposition. Analytic statements are a species of necessary truths. A traditional view, which have many supporters, is that such truths are true solely in virtue of the meaning of the terms there are expressed. […] The phrase ‘in virtue of’ inevitably suggests truthmakers, at least to those attracted to truthmaker theory. […] The words in which an analytic truth is expressed do not, save per accidens, refer to meanings. But the meanings may still be truthmakers for the truth (Armstrong 2004, 109).

How this works in detail is a matter for investigation, but I here simply point out the connection between Armstrong’s answer and the traditional empiricist account of necessary truths. According to a tradition, traceable back to Leibniz’s distinction between vérités de fait and vérités de raison, and to Hume’s distinction between matters of fact and relation of ideas, necessary truth is analytic truth, and analytical truths are true in virtue of the meanings of their constituent parts. Here, for example, is A. J. Ayer’s brief and somewhat unsatisfactory formulation in Language, Truth and Logic (1936, 103) : A proposition is analytic when its validity depends solely on the definitions of the symbols it contains.

This is problematic for those non-contingent truths which contain undefined symbols, but if we replace ‘definitions’ by ‘meanings’ and ‘validity’ by ‘truth’ we have the classic formulation. Speaking more specifically of logical truth, Quine writes of the “linguistic doctrine of logical truth”, which “has its attractions” — “that logical truths are true by virtue purely of the intended meanings, or intended usage, of the logical words (1976, 108)4 —, and further, of a logical sentence such as ‘Brutus killed Caesar or did not kill Caesar’, that “it is a sentence which, 3 4

Mulligan, Simons and Smith 1984. Page references are to the 1976 reprint of Quine 1960.

69 given the language, automatically becomes true, whereas ‘Brutus killed Caesar’, given the language becomes true only contingently on the alleged killing” (110). Quine is close to truthmaker talk here, and indeed later in the same paper he says of truths containing new notation that they “come into being through a conventional adoption of a new sign, and they become true through conventional definition of that sign together with whatever made the corresponding sentences in the old notation true” (118, my emphasis). So a modern version of the empiricist account of necessary truth is that necessary truths are true solely in virtue of the existence of the meanings occurring in them (more precisely, those occurring essentially in them, to use Quine’s term). As Armstrong puts it : “given all the meanings, all the analytic truths are fixed”. It is this attractive proposition that I shall be investigating. The vaporous notion of meaning To begin to analyse this theory, we first need to delve into what Quine scathingly calls the “vaporous notion of meaning” (1976, 114). Armstrong rejects scepticism about meaning and synonymy and hopes for a naturalistic account of meanings (2004, 109). I agree with the rejections and the hope, but to test the theory a little more detail is required. For anyone but a semantic platonist in the mould of Bolzano or Frege, meanings are not self-subsistent abstract entities but in some sense live in the actual, concrete use of language (which is not to say meaning is to be identified with use, as some bowdlerised versions of late Wittgenstein were wont to claim). Whether one tends to nominalism or not, it pays to start at the grass roots, among the concrete, individual employments of linguistic signs among members of a linguistic community. I endorse Husserl’s view that overt linguistic behaviour is only that, namely linguistic, because the active and passive participants in any linguistic situation are mentally so equipped as to take physical token events or objects to be meaningful, to ascribe meanings to them, in mental acts which, in Husserl’s vivid metaphor, animate the glyphs or noises in question. When a TV announcer says something that is broadcast, literally millions of such acts take place more or less simultaneously, in millions of different heads, whereas someone

70 listening to the broadcast who does not know the language simply has no such animation acts and for them the words remain mere noise without meaning. This is a commensense datum not in need of theoretical explanation: it is incumbent on any theory of meaning to take such data into account, not to deny them. When we talk about meanings in the abstract, as when noting (e.g. in a dictionary) that the adjective ‘wicked’ has acquired the new meaning of ‘good’ or ‘cool’in recent British English, it is clearly not the millions of individual acts of use that are being counted or spoken about, but rather something abstract or recurrent which is somehow inherent in many such acts, about the number and extent of which we rarely if ever have exact information. The reason is that ordinary average human beings can hack their way to a humanly average competence in at least one language in a period of a little more that ten years from a finite corpus of linguistic events, and secondly that lexicographers, grammarians and other linguists can summarize and codify their achievements with a remarkable degree of consensus. So while the details of the way in which meanings are wielded in concreto remain largely hidden and idiosyncratically variable, that it happens is not in doubt. Armstrong’s hope for a naturalistic account of meaning is therefore not a pious one, even though its detailed elaboration would be a task of many lifetimes. Examples I take it as read that there is synonymy of bits of language, even it is not an exact equivalence and therefore that the boundaries between different meanings are not always sharp. There are enough cases to be sure than synonymy is a real feature of language — Armstrong’s example of ‘father’ and ‘male parent’, Quine’s of ‘oculist’ and ‘eye-doctor’, or Lewy’s of ‘vixen’ and ‘female fox’ will serve as dissent-blocking examples, as will countless everyday examples of good translation from one language to another. What then are good examples of analytically true sentences ? Here are some categorized examples. Synonymy Pairs Vixens are female foxes Fathers are male parents Abelian groups are groups where the group operation is commutative

71 Even integers are those divisible by 2 without remainder Subsumptions Whatever is scarlet is red Whatever is square is rectangular All dogs are carnivores All electrons have negative charge —and by far most abundant examples (mostly trivial) Exclusions No whale is a fish No event is a body Nothing scarlet is green If the temperature outside is 80°, it is not 90° If this river is in Africa, it is not in Antarctica Logical truths If pigs can fly, then pigs can fly Brutus killed Caesar or it is not the case that Brutus killed Caesar If someone killed Caesar and Brutus did not, someone else did If there are six girls in the class and more than twice as many boys as girls then there are at least thirteen boys in the class Conventional truths 32°F = 0°C 1 inch = 2.54 cm Truths based on conventions A goal cannot be scored by a player judged to be in an offside position Two rooks can force checkmate but two knights cannot. In what way can we say that such truths, while not about meanings, as Armstrong points out, are true thanks to their meanings ?

72

Bearing in mind the primacy of actual usage, let’s pick one example, indeed one which may be considered to provide a good case for scepticism about analyticity, namely : No whales are fish. Those who know their bible will recall that in the story of Jonah, the whale is described as a great fish. The ancient scribes were not committing elementary errors; rather the meanings of ‘whale’ and ‘fish’ have undergone mutual adjustment since 1600, taking the class of whales out of the order of fish and re-placing it in the order of mammals. But, continues the sceptic, that whales are mammals rather than fish was an empirical discovery, hence a posteriori, therefore the proposition that whales are not fish is synthetic, not analytic. The defender of analyticity has an easy and convincing reply. In 1600, the term ‘fish’ comprehended many large free-swimming animals with fins, lateral symmetry and more or less streamlined shape. Closer examination and observation of whales showed them to be viviparous, endothermic, suckling, with a quadricameral heart, all characters found among furry terrestrial animals. As the terms ‘whale’ and ‘fish’ are now used — by biologists, not im Volksmund — mammals and fish (Pisces) analytically exclude one another, Cetaciae (whales and dolphins) are analytically included in Mammalia, so ‘No whale is a fish’, given current meanings, is analytically true, whereas an equiform token of the sentence understood as in 1600 would be analytically false. Note that it is not sentence types, but tokens, better, productions of meaningful sentence tokens and acts of comprehending them that are primarily analytic, ass they are primarily true or false. How does it work in practice? It means that anyone who is inducted into modern biological English learns, sooner or later and with more or less surprise or disruption to prior lay usage, that it goes against accepted and entrenched biological lore and terminology to classify a whale as a fish. That does not mean that this truth is intrinsically unrevisable, at least, it does not preclude possible future terminological upheavals. If future biological research were to show that whales had evolved their mammalian

73 characters directly from fish and not via intermediary terrestrial mammals, then the lore and its associate meanings would change again. Since whales appear to have evolved from goat-like ancestors, this is unlikely, but not inconceivable. The mutability of sentences-types serves to underline the non-substantive nature of analyticity better than if there never were such shifts. Empirical discoveries lead us to re-jig our classifications, but these follow the facts, they don’t precede them. Practice grounds Truth Take as given the extant, established practice of biologists conversing about whales, fish and the like. The practices are multifarious and complex, but running through them is an investigable regularity: speakers who sally forth into taking some whale to be a fish will be bullied, cajoled, persuaded or enjoined into desisting. Students saying so in examinations will be penalized. There may be recalcitrants or rebels, but they will show by their very behaviour that they understand one or more of the terms differently from the rest. Refusing to bow to pressure, to adjust your terminology so that certain sentences count automatically as true and others count automatically as false, is the surest indication that the difference is one of meaning, whether or not other factual disagreements accompany it. Since meaning depends on use as an intersubjective phenomenon, no other criterion is adequate and none other is needed. Thus the conformity of a group of speakers to a linguistic practice in respect of various terms is a necessary but not a sufficient condition of that practice grounding the truth or falsity of certain sentences. It is necessary because without the conformity there are no well-defined univocal meanings in the first place. It is not sufficient because the conformity may be accidental, or due to common acceptance of certain propositions which are themselves obviously contingent. For example, anyone knows that on average men are taller than women. But this common opinion fail to intrude into the meaning of the terms ‘man’ and ‘woman’, for one thing because it is a statistical rather than a universal generalization, and for another because it is fairly evident to all but the most rabidly chauvinistic that it is contingent and might gave been otherwise. Even a universal truth, that no human weighs more than a ton, does not get written into the definition of

74 ‘human’, though a one-ton human is, as we understand it, conceivable. Accepting a generalization on such a conformity becomes a candidate for grounding truths only when the generalized acceptance is enforced normatively as an explicit matter of terminology. That requires not only an established and pre-existing uniformity among speakers ; it requires a level of reflexive awareness that is not necessarily present in all cases, whether because of immaturity of the subject-matter, or distraction, or whatever. When normative terminological enforcement is in place and accepted by at least a sufficiently large body of speakers, then and not before is it possible to talk of the linguistic practice grounding truths independently of the facts. It is interesting how the inception of enforcement can change the status of a proposition without changing its truth-value. Before 1930, no one had thought of electrons as being anything other than negatively charged: physical theory and the data of experiment did not demand it. ‘No electrons are positively charged’ was true for want of a falsifying counterexample.5 Then Dirac’s theory and Anderson’s empirical investigations gave us knowledge of the positron. For a while the term ‘postive electron’ was bandied about as a name for the positron.6 Then the physics community collectively opted to reserve ‘electron’ for the negative case, and enforced this terminology normatively. ‘No electrons are positively charged’ was thenceforth true in virtue of meaning. Its truth-value did not change, but after the transitional uncertainty its truth was protected: nothing would be allowed to stand as a counterexample. The lack of counterexample— now guaranteed terminologically—is still the reason why the negative existential proposition is true. But the terminological enforcement is why it is now analytic, when before it was empirical. Since a truthmaker for ‘Necessarily p’ is also a truthmaker for p, the proposition may acquire a truthmaker whereas before it was not made true.

5

Whether anyone knew it or not—I am not endorsing verificationism. The large Oxford English Dictionary, being an historical record, accepts this episode as affecting the meaning and says that ‘electron’ can cover positrons. All other dictionaries reporting current usage, such as the Compact Oxford, do not. The 1911 edition of Encyclopedia Britannica, written well before the discovery of positrons, simply reports electrons as having negative charge. Anderson wanted to use the word ‘negatron’ alongside ‘positron’ and have ‘electron’ as the generic term, but his suggestions did not catch on.

6

75 Analyticity is thus a mark of maturity of linguistic sophistication.7 Quine highlighted this at the beginning of “Truth by Convention” when he wrote : The less a science has advanced, the more its terminology tends to rest on an uncritical assumption of mutual understanding. With increase of rigor, this basis is replaced piecemeal by the introduction of definitions. The interrelationships recruited for these definitions gain the status of analytic principles ; what was once regarded as a theory about the world becomes reconstructed as a convention of language. Thus it is that some flow from the theoretical to the conventional is an adjunct of progress in the logical foundation of any science. (Quine 1976, 77.)

This is very little I would disagree with in this passage. What I would suggest however — in the light of the whale and other examples — is that the flow is not all one way. A terminological decision may be undone, either by replacing it by another, or because of dissent about concomitant facts. Conventional replacement may be observed in the case of the metre, which was defined in terms of the standard metre in Paris, but is now defined as a fixed part of the distance travelled by light in vacuo in one second. It has thus become possible for the standard metre in Paris to be other that one metre long. Examples of crumbling assent are probably most visible in biology. For example, many biologists doubt the validity of the separation of hominids from the other great apes (Pongidae), while others dispute the validity of the paraphyletic taxon Reptiliae, and yet others classify birds, Aves, not as an order of its own but as a suborder of Dinosauria. What all these examples show is that Quine was quite right to deny the fixity and the exactness of the analytic/synthetic divide. However they do not show that it is no viable or useful distinction in the first place. On the contrary, they show that, carefully treated, we can observe and test analyticity in action, by looking at how linguistic communities expressly, overtly and self-consciously enforce linguistic / terminological norms. Analytic truths are not so much “truths by convention” as “truths by enforcement”. Sometimes there will be conventions, agreed and voluntarily entered into, which then become binding. Advanced sciences do support 7

Not necessarily of mature subject-matter—scientists can start laying down linguistic norms very quickly in new domains: they are merely less likely to secure general consent.

76 this sort of terminological activity, indeed sometimes there is more than enough of it among standards organizations. This sense of ‘convention’ is obviously a stricter and more specific sense than that trivial sense in which all language is conventional. Meanings as Truthmakers ? We accept that some truths result from words and other expressions meaning as they do : truths in virtue of meaning (analytic truth) exists, as does falsity in virtue of meaning. Does that mean that the propositions in question are true (false) solely in virtue of the meanings in question existing ? I have two reasons for denying that it does. The first is a general distrust of the vaporous notion of meaning. Meanings can be said to exist only insofar as meaningful acts of understanding exist in a community of speakers. So if we wish to point to the items which by virtue of existing render propositions true, then it should be these acts and the overt linguistic practices in which they are implicated, rather than their derivations, the abstract meanings. Secondly — and this is more delicate — the question arises as to whether the mere existence of the meanings in question — however one tells the story of their embodiment in linguistic practices — is sufficient to ensure the truth or falsity in question, i.e., to be truthmakers for the truth or falsemakers for the falsehood. Here is why I want to be careful. Imagine an established usage, e.g. of classifying whales among mammals, or of taking a point as having no extension. Suppose that there is consensus about these matters but they are not regarded as issues of terminology. What changes about the meaning if and when terminological decisions are made or conserved or enforced ? Have the terms in question undergone a change of meaning ? Their reference, by hypothesis, stays the same. So can they change in sense or meaning because of the additional role of terminological enforcement? The traditional answer is that they can, that new clauses need to be written into any lexical entry giving their meaning. The elasticity of this is obvious. What belongs in the lexical entry? Sometimes a dictionary contains encyclopedia-type general information, sometimes it merely reports usage. But reporting usage may fail to report extra enforcement of usage. It may be in principle impossible to report all that can be enforced. A lexical entry for ‘4’ does not list separately that it is enforced terminologically that 4 ≠ 2, that 4 ≠ 3, that 4 ≠ 5, etc. ad. inf.

77 It is not that there is never any point of incorporating terminological decisions or norms into a dictionary definition. What I am saying is that the concept of meaning is sufficiently slippery (vaporous) that, rather than introspecting about meanings, it is more sensible to focus attention on the terminological enforcement practices of linguistic communities. These practices if anything are those items which, by virtue of being there, preserve some propositions as true and others as false and insulate them from the contingent facts about their subject-matter. Truth in virtue of practice is the cash value of truth in virtue of meaning. A corollary of this is that where enforcement practices are not hard and fast and there is more than a trickle of exceptions (people who fail to or refuse to toe the terminological line), there is no sharp boundary between analytic and non-analytic truths. It remains to be considered whether the practices protecting truth and falsity, multifarious and dispersed as they are, deserve the appellation ‘truthmaker’. It is not clear to me that it is harmful to say they do. But perhaps this too is a terminological matter, to be settled by argument if possible.

REFERENCES

Armstrong. D. M. 2004. Truth and Truthmakers. Cambridge: Cambridge University Press. Ayer, A. J. 1936. Language, Truth and Logic. London: Gollancz. Mulligan, K., Simons, P. M. and Smith, B. 1984. Truth-Makers. Philosophy and Phenomenological Research 44, 287–322. Quine, W. V. 1936. Truth by Convention. In O. H. Lee, ed., Philosophical Essays for A. N. Whitehead. New York: Longman, 90–124. Reprinted in Quine 1976. References are to the reprint. —— 1960. Carnap and Logical Truth. Synthese 12, 350-374. Reprinted in Quine 1976. References are to the reprint.

78 —— 1976. The Ways of Paradox. 2nd revised and enlarged edition. Cambridge: Harvard University Press. Simons, P. M. 2000. Truthmaker Optimalism. Logique et analyse 169–170, 17–41. —— 2005. Negatives, Numbers and Necessity: Some Worries about Armstrong’s Version of Truthmaking. Australasian Journal of Philosophy 83, 253–261.

Truthmaker Explanations BARRY SMITH (IFOMIS/Buffalo) AND JONATHAN SIMON (NYU)

Abstract This paper is a fresh attempt to articulate the role of a theory of truthmakers. We argue that truthmaker theory constitutes a cornerstone of good methodology in metaphysics, but that a conflation of truthmaker theory with the theory of truth has been responsible for certain excesses associated with truthmaker-based approaches in the recent literature. We show that truthmaker theory retains its appeal as an instrument of metaphysical inquiry even when we agree with (or at least remain neutral about) the sorts of deflationist doctrines put forward by Ayer, Quine, Field and Horwich, and we argue further that its underlying intuitions become clearer when we separate them from a theory of truth, and above all from the attempt to provide a definition of truth.

Part One 1. Truth as Property The debate over the nature and definition of truth has been prominent in recent literature. Unfortunately, it has not been entirely clear what the subject matter of this debate is, since its participants share too little common theoretical ground. For this reason, two questions have been run together, one concerning the real definition of the property of truth, the other concerning nominal definitions of the meaning of ‘is true’. The first question, in particular, suffers from an almost terminal unclarity, not least because many participants in the debate (as in the related realist/anti-realist debate) shy away from metaphysics and consequently from any serious attempt to understand what properties might be. Moreover even for those, like Armstrong, who have worked-out theories of properties, the issue remains problematic, given that a property like truth will likely not be one of the basic properties which correspond to genuine universals. And even for those with more liberal theories of properties, problems will still arise. Necessarily, an entity is equiangular if and only if it is equilateral. Each of these properties is instantiated precisely where the

80 other is. But this does not indicate that either must feature in any real definition of the other; and this tells us that, even if a truthmaker principle of the general form: (M)

Necessarily, ‘P’ is true iff ‘P’ has a truthmaker

were correct, this need still not give us reason to believe that having a truthmaker is definitive of the property of truth, any more than being equilateral is definitive of the property of being equiangular. Even if these concerns were somehow addressed, there would still remain a major objection to the view that truth is to be given a real definition in truthmaker terms. As Lewis, Horwich and others have pointed out, the general validity of the disquotational truth schema (formulated to taste in terms of propositions or sentences): (T)

P iff ‘P’ is true.

implies that any interesting truthmaker principles along the lines of (M) can be reformulated in such a way as to avoid any mention of the property of truth. (M) together with (T) thus together yield: (M*)

P iff ‘P’ has a truthmaker.

And there seems to be no good reason for taking (M) as prior to (M*). 1 2. The Meaning of ‘Is True’ Our second question – concerning the meaning of ‘is true’ – is, in contrast, relatively easy to formulate. At the same time it is quite clear that truthmaker theory can play no part in providing it with a satisfactory answer. For an account of the meaning of each given predicate answers ultimately to those who competently use that predicate in thought or speech. This means, presumably, that such an account should present itself as something to which competent users would spontaneously assent, or at least that it 1

For instance see “Truthmaking and Difference-making”, Noûs 35:4, 2001, 602-615; David Lewis, “Forget about the ‘Correspondence Theory of Truth’”, Analysis 61:4, 2001 275-280

81 should shed light on the principles underlying the linguistic and mental practices of such users. But it is hard to see how a truthmaker theory could do either of these things. This is because, as additions to the disquotational schema (T), truthmaker principles like (M), however interesting, neither call forth spontaneous agreement from ordinary competent users of ‘is true’, nor do they shed light on the principles underlying the competency of those speakers. Thus, even if some principle along the lines of the universal generalization of the schema (M) were true, it is not clear why it would have any role in a theory of the meaning of ‘is true’. 3. Truthmaker Maximalism Yet in spite of the considerations presented above, many advocates of truthmaker theory accept the premise that a theory of truthmakers is necessary precisely to provide a definition (real or nominal) of truth. Among other things, it is this premise which provides the most straightforward motive for Armstrong’s maximalism, the view that every truth must have a truthmaker, and his factualism, the view that these truthmakers are, in general, proposition-shaped entities called ‘facts’ or ‘states of affairs’. Below, we discuss how rejecting this premise should lead us to reject maximalism and Armstrong’s factualism, and thereby help us on the road towards a better account of truthmaker theory as an instrument of metaphysical inquiry. Our most immediate target is truthmaker maximalism, the view that every truth has a truthmaker, or in other words: (MAX) ∀P (P is true iff ∃x (x is a truthmaker for P)), where the variable P now ranges over actual or possible bearers of truths (however these latter might be conceived). (MAX) has intuitive appeal because it appears to be an encapsulation of the eminently acceptable claim that every truth is true because of something in the world, or because of something about the world, or because of some way the world is. However, this platitude is acceptably regimented via (MAX) only to the extent that, for example, ‘There is something they are fighting for’ is acceptably regimented by: ∃x(Are fighting for (they, x)). We do not wish to discredit the commonsensical idea that truths are true because of some way the world is. But we also do not think that it can be

82 taken in the literal way that maximalists require. (Reiterating P is sometimes the best way of spelling out the way the world is in virtue of which it is true that P.) In any case, modus tollens shows us that there is no simple argument from common sense to maximalism, since if there were, it would turn out to be equivalently an argument for the existence of sakes we do things for, things we believe in, things whose non-existence we regret, and so forth. Respectable proponents of maximalism do not, of course, rely exclusively on the argument from common sense. It does seem, however, that Armstrong relies on the premise that truthmaker theory is essential to a satisfactory definition (real or nominal) of truth. And if the goal is providing such a definition, then (MAX) clearly provides the most elegant conceivable solution. It is elegant, not least, because its rejection seem to force a certain dualism in characterizing truths: on the one hand are those true in virtue of truthmakers, on the other hand are all the rest. In the absence of (MAX), then, we will be forced to split a nominal definition into clauses, so that ‘is true’ means ‘has a truthmaker’ in some cases but something else in others – with no evident means of specifying what it is in virtue of which both cases would deserve the name of ‘truth’. Similarly, a real definition would, in the absence of (MAX), appear to have to construe truth as an essentially disjunctive property – a consequence which would undermine the very purpose of providing an ontologically robust definition of the property of truth. Moreover, since it is not clear how truths are to be parceled out into the two classes, and also not clear what to do in the way of providing a definition for elements of the second class, the rejection of (MAX) threatens to stop the definitional project in its tracks. Yet (MAX) itself seems (unfortunately for its defenders) to face an obvious and devastating objection in light of the heavy ontological price it brings in terms of special entities needed to perform the truthmaker role for difficult kinds of truths. This becomes clearer when we couple it with another independently established constraint on the truthmaker relation, namely that it should satisfy the necessitation or entailment principle:

83 (NEC)

If entity x makes P true, then necessarily (if x exists then P is true),

a principle accepted in almost all the truthmaker literature thus far. For what entity is such that the proposition asserting its existence could entail the truth of a proposition such as ‘There is no phlogiston’? Nothing, to be sure, in the reality we know from common sense or science. Maximalists, therefore, must resort to the positing of special entities – negative facts in the case of Russell, totalizer facts in the case of Armstrong – which face the problem that they are supported by no arguments independent of maximalist versions of truthmaker theory. If, however, we are right that the friends of truthmakers have no business providing a definition of truth, then maximalism can be abandoned and therewith also those special entities which leave it vulnerable to an argument along the lines just presented. In other words, if a given ontological claim presents itself as intrinsically bizarre, and is motivated only by its satisfaction of some general principle dictating which truths should have which sorts of truthmakers, where this principle in turn is motivated only by the desire for a truthmaker definition of truth, then a modus tollens emerges against the principle in question as soon as we reject its ontological offspring as bizarre. 4. Factualism A position that tends to run hand in hand with maximalism is what Armstrong has dubbed ‘factualism’, the tripartite view according to which: 1. the world is populated with special entities called ‘facts’ or ‘states of affairs’, 2. truths correspond to many or all such entities, 3. many or all judgments are true if and only if there exist facts to which they correspond. The most extreme version of factualism is a variant of maximalism. It posits the existence, for every true judgment p, of a special proposition-shaped entity, the fact that p, precisely tailored to make p true. The factualist is then in the happy position that he can provide a definition of truth accord-

84 ing to which a judgment p is true if and only if there is an x such that x is the fact that p. More moderate versions of maximalist factualism, such as Armstrong’s own, privilege a certain subclass of truths (for example those of atomic logical form) and hold that only these come equipped with corresponding facts, while remaining truths are entailed by the truths belonging to this subclass. The Tractatus, with its two-sorted truthmaker theory of Sachverhalte and Tatsachen, is also of this variety. Distinct conceptions of factualism arise depending on how ontological priority is assigned to facts. On the one hand there is the view that facts are second-class denizens of reality – the plebeians of the ontological realm. Under this conception, facts supervene on, or are dependent on, a reality which in and of itself consists of more garden variety entities such as objects, qualities, processes, etc. We might also refer to this conception of facts as deflationary, since it suggests again that facts do not play any fundamental explanatory role in our metaphysics, and that our reference to them is primarily a matter of linguistic convenience. Pfänder2 and Mulligan3 are plebeian factualists who are also maximalists. On the non-maximalist factualisms defended by Daubert4 and by Smith5, in contrast, facts are the results of different sorts of carvings up of the material of reality, creating boundaries in reality which are analogous to the boundaries we create, for instance, when we carve out voting districts or portions of real estate. One implication of this demarcatory view is that there is a fact only where there is some positive material to be carved. There is a fact that John is kissing Mary because there is material to be carved that comprehends, in addition to John and Mary, some event or events involving certain movements of John’s lips. Such carvings are reflections of the judgments we make; hence (to echo Strawson6) if there were no judgments, there would be no facts. Facts are special sorts of fiat 2

Alexander Pfänder, Logik, Halle: Niemeyer, 1929. Kevin Mulligan, “Two Dogmas of Truthmaking,” in this volume. 4 Karl Schuhmann and Barry Smith,. “Questions: An Essay in Daubertian Phenomenology”, Philosophy and Phenomenological Research, 47 (1987), 353-84. 5 Barry Smith, “Fiat Objects“, Topoi, 20: 2, 2001, 131–148. 6 Peter F. Strawson, “Truth”, Proceedings of the Aristotelian Society, Supplementaryvolume, 1950, as repr. in Logico-Linguistic Papers, London: Methuen, 1971, p. 197. 3

85 entities. They are gerrymandered portions of reality dependent for their demarcations on our acts of judgment. On the other hand is the view that facts are true patricians in the order of reality – entities that exist independently of our cognitive acts and do genuine ontological work. Under this conception, facts do not supervene on non-factual reality. Rather, they are full-fledged ingredients of reality at its base level. So for example the fact that this apple is red does not exist simply because the apple and redness do. Rather, this fact is the nexus or tie that connects this particular apple to the universal redness, or rather (as on the view defended by Armstrong) the apple, the redness and the tie are themselves properly viewed as abstractions from the fact.7 Let us call the two views plebeian and patrician factualism, respectively. The former draws in part upon linguistic usage – stemming from the fact that we say things like ‘stemming from the fact that’, a turn of phrase which suggests that there are facts from which things stem. It draws its motivation also from the way it seems to facilitate a correspondence-style theory of truth and an associated maximalist definition of truth in terms of truthmaking at very little ontological price. With enough plebeian facts at our disposal we have, for every truth p (or for every ‘positive’ or ‘atomic’ truth p), a corresponding fact that can serve as that to which it corresponds. We hold, however, that those who countenance as valid the goal of providing a truthmaker-driven definition of truth should reject a plebeian factualism, since it is unable to provide the truthmakers required for such an enterprise. The entire purpose of a truthmaker-driven definition of truth is, after all, to highlight the way in which truth claims turn out to be in some sense equivalent to ontological claims. Yet plebeian accounts of facts are intended precisely to be ontologically modest, or ‘neutral’. Their talk of facts is supposed to be reducible to some non-fact-involving talk. This means, however, that any definition given in terms of plebeian facts should be no more than shorthand for some definition formulated in other terms. Even, therefore, if there were good reasons to look for an ontologically flavored definition of truth, it is doubtful that a plebeian conception of facts could play any prominent role therein.8 7

David M. Armstrong, A World of States of Affairs. Cambridge: Cambridge University Press, 1997. 8 See, again, Paul Horwich, Truth. op. cit., 105-106

86

Our principal objective here is not to argue with the plebeian factualist. Rather, it is to explore what happens when we wean ourselves away from the urge to define truth in truthmaker terms. If there are any good reasons to believe in plebeian facts, these will presumably survive even after this urge is quelled. At the same time, a truly deflationary conception will not carry with it any ontological excesses, and as such will not be vulnerable to the sort of modus tollens arguments which can be applied to more robust versions of maximalism and factualism. Patrician factualism draws its justification from deeper philosophical considerations, and we have no general brief against a well-modulated ontology of facts. Our argument is rather directed only against those forms of factualism which are motivated by maximalism to postulate factoid entities which, in spite of their metaphysically questionable nature, are yet held to play a fundamental role in the structure of reality. The most well-articulated formulation of the patrician factualist doctrine is Armstrong’s theory of states of affairs,9 which rests on the intuition that, since both the particular (the apple) and the universal (redness) can exist without the apple being red, something further must exist in order to explain how the two are tied together. Armstrong holds that it is the fact that the apple is red which must do this work. For Armstrong the fact is not, so to speak, a fancy way of framing the situation of interest: rather the fact is the situation of interest. Following Reinach,10 he sees facts as being essential also in accounting for the metaphysics of laws of nature, of possibility, of mathematics – in each of which some addition is required, on top of objects, properties, qualities, to explain the phenomenon in question. Thus, for example, if it is a law that Fs bring about Gs, then there is a requirement for some necessitation state of affairs to exist, over and above F, G and their various separate instances, to serve as truthmaker for the proposition that this law obtains. We hold the intuition behind such arguments to have some force, but we think the best response is to invest some toil in searching for solutions

9

A World of States of Affairs (op. cit.). Adolf Reinach, “On the Theory of the Negative Judgment”, in Barry Smith (ed.), Parts and Moments. Studies in Logic and Formal Ontology, Munich: Philosophia, 1982, 315–77.

10

87 more heterogeneous and more finely-tuned to each of the problems at hand. Thus for example, following in the tradition of trope-based theories,11 we hold that appeal to some version of the theory of what Aristotle called individual accidents (headaches, kisses, the redness of this apple) yields a less heavy-handed and more finely-tuned solution to the problem of explaining instantiation.12 It is not however problems such as this, but rather the need to postulate extra entities to serve as truthmakers for truths like ‘There is no phlogiston’ which leads Armstrong to make bizarre ontological posits, the so-called totalizer facts. Each such fact is essentially associated with a certain (possibly empty) collection of individuals and with a certain condition (for example being white or being a portion of phlogiston), in such a way that the totalizer fact exists if and only if the collection of individuals with which it is associated constitutes all and only the entities satisfying the given condition.13 Totalizer facts not only constitute a sizeable bullet for Armstrong’s theory to swallow, they also do not lead to any analysis of some puzzling issue (such as instantiation or the nature of laws) independent of their ability to save the principle of truthmaker maximalism. Since, to recap our arguments above, totalizers must be patrician facts if they are to serve Armstrong’s purposes (since on the plebeian view talk of totalizers would be in any case nothing more than a façon de parler about something else), they are just the sort of entities whose intrinsic bizarreness serves to actively discredit the principle of truthmaker maximalism when that principle is shorn of independent motivation. 5. Truthmaker Arguments Even for Armstrong, truthmakers were not originally intended to figure in the definition of truth. Rather, the question ‘where are the truthmakers?’ was first wielded (by C. B. Martin) in the battle against various reductionist theories which made complex and ambiguous claims seemingly in need of metaphysical analysis while simultaneously denying the very possibility of such analysis. Thus phenomenalism and behaviorism depended essen11

Kevin Mulligan, Peter M. Simons and Barry Smith, “Truth-Makers”, Philosophy and Phenomenological Research, 44 (1984), 287–321. 9 Op. cit.,. 13 David M. Armstrong, Truth and Truthmakers¸Cambridge: Cambridge University Press, 2004.

88 tially on counterfactual claims to account for truths about unperceived objects and unmanifested behaviors, but in such a way that the counterfactuals in question (involving what objects would have been seen, or what behaviors would have been manifested) were left as primitive. In this context, the truthmaker question was interpreted as the demand for some way of showing how the counterfactual claims in question might be understood as tethered to or grounded in reality. The core truthmaker commitment is in this respect what we might call the demand for ontological explanation, that is, for ontological posits that would serve to explain (account in a non-epistemic way for the truth of) propositions of given types. In many cases this demand for explanation will be trivially satisfied, as for instance when the truth ‘George exists’ is ontologically explained by George. It need not follow that every truth has even a partial ontological explanation, however advantageous this would be. Thus there is no ontological explanation of ‘there is no phlogiston’, given that the best answer to the question: ‘how must a possible world be, ontologically, if there is no phlogiston there?’ is simply: ‘there is no phlogiston there’. We hold that there are some sorts of truths that can clearly be explained ontologically and others that clearly cannot be so explained, but also that there is a large pool of unclear problem cases in between. We hold further that it is a methodological error to tether oneself in advance to any general principle about which truths have such explanations and which do not. The search for one – maximally all-embracing – principle along these lines is of course understandable in the context of a desire for a truthmaker definition of truth, but otherwise we cannot see what justification it might have. What purpose, then, do ontological explanations serve? Our answer is that they test metaphysical theories. Just as a scientific theory is proven by its ability to provide scientific explanations of seemingly extraneous phenomena (phenomena hitherto unanticipated by proponents of the theory in question), so an ontological theory will be vindicated by its ability to provide enlightening ontological explanations for seemingly extraneous truths. Our methodology below will be to present some instances of ontological explanation at work. We hold that, for truths of any given type, the demand for an ontological explanation is like the demand for a microphysical explanation given a particular type of simple or complex physical phenome-

89 non – a demand whose fulfillment is realizable only in light of a delicate set of constraints on overall theoretical harmony.14 On the methodology advocated here, therefore, the search for truthmakers provides at best defeasible or negotiable arguments for selected ontological posits, which must in every case be balanced against a variety of considerations of other types. The success of the methodology will thus involve weighing the quality of the ontological explanations which it provides against the cost of integrating the corresponding posits into our overall ontology. 6. Truthmakers and Ontological Commitment Our defeasible (and thus) non-apodictic approach to truthmakers can be used to throw light also on the notion of ontological commitment. Armstrong alleges that the approach to these matters favored by Quine, with his ‘to be is to be the value of a bound variable’, stacks the deck against a metaphysics of properties, since in the case of ordinary predications (‘the apple is red’) it demands only that we commit to the existence of apples.15 Armstrong’s substitute criterion, in contrast, asserts that we are ontologically committed to those entities which we construe as truthmakers for given sorts of truths. In this way universals like redness will turn out to be among the ontological commitments induced by truths like ‘the apple is red’. Quine might respond to Armstrong that his criterion of ontological commitment is the biased one, because it stacks the deck in favor of universals (among other things) by unduly broadening the range of possible arguments that can be used in support of them. At this point the dialectic 14

Related notions, with names like ‘metaphysical explanation’ and ‘grounding’ have been discussed in the literature. See Kit Fine, “The Question of Realism”, Philosophers’ Imprint, vol. 1 no. 1, 2001; Michael Gorman, “The Essential and the Accidental”, forthcoming in Ratio 18, 2005. 15 David Armstrong, Truth and Truthmaking, pp. 23 f.; “Against Ostrich Nominalism: A Reply to Michael Devitt”, Pacific Philosophical Quarterly, 61 (1980), 440-449. The Quinean criterion does not rule out a theory countenancing such entities as universals, though it does restrict the range of arguments that may be used in support of such a theory since it admits only arguments in terms of best syntactic regimentation. (See Barry Smith, “Against Fantology”, forthcoming in Johann C. Marek and Maria E. Reicher (eds.), Experience and Analysis, Vienna: HPT&ÖBV, 2005.)

90 mightbe thought to have reached an impasse, where a criterion of ontological commitment can be chosen only on partisan grounds, with friends of universals tending toward Armstrong’s account and nominalists tending toward Quine’s. It turns out, however, that a neutral criterion can be specified, one which has the chance of being accepted as satisfactory by all parties because it is a generalization of the criteria they have respectively proposed. This neutral criterion might be articulated as follows: A theory ontologically commits us to those entities whose existence is required to ontologically explain its constituent assertions. Alternatively: A person is ontologically committed to those entities whose existence is required to ontologically explain those assertions he countenances as true. The respective criteria suggested by Quine and Armstrong can both be seen as the results of adding to the criterion proposed above a specific thesis as to what sorts of ontological explanation are in general required. 7. Truthmakers In speaking of ontological explanation we deliberately employ a terminology more general than that of truthmaker theory in order to weaken the hold of the assumption that there is some single autonomous concept of truthmaking whose analysis can lead to substantive new factual discoveries (in analogy with concepts like knowledge or justice). Rather, for those who find it important that some rigorous sense be made of the notion, we offer a purely stipulative definition of truthmaking (a simplification of that defended in Smith’s “Truthmaker Realism”16): (TM) a TM p := p ∧ (E!(a) ↔ p),

16

Australasian Journal of Philosophy, 77 (3), 1999, 274–291.

91 where ‘E!(a)’ symbolizes: ‘a exists’ and ‘↔’ symbolizes co-entailment. Thus, a makes p true whenever: 1) p is true, and 2) the existence of a is (necessarily) both necessary and sufficient for the truth of p. In the language of possible worlds, we might say that a makes p true on our world whenever: 1) p is true on our world, and 2) p is true on all and only those worlds on which a exists. This definition singles out a certain group of propositions as those which have truthmakers, or which would have truthmakers if true.. They may be identified, roughly speaking, as those propositions whose sole demand on reality (all that they need the world to be like in order that they come out true) is that some entity exists. ‘Superman is real’, ‘I exist’, ‘This redness exists’ are obvious examples of judgments of this sort. There are less obvious examples. Thus the judgment, ‘Socrates is mortal’ seems at first glance to require something like the presence of a virtue of Socrates – namely: his being mortal – in order to be true. But Socrates is necessarily mortal. That is, he could not exist and yet fail to be a mortal. This means that it strictly suffices, for the given judgment to be true, that Socrates exists. Moreover, the entailment holds in the opposite direction: if Socrates succeeds in being mortal, then he thereby also succeeds in existing. ‘Socrates is mortal’ is thus a judgment which necessarily both implies and is implied by the judgment that Socrates exists. This definition captures the Armstrongian idea that truthmaking is necessitation, and also the idea that a proposition requires a truthmaker only if there is some entity whose existence is required to explain its truth.17 The definition avoids many of the challenges raised against the naïve Armstrongian characterization of truthmaking as necessitation (for example Restall’s argument to the effect that your refrigerator necessitates the truth of ‘2 + 2 = 4’18), by requiring the necessity to run in both directions. (Armstrong, in contrast, contents himself with an appeal to some unspecified relevance logic to save the day.) 17

It does not, however, provide us with everything we need to characterize the notion of ontological explanation. For the latter, intuitively, admits of degrees. (Thus Socrates affords a higher degree of explanation to the proposition ‘Socrates exists’ than to the proposition ‘Socrates is mortal’, even though Socrates is a truthmaker for both of these. 18 Greg Restall, “Truthmakers, Entailment and Necessity”, Australasian Journal of Philosophy, 72, 1996, 331-340.

92 Part Two : Some Ontological Explanations

We shall now see how the demand for ontological explanation can be used as a means of putting to the test one specific ontology, an ontology which accepts both independent substances and tropes. We will show that this ontology allows us to provide ontological explanations for a broad range of difficult kinds of truths, in a way which involves appeal only to entities in whose existence we may be independently motivated to believe. In this way we throw new light on the original use of truthmaker considerations against phenomenalists and behaviorists by Martin and Armstrong. The methodology employed there is to show that some view is inadequate because it fails to specify appropriate truthmakers for some of its claims. We have argued that this methodology is weakened – or even crippled – to the degree that it is associated a priori with a particular theory of truthmakers (that is, a set of non-negotiable principles dictating what propositions must have truthmakers, and what characteristics these truthmakers must have). Our examples are designed to point at the way in which a truthmakerbased methodology for doing metaphysics may be fruitfully employed when it is not so weakened. 1. Singular Existentials, Essential Predications Examples : ‘John exists’, ‘Socrates is mortal’, ‘That event is a kissing’. Judgments in this group are true if and only if the entity to which existence is attributed, or of which something essential is predicated, does in fact exist. The existence of that entity yields an ontological explanation of the corresponding truth. Our trope ontology allows us to deal with indexical judgments referring to events under the same heading. Thus, ‘That event is a kissing’ will be true if and only if that event itself exists, since that event could not have been other than a kissing event. 2. Standard Existential Assertions Examples: ‘There are rabbits’, ‘There is a man’.

93 The judgment ‘There are rabbits’ is true at a world if and only if there is some rabbit there. Which of all possibly existing rabbits it must be changes from world to world, and there is no particular entity whose existence is necessary and sufficient for the truth of the judgment. Thus it is not the case that Harvey, your favorite pet rabbit, makes it true that there is a rabbit (recall the definition of truthmaker provided above).19 Yet we may still say that Harvey’s existence is ontologically explanatory to some degree of the truth of ‘there are rabbits’, among other things since this truth is entailed by a truth that Harvey makes true (namely, ‘Harvey is a rabbit’). 3. Standard Predications in the Category of Accident Examples: ‘John is hungry’, ‘John is running’. The first case involves the existence of a quality (or trope) of being hungry, the second of a process of running. In both cases the entities in question are existentially dependent on a certain substantial bearer, namely John. The judgments here are ontologically complex (as Ramsey and Davidson saw): they are in effect existentially quantified and assert the existence of some state, quality or process satisfying a certain description. 4. Standard External Relational Judgments Example: ‘John is kissing Mary’, ‘Mary is slapping John’. These cases, too, involve an event (a kiss, a slap) whose existence necessitates the truth of the relevant judgment. As in the previous section, what is entailed by the truth of judgments in this class is only that an event of the given sort exists. Thus a partial ontological explanation of the corresponding judgments is provided if we say that a John-kissing-Mary event exists, a Mary-slapping-John event exists, etc.

19

This points to a divergence of the present account of truthmaker with that in Smith’s “Truthmaker Realism”. There, erroneously, Harvey was considered a truthmaker for “There are rabbits”.

94 5. Standard Contingent Negations Examples: ‘John is not hungry’, ‘John is not kissing Mary’, ‘There is no phlogiston’. One of the principles underlying our position is that special entities are not required to account for how the world is when something fails to be the case. If there is no golden mountain, then there does not need to be some other entity whose existence (demotically) entails that this is true.20 Rather, all that is needed is that there be no golden mountain. We therefore claim that such standard negative claims are not the beneficiaries of any ontological explanation. 6. Totalizer Judgments Examples: ‘Everyone is hungry’, ‘No one is kissing’. It is notoriously difficult to find entities that necessitate judgments like these. This is not surprising, given that there is no intuitive reason why the existence of some entity would be either necessary or sufficient for the truth of such a judgment. This is because like standard negations, these judgments do not admit of ontological explanation. 7. Logical Truths Examples: ‘Every thing either is a human or is not a human’, ‘It is not the case that some thing is a human and is not a human’. Logical truths are true no matter what. We might say that they need no explanation of any kind: they entail no ontological posits whatsoever, as there is no condition that the world must satisfy when they are true. This is in agreement with Wittgenstein: ‘A tautology has no truth-conditions, since it is unconditionally true.’ (Tractatus, 4.461) Some hold that such truths are true in virtue of their meaning; in particular in virtue of the meaning of logical terms like ‘every’, ‘or’, ‘is’, ‘not’. If you hold that truth is a property of particular judgments rather than abstract propositions, then you will 20

Raphael Demos, „A Discussion of a Certain Type of Negative Proposition“, Mind n.s. 26, 1917, 188-196

95 in a sense agree, since if the utterance in question had meant something else, then it might not have been true. But this holds of all judgments. We might single out the logical (or, more broadly, the analytical) judgments as special in that in their case it is exclusively meanings which determine truth: once the meaning is fixed, then there is no further way that the world must be in order that the judgment be true. However, ontological explanation, and talk of how the world must be if a certain judgment is true, come after meaning is fixed. Otherwise it would be necessary to mention the meaning component of every truth in giving its ontological explanation. Moreover, there are necessary truths which are not logical truths, such as the truth that Socrates is mortal if he exists, and the in-virtue-of-meaning approach would seem to cover such cases as well. Thus, we hold to the claim that logical truths are simply true no matter what, or true without entailing any ontological posits whatsoever. In this way, questions of meaning and sense may be avoided while attending to the project of ontological analysis. Our stance does not necessarily lead to the conclusion that logical truths lack a sense, as Wittgenstein thought. But that is more properly a question for a theory of meaning. There are logical truths which do bear specific existential presuppositions, such as ‘John is hungry or it is not the case that John is hungry.’ This proposition is a logical consequence of something which is a logical truth in the above sense (namely, ‘Everything is either hungry or not hungry’) as long as we allow that logical consequences of general judgments may involve proper names. We might call these judgments ‘impure’ logical truths: identity statements bearing rigidly designating names (e.g. ‘Hesperus is Hesperus’) are among their number – these follow from the logical truth that everything is self-identical. These truths are made true (in the strict sense of [TM]) by the existence of the entities named. Judgments predicating necessary intrinsic properties, like ‘Socrates is human’ also require only that the named entities (here: Socrates) exist in order to be true. Yet judgments such as this are not impure logical truths, since they are not logical consequences of any pure logical truth. 8. Contingent Intrinsic Predications (Judgments of Internal Relations) Examples: ‘John is two meters tall’, ‘Jones is in Thailand today’, ‘Mary’s arm is a part of Mary’s body’, ‘John is taller than Mary’.

96 These judgments express contingent, temporary, localized matters of fact, and seem to be akin to the predications of accidental and external relations considered under 3. and 4. above. Yet where, for ‘John is hungry’, there is a hungering (a growling of the stomach, a transmission of neurotransmitters to the brain), and for ‘John is kissing Mary’ a kiss (a congress of lips), what could motivate us to hold that there are token parthood-processes, or tallness-processes? Processes have very many of their properties essentially – they could not have been much otherwise than they actually are. If the Titanic had sunk an hour later than it did, the process that would then be referred to by the description ‘the sinking of the Titanic’ would have been a different entity from the process that is in fact referred to by that description, and likewise if a different iceberg had been involved, or if events had occurred in a different region of the Atlantic. This particularity of essence is unique to processes. Objects like people and oceanliners are such that their lives could have been filled with different events than those which actually did occur. John had oranges for lunch, but he could have had bananas instead. The Titanic could have made it to America. We might thus be tempted to say that it is a contingent matter that a certain process is a part of a life. But what is contingent is not that this process was a part of that life (the latter being itself an extended process of a certain sort). Rather, what is contingent is that this particular extended process, having yesterday’s eating-oforanges incident as a part, was that life. It is contingent that this particular collision and tragedy was the (conclusion of the) history of the Titanic. Lives are processes occupying regions of spacetime. They correspond to what are called the ‘spatiotemporal worms’ whose instantaneous temporal parts exactly coincide with those substances whose lives they are at each corresponding instant. John’s life is, roughly, the maximal event in which John is the exclusive or principal participant (and we may similarly speak of the lives of other sorts of things, including for example ships, arms, and countries). John’s life is existentially dependent on John – John’s life could not have been if John had not been. Crucially, again, the converse is not true. John could have lived differently. His life would then have been different (a different entity), though John would still have been himself. Lives are useful components of ontological explanations for the propositions with which we are presently concerned: among the essential proper-

97 ties of John’s life are its spatial location and material composition at every instant during which it is occurring. John’s life is therefore precisely the entity we need to bear ontological witness to the truth of the predications of formal measurement properties, contingent parthood relations, and the like. A partial ontological explanation of ‘John is two meters tall’ is then: There is an entity which is the now-slice of John’s life, and its maximal spatial span is two meters. A proposition similarly helping to explain ontologically ‘Jones is in Thailand today’ is: There are entities which are the today-slice of Jones’ life and the today-slice of Thailand’s life, and the today slice of Jones’ life is located in a spatial region which is a part of the spatial region in which the today-slice of Thailand’s life is located. And similarly helping to explain ontologically ‘Mary’s arm is a part of Mary’s body’ is : There are entities which are the now-slice of Mary’s arm’s life, and the now-slice of Mary’s life, and the former is a part of the latter. And similarly helping to explain ontologically ‘John is taller than Mary’ is : There are entities which are the now-slices of John and Mary’s lives, and the maximal spatial span of the former is greater than that of the latter.

Conclusion The project of defining truth in truthmaker terms is to be abandoned (and it is in any case unrealizable). But this does not undermine the foundations of truthmaker theory in its truly productive aspects. Indeed the effects of the rejection of this project are liberating. They draw attention to the true force of the truthmaker idea – the idea of ontological explanation – as a valuable type of accessory tool for metaphysical theorizing, rather than as a mere component of the enterprise of defining some single concept or property, however central it might be. An ontological explanation is in effect an account of what there must be in reality for a given judgment to be true. The work, for each of us, lies in es-

98 tablishing how to find ways to formulate such accounts each within the framework of his preferred ontological theory. We have provided one ontological theory – involving both substances and tropes of various kinds – which yields what we believe is the maximally satisfactory set of ontological explanations for a large group of cases. In this way we have illustrated how truthmaker considerations can serve as one important means of putting metaphysical theories to the test.

Truthmakers for negative truths, and for truths of mere possibility D.M. ARMSTRONG University of Sydney

1. Negative truths In my recent book on truthmakers I embraced Truthmaker Maximalism, the doctrine that every truth has a truthmaker. Even among devotees, not many are found who accept my stand, though it has some considerable theoretical advantages. One advantage is that it permits an univocal theory of truth. (I take it that truthmaker theory, as opposed to suggestions about what particular truthmakers we should postulate, is part of the theory of truth.) Perhaps it is rather uneconomical in what D.C. Williams wittily called the ‘gross tonnage’ sense, but I’d argue, as Williams did, that theoretical economy is very much more important than gross tonnage. (See Donald Williams, 1966, p. 133, ‘true logical economy consists in the assumption of as few independent principles as possible.’ His whole discussion is greatly worth reading.) One interesting application of this point is to be found in the problem of finding truthmakers for negative truths. This problem, I have argued for some time now, is best solved by first picking out a sub-set of the negative truths: the general truths. If you have truthmakers for all the general truths, then it seems a plausible claim that the other negative truths will supervene. (Slogan : once you have set the limits, the absences will take care of themselves.) And if so, it is further plausible that the truthmakers for these other negative truths, such truths as , will be found among the truthmakers for the general truths. (, where the such and such is a list on which the property of blueness does not appear.)

100 But we can perhaps go further than this, and get a single general truth that will give all that is needed. Consider the truth that lists all the positive truths with one exception. It lists all the positive entities that exist, exist omnitemporally I’d say, and then says of these entities that they are all the positive entities. (The point of saying ‘positive’ is to help with the problem of self-reference, which might be thought to arise if we say ‘all the entities’.) The list may be an infinite one, so that no finite mind could possibly assert or contemplate it. If you are, as I am, prepared to allow such a proposition, then providing a truthmaker for this general truth, seems to provide a truthmaker (in general not a minimal truthmaker) for all the other negative truths, including all the other general truths. You will of course need a truthmaker for the existence of truths, and more generally of propositions. I’ve argued in 2.6 of my 2004 book that this is not too difficult a task. Unexpressed truths are mere possibilities. These modal truths can, in turn, be given relevant but ontologically economical truthmakers, but that is the second part of this paper This huge general truth (let us call it ‘the totalizer proposition’) will entail all the other negative truths, whether they are general truths or the other negative truths that are more obviously negative. The Entailment principle – that, in general at least, the truthmaker for the entailing truth will be a truthmaker for what is entailed – can, it seems, be appealed to here. If this is so, and if we have a truthmaker for the totalizer – the totalizer fact or state of affairs – then we will have truthmakers for all negative truths. The totalizer fact will be a negative fact, but it will be the only one. (It will be like a Sabbath, where God can rest.) Negative truths can flourish, but in a sense there will only be one negative truthmaker. (For ordinary negative or general truths the totalizer fact will not, of course, be a minimal truthmaker. Lesser positive totalities will suffice. But these smaller positive totalities are just proper parts of the great fact.) If you think that the totalizer fact is too big a fact, I reply that it is very big in a gross tonnage sense, but it helps towards giving us that great theoretical simplification in truthmaking theory: a truthmaker for every truth.

101 The totalizer’s truthmaker (its only truthmaker) would, I think, have the same form as I have argued for in the case of other general truths. You have a mereological sum of some sort that ‘totals’ some property or other – not necessarily a natural property. A certain very large mereological sum, the sum of all positive entities, totals the (rather dilute) property of being something positive. Is this fact or state of affairs an addition to the very large sum ? It is and it isn’t. It is because you need a truthmaker for ‘That’s all’ (by truthmaker Maximalism.) It isn’t because it is a negative fact, and so, strictly, is no addition of being. 2. Truths of ‘mere possibility’ Truthmaker Maximalism demands that we supply truthmakers for all modal truths. I originally approached this problem by thinking about truths of mere possibility, truths of the form ‘it is possible that not-p’, where p itself is a true proposition. There is a very simple one-one correlation between contingent truths and the truths of mere possibility. What is more, the contingent truth entails the corresponding mere possibility, an entailment that would seem to be analytic. This consideration, though, led me to make a sad blunder. (See Armstrong 2004, 7.2.) I thought that all we need do is to consider some truthmaker of a contingent truth, and then use the Entailment principle to show that this truthmaker was also a truthmaker for the entailed mere possibility. This is clearly wrong. To get an entailment we need that the truth is a contingent one, and this means that we need, not the truthmaker for p, but a truthmaker for the truth

. It may be, though, that the situation can be saved, and the Possibility principle sustained. Let T be a truthmaker for contingent p. Can it be argued that T is also a truthmaker for

? Perhaps it can. T, whatever sort of existent entity it is, is a contingent being. In virtue of what is it a contingent being ? A rather good hypothesis, I suggest, is that it is a contingent being in virtue of what it is in itself. ‘What it is in itself’ is here intended to contrast with what it is in virtue of some relation T has to some-

102 thing else. ‘What it is in itself’ is T taken non-relationally or, if you prefer the term, intrinsically. We have truths that are contingent and truths that are necessary. I assume that this is a real and objective distinction among truths. If the distinction is objective, something that we do not impose upon truths, then it would seem that there must a real and objective distinction between the truthmakers for these sorts of truth. Traditionally, this is the distinction between contingent and necessary beings. Given permissive mereology, there can, of course, be beings that are wholes containing both sorts of being. Taken strictly, such a mixture is a contingent being, but in any case we can stipulate here that T is a purely contingent being. It seems that for each contingent truth there must be at least one purely contingent being to be its truthmaker. We have the usual difficulty here of proving a negative, the negative here being that there is no relational property of T that could serve as a truthmaker for T’s contingency. If T is merely ‘an aspect of the absolute’ or something like that, it might be argued that T’s contingency lies outside itself. But given a realist view of the world, it seems that T itself that is truthmaker for T’s contingency. But we seem to be able to do better than this. Consider nature, that is to say, space-time. (Current physics and cosmology suggest that ‘space-time’ may be a relatively superficial description of this reality. But that seems not relevant here.) Philosophers generally assume that nature is made up of contingent beings, and often that nature itself is a contingent being. Let us make these assumptions. (This, it may be noted, is even consistent with there being necessity in nature. One can abandon the neo-Humean assumption that there is no necessary connection between wholly distinct existences, yet still think that the world is a contingent being and made up of contingent beings. This can be done if one maintains that necessary connections in nature do exist, but always hold between contingent entities. Then the instantiation of the necessary connection, the whole state of affairs, is contingent.)

103 Now consider some contingent being in nature. It might not have existed. But can we not add : its existence or non-existence as a contingent being is not logically dependent on the existence or non-existence of any further contingent being ? A counterfactual holds : it might have been there, but unaccompanied. And if so, must not the truthmaker for the contingency of its existence be itself, T ? So if T is a truthmaker for some contingent truth p, then it will also be a truthmaker for

. It remains to add that if there are contingent entities that are not spatiotemporal entities, the same line of thought seems to apply. Notice that this account of truths of mere possibility will not be applicable in full generality unless there are truthmakers for all negative truths. It is true that there is no rhinoceros in this room now, but it seems to be a possibility that there should be one − the absence of the animal seems to be a contingent one. A truthmaker for the negative truth is required if we are to use the Possibility principle to give a truthmaker for the possibility of the presence of the rhinoceros. 3. Might there have been nothing at all? A note for the fun of it : if the Possibility principle is adopted, then it seems relatively easy to provide a truthmaker for the disputed proposition , or at least . The proposition is, plausibly, both contingent and true. If so, then it is easy to provide truthmakers for . Any contingent entity will do. And if there cannot be necessary beings, as I incline to think, it is possible that there might have been nothing at all.

REFERENCES Armstrong, D.M. (2004) Truth and Truthmakers, Cambridge: Cambridge University

104 Press. Williams, Donald C. (1966) Principles of Empirical Realism, Springfield, Illinois: Charles C Thomas.

A World of Truthmakers PHILIPP KELLER

Abstract I will present and criticise the two theories of truthmaking David Armstrong offers us in Truth and Truthmakers (Armstrong 2004), show to what extent they are incompatible and identify troublemakers for both of them, a notorious – Factualism, the view that the world is a world of states of affairs – and a more recent one – the view that every predication is necessary. Factualism, combined with truthmaker necessitarianism – ‘truthmaking is necessitation’ – leads Armstrong to an all-embracing totality state of affairs that necessitates not only everything that is the case but also everything else – that which is not the case, that which is merely possible or even impossible. All the things so dear to realists – rocks, natural properties, real persons – become mere abstractions from this ontological monster. The view that every predication is necessary does in some sense the opposite: it does away with totality states of affairs and, arguably, also with states of affairs. We have particulars and universals, partially identical and necessarily connected to everything else. Just by the existence of anything, everything is necessitated – the whole world mirrored in every monad. Faced with the choice between these two equally unappealing alternatives, I suggest returning to Armstrong’s more empiricist past: the world is not an all-inclusive One, nor necessitated by every single particular and every single universal, but a plurality of particulars and universals, interconnected by a contingent and internal relation of exemplification. While a close variant, truthmaker essentialism, can perhaps be saved, this means giving up on truthmaker necessitarianism. This, I think, what it takes to steer a clear empiricist course between the Scylla of Spinozist general factness and the Charybdis of a Leibnizian overdose of brute necessities.

0. Introduction As realists, we hold that truth depends on the world. What we hold true, we would like to be able to say, commits us to certain views about what exists and what does not. As serious metaphysicians, we should be prepared to pay the ontological bill of what we assert. But how are we to determine the price? A venerable method, championed by Quine, is to look at the domain of quantification of the variables occurring in (some regimentation of) what we are asserting. In his early work, David Armstrong (1978, 1978a) pointed out that this is not always satisfactory: the ontological ground of

106 our alleged truths does not only consist of things, but of their properties as well: we need an ontologically robust account of properties in virtue of which the alleged truths are true. In recent years, truthmaker realism has seen something of a renaissance and it is its recent defence in Truth and Truthmakers (Armstrong 2004) I mostly want to discuss in the following. First of all, let me emphasise the high degree of agreement I have with Armstrong’s views. I agree with him that asking the truthmaker question is a promising way to regiment metaphysical enquiry (Armstrong 2004: 4), that, in particular, “continually to raise the truthmaker question about properties makes for ontological honesty” (2004: 43) and that there is, “in the general case, no cheap and easy way to determine the truth-makers even of simple descriptive sentences via linguistic transformations” (Mulligan et al. 1984: 300, cf. Armstrong 2004: 16). I agree that “philosophy is not meant to be easy” (Armstrong 2004: 117) and that part of its difficulty comes from thinking metaphysics through from a truthmaker perspective. I also think that answering the truthmaker question commits us to an ontology of sparse properties, “in terms of which the world’s work is done” (2004: 17), and that this is motivated by the fact that, intuitively speaking, we do not need the whole of the particular to make non-relational predications true (2004: 41). I also think that the cash value of truthmaking is most visible in its critical use, e.g. as against ungrounded phenomenalist counterfactuals about unobserved objects or Rylean unactualised dispositions to behaviour. In these uses, the truthmaker intuition consists in roughly the following two tenets: • Truth is relational: being true is being made true by something. It is then a further question whether the things in virtue of which truthbearers are true are states of affairs, some objects or ways they are. • Truth is grounded: true truthbearers are true because the world is how it is; truth is not brute. It is a further question whether some truthbearers may ground themselves and what the grounding in question comes to. These rough intuitions, of course, do not amount to a theory. There are different ways to flesh them out, three of which, all at some time put forward by Armstrong, I will discuss in the following. The first theory, advocated

107 by him in 1978 and a variant of which I would myself like to advocate, holds that the world is a world of particulars and universals, which are connected by a relation of exemplification. Armstrong never says much about this relation,1 except that universals are “immanent”, i.e. are “constituents” of things and “part of [their] internal structure” (1989: 77),2 that exemplification is a ‘non-relational tie’ (1978: 109) making for an identity in nature of particulars that is “literally inexplicable”: “I take it that the Realist ought to allow that two “numerically diverse” particulars which have the same property are not wholly diverse. They are partially identical in nature and so are partially identical.” (Armstrong 1978: 112)

Both David Lewis3 and Keith Campbell4 have interpreted Armstrong as holding that universals are non-spatiotemporal parts of the particulars exemplifying them and this is the view I want to defend in section 4. 1

Of exemplification, he said in 1978 that “it is interesting, but somewhat saddening, to notice that the great modern defenders of transcendent universals, Moore and Russell, do not even consider this problem of the nature of the relation between particulars and Forms to which Plato gave such close attention.” (Armstrong 1978: 67) It is equally interesting, but somewhat saddening, that the same can be said of the great contemporary defender of universals. 2 Armstrong characterises the alternative position, transcendentalism, as the view that “put[s] properties ‘outside’ their particulars”: “A theory that has particulars instantiating transcendent universals seems to put properties ‘outside’ their particulars. It offends against the original insight that the thing itself should serve as truthmaker, even if not as minimal truthmaker, for truths that particulars have certain (non-relational) properties. A theory of immanent universals is required if the truthmaker for a nonrelational property of a particular is to be found ‘within the particular’.” (2004: 42) 3 “A universal is supposed to be wholly present wherever it is instantiated. It is a constituent part (though not a spatiotemporal part) of each particular that has it. […] Things that share a universal have not just joined a single class. They literally have something in common. They are not entirely distinct. They overlap.” (1983: 10-11). Cf. also Lewis (1986a: 80): “Whenever it [a universal] is instantiated, it is a nonspatiotemporal part of the particular that instantiates it.”; “[The universal of charge] is located there, just as the particle itself is. Indeed, it is part of the particle. It it not a spatio-temporal part…[…] I reserve the word “universal” strictly for the things, if such there be, that are wholly present as non-spatio-temporal parts in each of the things that instantiate some perfectly natural property.” (1986: 64, 67, cf. also 204-205) 4 “This [Armstrong’s] view requires us to acknowledge that there can be parts other than spatio-temporal parts.” (Campbell 1990: 39); “The most promising reply to [the ‘Third Man’ argument] is that the substance substratum of Socrates neither contains nor resembles humanity, while the complete substance Socrates does contain humanity (has humanity inhering in him) and in that way resembles humanity. It is a one-sided

108 Although Armstrong introduced them already in 1978,5 non-supervenient states of affairs ‘officially’ entered his ontology via another truthmaker argument, providing entities ‘encapsulating’ the fundamental tie of exemplification and necessitating the corresponding predications: Because the truthmaker for the contingently true predication “Fa” must necessitate its truth, it cannot be F or a alone, nor their fusion, for all three of them could exist without “Fa”’s being true. Hence it is the state of affairs a’s being F (cf. 1989: 88, 1997: 115), which, by necessity, exists if and only if a is F: “If it is said that the truthmaker for a truth could have failed to make the truth true, then we will surely think that the alleged truthmaker was insufficient by itself and requires to be supplemented in some way. A contingently sufficient truthmaker will be true only in circumstances that obtain in this world. But then these circumstances, whatever they are, must be added to give the full truthmaker.” (Armstrong 1997: 116)

By this ‘sufficiency argument’, as I will call it, we arrive at the following: Truthmaker Necessitarianism: The determining of a truth by a truthmaker is an absolute necessitation (Armstrong 2004: 5).

1. Truthmaking by thick particulars Truthmaker necessitarianism, coupled with the view that every truth has a truthmaker (‘truthmaker maximalism’), populates the world with entities that, by necessity, exist only if some corresponding truthbearer is true. If these two categories of entities do not overlap, truthmaker necessitarianism violates combinatorialism, the view that there are no necessary connections between distinct existents.6 Truthmakers and truthbearers, while different, stand in the truthmaking relation in every world in which the former exists, thereby ruling out combinations of both without the truthmaking relation

case of partial identity (a non-spatio-temporal part of Socrates is identical with humanity).” (1990: 42) 5 At the time, he did not take them as basic: “I do not think that the recognition of states of affairs involves introducing a new entity.” (Armstrong 1978: 80) 6 I use “combinatorialism” for what Armstrong (1989a: 116, 2004: 71) calls the “Distinct-Existence Principle”, that each of any two wholly distinct things may exist in the absence of any part of the other, which follows from his combinatorial theory of possibility. In (1997: 139), he calls it “Independence”.

109 holding between them.7 If the truth of truthbearers requires the existence of the things they are about and if these things are not mereological parts of the respective truthmakers, combinatorialism is even doubly violated: for then not only the truthbearer but also the things it is about are necessitated by the truthmaker.8 If this truthmaker is a state of affairs a’s being F, then it necessitates not just that “Fa” is true, but also that a and F exist and are related by the exemplification relation.9 7

Armstrong has a peculiar account of truthbearers: to fit propositions into his naturalistic world-view, he identifies them with equivalence classes of actual and possible states of mind (1997: 131, cf. also 2004: 13). Unexpressed propositions are (merely possible sets of) “merely possible mental or statement tokens” (1997: 131) or properties of merely possible mental states (2004: 13). This view has at least two problems: What could justify our belief in the existence of such merely possible propositions? On Armstrong's actualist views, the merely possible cannot stand in any external relation to the actual: “Given this absence of external relation, in particular causal relation, of the merely possible to the actual, it becomes very hard to see how we could know or even have any reason to believe in the existence of merely possible entities. Our beliefs have causes.” (1997: 149) A merely possible proposition, prior to its being believed or known, cannot have any influence on the believer. The second problem is that the distinction between expressed and unexpressed propositions imports a radical asymmetry into the account of truthmaking: unexpressed propositions are not exemplified. Unexemplified properties are analysed as mere possibilities of the exemplification of such properties (2004: 15-16). Hence the truthmaker of an unexpressed proposition (which necessitates its existence) is a truthmaker for the claim that it could be expressed, i.e. for the claim that it is not actually expressed (1997: 91). This will be a totality state of affairs: that, at some time, some propositions are all that have been expressed. How can this state of affairs make true the (hitherto unexpressed) proposition that no atom bomb exploded in Sydney on January 5, 2007? And how can it be explained that its truthmaker now, as the proposition became expressed, no longer involves any mental states and propositions, but just what happened some time ago in Sidney? Whatever the virtues of this two-tiered account of propositions, merely possible mental states are in any case wholly distinct from their truthmakers: while the latter actually exist, the former do not. 8 This has been pointed out by Fox (1987: 196-197). Lewis has advanced both recombinatorialism (1998: 219) and reluctance to accept (and inability to understand) nonmereological composition (1986b: 109) as reasons to reject the truthmaker principle, where the complaint about non-mereological modes of composition is subsumed by the worry about necessary connection between distinct existences (2001: 611). 9 If Lewis’ charge is taken to concern just the necessary connection between the state of affairs and its components, then it is not a problem for truthmaking in general but rather for truthmaking by states of affairs, as Daly (2000: 96) rightly points out. There is another necessary connection, however, between the truthmaker, the truth and its ontological commitment. Contra Daly (2000: 97), this necessary connection is not

110 This is a considerable price to pay. Combinatorialism underlies both Armstrong’s and Lewis’ recombinatory theories of possibility and is our best handle on what possibilities there are. It seems worthwhile, therefore, to reconsider the argument why it is that, whenever a makes it true that p, it has to do so in all worlds in which it exists. The sufficiency argument for this claim is that if there were a world where a would not make it true that p, say w, then the question what it is that makes it true that p was (partly) the question what distinguishes our world from w.10 Because that difference not only concerns a but also something else, this something else has to be ‘brought into’ the truthmaker. The property of making it true that p, in other words, has to be an intrinsic property of the truthmaker. The sufficiency argument, as Armstrong (1997: 115) says, establishes that the truthmaking relation is internal. This brings out a viable intuition: the truthmaking relation cannot depend on facts about things outside the items it relates. If a makes it true that p, nothing else than a and p have a bearing on whether the truthmaking relation holds. If the truthmaking would depend on something outside of them, this additional circumstance would have to be brought into a, as Armstrong says. Another reason to take the truthmaking relation to be internal is the following: external, but not internal relations are ontological additions to their terms. If truthmaking were an external relation, it would be an addition to the “ontology of the situation” (Armstrong 2004: 9) – it itself would have to be brought into the truthmaker, creating an infinite regress. Whether we get truthmaker necessitarianism out of truthmaker internalism (the thesis that truthmaking is an internal relation), however, depends on what we mean by “internal”. “Internal relation” is a notoriously ambiguous term. Bradley (1893: 392) used it to characterise relations that “essentially penetrate […] the being of [their] terms”, Moore (1919-20: 291) for relations that supervene on monadic foundations which are critical to the identity of their terms in the sense that without them, they would not be what they are, and Wittgenstein in the Tractatus for relations the relata of which are inconceivable without them (1921: §4.123). Armstrong (1978a: 85) said that two or more particuavoided by truthmaking by tropes: the F-ness trope that makes it true that a is F is necessarily connected to a, if “Fa” could not be true if a did not exist. 10 Bigelow (1988: 126) gives essentially the same argument: “…unless the existence of a thing does entail a truth, that thing cannot be an adequate or complete truthmaker for that truth.”

111 lars are internally related if and only if there exist properties of the particulars that logically necessitate that the relation holds. They are externally related if and only if there are no properties that necessitate the relation or a part of it. As the context of the passage makes clear, the properties in question must be understood as intrinsic properties. We thus get the standard account of internal relations: Internal relations: A relation is internal if and only if it supervenes on the intrinsic properties of its relata.11 Armstrong also characterises internal relations somewhat differently: “I mean by calling a relation internal that, given just the terms of the relation, the relation between them is necessitated.” (Armstrong 2004: 9)

This turns truthmaker internalism into truthmaker necessitarianism. How is such a transition to be justified? Armstrong (1997: 12, 87, 115) says that a relation is internal if and only if it is impossible that its terms should exist and the relation not exist, where the joint existence of the terms is possible. He adds that “to fall under our definition of internal relations, the particulars involved must be taken as having their non-relational properties” (1997: 88). The terms necessitating the internal relations are “thick particulars”, particulars ‘taken together’ with their intrinsic properties.12 The thesis that truthmaking is internal in the sense of supervening on intrinsic properties of truthmaker and truthbearer is at least prima facie different from necessitarianism because it can be reasonably doubted whether all intrinsic properties are “given just the terms of the relation”. It may well be that some intrinsic properties of some truthmaker are not essential to it, i.e. such that the truthmaker could exist without them.13 This is reason enough to distinguish truthmaker internalism from necessitarianism. 11

Lewis (1986: 62) calls an internal relation in this sense “intrinsic to its relata” (cf. also 1983: 26, fn. 16). An intrinsic relation that is not internal is called “intrinsic to its pairs” by Lewis (1983: 26, fn. 16) and “external” by Lewis and Langton (1998: 129). 12 This matches Armstrong’s other definition (1989a: 105): particulars having certain properties are internally related by a relation R iff in each possible world which contains them and where they have these properties, they are related by R. Similarly, Armstrong (2004: 116) says: “Where a pair stands in a fixed relation, one that is fixed, that is, necessitated, by the nature of the pair, there we have an internal relation.” 13 Being n meter tall is an intrinsic, but not an essential property of mine. Armstrong (1997: 92) himself warned against the confusion of intrinsic and essential properties.

112

Truthmaker internalism: Truthmaking is an internal relation. Truthmaker internalism brings out the sense of sufficiency we are after in our quest for truthmakers, for it means that the truthmaking powers of something are a matter of how this thing is itself. We only have chosen our truthmaker inclusive enough if its truthmaking ties do not depend on anything ‘outside’ of it, i.e. if they cannot be made to vary by variation in the intrinsic properties of things disjoint of it. Such a relation, however, may still be contingent. It is one thing to say that what makes it true that an internal relation obtains are just the terms of the relation (Armstrong 2004: 92, 98, 104, 139) and that internal relations are ontologically innocent (2004: 104). It is quite another thing to take this to entail necessitarianism. Why does Armstrong link internalism and necessitarianism so closely? To understand his reasons to do so, we must discuss his distinction between thick and thin particulars, which, I think, has done a lot of damage to his metaphysical system. The paradigms of truthbearers in need of truthmakers are singular existentials, claims to the effect that such and such an entity exists. In such cases, it seems incontestable that the entity in question, iff it exists, makes the corresponding claim true.14 But how is this compatible with the world’s being one (solely) of states of affairs? John’s existence, after all, is not a state of affairs (Armstrong 2004: 6). But perhaps John is? John is a non-mereological component of the state of affairs of John’s being human, which makes it true that John is human and hence, by the Entailment Principle (truthmaking distributes over entailment),15 also that at least one human being exists (2004: 21). Is John’s being human a minimal truthmaker? Could not the remainder of the state of affairs be abstracted, leaving us just with John? Armstrong says it can: “Minimal (or at least close to minimal) truthmakers for this existential truth [] will be each individual horse” (2004: 55). Though every state of affairs involving humans is a truthmaker for the truth that at least one human exists, only the individual human beings are minimal truthmakers. But

14

Cf. e.g. Mulligan et al. 1984: 300. Armstrong (2004: 6) calls the relation between John and the proposition that John exists “the simplest of all truthmaking relations”. 15 Armstrong (2004: 11) restricts the Entailment Principle to ‘purely contingent truths’, i.e. truths that do not contain any necessary conjunct on any level of analysis. If “John is human” entails John’s existence, then it is clearly contingent.

113 are they necessitating it? Only, it seems,16 if they are essentially human beings, i.e. cannot exist as non-humans. But let this be assumed.17 In some sense, then, John is more minimal a truthmaker than John’s being human. Sometimes, however, the (non-mereological) inclusion relation goes in the other direction: while the mereological fusion of Venus and Mars makes it true that Venus is greater in size than Mars, it is not a minimal truthmaker: “For this truth, it seems that we do not need all the properties of the two objects, or even all their non-relational properties. It is enough that Venus is a certain particular size, and that Mars is a certain particular size. These are states of affairs. The minimal truthmaker appears to be the mereological fusion of these two states of affairs. The other properties of Venus and Mars seem irrelevant.” (Armstrong 2004: 50) 18

Here, the inclusion goes the other way round: Venus’s being of size m + Mars’s being of size n is here said to be more minimal than Venus + Mars. A distinction is needed. In response to the criticism of Devitt (1980: 98) that his account renders exemplification obscure, Armstrong (1980: 109110) claims that while we can distinguish the bare or ‘thin’ particular from its properties and the universal from its exemplifications in ‘thick’ particulars, neither can exist without the other. The thin particular is the “thing taken in abstraction from all its properties” (1978: 114),19 the particular “taken apart from its properties” (1989: 95), it is “the particularity of a par-

16

Cf. Fox (1987: 194), Restall (1996: 332) and Lewis (1998: 218). Armstrong extends this account to merely possible entities. He says that the minimal truthmaker for the truth that there are no arctic penguins is the totality state of affairs that some fusion comprises all the arctic animals (2004: 75-76). He then continues: “In the same way, if we work with the totality of all birds, we eliminate the phoenix” (2004: 76) This presupposes that the phoenix, if it existed, would be essentially a bird. In the same spirit, the minimal truthmaker for “there are no unicorns” is said to be the totality state of affairs that all ‘horse-like creatures’ lack ‘unicorn-making characteristics’ (2004: 36, 76) – but for this to exclude unicorns, it has to be assumed that unicorns are essentially horse-like and essentially have their unicorn-making characteristics. But if the possibility of unicorns is conceded, then why not also the possibility of unicorns that lost their horn or some other of their ‘unicorn-making characteristics’? 18 In the same vein, Armstrong (2002: 34) says that O itself is a truthmaker of “O has a mass of five kilograms”, albeit not a minimal one. 19 In (1978: 118), Armstrong identifies the thin particular with its total spatio-temporal position, though he seems to have retracted this claim. 17

114 ticular, abstracted from its properties” (2004: 105).20 It is the thin particular John that is contained, as a proper but non-mereological part, within the state of affairs of John’s being human. The thick particular, on the other hand, is the “particular taken along with all and only the particular’s non-relational properties” (Armstrong 1997: 124). It is the state of affairs of the (thin!) particular’s having all its nonrelational properties (1989: 95), the particular “with all [its] (non-relational) properties upon [it]” (1997: 176).21 These properties are said to be “‘contained within it’” (the scare quotes are Armstrong’s) and it “enfolds” these properties “within itself” (1989: 95). It is in the fusion of the thick particulars that Venus’s being of size m and Mars’s being of size n are contained. Here we have a third violation of combinatorialism: the thick particular depends on the thin and the thin on the thick. They are ‘wholly distinct’ in the sense that they do not overlap in a mereological part. The thick particular could not exist without a ‘hook’; it is not a mere bundle of properties. The thin particular, however, is a mere abstraction, which does not enjoy independent existence: though there is no thick particular of which is must be a component, it must be a component of at least one (Armstrong 1989a: 52). It is an equivocation between thin and thick particulars, I think, that made Armstrong infer necessitarianism and not just internalism from the sufficiency argument. If truthmakers are to be sufficient for the truthmaking they do, this just means that their standing in the truthmaking relation to certain truthbearers cannot depend on anything external to them, i.e. that it supervenes on their intrinsic properties. Only if these intrinsic properties 20

Armstrong (1997: 109) says it is “the particular abstracted in thought from its nonrelational properties”, but then makes it clear later that he means all properties (1997: 123). Sometimes, e.g. in (1989: 95) and (1989a: 52), Armstrong says that the thin particular has some properties: though it is thin, it is still clothed and not bare. It is not clear, however, which properties these might be. They are not its essential properties, for the thin particular together with its essential properties is intermediate between the thin and the thick particular (1997: 124). Presumably, the thin particular has just its formal properties, like being a particular (cf. Hochberg 1999: 68). If we arrive at our concept of thin particulars by ‘partial consideration’ (Armstrong 1997: 109), then their properties would be those we cannot subtract even in thought. 21 That thick particulars are states of affairs (cf. Armstrong 1978: 113, 1997: 125) is overlooked in Rissler’s discussion of the need for states of affairs in Armstrong’s later theory (2006: 200, fn. 4).

115 are ‘enfolded’ within thick particulars is the truthmaking relation itself necessitated by the mere existence of the truthmaker. Thin particulars, or more generally particulars having not all their intrinsic properties essentially, can be ‘sufficient’ for their truthmaking job without being so of necessity. This is most apparent in the case of singular existentials: if John is to make “John exists” true, then the thick particular John cannot be its only possible truthmaker. For thick John could fail to exist (i.e. John could have different intrinsic properties) and it still be true that John exists. A transworldly permanent truthmaker would have to be thin John. But thin particulars are mere abstractions in Armstrong’s ontology.22 The “cross-categorial unity” of thin particulars and universals indeed comes to appear as “the most puzzling unity of all” (2004: 267).23 But it is not just puzzling what it is, but even how it can be possible at all. Exemplification between a ‘thin’ particular and some properties, it seems, is an external relation, connecting the particular with something outside itself.24 The sufficiency argument then requires us to bring this external relation into the truthmaker –

22

It is even doubtful whether thin particulars can make true the statement that there are thin particulars. For if the world is a world of states of affairs and truthmaker theory is our guide to ontology, then, as Armstrong repeatedly argues, all truthmakers are states of affairs, i.e. what thin particulars precisely are not. This reflects a general problem for all necessary relations: whenever two things are ‘internally’ (essentially) related, Armstrong says repeatedly, any statement to this effect is made true just by the two things themselves (cf. e.g. 1997: 2-3, 89 and 2004: 50, 121). Because the things could not both exist without standing in that relation, their joint existence itself makes it true that they do so. But if there are internal relations between universals, like resemblance, parthood and identity, then at least some truthmakers are not states of affairs. 23 As Armstrong recognises, the puzzlement is not avoided by speaking of a nonrelational tie. This is just to label the problem: “One’s first response to this is naturally extremely negative: are there two constituents involved or not? If so, how can they fail to be distinct terms? If they are distinct terms, how can they be ‘tied’ together except by a relation? It is no good simply talking about non-relational ties: or, to put it another way, one philosopher’s solution is another philosopher’s problem.” (Campbell 1990: 15) “A non-relational tie between distinct things is pretty mysterious. Seemingly, if the things are distinct then the tie is a relation. If the tie is not a relation then they are not distinct. So a non-relational tie could hold between distinct things only if they are not distinct.” (Baxter 2001: 449) 24 Numbering relations, e.g., would be external if they held between properties and thin particulars (Armstrong 1997: 176).

116 requires us to bring this external relation into the truthmaker – ontological explosion through Bradley’s regress is the dire consequence.25 Exemplification, however, is no less mysterious when considered a relation between the thick particular and its properties (cf. Aune 1984: 165). The ‘thick’ particular “is conceived as already possessing its properties” (Armstrong 1978: 114) and thus does not need to exemplify them. Armstrong (1989a: 52, 1997: 125) says that the ‘thick’ particular has its properties necessarily. But not only contingent properties are problematic: strictly speaking, the ‘thick’ particular does not exemplify any of its (first-order) properties (except perhaps its relational properties). It is, so to say, already ‘saturated’ (Armstrong 1980: 109); properties exemplified by it are second-degree properties. Second-degree properties, however, would give us second-degree states of affairs, which are different from first-degree ones. It seems mysterious, then, how either the thin or the thick particular could have any properties. But even if they can, they do not exemplify them in a way that helps us in our quest for truthmakers for contingent predications. The thin particular, even in conjunction with its properties, does not necessitate any contingent truths about it. The thick particular does necessitate these truths, but only because it necessarily has the property attributed to it. Factualism thus is incompatible with necessitarian truthmaking of contingent predications by ordinary particulars.26

25

In reply to Aune (1984), who presses him on this point, Armstrong seems to agree: “The particularity of a first-order particular, in abstraction from all properties and relations, the mere thisness of a thing as a Scottist would put it, can have no properties. It is a bare principle of numerical difference.” (1984: 254) 26 This means that states of affairs do not explain the relation of exemplification, contra, e.g., Linsky: “The notion of a fact is introduced precisely to provide an explanation where others just provide truth conditions. Facts are deemed necessary in order to show what it is for an object to have a property.” (1994: 193) Armstrong is much more cautious: he says that we need states of affairs because something “is needed to weld [universals and particulars] together” (1997: 114-115) and that “we may think that some ontological connection between subjects and predicates is required, and thus, perhaps, be led to postulate facts or states of affairs among our truthmakers” (2002: 33). States of affairs presuppose that we can already make sense of particulars and universals combining into entities that exist if and only if a proposition is true. They do not, contra Armstrong (2004: 24) provide the “ontological connection between subjects and predicates” but presuppose that such a connection has already been made.

117 2. Allness But perhaps the very project of rescuing a notion of particulars from factualism was ill-conceived. Perhaps adopting factualism is a one-way street: we just have to accept states of affairs as primitive particulars; while they are, in some sense, ‘composed’ out of (ordinary) particulars and universals, these are not retrievable from them other than as bloodless abstractions. So let us take this leap of faith and pretend we understand what states of affairs are. Let us suppose that the world is a world only of states of affairs and that they are the only truthmakers there are. Will the first-order states of affairs give us truthmakers for all the truths? No, says Armstrong: to make it true that it is a law of nature that all Fs are Gs, for example, we need a further, non-supervenient and higher-order truthmaker, i.e. the state of affairs that F-ness necessitates G-ness (1983: ch. 6). If it is a nomically contingent fact that a certain number of states of affairs are all there are, then we need also another type of higher-order state of affairs:27 “If it is true that a certain conjunction of states of affairs is all the states of affairs, then this is only true because there are no more of them. […] That there are no more of them must then somehow be brought into the truthmaker. […] The truthmaker must be the fact or state of affairs that the great conjunction is all the states of affairs.” (Armstrong 1997: 198)

Before pointing out the several intricate problems presented by totality states of affairs, let us first note that this argument in their favour is not quite compelling: it is not true in general that any necessary condition for a truth must somehow be “brought into” its truthmaker. It is, e.g., a necessary condition for it’s being true that 2+2=4 that at least one truthbearer exists, but no truthbearer has to be brought into the truthmaker of this arithmetical fact.28 Armstrong’s real motivation for totality states of affairs, I presume, is not that truthmakers must include all necessary conditions for some truthbearer’s being true, but his construal of truthmaking as an internal relation – it is because it is an extrinsic property of the big conjunction that it 27

The qualification is important: if it is a law of nature that some totality of states of affairs exhausts all there is, then this truth is made true by the laws of nature themselves, without any help from any other higher-order states of affairs. 28 The argument is easily generalised: every necessary truth is a necessary condition for everything else, but there are, I hope, at least some truths the truthmakers of which do not contain all (truthmakers of) necessary truths.

118 is all there is that there must be something else to make this true, something that intrinsically is all there is. This is some totality state of affairs: every fusion of states of affairs which are of the same ‘sort’ F is an object which may stand in a contingent and external relation to some ‘unitproperty’ G that Armstrong calls “alling” or “totalling” and which he takes to be a universal (cf. 1989a: 93, 1997: 199, 2004: 73). The sort of the fused states of affairs F and the ‘unit-property’ G, on the other hand, are normally non-fundamental, ‘second-’ or even ‘third-degree’ properties. The mereological fusion of the black swans on the lake now (the thick swans, including their properties), for example, totals the “distinctively secondrate property” (being a) black swan on the lake now (Armstrong 2004: 72). Totality states of affairs violate combinatorialism in yet another, fourth way.29 The all-inclusive totality state of affairs makes it true that there are no unicorns by ruling out the existence of unicorns. The absence of unicorns entails the existence of some unicorn-free totality state of affairs.30 By their very nature, totality states of affairs constrain what lower-level states of affairs there can be. Armstrong takes the damage done to combinatorialism to be quite limited. For he thinks that there is just one totality state of affairs that suffices as truthmaker for all negative and general truths: “These states of affairs [i.e. the fusion of all states of affairs totalling both being a state of affairs and its totalling being any existent at all, which Armstrong takes to be the same state of affairs] are the biggest states of affairs of all. Given these huge states of affairs, each positive, all the lesser totality or limit states of affairs are also given. In the great catalogue of being, as it were,

29

The other three were the connections between truthmakers and truthbearers, truthmakers and what their truthbearers are about and between thick and thin particulars. 30 Lewis (2001: 610) has called such things “unicorn-replacements”, complaining that they are necessarily incompatible with unicorns while being wholly distinct from them. Armstrong (2004: 71) disagrees, pointing out that the totality state of affairs of everything being different from a unicorn contains the big molecular state of affairs which is the ‘conjunction’ (fusion) of all first-order states of affairs as a nonmereological part. But Lewis’ worry concerned the connection between some merely possible unicorn and its this-worldly replacement – and the merely possible unicorn is not a constituent or part of the fusion of all states of affairs.

119 you need neither have any of the lesser allings nor, I have claimed, any other negative state of affairs.” (Armstrong 2004: 74)31

The biggest totality state of affairs – which Armstrong calls “limit state of affairs” (2004: 71) and I will call “Porky”, following Forrest and Khlentzos (2000: 7) – “fixes” all the negative facts (1989a: 96), all negative facts supervene on it (1997: 200) and it is a truthmaker for all the lesser totalities (2004: 59): “Once you have set the limits, the absences will take care of themselves” (2004c).32 It is not a minimal truthmaker, however, for the totality of the properties of some swan’s plumage will do as truthmaker for it’s not being white and the totality of the arctic animals makes it true that there are no arctic penguins (2004: 75-76). But in what sense does Porky ‘include’ these more minimal truthmakers? We already met three ways in which truthmakers can be ‘more minimal’ than or included in others. They can involve only the thin, in contrast to the thick particular, only mereologically proper parts of either the particular or the universal component of the other, or they can be predications of more or less properties (where the ‘inclusion’ of F within the conjunctive universal F&Q is non-mereological (Armstrong 1989a: xi)). But in none of these senses are lesser allnesses included in the limit state of affairs. Take some lesser allness, e.g. the state of affairs of some fusion of properties comprising all of Theaetetus’ properties – what Armstrong proposes as truthmaker for “Theaetetus is not flying”. In what sense can Theo, as we may call this state of affairs, be said to be “given by” or “contained in” Porky? Only the positive states of affairs about Theaetetus are totalled in 31

Even within this passage, it is not clear whether Armstrong really claims that they are positive. In response to Molnar’s worry (2000: 81) that they are negative after all, because “The Gs are the only Fs” is equivalent to “¬∃x(Fx&¬Gx)”, he (2004: 70) agrees that “[t]here is no getting away from negativity altogether”. He goes on, as cited above, to invoke a dubious principle of economy, which concerns the need for only some, but not all, of the (epistemically possible) negative facts (cf. also 1997: 200). It is this concern about theoretical economy in the “gross tonnage sense”, a phrase Armstrong (2006b: 229) takes from Keith Campbell, that I address in the following. 32 The same ontological economy is allegedly achieved also at the level of states of affairs involving one and the same individual, say Theaetetus: “We get rid of the ontological nightmare of either a huge number of negative properties or a huge number of negative states of affairs, and substitute for them a single all state of affairs. It is a state of affairs (admittedly, a pretty large state of affairs, subsuming innumerable lesser allnesses), one that will serve as a truthmaker for the huge number of negative truths about Theaetetus among other particulars.” (Armstrong 2004: 57)

120 Porky. Porky, however, makes Theo redundant: for the totality of properties F, G etc. of Theaetetus, Porky entails that Theaetetus is F, that he is G etc. and that he has no other property. Porky is a truthmaker for the truth that Theaetetus is not flying, and it will also be a minimal truthmaker if, as Armstrong says, the limit state of affairs contains only positive states of affairs. Porky contains, by definition, all the states of affairs there are, and therefore excludes, rather than ‘includes’, the lesser allnesses – a fifth violation of combinatorialism. But perhaps Theo nevertheless exists, and is part of the fusion totalling being any existent at all. Even then, however, Theo would only in a trivial sense be included in Porky, in the same way in which it is ‘contained in’ the truthmaker of “Theo and Porky are Armstrong’s favourite states of affairs”. If this truthbearer is true, it has a truthmaker, part of which is a state of affairs ascribing to Theo the property being one of Armstrong's favourite states of affairs. Theo is ‘contained’ in this higher-order state of affairs in the same way it is ‘contained’ in Porky. It must exist if either of them does, but it does not exist because they do. We have a Eutyphro dilemma here: Theo does not exist because Porky does, but rather it is because Theaetetus has only these properties that Theo is an available candidate for being Armstrong’s favourite and included in Porky: we must acknowledge its existence prior to encapsulating it in further higher-order states of affairs. Besides their promise of ontological economy, another motivation for totality states of affairs is that they are needed to provide truthmakers for modal truths. While Armstrong (1989: 88) restricted the truthmaker principle to contingent truths, he came to think that their lack of truthmakers would be “an enormous and implausible disvaluing of modal truths” (1997: 149), proposing that the “truthmakers for a particular modal truth will make that truth true in virtue of nothing more than relations of identity (strict identity) and difference between the constituents of the truthmakers” (1997: 150). As these are internal relations, the mereological sum of the constituents themselves will make the modal truth true. To secure the supervenience of the modal on the actual, Armstrong (2004: 83-85) appeals to what he calls the “Possibility Principle”: that truthmakers for contingent truths are also truthmakers for the possibility of their contradictories. Hence Theo makes it true not just that Theaetetus is not flying, but also that he might fly. Armstrong (2000: 155, 2004: 84, 2006c: 247)

121 argued for the Possibility Principle using the Entailment Principle and the claim that, for any contingent truth p, p entails “it is possible that ¬p”.33 Even if we grant him the Entailment Principle,34 the minor premise is highly questionable: Even if “it is of the essence of contingency that the contradictory of a contingent truth be a possibility”, the connection between contingency and the possibility of the contradictory is analytic and “holds in virtue of what we mean by the phrase ‘contingent proposition’” (2004: 84), this does not show that p entails “it is possible that ¬p” given that p is contingent: even if being unmarried is of the essence of bachelorhood, we cannot say that “Sam is happy” entails “Sam is happy and unmarried” ‘given’ that Sam is a bachelor. We also need a truthmaker for the claim that Sam is a bachelor (and for the claim that p is contingent). In earlier and better versions of the argument (2000: 155, 2002: 35), the claim that p is contingent was enlisted as an explicit premise (rather than a ‘presupposition’): the truthmaker for “it is possible that ¬p” will then be at least the sum of a truthmaker for p – call it “a” – and a truthmaker of the claim that p is contingent. An appeal to the Entailment Principle is then no longer necessary: if it is true that p is contingent, there is, by maximalism, a truthmaker b for it. If “p is contingent” is equivalent to “it is possible that p and it is possible that ¬p” (2004: 83), we need much weaker principles than the Entailment Principle to conclude that b makes it true that it is possible that ¬p: distribution of truthmaking over necessary (or even analytic) equivalence (2004: 25) and conjunction will suffice. Now a will no longer do any work – the truthmaker for “it is possible that ¬p” will just be one for “p is contingent”. This is more perspicuous in the argument Armstrong gives in (2004: 111 and 2005: 271) for the Possibility Principle: (i) (ii) (iii) (iv) (v) 33

Suppose p is a contingent truth. Hence it has a truthmaker, a. By truthmaker necessitarianism, a is contingent. a is the truthmaker not only for “a exists” but also for “it is possible that a does not exist”. Hence a is the truthmaker for “It is possible that ¬p”.

As stated by Armstrong (2004: 10), the Entailment Principle is inapplicable (cf. fn. 15) since he takes “it is possible that p and possible that ¬p” to be necessary for contingent truths p (2004: 85). He says that “it is possible that ¬p” “is very tightly linked to the truth [p]” and that the principle can therefore nevertheless be applied (2004: 84). 34 Simons (2005: 254) points out that it is relevantly invalid.

122 Aside from premise (iv),35 the crucial step is from (iv) to (v). Armstrong does not do much more than state that it is obvious.36 But it is not: even if a is the truthmaker for p, “a exists” and “a might not have existed”, it does not follow that it is also the truthmaker for “it is possible that ¬p” – that there is a world without a does not show that there is a world where p is false, for p might be made true by something else in that world. Armstrong produces something that sounds like a transcendental argument: “If [a] is the only minimal truthmaker that p has, then the possible nonexistence of [a] must be reflected at the level of propositions by it not being that case that p is true. Hence [a] will be truthmaker for , which is what is being argued for.” (Armstrong 2005: 272)

It is a pivotal principle of Armstrongian truthmaking, however, that it does not have to be one-one, i.e. that there may be many different (and many different minimal) truthmakers for one truth. Whenever this is the case, the ‘possible non-existence of [a]’, the actual truthmaker, is not ‘reflected’ by the possible falsity of p – in worlds where I do not exist, someone else may still make it true that there are humans. Armstrong (2005: 272) seems to think that this can be remedied by taking the mereological sum of all minimal truthmakers. This will not do, however, for the worry concerns not just actual, but also merely possible non-uniqueness of minimal truthmakers: Suppose Theo makes it true that Theaetetus is not a poached egg and is a minimal truthmaker for this truth. But its possible non-existence (e.g. in worlds where Theaetetus is flying) does not reflect the possibility that Theaetetus might be a poached egg; it might still be impossible that Theaetetus is a poached egg.37 Necessary truths may have contingent truthmakers: If truthmaking distributes over disjunction introduction (Arm35

I think that it may be granted that contingency is a feature of the nature of the things to which it applies (cf. Almog 1996: 423-424). (iv) only requires in addition that it is intrinsic, a matter of “what [the contingent being] is in itself” (Armstrong 2004c). 36 “Whether we need a property of contingency in re, a special categorial property of the truthmaker, is a difficult question of metaphysics that I trust need not be entered into here. […] But, however one resolves that matter, it is difficult to quarrel with the idea that any truthmaker for p is also the truthmaker for

.” (2003: 15) “Given that [a] is contingent, it necessitates the possibility of p.” (2004: 111) 37 Taking the mereological sum of possible unique truthmakers will not do either, for that sum is not contingent. Armstrong (2004c) explicitly assumes that any contingent truth has a purely contingent truthmaker (every part of which is contingent).

123 strong 2004: 21), Sam is a truthmaker for “either Sam is human or he is not” – a unique minimal truthmaker that is contingent but makes its truthbearer true without making it contingent (because it is not). For the step from (iv) to (v) to go through, we need a reason to think that the truthmaker of “p is contingent” cannot have any other truthmaker than the one p actually has. The truthmaker of p, if p is contingent, must be a contingent existent. So there is a world where it does not exist and hence is unavailable to make it true that p is contingent – which is, given S5, if true, necessarily true.38 Hence something else must make it true in that world.39 The Possibility Principle and S5 are incompatible.40 Given S5, the truthmakers for both ‘statements of mere possibility’ and the possibility of aliens are the truthmakers for the necessary statements that some proposition or some state of affairs is contingent and hence do not ‘reflect’ this contingency.41 For necessary truths quite generally, Arm38

Cf. 2000: 155, 2004: 84. Armstrong (2002: 35) uses this claim to support premise (iv). The necessity of contingency follows from the claim that S5 is the logic of metaphysical necessity, an idea Armstrong (1997: 171, 2003: 14, 2004: 84-85) finds appealing. Recently, however, Armstrong seems to have given up S5 (cf. fn. 40 below). 39 This worry cannot be countered by the claim that we are looking for truthmakers not in other worlds but only in this one, which is the only one that exists. Armstrong (2004: 91) relies on this claim to counter the objection that an empty world lacks unicorns and this truth has to be made true even there, in the absence of any totality states of affairs (Lewis 2001: 611). Given S5, if p is contingent, it is necessarily so. Hence the necessity, not just its possibility is in need of a truthmaker. 40 It is not clear whether Armstrong really accepts S5. Armstrong (2003: 18, 2004: 90) argues from the Possibility Principle to the claim that any contingent existent makes it true that there might be nothing, a claim which he (1989a: 24-25) thought “attractive [only] at a shallow level of reflection”, which he later (2000: 158) still doubted and about which he is again (2004a: 144) “deeply uncertain”. To argue that it is true, Armstrong (2003: 18) needs to assume that it is possible that there is nothing, but it is not necessary that it is possible that there is nothing – which rules out S5 (and makes the existence of necessary beings incompatible with the existence of any of the actual existents). Armstrong (2004: 90) provides an argument that seemingly does not rely on this premise – but this is only because he forgets to enlist the contingency of “there is at least one contingent being” as a premise. For the Entailment Principle to be applicable to it, “it is possible that there is nothing” has to be a contingent truth (cf. fn. 15). 41 While Armstrong (1989a: 21) thought that he would need a realistic theory of possibilities to provide truthmakers for the claim that alien properties and relations are possible, he then (1997: 165) accepted them in the ‘outer sphere of possibility’, in particular to provide possible exemplifiers for mathematical properties (1997: 181) and to

124 strong (2002: 36) expressed the hope that they “set up an internal relation between entities” which will then themselves serve as truthmakers for it.42 As we have seen, however, more than just the truthmaker of p is required to make “it is contingent that p” true. It seems that the proposition p itself has to be brought into the truthmaker of the contingency claim. In this case, the propositions themselves would make it true that they are contingent – no special work for totality states of affairs here. This is fortunate, for totality states of affairs suffer from a serious problem: they are impossible, and demonstrably so.43 If there were any, some truthbearer of the form “These are all the totality states of affairs there are” would be true. If some such truthbearer were true, it would be made true by some totality state of affairs. This totality state of affairs, however, cannot be one of the totality states of affairs in the totalling fusion. So it would have to be some other totality state of affairs. But then the truthmaker of keep S5 as his logic of metaphysical possibility (1997: 170). The truthmaker for “there could be alien particulars and properties” are the “actual constituents [of the maximal state of affairs W] and their [internal] relations of mutual difference” (1997: 167, but cf. fn. 48 below). For any alien particular a, this state of affairs makes “a is possible” true. If the latter truth is necessary, however, it will be possible that it is made true by many different maximal states of affairs. 42 Cf. 2000: 156, 2003: 21 and also: “Consider the truth . Given the number 7 and the property of being prime, then the truth is necessitated. This entity and this property, then, can serve as truthmakers for the truth. A predicative tie is not required. All we need are truthmakers for the existence of the number and the property.” (2004: 99) 43 The paradox to be discussed is not the one raised by Cox (1997: 56) and anticipated by Armstrong (1997: 198-199) concerning a regress of higher- and higher-order states of affairs. Cox’s ‘paradox’ can, but I think mine cannot, be met by turning the tables on the regress and suggesting that the very fact that the higher-order states of affairs are necessitated by their predecessors in the regress means that all we have is a regress of truths sharing as their truthmaker the totality state of affairs of the lowest order (cf. Armstrong 1989a: 94, 1997: 198, 2004: 78, but cf. 2006d: 246). Even if this answer is generally acceptable (and we will return to this on p. ??), however, it needs some finetuning: there are, Armstrong (2004: 74) says, at least two most inclusive second-order states of affairs, the totalling of being a state of affairs (or rather: being a first-order state of affairs) and the totalling of being any existent at all. If naturalism is true, then there is also a third one, the totalling of being in space-time. Naturalism, i.e. the doctrine that the world of space and time is all there is, is a contingent thesis (Armstrong 1997: 35, 2004: 112). Hence the state of affairs that there are three most-inclusive second-order states of affairs is itself contingent, i.e. not necessitated by the second-order states of affairs. The regress therefore stops at the second stage at the earliest.

125 “These are all the totality states of affairs” would not total all the totality states of affairs; hence it would not total any. Assume, again, for reductio that there are totality states of affairs and that totalling is a universal, which occurs as predicative component in each and every totality state of affairs. If there are totality states of affairs, there is a totality of them: “The Tot relation is to be found even where there is just one object of a certain sort.” (Armstrong 2004: 73). Call “Total” the totalling relation’s holding between the fusion of all totality states of affairs and the (second- or third-grade) property being a totality state of affairs. Total is impossible: if the totalling relation holds, then the fusion has to be the fusion of all states of affairs. The fusion, however, cannot contain Total itself, because it is a proper part of Total (Armstrong 2004: 56, 71).44 Could some other property than being a totality state of affairs be totalled in Total? No, it seems, if Total really is the totality of all totality states of affairs. Could the totalling relation fail to hold? Only, it seems, if the fusion were not the totality of all totality states of affairs. But then there would be some other totality state of affairs not contained in it, and Total would not be the totality of totality states of affairs, contrary to what we assumed. There are other paradoxes in the vicinity.45 We have seen that a totality state of affairs is the obtaining of the totalling relation between some fusion of states of affairs and some ‘unit-property’. There is an important distinction between two types of totality states of affairs. In cases like the one of the black swans on the lake, the totalled property, though second-rate, occurs as a ‘predicative component’ in the states of affairs (thick particulars) fused into the aggregate totalling it.46 In some other cases, however, this is not the case: the property of being a first-order state of affairs, for example, is not itself a predicative component of the first-order states of affairs (all states of affairs of which it is are at least second-order). It is a state-of-affairs type that cannot be obtained by abstraction from the states of affairs of which it is the type: let us call such states of affairs “nonpredicative”. Some such states of affairs exist, for example Theo (for being a property of Theaetetus is not a property of Theaetetus). This means that there is a totality, call it “Russell”, of all and only the non-predicative total44

That totality states of affairs are ‘ampliative’ follows from, but does not imply, Armstrong’s earlier assertion that the totalling relation is external (1997: 199). 45 The following Russell-type paradox has independently been noted by Greg O'Hair. 46 This is also the case for the (many!) numbering relations (Armstrong 2004: 116).

126 ity states of affairs. With respect to Russell, we may now ask whether the property that is totalled in it, the property of being a non-self-predicative state of affairs, is a component of any of the states of affairs totalling it. We may ask, in other words, of Russell, whether it is self-predicative. If it is self-predicative, then the property of being a non-self-predicative state of affairs occurs in some state of affairs in the totalling fusion. So it is the property totalled by at least one of the state of affairs in this fusion. But what fusion is totalling it? It cannot be the fusion of all the non-selfpredicative states of affairs, for otherwise Russell would contain itself as a proper part. But it cannot be any other fusion: the fusion totalling the property of being a non-self-predicative state of affairs must be the fusion of all the non-self-predicative states of affairs. If Russell is not self-predicative, on the other hand, then it belongs to the fusion totalling the property, so the property of being a non-self-predicative state of affairs is a component of a state of affairs in the fusion. So it is self-predicative after all. Hence Russell is neither self-predicative nor non-self-predicative. Faced with these paradoxes, none of the familiar options seems plausible. Given unrestricted composition, we cannot deny that there is a fusion of all totality states of affairs or of all non-self-predicative totality states of affairs, as long as at least one of them exists. We could, perhaps, replace the totalling universal with an infinite family of totalling relations, each indexed to one order in the hierarchy. But this would leave us with no index for the totalling of the fusion of all totality states of affairs. We could adopt a limitation of size principle, but this would break the connection between generality and negation. For any totality state of any order has countless negative properties (for example, not being a black swan), and to account for these, we need another totality state of affairs one order higher up. Could we say that the totality of all totality states of affairs supervenes on them? Suppose, the earlier arguments notwithstanding, that there is just one totality state of affairs. Would it not necessitate the state of affairs of its being the only one? The problem with this reply is that it undermines the motivation to introduce totality states of affairs in the first place:47 “…David Lewis has raised with me the question whether the fact of totality is in fact, as Russell claims, non-supervenient. […] How, asks Lewis, could two worlds be exactly alike in all lower-order states of affairs, yet differ in this higher-order state of affairs? The answer, of course, is that the two worlds 47

Thanks to Frank Jackson for drawing this passage to my attention.

127 could not differ. But I claim that this is so only because a totality state of affairs has already been written into the description of the case. Suppose we had a list of the states of affairs in the two worlds, but with no totality condition given. It would not be the case that every world that contained those states of affairs was the same world. You get that result only if you add that the worlds contain just those states of affairs, that is, those states of affairs and nothing more. The ‘nothing more’ must have a truth-maker. I claim that that truthmaker is a totality fact or state of affairs, having the form I have tried to describe.” (Armstrong 1989a: 94)

What holds for states of affairs holds for totality states of affairs. Suppose there is just one state of affairs, a’s being F.48 Why add the totality state of affairs of a’s totalling F? No world can differ just with respect to it. The reason it is necessary, Armstrong says, is to distinguish the first world not from a ‘complete’ world (where completeness is ‘written into the description of the case’), but from an (a-centred) ‘sub-world’ of a world where a is F and another b is also F. An exactly parallel argument shows the nonsupervenience of totality states of affairs: Suppose there is a world with just one totality state of affairs, a’s totalling F. How can a world differ from it just with respect to this totality of one totality state of affairs? This does seem impossible only if we forget about sub-worlds, e.g. the F-subworld of a’s being F, a’s totalling F, and a’s being G. The only difference between them is that without a’s being G, there is just one totality. To suppose otherwise is to ‘write [completeness] into the description of the case’. If, as Armstrong says (1989a: 88, 1997: 196, 2004: 75), totality states of affairs are not supervenient, his only option at this point, I think, is to withdraw his claim that totalling is a universal and may be a component of states of affairs.49 What makes it true that some totality is all there is just this totality itself – all there is, even if there might be something more. Giving up necessitarianism for general truths seems a viable option then. 48

This is problematic for the reasons mentioned on p. ??: it would have to be a totality state of affairs and hence contain itself as a proper part. Another argument for this does not rely on (totality) states of affairs being ‘ampliative’: If there is a totality state of affairs, some property is totalled ‘in’ it. This property must be exemplified, and it must be exemplified by something else than the totality state of affairs in question; for it to be ‘available’ as a constituent of the totality state of affairs, it must exist prior to and independently of the latter. If the property is being something positive, as Armstrong (2004c) proposes, it clearly cannot be exemplified by the limit totality state of affairs. 49 Could Armstrong give up the ampliativity of states of affairs? He cannot, if he wants to stay realist about them and does not want to accept, as parts of the natural world of space-time, things that may contain themselves as proper parts.

128

It still leaves us, however, with states of affairs, and hence with their fusion, which Armstrong (2004: 122-123) calls “W, the whole world, the whole that contains absolutely every thing that exists”, that “greater than which nothing exists”. It cannot be part of any state of affairs: “States of affairs are ampliative, that is, they embed their subjects in something further. But if W really is everything, then there is nothing further, not just no further particulars, but no further properties or relations or anything else.” (Armstrong 2004: 123)

But if W cannot be put into any state of affairs, then it cannot have any property and cannot stand in any relation. So, in particular, it cannot stand in the totalling relation to the property being a state of affairs. If it were everything, it would need to do so, and also to stand in the totalling relation to being an existent and, perhaps, also to being in space-time, hence be a proper part of (at least) one other thing, namely Porky. Even if Porky is (somehow) not an ‘ontological addition’ to W, it certainly exists: it is required as the actual truthmaker of all truths asserting the possibility of something non-actual50 and it may also occur in merely possible states of affairs, e.g. its singleton.51 50

Armstrong gives two conflicting accounts of the situation: he says, on the one hand, that “W is the totality of being” is a contingent truth, having W as its truthmaker. By the Possibility Principle, W is also the truthmaker for “it is possible that W is not the totality of being” (2004: 123, 1997: 167; but cf. fn. 41 above). The latter truth, on the other hand, is equivalent to “it is possible that there are alien particulars or properties” and this truth, Armstrong (2004: 88, 2000: 156, 2002: 36, 2003: 17) says, is made true not by W but by Porky, the totality state of affairs that W is all there is. 51 Cf. Armstrong (1997: 194-195, 2004: 123). There is some doubt, however, that {W} is possible. Armstrong (1997: 193) distinguishes between empirical (existing) and non-empirical (merely possible) singletons and holds that {W} is merely possible (1997: 194, 2004: 123). But all the things exemplifying unit-properties have empirical singletons and it seems that all these singletons will themselves exemplify unitproperties: for take a, and some unit-property being an F. Hence a exemplifies having some first-order unit-determining property and this state of affairs is {a}. But then it seems that {a} cannot fail to exemplify being the exemplification of some unitproperty by a. There will normally be more than just one state of affairs exemplifying this property, and they are countable: hence, being the exemplification of some unitproperty by a is a unit-property and its exemplification by {a} is the state of affairs {{a}}. Given that unit-properties may be second-class (Armstrong 1997: 190), disjunctions and universal quantifications of unit-properties are unit-properties. Hence the procedure may be applied to arbitrary sets: the unit-property of {a,b}, for example, is being either the exemplification of some unit-property by a or the exemplification of

129 W, this thickest of all particulars, ‘enfolds’ all properties and particulars there are and makes true every truth, including that Theaetetus is not flying. How it accomplishes this difficult task, however, must be left unexplained: no property can be (truly) attributed to it and it cannot (truly) be said to stand in any relation. We cannot even truly say of it that it is all there is. If there is no totalling universal, moreover, there is no relation holding between Theaetetus’ positive properties and being a property of Theaetetus – W is then the unique minimal truthmaker for the truth that Theaetetus is not flying! If it is true that “the candidates for unique minimal truthmakers that a particular philosopher upholds take us into the heart of that thinker’s metaphysical position” (Armstrong 2004: 22), then this Spinozist One should give us pause. It is fortunate, therefore, that Armstrong has another, and different, theory of truthmaking to offer.

3. Aspectual truthmaking According to the factualist account of truthmakers for contingent intrinsic predications, the truthmakers of “Fa” are required to necessitate that a is F. We discussed some difficulties for this account: the minimal truthmaker cannot be the thin particular a, which does not necessitate “Fa”, nor can it be the thick particular, which necessarily exemplifies all properties ‘contained’ within it. Because the thin particular is not a truthmaker and the thick is not a minimal one, the minimal truthmaker must be an ‘intermediate’ entity, a’s being F, which ‘enfolds’ just F. This ‘intermediate’ entity is itself a particular and depends on F: it could not be the entity it is without having F as its predicative component. But it also contains a, and it also does so essentially, creating a necessary connection between a and F. This connection is not symmetrical, however: while the thick particular necessitates the universal, the universal only generically depends upon it. some unit-property by b. But this means that a union of sets having empirical singletons will have itself an empirical singleton. If {W} is possible, it would be the union of all empirical singletons, hence itself empirical (this also follows directly from Lewis’ 2001 analysis of union as fusion which Armstrong accepts). Armstrong (1997: 195) says that the fusion of all empirical singletons “would seem to be W, and certainly cannot be anything more”. So if {W} is empirical, then it is a (proper or improper) part of W, which violates, again, the ampliativity of states of affairs.

130 The thick particular could not be what it is without enfolding F, but F could be what it is without being enfolded in this thick particular. On this account the “identities [that] run across the states of affairs” are “somehow mysterious” (Armstrong 1997: 265). a’s being F and b’s being F, while sharing their predicative component, are non-identical, mereologically disjoint and capable of independent existence. Contra Armstrong (1997: 265), the same does not seem to be true of the states of affairs of a’s being F and a’s being G – these literally share a component, namely the thin particular a, that in turn depends on the thick particular which enfolds both F and G. The same asymmetry shows up in other places as well: While Armstrong always rejected the identity of indiscernible particulars (cf. e.g. 1978: 95), he held indiscernible universals to be identical.52 Particulars, on this conception, are something over and above the states of affairs in which they occur: they can differ by “bare numerical difference” (1997: 109). Universals, on the other hand, can be reconstructed as “stateof-affairs types”.53 The identities running through the states of affairs, then, are indeed mysterious: universals, but not particulars, depend on them. This is an unstable position: being a a posteriori realist about universals, it is unclear what resources Armstrong can draw on to a priori exclude the possibility of a universal that, by necessity, is had by at most one particular, say a. In such a case, however, generic dependence becomes specific: whether or not a exists determines whether such an F exists (cf. Armstrong 2005: 274). Another source of instability is the ampliative nature of states of affairs: if both particulars and universals are components of states of affairs, why is it, we may ask, that only the latter can be retrieved from them

52

Armstrong expresses this by saying that universals are wholly ‘qualitative’: there is nothing that could distinguish two universals sharing all the qualitative features they bestow (cf. 1978a: 110 and 1989: 106). For his later change of mind, cf. p. ?? below. 53 Cf.: “The universal is a gutted state of affairs; it is everything that is left in the state of affairs after the particular particulars involved in the state of affairs have been abstracted away in thought.” (1997: 29) I am not sure how this abstractionist conception allows Armstrong to maintain his realism about universals. Would universals still exist if no one ever had ‘abstracted’ them from their states of affairs? If universals are states-of-affairs types, they are rather like functions from particulars (individuals) to particulars (states of affairs). Why should we not then identify them with sets of pairs of such particulars? And even if we grant an independent ontological status to functions, they seem to be particulars.

131 as ‘states-of-affairs types’? Would not a similar process of abstraction yield the particulars? If the link between a and F were itself necessary, the necessary connection would be symmetrical: not only would the particulars and universals be fixed given the states of affairs, but the states of affairs would be fixed given the particulars and universals (Armstrong 2004: 84). No need then to postulate them as truthmakers: they come for free as a supervenient lunch. While Armstrong (1997: 267) thought this would go against “the contingency of states of affairs [which] cannot be abandoned”, he “now [has] sympathy with the view that predications are necessary truths” (2004: 51, cf. also 126). I will call this view ‘Leibnizianism’ in the following:54 “What is contingent might not have existed. Suppose a to be F, with F a universal. If this state of affairs is contingent, then it might not have existed. Suppose it had not existed. The particular a, the particular with all its nonrelational properties, what I have in the past called the ‘thick particular’, would not then have existed. Something quite like it could have existed instead: a particular with all of a’s properties except F. But that would have been only a close counterpart of a, because the intersection with F, the partial identity with F, would be lacking. Equally, it now seems to me, the universal F would not have existed. A universal very like F could have existed: a universal that had the same instantiations as F except for instantiating a. But that would have only been a close counterpart of F, because the intersection with a, the partial identity with a, would not have existed. So, strictly, if a and F exist, then they must ‘intersect’. They themselves can be, and I think are, contingent beings. But if a exists and F exists, then a must be F: a necessary connection between contingent beings.” (Armstrong 2004: 47, his italics)

Here we have another, and even more radical, abandon of combinatorialism: both particulars and universals are now conceived of as ‘thick’ – they overlap in states of affairs (Armstrong 2004: 47, fn. 6), they necessitate them because they have the states of affairs ‘built into them’:

54

Cf. Armstrong 2004a: 142. In the meantime, Armstrong has given up Leibnizianism: “‘Partial identity’, I now think, is a somewhat misleading phrase. Particulars enfold their universals – and that is a sort of partial identity – but universals do not enfold their particulars. In the envisaged ‘deleting’ [of the a that is F], the universal continues to exist identically in other particulars, unless, indeed, a is the only particular to instantiate the universal.” (2005: 274) I will argue in the following that he did so for the wrong reasons – giving up on ‘thick universals’, while retaining the ‘thick particulars’.

132 “Given a and given F, as opposed to mere counterparts of this particular and this universal, then the state of affairs of a’s being F is automatically there. It is built into the two constituents of the state of affairs.” (2004: 49)55

The way in which a’s being F is built into both a and F is not mereological, however. Even though Armstrong (2004: 103) characterises partial identity as a relation “where one entity contains another with something to spare, or else where entities overlap each other”, partial identity is not identity of a part: “…what is involved in a particular instantiating a property-universal is a partial identity of the particular and universal involved. It is not a mere mereological overlap, as when two streets intersect, but it is a partial identity.” (Armstrong 2004: 47)56

How are we to understand this ‘partial identity’ of particulars and universals? Armstrong (2004: 47) refers to Donald Baxter’s “Instantiation as Partial Identity” (2001), so perhaps this is where elucidation can be found. Baxter (2001) has provided a new answer to the empiricist worry about universals having multiple locations, saying that even if it begs the question by assuming that if something is at one location, it is at no separate location, we are left with the task of explaining its attractiveness. According to Baxter, it resides in its having a close and true variant, namely:

55

In other passages, Armstrong does not draw this radical conclusion, claiming e.g. that even on the ‘predication is necessary’ view, external relations can be distinguished from internal ones by “demand[ing] states of affairs” (2004: 52). He does not say that Leibnizianism entails that there are no external relations, though it entails, e.g., that causation is a necessary connection in re (2004: 126) and hence internal (2004: 52). 56 The relation discussed under the label of ‘partial identity’ by Armstrong (1997: §2.3.2) should not be confused with the partial identity involved in Leibnizianism, for the first, but not the latter is strictly mereological: “These cases [like the identity of the morning and the evening star] tempt us to overlook such a case as that of Australia and its state of New South Wales and also that of two adjoining terrace or town houses that have a wall in common. These are partial identities. One is whole/part, the other is overlap. Mereology which deals with these notions, may be thought of as an extended logic of identity, extended to deal with such cases of partial identity.” (1997: 18) It is therefore highly misleading for Armstrong to provide mereological models, even only ‘rough’ ones: “The particular and the universal intersect. Consider a cross that has been cut out of a single piece of wood. The intersection of the vertical position of the cross (which models the particular) and the horizontal portion (which models the universal) gives a rough, but perhaps helpful, model for a’s being F.” (2004a: 141)

133 “A universal insofar as it is in one location, is not in another. Insofar as it is in one location, it is separate from (spatially discontinuous from) itself insofar as it is in the other.” (Baxter 2001: 451)

The explication of “insofar as” leads Baxter to an ‘aspect’ theory of universals, according to which universals are aspects of particulars and only formally or ‘loosely’ distinct from them: “…to take many things to be a single thing is to take them to be aspects of a single thing, in my sense of “aspect”.”(Baxter 2001: 600, fn. 14)

The universal insofar as it is there and the universal insofar as it is here are ‘loosely’ identical with just one universal, of which they are aspects. Baxter’s aspect-theory is therefore rather different from Armstrong’s ‘loose identity’: whereas the latter is a matter of equivalence classes,57 the first is a conceptualist substitute for real identity (numerical identity of aspects).58 Baxter explains the difference between strict and loose identity in terms of different ways of counting. His ‘partial’ identity (what he calls “many-one identity” in 1988: 577 and 1988a: 193) is identity across different counts: [It is a kind of identity] “that holds between distinct things (counted on a strict standard) and a single thing (counted on a looser standard). It is identity because the several things (counting strictly) are identical with each other (counting loosely).” (1988: 576)

Partial identity is not overlap (in neither a mereolo-gical nor a nonmereological sense), because each of the – strictly counted – many things (and not only the fusion of all of them) is not numerically distinct from the – loosely counted – one thing, as a proper part or a state-of-affairs compo-

57

Armstrong calls particulars ‘loosely identical’ if they exhibit “sameness of type in the absence of identity of the universals involved” (1997: 15). 58 Baxter’s theory can be formulated as a reinterpretation of the attribution of properties: A predication is contradictory only if it ascribes some property to something under some aspect and denies it from it under the same aspect; and this holds even though the aspects of a property are numerically identical with it (2001: 449). The universal is located here under some aspect (insofar as it is exemplified by one particular), but located there under some other aspect (insofar as it is exemplified by a different particular). Even if a and b are identical, there might be an aspect x of a and an aspect y of b such that a as x is discernible from b as y (Baxter 1989: 130).

134 nent would be (1988: 578-9). Aspects are not proper parts of the things of which they are aspects, but numerically identical with it.59 This may explain the appeal of the multiple location objection, but does it explain exemplification? It does, Baxter thinks, if we “think of a particular as like a universal in having aspects” (2001a: 453). Baxter gives rather enigmatic advice on how to accomplish this: “Here is the proposal in brief: the non-relational tie is the identity of an aspect of a universal with an aspect of a particular. If you think of aspects as parts, then the non-relational tie is the ‘partial identity’ of particular and universal. That’s putting it Armstrong’s suggestive way [making reference to 1997: 17]. The aspect is the part they have in common.” (Baxter 2001: 453)

Mentioning ‘partial identity’ in this respect is very misleading, even if Baxter immediately goes on to stress that it means “think[ing] of aspects in the count in which the whole counts as one” and that his notion of partial identity is like the one of Bradley and unlike the one of Brentano, which, he says, is closer to Armstrong’s. The loosely identical particulars are the exemplifications of one universal of which they are aspects. The loosely identical universals, however, are not, as they were in Armstrong’s reconstruction of the empiricist worry (1997: 15), a strictly identical universal ‘wholly present’ in different locations, but the strictly different universals exemplified by the one particular of which they are aspects. We count the similar particulars strictly as many and loosely as one. When we count them loosely as one, we have the universal. We count the properties of one and the same particular strictly as many and loosely as one – when we count them loosely, we have the particular. If a particular exemplifies a universal, it is an aspect of it. The universal exemplified by the particular is then an aspect of the particular. The aspect of the universal is numerically identical with the universal, the aspect of the particular numerically identical with the particular. If both aspects are identical, then so are the universal and the particular. This is why such “identity in difference” (Baxter 2001: 453) has nothing to do with the mereological notion of partial identity discussed by Armstrong (1997: 17). 59

Even granted that composition is identity, I think it is hopeless to think of aspects as parts: “On standard conceptions, the [proper] parts are all numerically distinct from each other, and each is numerically distinct from the whole they compose. Aspects aren’t like this. They are numerically identical with each other and the whole. Think of parts likewise.” (Baxter 2001: 453) I am sorry to say that I failed.

135 It is also why it is understating the radicalism of his proposal when Baxter gives the following example: “Suppose Hume is a particular, Benevolence is a universal, and Hume is benevolent. Then Hume has an aspect, Hume insofar as he is benevolent. Also Benevolence has an aspect, Benevolence insofar as Hume has it. These are the same aspect – Hume’s benevolence.” (Baxter 2001: 454)

It is, of course, tempting to take the shared aspect, Hume’s benevolence, to be a state of affairs. According to Baxter, however, both Hume and Hume insofar as he is benevolent are numerically identical and so are Benevolence and Benevolence insofar as Hume has it. So Hume’s benevolence is both numerically identical to Hume and to Benevolence! But Benevolence, if it is multiply exemplifiable, is not just numerically identical to Hume, but also, say, to Mill. If Mill and Hume are not numerically identical, then Benevolence is numerically distinct from itself. This, according to Baxter, is “Boethius problem[,] the deep problem […] underlying the multiple location problem” (2001: 454). Baxter’s solution is to bite the bullet: Hume and Mill are identical insofar as they are the same universal, Benevolence (2001: 455). There are two particulars in one count, one universal in another, where the counts compete but are equally strict. Armstrong’s Leibnizianism is different from Baxter’s aspect theory. Rather than a theory of partial identity, it is one of entanglement: the natures and essences of both particulars and universals are tied up with each other.60 Rather than ‘following’ from partial identity,61 the doctrine that ‘predica60

Already Armstrong (1997: 268) said that if predication were necessary, “[t]hen we shall have to say that particulars and universals are not “distinct existences” but that their identities are in some way entangled with each other”. 61 This is how Armstrong puts it: “I find the partial identity very attractive, but it seems to me that partial identity, like any identity, brings necessity with it. If a universal is partially identical with a certain particular, then to try to consider that very universal without it being instantiated by that particular is to consider a mere counterpart of the universal in question.” (2004: 80) This is thirdly misleading: first, because the ‘partial identity’ is not mereological overlap, second, because even if it were, we would need mereological essentialism as a further premise, and third, because the ‘partial identity’ among states of affairs having the same constituents does not add up to identity (in contrast to how Armstrong (1997: 18) characterises partial identity): as Lewis (1986a) pointed out, and Armstrong (1989: 90, 1997: 120) acknowledges, Fa&Gb and Ga&Fb have the same constituents, but are not identical states of affairs, let alone necessarily so (Armstrong (1989a: 59) calls this position ‘weak Haecceitism’).

136 tion’ is necessary is better taken as a substantive claim about the nature of universals and particulars: “The property F must have all its instances and it cannot have any others” (Armstrong 2004: 80-81), “because the instantiations of any universal are part of what that universal is” (2004: 136).62 Leibnizianism restores the symmetry in Armstrong’s theory. He already had thick particulars, enfolding their properties. But these properties were only generically dependent on particulars. So he needed states of affairs to provide necessitating truthmakers. Leibnizianism now gives him thick universals, enfolding their particulars. States of affairs are no longer needed – they are the intersections of thick particulars and thick universals and come in as a free lunch. Leibnizianism is not a consequence of the adoption of thick universals alone. Baxter has a simple explanation why some predications are contingent: if the aspect of the particular exists, then it is numerically identical with the particular and necessarily so – but if it does not exist, then the particular might still exist and perhaps be necessarily numerically identical with other aspects (2001: 458). Aspects are contingent beings and their contingent existence makes the propositions they make true contingent. In this respect, aspects are rather like tropes.63 Armstrong’s universals are rather different: even if they depend on all their particulars, they are still ‘ones over many’, wholly present in numerically distinct particulars. If both a and F exist, a is necessarily F. But the exis62

This is also how Armstrong reports Baxter’s claim: “Baxter’s suggestion is that particulars really do participate in their universals (as the young Socrates suggests to Parmenides and Zeno in Plato’s Parmenides!).” (2004a: 140) 63 Armstrong thinks that advocates of non-transferable tropes are equally committed to Leibnizianism about predication: “The idea is that the mass is held to be the mass of this stone by necessity. It is an identity condition for the property. Every property then becomes an essential property.” (2004: 46, cf. also 2004a: 144) This is a misunderstanding of non-transferability, as Simons (2005: 259) points out: while being part of its subject is essential to the trope, it is not essential to the subject to have the trope among its parts. Even if the mass trope is non-transferable, it can still be held that it is only contingently the mass trope of this stone. While it could not have been the mass trope of another stone, it is itself a contingent being and could not have existed. If the stone has it, the trope exists and could not be the mass trope of any other stone. But just given the stone, the existence of the mass trope and hence the predication is not necessitated. The situation is asymmetrical: while the trope depends on the stone, the stone does not depend on the trope.

137 tence of F is sufficient for the F-ness of many other particulars beside a. If a is F, many other things (i.e. all the Fs) are bound to be F too. Conversely, if a ceases to be F, all these other particulars cease to be F to, for F then ceases to exist (Armstrong 2004a: 144). This is the fatal stab to combinatorialism. If a and b are wholly distinct existences and both F then if a ceases to be F, b ceases to be F too: for both a and F will cease to exist, and hence so does b – if only one thing changes, all things sharing a property with it pop out of existence. Another crucial difference between Baxter and Armstrong is ontological. Even though Baxter (2001: 455) calls his view “realism”, it is realism either about universals or about particulars, or rather realism about something else of which both universals and particulars are aspects. No need to have entities of both categories if you can just count differently the entities in one to get those in the other. Armstrong, however, needs both thick particulars and thick universals. Only if they both exist, their intersection is necessitated.64 Armstrong has necessary predications because he conditionalises them both on the existence of the particular and of the universal.65 While he is an eliminativist about contingency,66 Armstrong says he can offer counterparts for it: “I re-emphasize that such a theory can supply a substitute for contingency by offering counterparts. That a is F is necessary, but contingent a might not have existed and an a-like object that is not a might have existed that is not F. The situation is much the same as David Lewis’s counterpart theory. For Lewis, an a that is an F strictly cannot exist in ‘another possible world’ without property 64

This conditional is also true if F is a non-transferable trope – the difference lies in the respective existence conditions of universals and tropes. Since 2004, Armstrong has possibly changed his view on this matter: “As I now see it, universals are to be thought of as a special sort of part of the particulars that instantiate them.” (2005: 274) This would, I think, make a rather big difference to the 2004 theory (cf. sct. 4 below). In particular, it may, but does not have to be, conjoined with mereological essentialism about these ‘universal’ parts. 65 It may still be true that both the totality of thick particulars and of thick universals singly constitute the whole of reality (Armstrong 2004: 143). But only if both are given, states of affairs (minimal truthmakers) are yielded as their intersections. 66 This is how he characterises the eliminativist strategy: “Eliminativists usually provide what one might think of as ‘counterpart’ truth that correspond to a degree to the propositions that they hold to be false.” (2004: 33) It is false, ‘strictly speaking’, to say that a might not be F, but it is true that something quite like a (except for being F) might exemplify something quite like F (except for being a property of a).

138 F. All that can exist in the other world is a more or less close counterpart of a. He seems to be prepared to call this ‘contingency’, but it is contingency in only a loose sense. Strictly, I think, he is (or he should be) a necessitarian about predication.” (Armstrong 2004: 48, cf. also 2004a: 144-145)

But Lewis is not. If a is contingently F, this means that F, the very same F, can fail to be a property of some otherworldly counterpart of a. While a does not exist in other worlds, F does. This is real contingency, not a counterpart for it: given just (world-bound) a and (trans-world) F, it is still open whether all or only some of a’s counterparts are F. Armstrong’s new picture is relevantly different: given just the truth that a is F, we have the thick particular a and the thick universal F. Given them, we have their intersection, hence the minimal truthmaker necessitating the truth. There is a ‘royal road’ to truthmakers after all. If we have not only thick particulars, but also thick universals, no other states of affairs than their intersections are needed; in particular, no totality states of affairs are needed to make true general truths: “…the conjunction of states of affairs a’s being F & b’s being F… will serve as truthmaker for the truth . Allness will supervene in this situation. A Russellian general fact or state of affairs will not be needed in addition. General facts seemed needed only because was taken to be contingent.” (Armstrong 2004: 81)67

Even if restricted to states of affairs where the property totalled is the common predicative component of the states of affairs fused together (‘self-predicative’ totality states of affairs in the terminology introduced earlier),68 this is misleading. We do not need the conjunction, every single state of affairs will serve as the truthmaker: given just a’s being F, we have both a and F and the latter could not exist without being exemplified by the conjunction of all the particulars that (as we would say) happen to be F.

67

Armstrong (2004a: 148) calls this a “notable ontological economy”. The solution will not work, for example, for the truth that such-and-such a collection comprises all the first-order states of affairs. For the states of affairs in the fusion totalling the property being a first-order state of affairs do not contain the property of being a first-order state of affairs (else they would be second-order). We can still say, of course, that being a first-order state of affairs, like any other property, has all its particulars essentially – given the property, the first-order states of affairs are fixed. But this shows that what is doing the work is the thick second-order universal, not the firstorder necessary states of affairs. 68

139 This is important for the truthmaking of negative truths, where we now have a vast abundance of truthmakers. That Theaetetus is not flying, e.g., is made true just by Theaetetus: Theaetetus, the thick particular, could not exist and fly. It is also made true by the property of flying, for it could not exist and be exemplified by Theaetetus. It is also made true by the secondorder property being a property of Theaetetus, which could not be exemplified by flying. In a similar way, every single black raven makes it true that there are no white ravens, and so will being a raven, being black, being white, being a property of a raven, being co-exemplified with blackness and so on: an indefinite multiplicity of truthmakers and no way of singling out one of them as the ‘minimal’ one. Surprisingly, Armstrong thinks Leibnizians still need at least one totality state of affairs: “…there seems to be need for at least one totality state of affairs. For even if it is extensionally correct to say, for instance, that reality is exhausted by states of affairs having particulars and universals as their constituents, it seems not to be a necessary truth that this is so. If this is correct, then the further truth that will require a further truthmaker, a totality state of affairs as I have argued.” (Armstrong 2004: 81)

This seems, however, to underestimate the power of thick universals. If being an existent, being a state of affairs and being in space-time are properties, then they too have their particulars essentially. Instead of a superthick particular, the totalisation of the fusion of all states of affairs to which no other particular or universal may be added, we now have a super-thick universal, exemplified by everything there is. Given just this property, everything else is fixed.69 There never was a richer free lunch, if only we could stomach it. This is a very Leibnizian picture indeed: Suppose there exists some thing, say a. Then the truth that a exists will be necessitated by some state of affairs. This state of affairs is or contains the intersection of the thick particular a with the super-thick universal exemplified by everything there is.70 69

Simons (2005: 259-260) says that if there are enough external relations, then on Armstrong’s Leibnizian theory, the falsity of any simple predication entails the nonexistence of large parts or even of the whole of the universe. I think that external relations are not needed to derive this undesirable result. 70 I am not assuming what Armstrong (2003: 23, 2004: 6) denies, namely that a’s existing is a state of affairs, but only that it is made true by some state of affairs. Arm-

140 The existence of every single thing, then, gives us the state of affairs making it true that it exists, containing the super-thick universal, which, in turn, gives us everything else. Anything makes true everything; the whole world is mirrored in every single monad. 4. The riddle of exemplification I take both positions reached to be somehow uncomfortable. The classical, states-of-affairs theory forces us into the infelicitous dichotomy of thin and thick particulars and gives us paradoxical totality states of affairs. The new theory eliminates contingency and leads to truthmaker monism. In this section, I argue that we should step back and return to the 1978 theory. I do not think Leibnizianism is to blame for our difficulties – it has, even apart from guaranteeing truthmaker necessitarianism, obvious advantages. Shedding some light on the relation of exemplification, it removes the need for a non-mereological mode of composition of states of affairs: the argument that a’s being F cannot be the fusion of a and F (because they could both coexist with a’s being ¬F) no longer goes through. The existence of the fusion gives us its parts; the parts, in turn, necessitate the truth. Leibnizianism also fits well with the one-over-many argument for universals: universals, after all, were introduced to account for the Moorean fact that different particulars were “identical in nature” (Armstrong 1978: xiii). Partial identity is an obvious explanation and, I think, a plausible one. The symmetry introduced by “think[ing] of a particular as like a universal in having aspects” (Baxter 2001: 453) and identifying the aspects of particulars with universals, presupposes that a prior distinction can be made between particulars and universals.71 The problem with Leibnizianism is strong (1989a: 95) says that being a state of affairs “could perhaps be taken to be a universal”, but this is not a premise of the argument either. The state of affairs in question could just be a’s being in space-time. In short, whatever the property that is totalled in Porky, the putative limit totality state of affairs, this property is also the ‘universal component’ in the state of affairs making it true that a exists. 71 This is acknowledged by Armstrong (1999: fn. 2, 2004a: 146). In (1989a: 44), he draws the distinction in terms of universals’ having a definite adicity. This criterion becomes inapplicable, as Fraser MacBride (2005) has observed, if we admit multigrade universals (which Armstrong 1978: 94, 1989: 40, 1997: 85, 2004a: 147 rejects). Baxter (2001: 461) draws the distinction in the following terms: universals can be instantiated by many particulars while particulars cannot; a particular cannot merely be

141 not its introduction of thick universals, but rather that they are added to thick particulars. The thick particulars, in my view, are responsible for the rationalistic flavour of the resulting ontologies.72 Once we dismiss thick particulars, we may accept thick universals without turning everything into a Leibnizian monad mirroring the whole world. Particulars are just what they are, neither thick nor thin. They exemplify properties, some essentially, others intrinsically and they stand in internal and external relations to other particulars. The universals to which the exemplification relation connects them are importantly different: these are generically dependent entities, nothing but the qualitative features they bestow on their exemplifications. Universals are ways things are and their nature is exhausted by how they make things to be. Indiscernible universals, universals bestowing the same qualitative features, are just identical – there is nothing by which they could differ.73 The aspects of a universal are indeed the particulars exemplifying it, loosely counted as one. The aspects of a particular, however, are not the universals it exemplifies. What we get if we loosely count as one the (strictly) different universals exemplified by one particular is not the particular, but its nature or ‘type’, the most inclusive property it exemplifies (Armstrong 1997: 125). Different particulars could exemplify this property, because indiscernible particulars need not be identical. We should combine Baxter’s insight into the nature of universals not with Factualism – thick particulars, ampliative states of affairs – but with Armstrong’s 1978 realism about particulars and universals, connected by a contingent relation an aspect of something with other aspects. Armstrong seems to concur: “It is of the essence of particulars to be collectors (though they might collect one property only) and it is of the essence of universals to be instantiated (though they might have one instantiation only)” (2006a: 211). But this presupposes a prior understanding of how exemplification can be asymmetric. 72 Armstrong (1997: 183) characterizes rationalism as “providing necessities in re and a faculty of Reason to know these necessities”. 73 Armstrong (2004b: 188) suggests that in addition to ‘thick’ universals, which ‘enfold’ their properties, there are also thin universals that can differ by mere numerical difference. This is foreshadowed in Armstrong (1997: 168), where he plays with the idea of postulating quiddities for universals, letting the difference between universals of the same adicity only be identified, though not constituted by, the different causal powers they bestow. This notion of thin universals that can differ in “bare numerical identity” only (2004: 146) has to be rejected on the conception I am advocating here.

142 of exemplification.74 But did Armstrong not produce arguments aiming to show that exemplification cannot be a relation? We now have to consider these. Armstrong’s main argument is based on Bradley’s regress (which he also calls “relation regress”): If exemplification were a relation between, say, a particular a and a property F, and hence a universal, a further relation would be needed to connect a, F and the exemplification relation (1978: 20, 41, 54, 70). An ontologically and epistemologically vicious regress would follow.75 This argument, however, assumes that if exemplification were a relation, it would be an external one.76 If exemplification is an internal relation, supervening on intrinsic properties of the exemplifying particular and the exemplified universal, then the regress, I think, is as harmless as the truthregress (if p is true, it is true that p is true etc.) of which Hochberg says:77

74

Armstrong (2004: 142) says of Baxter’s theory that its great attraction is “that it involves nothing but the particulars and universals”: “Because the suggested link between the two is partial identity, any need for a fundamental tie, a copula, or what have you, seems to be eliminated. All the trouble that this tie has caused to those of us who accept universals alongside particulars, the tie that so many others use as a major reproach against the postulation of universals, is at a stroke removed.” (2004: 142) I agree that this is the main attraction of the theory that exemplification is partial identity and try to make it compatible with the contingency of predication. 75 “It appears, then, that the Relation regress holds against all Relational analyses of what it is for an object to have a property or relation. If a’s being F is analyzed as a’s having R to a θ, then Raθ is one of the situations of the sort that the theory undertakes to analyze. So it must be a matter of the ordered pair having R′ to a new θ-like entity: θR. If R and R′ are different, the same problem arises with R′ and so ad infinitum. If R and R′ are identical, then the projected analysis of Raθ has appealed to R itself, which is circular.” (Armstrong 1978: 70-71) 76 ”But in general at least and perhaps in every case, the fact that an object instantiates a certain property does not flow from the nature of the object and the nature of the universal that are involved.” (Armstrong 1989: 109) In (1997: 101), he says that the “connection between things and their properties” is an external relation. 77 The truth-regress is taken to be harmless on all sides (Armstrong 1978: 56, 1997: 119, 2004: 78-79, Hochberg 1999: 196). One could even consider it a special case of the exemplification regress (starting at its second stage): if a is F, then a exemplifies F (it is true that a is F), then exemplification is exemplified by a and F (it is true that it is true that a is F).

143 “The subsequent facts in the chain are not involved in the specification of the truth conditions for the initial statements, which is what would make the chain a vicious regress.” (Hochberg 1988: 193)

While exemplification is exemplified by the particular, the universal and the exemplification relation, this fact supervenes on the particular exemplifying the universal: “the predicates may ascend, but not the reality in virtue of which they apply” (Armstrong 2004: 106). Armstrong, even in his non-Leibnizian period, had arguments against exemplification being an internal relation. If it were, would it not then hold necessarily? This testifies to the same confusion of internal and essential relations we noted earlier. A relation is internal if it is necessitated by the intrinsic properties of the relata. In this sense, exemplification of intrinsic properties is an internal relation: given a particular has the properties it in fact has, it exemplifies exactly the universals it in fact exemplifies. This does not, as Armstrong seems to think,78 imply that it does so necessarily. There is an important distinction to be drawn between intrinsic and essential properties of particulars. How ‘external’ vs. ‘internal’, when used in Armstrong’s sense, becomes a false dichotomy, is particularly clear in Baxter’s presentation of Armstrong’s argument that exemplification, if it were a relation, could be neither internal nor external: “If you believe in universals and particulars, and you believe that neither are simply bundles of the other, then you need to make sense of instantiation…[…] It needs to be a ‘non-relational tie’ […] That is, it can be neither an internal nor an external relation, as Armstrong construes them […]. Internal relations are always necessary – the relata can’t exist without them …[…] External relations are or involve additional entities…” (Baxter 2001: 449)

78

It is difficult to find Armstrong explicitly advocating this doctrine. The argument for exemplification being external quoted in fn. 76 continues with “The connection is contingent.” (1989: 109). The sufficiency argument by Armstrong (1997: 115-116) quoted on p. ?? is preceded by the following passage: “The assumption here is that the truthmaker for a truth must necessitate that truth. […] Using the distinction between internal and external relations […], the truthmaking relation is an internal one. This seems evident enough if we consider for a moment the idea that the relation should be external, contingent.” Armstrong (2004: 9, 50) says that the truthmaking relation is internal because it is necessitating and that internal relations are those that are had necessarily (cf. 2004: 105). The clearest endorsement is recent: “Will not the relation between truthmaker and truth-bearer be an internal one? It will depend on the nature of the terms involved and on them alone. If so, it will be necessary, I think.” (2005: 275)

144 It can – and should – be accepted that exemplification is neither internal nor external in these senses, but it still can – and should – be held that exemplification is internal in the sense defined earlier, i.e. supervening on intrinsic properties of its relata. Exemplification is a relation that holds only if exemplified, but the exemplification of which does not require a further and ontologically substantial relation of exemplification, but just the two relata, together with their properties, including their relational properties of standing in the exemplification relation with respect to each other. If a exemplifies F, there is a relation holding between them – which is to say that exemplification E is exemplified by them. But we do not need a second exemplification relation E′ to account for the fact that E(F,a), for “E(F,a)” is made true by what a is and by what F is.79 The truth-conditions for “E(F,a)” do not involve further exemplification relations, but only a and F. If exemplification is a relation, what kind of relation is it? My answer is simple, but perhaps surprising: it is partial identity – partial identity not in the rather special sense Armstrong takes from Baxter, but ordinary mereological overlap: the universal is literally part of the particular that exemplifies it, two resembling particulars literally share a universal as their common part. If you think that only material or concrete objects can literally have parts, think of the particular as extended in more than three (or four) dimensions, as a location in quality space as it were: add a dimension for every degree of independent qualitative variation, in which it either is or is not extended (or extended to some degree in the case of quantities). Its extension in these dimensions are the universals it exemplifies. Even if some sense can be made of properties being parts of particulars that intrinsically exemplify them, they will be contingent parts – so how could they be truthmakers? I agree that if a contingently has the intrinsic property F, it is a contingent and accidental property of a that it has an F-part – a could have lacked it and still be what it is. Even though a has its properties as parts, it does not ‘enfold’ them; it is not a thick particular having its ‘property parts’ essentially. But may a contingent part of a be a truthmaker for the intrinsic predication that a is F? Surprisingly, Armstrong accepts this for some lesser allnesses, claiming with respect to the ‘ordinary general proposition’ “All ravens are black”: 79

A similar point is made by Forrest (1993: 56).

145 “There are, prima facie, two totalities: the mereological whole of the black ravens and the mereological whole of the ravens. […] It then becomes clear that if and only if the two totalities are identical, then the proposition is true, and this one totality is its (minimal) truthmaker. If there are two distinct totalities, with the totality of the black ravens no more than a proper part of the totality of ravens, then the proposition is made false…” (Armstrong 2004: 74)

Suppose the proposition “All ravens are black” is true. Then there is some fusion, which is the fusion of all the ravens and also the fusion of all the black ravens. It is the truthmaker of the proposition that all ravens are black. But is it necessitating this truth? It does not seem so. The fusion of the black ravens could very well exist, and be the very same fusion, without making it true that all ravens are black (if there were, say, another white raven). It would not be, to be sure, the fusion of all the ravens – but this is not a fact of existence, but a fact about the fusion having this or that property. Armstrong might reply that the real truthmaker is not the fusion of the black ravens, but the state of affairs that the fusion of the black ravens is (identical to) the fusion of the ravens. But this, it seems, is just the fusion itself, for the truthmaker of “a=b” is just a (2004: 39). Necessitarianism goes by the board then. But internalism does not: the fusion of the ravens is a truthmaker not just because it exists but in virtue of its internal relation of being identical with the fusion of the black ravens.80 Generalising from strict to merely partial identity, we may say: It is in virtue of its standing in the internal, mereological relation of having an F-part that a makes it true that it is (intrinsically) F; it is in virtue of F+a being the very same fusion than a that it makes it true that a is F. What makes it true that a is F (for intrinsic F), is just a (= a+F) – but it does so in virtue of how it is.81 While this view has obvious problems with which I cannot

80

This is not the only place where Armstrong claims that totality states of affairs involve an internal relation. Cf. e.g.: “Thus, it is true Theaetetus is not flying, but the truthmaker for this, I hold, is the totality of Theaetetus’s properties, and the difference of each of these properties from the property of flying.” (2006b: 230) For “Theaetetus is not a centaur”, he gives Theaetetus himself as truthmaker, and for “No men are horses” the sums of all men and of all horses (2006b: 231). 81 Truthmaking of general truths by internal relations (and hence their terms) meshes nicely with what seems to be Armstrong’s new view: “a might have had property F” is made true by the mereological sum of a and F (2006d: 282).

146 deal here,82 it at least shows that there is room in logical space for accepting truthmaker internalism and rejecting truthmaker necessitarianism. 5. Thick universals But still, we may have wished to do better. I think that Baxter’s insight into the nature of universals – that they have their exemplifying particulars essentially – may help us here. We do not quite get truthmaker necessitarianism, but we may perhaps get something that many consider as good as it: truthmaker essentialism. Given a more plausible view of essence, however, truthmaker essentialism is weaker than truthmaker necessitarianism.83 The account of essential properties I find plausible takes the characterisation of a property as essential to be independent of an account of its modal behaviour. For F to be an essential property of a, it is neither necessary nor sufficient that, necessarily, a is F if a exists.84 I will also assume that the two 82

A first and obvious worry concerns the question whether it can be extended to extrinsic predications. I think it can. Whenever a is extrinsically F, a could cease to be F through variation in the outside world. Because truthmaking is internal, the circumstances on which the exemplification of F by a depends must be brought into the truthmaker. What makes it true that a is extrinsically F will hence be something that is intrinsically such that it makes it true that a is F. Other obvious problems arise with asymmetric relations. What distinguishes, for an asymmetric relation R, the truthmaker for a’s being R-related to b from the truthmaker for b’s being R-related to a? A first reply here is ‘tu quoque’: these problems equally arise with states of affairs. Discussing his principle that the same ultimate constituents constitute different states of affairs only if they are differently organised, Armstrong (1997: 121-2) claims that (at least asymmetric) relations have a “direction”, which he represents by indexing the blanks in the corresponding state-of-affairs type. It is not clear to me, however, what this ‘direction’ is supposed to be. It cannot be a second-degree property of the relation, for we would still not be able to explain the difference between Rab and Rba and at the same time maintain that they ‘contain’ the same relation. Rather, it has to be an additional, negative, state of affairs (cf. Armstrong 2004b: 193), or an ontological feature of the relation itself (an idea discussed by Armstrong (2004: 151) that Fine (2000) calls ‘positionalism’). Another problem that has its parallel in the states-of-affairs case concerns the structure of complex truthmakers. The truthmaker for “Fa&Gb”, I hold, is a+b (= a+b+F+G) – unfortunately, this is also the truthmaker for “Fb&Ga”. Hence, some coexemplification requirement is needed (Armstrong 1997: 36): the conjunction of F and G has to be structural. (Thanks to David Armstrong for pointing this out.) 83 I call “truthmaker essentialism” the view that if a makes it true that p, then it is essential to a to make it true. Parsons (1999: 328) uses it for truthmaking internalism. 84 This is how Armstrong (1983: 166) defines “essence” in terms of ‘weak necessity’. I do not have space to defend my unorthodox account here. One direction of the inde-

147 de-relativisations of a binary relation may differ with respect to whether or not they are exemplified essentially.85 Baxter’s insight that a universal would not be the universal it is if it had different exemplifications is best brought out in terms of possible worlds: framed in this language, the claim becomes that properties do not stand in non-trivial counterpart relations: they are strictly identical across possible worlds (Lewis 1986: 205).86 And it is the strictly transworld-identical properties that are most aptly called “universals”. To say what they are, we have to say how the particulars are like that exemplify are. But this means pendence claim has forcefully been argued for by Fine (1994): Necessarily, if a exists, it is a member of its singleton; however, a is not essentially a member of {a}. 85 Again, I cannot argue for this claim here in full, but just give some arguments from authority: Aquinas thought (I have been told) that it is essential to the world to have been created by God, but not essential to God to have created the world. Kripke thought that it is essential to me that I have my actual parents, while it is presumably not essential to my parents to have begotten me. Fine thinks it is essential to the set {a,b} to have a as a member, while it is not essential to a to be a member of this set. 86 Based on counterpart relations between particulars, we may of course introduce ‘counterpart’ relations for at least some extrinsic properties, e.g. one in which the property of being the biggest pig in w counts as a counterpart of being the biggest pig in v, and we may say that the first, but not the second, is exemplified by the oldest pig (in w and v respectively). However, these property nominalisations do not designate the property of being the biggest pig (whereas both “I” and “my counterpart in w” do designate me, albeit in possibly different worlds). They designate, respectively, being the biggest pig in w and being the biggest pig in v. This ‘counterpart’ relation does not play the role counterpart relations among particulars play in the regimentation of our modal talk. When we say that Sam, actually the oldest pig, is the biggest pig but might not have been, we do not say that Sam and his counterpart in v differ in that Sam has the first property, but his counterpart lacks the latter: rather we say of one and the same property that they differ with respect to it. Mark Heller (1998) defines the similarity relation making for counterparthood of properties as similarity between the roles they play in their respective worlds: “To describe a property P’s role completely, we say ‘it is such that …’, where the ellipsis is filled in with the rest of the description of the entire world: P is such that it has such-and-such a distribution among other properties P1, P2, and so on, that have so-and-so distributions. Where a world is a Ramsey sentence […], a property’s role in that world would be the open sentence that results from dropping the existential quantifier that binds that property.” (1998: 301-302) If ‘roles’ are taken to be open sentences, I do not see how properties can have similar roles that are not identical: either they satisfy the sentence, i.e. have the role, or not. If by similarity of role he means similarity in the patterns of property distributions (1998: 303), then he has not done away with cross-world property identity: for to be so-and-so distributed is a property that is identical across the respective patterns.

148 that, given what the property is, it could not have been exemplified by (qualitatively) different particulars: the property has a nature, a quiddity, it bestows on its particulars. By contrast, we may very well specify what a particular is without mentioning all its properties. This is the metaphysical asymmetry between universals and particulars.87 Whenever a exemplifies F, two relational properties are exemplified by a and F respectively, namely having F as a property and being a property of a. The first of these just mimics F: it is essential to a iff F is. The latter, however, differs from F in at least one important respect, or so I want to claim: whenever it is had by a property G, it is an essential property of G. Why should we believe this? Suppose we are modal realists and convinced by the argument from accidental intrinsics that anything having a property contingently can exist only in worlds where it has that property. This commits us to counterparts for ordinary particulars: what makes it true that a could have lacked its intrinsic property F is some ¬F-counterpart a′ of a in another world. But is it really F that a′ lacks, not just a counterpart of it? If there were no literal identity of type among things in different possible worlds, there would be no way of saying why a′ counts as a counterpart of a.88 There must be something unifying the counterparts, and this must be a ‘one over many’ – genuine, not surrogate unity.

87

I hold, contra Armstrong (2004a: 146, 2004b: 188), that two indiscernible universals (universals exemplified by the same possible particulars) are identical (cf. fn. 73). 88 John Hawthorne has pointed this out in personal communication quoted in Armstrong (2004a: 145, fn. 7): “…what would ground the counterpart relation of similarity? We now see that the world without the particular named ‘a’ would, strictly speaking, be a world in which none of the universals and particulars in the original grid world would exist. So what would make a property in another world a counterpart of “a”? It cannot be similarity between this world and that, construed as some kind of sharing of particulars and universals. So how does one think about the relevant notion of similarity that is to undergird the counterpart relation and in turn the “loose and popular sense” of transworld identity?” Suppose we ask whether it might be the case that some green table is not coloured. A ‘counterpart’ relation R exists that correlates the table with a pig, being green with being pink and being coloured with flying. Because there is a possible world where some pink pig flies, the answer will be in the affirmative. Everything turns out to be possible. How are we to argue that R is not a relation of similarity if there is no strict identity of anything across possible worlds?

149 Baxter’s insight gives us a more direct route to the same conclusion: if a is F, F has the property of being exemplified by a. If Baxter is right, then this property (or ‘aspect’ as Baxter would call it) is part of what F is. F being what it is, it must have the property of being exemplified by a, though it lacks – if F is a contingent property of a – the property of being exemplified by x, for at least some counterpart x of a. Here is another, somewhat less conclusive, argument that does not rely on modal realism: whether or not something could lack a property it actually has depends on whether it could exist without having that property. If we are to determine this, we hold some things constant while varying others. If the thing in question is a particular, this is a fairly simple task: we ask of this thing, concrete and determinate as it is, whether it would persist if stripped from some feature – we hold constant the thing and vary its properties. If the thing in question is a property, however, our task is more difficult: could the property being red fail to be a colour property, monadic or more similar to orange than to green? When wondering about these questions, we hold constant the property, but thereby also hold constant its particulars: if the colour in question really is being red, no other than red things can exemplify it. It could fail to be exemplified by the things that are in fact red only if these things were different, it seems. But this is a possibility for the things, not for the property. In this respect, properties are rather like sets. Sets have their members essentially89 – does it follow that the set of all and only the green things contains essentially some contingently green thing a? It depends: if we are talking rigidly about the set S, which we, in this world, pick out by S = {x | x is green}, the answer is yes; if we are talking about {x | x is green} tout court, however, the right answer seems no: we are not talking about one set in particular, but rather using a singular term whose referent varies from world to world.90 In the case of universals, I submit, only the first reading 89

Fine has called this feature of sets “rigidity of membership” (1981: 179). A related phenomenon has been argued for by Fine a long time ago: Think of propositions as sets of possible worlds and consider the set of all possible worlds. Viewed as a proposition, Fine says (1977: 141), this set exists necessarily: whatever our possible worlds, they necessarily form a set (or a proper class for that matter). Viewed as a set, however, its existence depends on the existence of each possible world. If their existence was contingent, the existence of their set would be contingent too. While the universal proposition is what it is independently of what possible worlds there are, sets depend for their existence on their members. Armstrong (1989a: 95) made the same 90

150 is available: If “being red” would pick out different properties P1, P2 etc. in different possible worlds w1, w2, etc., we should rather say that it (rigidly) stands for the disjunctive property: being P1 in w1 or being P2 in w2 or … Properties are best characterised by what they bestow on their particulars. They are what they are because these (i.e. such-and-such), and not others (i.e. different), particulars exemplify them. They do not only owe their existence, but their nature to these particulars: with other particulars, the universal would not be what it is. Given that the universal is these particulars, counted loosely as identical, it could not fail to be exemplified by them.91 Thick universals give us more than just truthmaker internalism: what makes it true that a is F is just a and F, i.e. a, because F is a mereological part of it. If F is a thick universal, there is more to be said: there is something, i.e. F, that is essentially such that a is F; F could not be what it is without making it true that a is F. Do thick universals bring back Leibnizianism? Suppose a is F, hence a and F both exist. Even if F essentially has the property being exemplified by b (for a≠b), this does not mean that b has to be F: for b to be F, b also has to exist – and because the property being exemplified by b is ‘world-specific’ (i.e. is a different property than bedistinction between the maximal ‘fact of totality’ “as a determinable” and “as a determinate”: only the former supervenes on the existence of the world. 91 It might be worried that this argument, if sound, rules out contingent properties of universals: it seems possible, e.g., that the property of being the most popular property among philosophers is now exemplified by being a bachelor, but will be exemplified by being a vixen in the future. But this clearly does not show that being a bachelor will cease to exist in the future. “The most popular property among philosophers”, however, does not rigidly designate a universal, identical across possible worlds. The fact that two properties, in different possible worlds, both are the most popular among philosophers in the respective worlds, does not entail that they are similar – because the second-level property is relational and the philosophers in question will be different in the corresponding possible worlds (at least in the perhaps unimportant respect of their property predilections). But “being exemplified by a” is not relational in this way. To attribute the second-level property of exemplifying a to a universal, we have to decide on whether we mean a-as-it-is-in-the-actual-world or a-as-it-would-be-in-somecounterfactual-circumstances, in the same way as we have to decide, when specifying a set as the set of all and only the green things, which one of the actual and possible green things we want to include. If a merely possible particular a in w is F, then being exemplified by a is a property of F already in our actual world. There is no possible world where F lacks this property. So being exemplified by a is an essential property of F, as is having a as a member for a set S that contains a.

151 ing exemplified by b′, where b′ is a counterpart of b), just the existence of b is not enough: b has to exist just as it is, i.e. including F. Contingency is thus salvaged, but necessitarianism is lost: it is only given that a has an F part, that it makes true that a is F. If a and F both exist, but the latter is not a part of the former, no truthmaking relation holds. What about negative and general truths? The truth that Theaetetus is not flying is not made true by Theaetetus nor by any of its parts. It is made true by the property of flying which would not be what it is if it were a property of Theaetetus. This allows for negative truths about alien particulars – Pegasus is not yellow in virtue of being yellow being what it is.92 What about general truths? That all ravens are black is made true by the fusion of the ravens, including the blackness and raven parts they have in common. Given that the black ravens are all and only the ravens there are, nothing else, and a fortiori nothing non-black could have been a raven. What about the all-inclusive totality, the world? The world could, of course, have contained more or less things. But existence would not have been the same.93

REFERENCES Joseph Almog, 1996, “The What and the How II: Reals and Mights”, Noûs 30(4), pp. 413-433. D.M. Armstrong, 1978, Nominalism & Realism: Universals and Scientific Realism, Volume I, Cambridge: Cambridge University Press. ——1978a, A Theory of Universals: Universals and Scientific Realism, Volume II, Cambridge: Cambridge University Press. ——1980, “Against ‘Ostrich’ Nominalism: A Reply to Michael Devitt”, Pacific Philosophical Quarterly 61(4), pp. 440-449, reprinted in Mellor and Oliver (1997: 101-111). 92

Does it allow for alien properties? It does on some relaxation of Aristotelianism. Properties may then be characterised not just by their actual, but by all their possible particulars. Hence, if they exist, provided they have possible exemplifications, they are here to make it true that they have no actual exemplifications. 93 Many thanks to David Armstrong, Davor Bodrozic, Ghislain Guigon, Kevin Mulligan and Gianfranco Soldati for comments on and discussion of previous versions.

152 ——1983, What Is a Law of Nature, Cambridge: Cambridge University Press. ——1984, “Reply to Aune (1984)”, in R.J. Bogdan (ed.), D.M. Armstrong, Dordrecht: Reidel, pp. 251-256. ——1989, Universals: An Opiniated Introduction, Boulder, Colorado: Westview Press. ——1989a, A Combinatorial Theory of Possibility, Cambridge: Cambridge University Press. ——1997, A World of States of Affairs, Cambridge: Cambridge University Press. ——2000, “Difficult Cases in the Theory of Truthmaking”, The Monist 83(1), pp. 150160. ——2002, “Truth and Truthmakers”, in R. Schantz (ed.), What Is Truth?, pp. 27-37, Berlin: Walter de Gruyter. ——2003, “Truthmakers for modal truths”, in H. Lillehammer and G. RodríguezPereyra (eds.), Real Metaphysics – Essays in honour of D.H. Mellor, London: Routledge, pp. 12-24. ——2004, Truth and Truthmakers, Cambridge: Cambridge University Press. ——2004a, “How Do Particulars Stand to Universals?”, in D.W. Zimmerman (ed.), Oxford Studies in Metaphysics, vol. I, Oxford: Clarendon Press, pp. 139-154. ——2004b, “Théorie combinatoire revue et corrigée”, in J.-M. Monnoyer (ed.), La structure du monde: objets, propriétés, états de choses. Renouveau de la métaphysique dans l’école australienne de philosophie, Paris: Libraire Philosophique J. Vrin, pp. 185-198. ——2004c, “Truthmakers for negative truths and truths of mere possibility”, Talk presented at the Colloque International de Métaphysique – Vérités et Vérifacteurs, 20 ans après – 9-11 Dec. 2004, Département de Philosophie, Aix-en-Provence. ——2005, “Reply to Simons and Mumford”, Australasian Journal of Philosophy 83(2), pp. 271-276. ——2006, “Particulars Have Their Properties of Necessity”, in P.F. Strawson and A. Chakrabarti (eds.), Universals, Concepts and Qualities. New Essays on the Meaning of Predicates, Aldershot: Ashgate Publishing, pp. 239-247.

153 ——2006a, “Reply to Rissler”, Australasian Journal of Philosophy 84(2), pp. 211212. ——2006b, “Reply to Forrest”, Australasian Journal of Philosophy 84(2), pp. 229232. ——2006c, “Reply to Heil”, Australasian Journal of Philosophy 84(2), pp. 245-247. ——2006d, “Reply to Efird and Stoneham”, Australasian Journal of Philosophy 84(2), pp. 281-283. Bruce Aune, 1984, “Armstrong on Universals and Particulars”, in R.J. Bogdan (ed.), D.M. Armstrong, Dordrecht: Reidel, pp. 161-169. Donald L.M. Baxter, 1988, “Identity in the Loose and Popular Sense”, Mind 97(388), pp. 575-582. ——1988a, “Many-One Identity”, Philosophical Papers 17(3), pp. 193-216. ——1989, “Identity through Time and the Discernibility of Identicals”, Analysis 49(1), pp. 125-131. ——2001, “Instantiation as Partial Identity”, Australasian Journal of Philosophy 79(4), pp. 449-464. ——2001a, “Loose Identity and Becoming Something Else”, Noûs 35(4), pp. 592-601. John C. Bigelow, 1988, The Reality of Numbers: A Physicalist’s Philosophy of Mathematics, Oxford: Clarendon Press. F.H. Bradley, 1893, Appearance and Reality – A Metaphysical Essay, Oxford: Clarendon Press, 2nd edition 1930. Keith Campbell, 1990, Abstract Particulars, Oxford: Basil Blackwell Publishers. Damian Cox, 1997, “The Trouble with Truth-Makers”, Pacific Philosophical Quarterly 78(1), pp. 45-62. Chris Daly, 2000, “Properties as Truthmakers”, Logique et Analyse 43(169-170), pp. 95-107. Michael Devitt, 1980, “‘Ostrich Nominalism’ or ‘Mirage Realism’”, Pacific Philosophical Quarterly 61(4), pp. 433-439, reprinted in Mellor and Oliver (1997: 93100).

154 A.C. Ewing, 1934, Idealism, A Critical Survey, London: Methuen & Co. Kit Fine, 1977, “Properties, Propositions and Sets”, The Journal of Philosophical Logic 6(2), pp. 135-191. ——1981, “First-Order Modal Theories I – Sets”, Noûs 15(2), pp. 177-205. ——1994, “Essence and Modality”, in J.E. Tomberlin (ed.), Philosophical Perspectives 8: Logic and Language, Oxford: Basil Blackwell Publishers, pp. 1-16. ——2000, “Neutral Relations”, The Philosophical Review 109(1), pp. 1-33. Peter Forrest, 1993, “Just Like Quarks? The Status of Repeatables”, in J. Bacon, K. Campbell, and L.R. Reinhardt (eds.), Ontology, Causality and Mind: Essays in Honour of D.M. Armstrong, Cambridge: Cambridge University Press, pp. 4565. Peter Forrest and Drew Khlentzos, 2000, “Introduction: Truth Maker and Its Variants”, Logique et Analyse 49(169-170), pp. 3-15. John F. Fox, 1987, “Truthmaker”, Australasian Journal of Philosophy 65(2), pp. 188207. Mark Heller, 1998, “Property Counterparts in Ersatz Worlds”, The Journal of Philosophy 95(6), pp. 293-316. Herbert Hochberg, 1988, “A Refutation of Moderate Nominalism”, Australasian Journal of Philosophy 66(2), pp. 188-207, elaborated into Hochberg (2001). ——1999, Complexes and Consciousness, Stockholm: Thales. ——2001, “A Refutation of Moderate Nominalism”, in Russell, Moore and Wittgenstein. The Revival of Realism, Egelsbach: Dr. Hänsel-Hohenhausen, pp. 175204. David Lewis, 1983, “New Work for a Theory of Universals”, Australasian Journal of Philosophy 61(4), pp. 343-377, reprinted in Lewis (1999: 8-55). ——1986, On the Plurality of Worlds, Oxford: Basil Blackwell Publishers. ——1986a, “Against Structural Universals”, Australasian Journal of Philosophy 64(1), pp. 25-46, reprinted in Lewis (1999: 78-107). ——1986b, “Comment on Armstrong and Forrest”, Australasian Journal of Philosophy 64(1), pp. 92-93, reprinted in Lewis (1999: 108-110).

155 ——1991, Parts of Classes, Oxford: Basil Blackwell Publishers. ——1998, “The truthmakers (review of Armstrong (1997))”, Times Literary Supplement, 13.02.98 (4950), p. 30, reprinted as “A world of truthmakers?” in Lewis (1999: 215-229). ——1999, Papers in Metaphysics and Epistemology, Cambridge: Cambridge University Press. ——2001, “Truthmaking and Difference-Making”, Noûs 35(4), pp. 602-615. David Lewis and Rae Langton, 1998, “Defining “intrinsic””, Philosophy and Phenomenological Research 58(2), pp. 333-345, reprinted in Lewis (1999: 116132). Bernard Linsky, 1994, “Truth Makers for Modal Propositions”, The Monist 77(22), pp. 192-206. Fraser MacBride, 2005, “The Particular-Universal Distinction: A Dogma of Metaphysics?”, Mind 114(455), pp. 565-614. David Hugh Mellor and Alex Oliver (eds.) 1997, Properties, Oxford: Oxford University Press. George Molnar, 2000, “Truthmakers for Negative Truths”, Australasian Journal of Philosophy 78(1), pp. 72-86. George Edward Moore, 1919-1920, “External and Internal Relations”, Proceedings of the Aristotelian Society 20, pp. 40-62, reprinted in Philosophical Studies, London: Routledge and Kegan Paul, 1922, pp. 276-309. Kevin Mulligan, Peter M. Simons, and Barry Smith, 1984, “Truth-Makers”, Philosophy and Phenomenological Research 44(3), pp. 287-321. Stephen Mumford, 2005, “The True and the False”, Australasian Journal of Philosophy 83(2), pp. 263-269. Josh Parsons, 1999, “There is no ‘Truthmaker’ Argument Against Nominalism”, Australasian Journal of Philosophy 77(3), pp. 325-334. Greg Restall, 1996, “Truthmakers, Entailment and Necessity”, Australasian Journal of Philosophy 74(2), pp. 331-340.

156 James D. Rissler, 2006, “Does Armstrong Need States of Affairs?”, Australasian Journal of Philosophy 84(2), pp. 193-210. Peter M. Simons, 2005, “Negatives, Numbers, and Necessity. Some Worries about Armstrong’s Version of Truthmaking”, Australasian Journal of Philosophy 83(2), pp. 253-261. Ludwig Wittgenstein, 1921, “Logisch-philosophische Abhandlung”, Annalen der Natur- und Kunstphilosophie 14, pp. 184-261, cited after Logisch-philosophische Abhandlung / Tractatus logico-philosophicus, Frankfurt a.M.: Suhrkamp Verlag, critical ed. by Brian McGuiness and Joachim Schulte, 1998.

Reply to Keller D.M. ARMSTRONG

Philipp Keller’s paper is exceedingly long, and I cannot reply to everything in it, so will have to be selective. First a complaint, and then I will take up five points. My complaint is this : Keller says at the beginning of his paper that it is my defence of truthmaker realism in my book Truth and Truthmakers that he wishes to discuss. Yet he freely quotes from other work of mine without much consideration of whether my views expressed there are compatible with the book he proposes to examine. 1. In his Abstract Keller describes my ‘all-embracing totality states of affairs’ as an ‘ontological monster’. ‘All the things so dear to realists – rocks, natural properties, real persons – are just abstractions from this … monster’. The all-embracing state of affairs, as I see it, has as its subject all the lesser states of affairs, and therefore, as I claim, all being, where being is taken omni-temporally. It ‘says’ of this subject that it is all being (or all positive being, as I’d now like to say). Rocks and real persons are mereological (proper) parts of this huge object. Natural properties are parts of the objects they are properties of in some more sophisticated sense to which some sense of the slippery term ‘abstraction’ may apply. Realists can sleep soundly. 2. The early part of Keller’s paper (before 2 : Allness) is devoted to exposing my sins against what he calls ‘combinatorialism’. This is his word for the Humean (not necessarily Hume’s) principle: no necessary connection between (wholly) distinct existences. (The addition of ‘wholly’ is very important. If it is omitted, then the principle can be refuted rather easily.) Here is one of his lines of thought. He notes that I maintain that the relation between John (the truthmaker) and ‘John exists’ (true proposition, so the truthbearer) is an instance of the simplest of all truthmaking relations. (John is a substitution instance of T, and ‘John exists’ an instance of ‘T exists’) Here being and truth are connected with the greatest perspicuity. No-

158 tice that this holds whatever be the detail of our metaphysics of John – a topic known to be fraught with difficulty. Keller then raises the question what, within my system of thought, is the minimal truthmaker for ‘John is human’. He notes that I think that any truthmaker must necessitate the truth it is truthmaker for. He concludes that this necessitating condition can only be satisfied in this case if John is essentially human, i.e. cannot exist as a non-human. This would violate combinatorialism, that is, violate Hume’s principle, by setting up a necessary connection between the particular, John, and his humanity. For myself I am now not at all sure that Hume’s principle holds across the board. But I don’t think that the principle is violated in the case of truthmaker / truthbearer connections. This is because being and truth are connected to each other very closely, so closely that we won’t have wholly distinct existences there. And I don’t think that the principle is violated for John and his humanity, or, if it is, that there is anything special about his humanity. John, a contingent being, has among his properties those that make him an instance of the kind: human being. And it is the state of affairs of his having these particular properties that is the minimal truthmaker, a necessitating truthmaker, for the truth of ‘John is a human being’. But I reject essential properties, and I don’t see that Keller has said anything that puts John’s ‘human-making properties’ in a special position among his other properties. Instead, I can have very much the same analysis as my analysis of the truthmaker for ‘Venus is greater in size than Mars’, an analysis which Keller immediately contrasts with ‘John is human’. 3. I pass on to the very interesting topic of totality states of affairs. These are what Russell called general facts, which he argued were needed as truthmakers for such truths as ‘all men are mortal’ and of which he said in his Logical Atomism lectures he did not know what their proper analysis is. I have suggested that these facts or states of affairs are constituted by a totalling relation holding between a certain mereological sum (fusion), e.g. the sum of all humans and a property that totals this sum, e.g. the property being a human. (It will be observed that the totalling property need not be a ‘sparse’ one.)

159 Keller ingeniously suggests that a paradox results from considering a very special, higher-order, totality state of affairs : the totality of totality states of affairs. (As he points out, this is not the regress argument proposed by Damian Cox, 1997: 56, which Keller – and I − think can be answered.) If the pattern I suggest for the form of totality states of affairs is correct, then the totalling relation involved would have to hold between the mereological fusion of the totality state of affairs and the property of being a totality state of affairs. But this extra totality state lies outside the contemplated mereological fusion of the totality states of affairs. So, Keller suggests, this is a reductio of the attempt to set up a fusion of all the totality states of affairs. I think the moral to be drawn from this is that there can be no such higherorder totality state of affairs, that sums all lesser totality states of affairs. (A useful discovery for which we must thank Keller.) The situation seems formally not so different from Cantor’s paradox about the class of all classes. There can be no such class because it would have to include itself in the putative class. Similarly, the putative totality state of affairs would have to include itself along with the sum, the fusion, of the lower-order totality states of affairs. There can be a fusion of all the fusions associated with the lesser totality states of affairs, and it would seem that there could be a fusion of all the lesser totality states of affairs. (The result of both fusions would be the whole world.) There could even, it seems, be a rather uninteresting property being a lower-order totality state of affairs. And perhaps an infinite regress of higher-order truths concerning totality states of affairs can be manufactured. But if there is such a regress, then one may wheel in the same solution to the problem it appears to pose as that which solves Cox’s paradox. There will be a regress of truths without a regress of truthmakers. The truthmaker will always be the world, and the limit state of affairs that determines it is the world. (Compare the truth regress. If proposition p has a truthmaker, that truthmaker will suffice for ‘it is true that p’, ‘it is true that it is true that p’ and so to infinity.) 4. I’d like to fill out a little the discussion in my 2004 about the typical general proposition ‘All ravens are black’. I said: There are … two totalities : the mereological whole of the black ravens and the mereological whole of the ravens. … If and only if the two totalities are identical, then the proposition is true. And this one totality is its (minimal) truthmaker. If there are two distinct totalities, with the totality of the black ravens no

160 more than a proper part of the totality of ravens, then the proposition is made false … (2004, p.74.)

This was not well expressed, and I cannot blame Keller too much for his misreading of it. My idea is that we consider here two different totality states of affairs. In the first of these a certain mereological fusion totals the property being a black raven, and in the second a certain mereological fusion totals the property being a raven. I then switch to consider the two mereological fusions involved in these two totality states of affairs. I call attention to two possible cases. The first possibility is that the ‘two’ fusions are the very same object. In that case the fusion of the two different totality states will be the truthmaker for the truth ‘All ravens are black’. But the second possibility, where the totality of black ravens is a proper part of the totality of the ravens, the fusion of the two totality states of affairs will be falsemaker for ‘All ravens are black’. All this is important because the original cases I considered of totality states of affairs involve a relation involving just one property and the fusion of the members that instantiate that property, for instance the property of being a raven and being a black raven. They only yield the truthmakers for ‘This is the totality of ravens’ and ‘This is the totality of black ravens’ which are propositions that we are normally not very interested in asserting because of the difficulty of counting off all the ravens. But we are very interested in asserting or denying propositions that involve a subject property and a predicate property, e.g. being a raven and being black. What I am arguing is that the fusion of two totality states of affairs – in this case involving first being a raven and second being a black raven – will give us the needed truthmaker. 5. But the next passage that Keller quotes involves a mistake on my part: States of affairs are ampliative, that is, they embed their subjects in something further. But if W [the whole world] really is everything, then there is nothing further, not just no further further, not just no further particulars, but no further properties or relations or anything else. (p.123.)

But, Keller objects, “if W cannot be put into any state of affairs, then it cannot have any property and cannot stand in any relation. So, in particular, it cannot stand in the totalling relation to the property being a state of affairs.”

161

W is a particular, and it has intrinsic (non-relational) properties. So there is at least one state of affairs involving W, perhaps better written ‘w’. This is the giant structural property S that w instantiates, the structural property that renders the whole positive nature of the world. It seems clear that, by definition, nothing can be added to S, and so to w, except perhaps for some totality state of affairs. (That was what was right in what I said.) But is a totality state of affairs a metaphysical addition to the world ? I think not. These states of affairs are negative states of affairs – fortunately, I think, the only sort of negative state of affairs that we need to admit among our truthmakers. ‘There is w and it has property S’. That proposition is made true by the state of affairs of w’s having S. We then need a truthmaker that makes true the proposition ‘there is w and it has property S and that is all’’. So, I say, a totality state of affairs is needed. But it seems wrong to think of this truthmaker as an addition to the monadic state of affairs : w’s having S. If it really was an addition, then the world would be bigger. But a totality state of affairs does no more than set a limit. It limits the positives. I can see, of course, that this can be seen as raising a dilemma that is best resolved by giving up on totality states of affairs. But my feeling, as it seems was Russell’s feeling also, that it is better to accept these ‘closure’ truthmakers than to giving up on truthmakers at this point.

REFERENCES D.M. Armstrong, 2004, Truth and Truthmakers. Cambridge: Cambridge University Press.

Relational Truthmakers FRANÇOIS CLEMENTZ

Truthmaking theory is a theory (though, for obvious reasons, not a definition) of truth. More accurately, it is a theory about truth – and, thus, part of an overall theory of truth. It is not, at any rate, an ontological doctrine. That is, while it should be certainly regarded as an essential component of any realist account of the nature of truth, it does not seem to imply, just by itself, any particular thesis as what the most general features of reality might be. Nonetheless, one may wonder to what extent considering with full metaphysical seriousness the broad requirement that there should be something, generally, in virtue of which true propositions are true can help us to lay bare the fundamental structure of the world. The aim of this paper is to inquire into the nature of the contribution that the truthmaker requirement can be expected to make to the ontology of both relations and relational properties. Thus, I shall not examine such questions as whether every true proposition needs a truthmaker (Truthmaker Maximalism), or whether we should say that entity e is a truthmaker for p if and only if the existence of e necessitates p’s truth (Truthmaker Necessitarianism), although I am in fact inclined to endorse both views (with some qualification). At the same time, I shall be led to ask how the truthmaker principle relates to, or coheres with, two other widely accepted principles in contemporary metaphysics : viz. the « ontological free lunch » doctrine, as David Armstrong calls it (that is, the doctrine that the supervenient is no ontic addition that what it supervernes upon), and Plato’s socalled « causal criterion » of existence. Section I briefly considers different views on the nature of truthmakers. In sections II and III, I examine the connections between various traditional distinctions (intrinsic/extrinsic properties, genuine change/bogus change, internal/external relations) and I inquire, with the truthmaker question in mind, about the justifications of the familiar claim that relational properties should not be counted among genuine properties. Section IV hints at the possibility of some form of local asymetry (or « mismatch ») between the ontological status of relational properties and that of relations themselves. Finally, section V ex-

164 plores a different, more radical, line of thought, according to which we simply do not need relational properties, in addition to particularized relations. I –Truthmaking theory and metaphysics What should we actually expect from truthmaking theory, as far as the ontological question of what there is - the question, as Russell would have put it, of the « basic furniture of the world » - is concerned ? Every friend of realist metaphysics will certainly agree with D. Armstrong (2004, p. 20) that « in metaphysics we should primarily be concerned with truthmakers ». However, in Armstong’s own words, although « to ask the truthmaker question (…) is a promising way to regiment metaphysical inquiry » (p. 4), there is no royal road (ibid), no « « easy and automatic road » (p. 23), in such matters. For, as soon as we allow that a distinction should be made between the general theory of truthmaking, on the one hand, and the « particular answers that may be given to truthmaking questions » on the other hand (p. 4), there is no reason why « the piecemeal task of providing plausible truthmakers for important classes of truths » (p. 8) should turn out to be less difficult than the enterprise of metaphysics itself. No wonder, then, that it is a controversial issue, among the main contemporary advocates of truthmaking, « what sort – or sorts – of entities », in general, truthmakers are (Mulligan, Simons & Smith, 1984, p. 289). On one view, truthmakers are, basically, facts or states of affairs. On another view, they are particularized properties, moments, modes or tropes. And there might, of course, be still other views. To quote Armstrong once more (op. cit., p. 23), one philosopher’s truthmakers are just the sort of things he is «ready to quantify over ». According to Armstrong, the main advantage of the search for truthmakers over Quine’s own account of ontological commitment is that it puts the metaphysical implications of the subject terms of propositions and those of their predicates on an equal footing (p. 23). Now, suppose that this - along with other, more compelling, considerations - leads us to admit properties into our ontology. Again, there is no easy road in these matters. A first, well-known, reason for this is that there is no one-one correspondence between predicates and properties. A further, related, reason is that it is simply not true that every property is a genuine property. Of course, what goes for properties goes for relations as well. Again, « we should not expect that

165 there is any one-one or other neat correlation » between polyadic predicates and « the true and objective relations» (p. 51). Philosophers, however, do not only hold different views on which truthmakers there are. They also disagree as to what extent one should do justice to what may be regarded, perhaps, as the major insight behind the truthmaking theory : that ontology should free itself, at last, from the sway of logic and semantics. Thus, those who reject facts will argue that there is no reason why truthmakers – the true truthmakers, as it were – should be tailored after the logical form of truthbearers (and all the more so as we have no guarantee that there exists any such thing, in the end, as the logical form of most natural language sentences). Indeed, this, in their view, provides a further reason for refusing to regard truthmaking theory as a version of the so-called « correspondence » theory of truth, in the narrow sense, that is, of a theory which postulates the existence of some sort of isomorphism between the structure of truthmakers and that of truthbearers. Of course, both parties may well agree that there are facts, as long as a « fact » is no more than a true proposition. Actually, some of those who oppose factualism might even concede that we need to posit « facts » as the immediate truthmakers for true propositions, even though such ad hoc entities are, in effect, nothing but the ontological shadows cast upon the world by those propositions1. But they will insist that there are also ultimate truthmakers, whose structure do not necessarily mirror that of truthbearers − while friends of facts will contend that there is a deeper, more substantial, concept of a fact, which can more plausibly fulfil the role of a truthmaker. The main trouble with facts, according to the anti-factualist, is that they are utterly logic-dependent entities, whereas the main lesson that ought to be drawn from the recent « ontological turn » in philosophy is that we should not try to read off ontology from logic or semantics. The hardnosed factualist’s claim, on the other hand, is there are, on the contrary, logic-independent, both epistemological and metaphysical, reasons why we should admit facts or states of affairs stricto sensu into our ontology − and, indeed, give them some sort of ontological priority over other kinds of entities −, one such reason being that we need states of affairs in order to solve the perennially intringuing problem of how properties and relations connect with particulars.

1

See Mulligan, 2003

166 But it is hard to see, then, why the discussion should not extend to wouldbe constituents of facts such as « objects » or « properties ». For, after all, such ontological categories – especially properties considered either as universals or as particularized predicables − are no less logic-dependent that states of affairs themselves2. Note, however, that those same philosophers who show some reluctance in allowing properties, as traditionally conceived, among the basic constituents of the word, do not appear to extend this move to relations (though they might, of course, urge that we should conceive of relations as non-predicable relational tropes). Now, suppose that we have some good reasons altogether, beyond those provided by logic or semantics, to countenance properties in the end – on the ground, for instance, that they provide the best explanation of observed resemblances among particulars, or because any adequate account of causation ought to make sense of the common-sense intuition that things causally interact in virtue of their properties. And suppose further that we have no reason whatsoever, on the other hand, to deny the full-fledged « reality » of at least certain categories of relations. Even so, the question immediately arises whether we should allot any serious metaphysical standing to those hybrid, Janus-like entities : relational properties. Should we not we reject them, at least, as being, as it were, logic-overdependent ? II – Relational and extrinsic properties Most philosophers, today, seem to take it for granted that relational properties − such as being north of Marseille, being George's father, or just being a father − are not genuine properties. The point is usually made in connection with the issue of "genuine", or "real", change, as opposed to what Peter Geach called "mere Cambridge changes". In Geach's classic words, a Cambridge change is one which takes place whenever some predicate comes to be true of an object. But then it seems pretty obvious that every Cambridge change cannot be a genuine change − or else we would have to allow that Socrates changes « posthumously …every time a fresh schoolboy to admire him », or that the number five undergoes a genuine change whenever it ceases to be the number of somebody’s children (Geach, 1969, p. 65 ff). Now, as has been observed by Sydney Shoemaker as well as by many other philosophers, there is certainly "a broad sense of the word 'property' in which there is a property corresponding to any 2

Mulligan, op. cit., p.19

167 grammatical predicate" (Shoemaker, 1979, p. 331). But there is also a narrow (and philosophically more interesting) sense of 'property', which is "correlative with our usual sense of 'change'" (ibid). Just as there are mere Cambridge changes, then, there are mere Cambridge properties. And, as Geach own’s examples seem to suggest, relational properties, specifically, are « not genuine properties » (Shoemaker, ibid). My aim, in this section, is not so much to reject this widespread assumption as to ask why, and to what extent, we should accept it. I begin with a few preliminary remarks on the very concept of a relational property. The notion is usually defined by means – indeed, upon the model − of the logico-linguistic distinction between monadic and polyadic predicates. As every first-year student in philosophy should know, modern logic conceives of predicates used to express properties as the limiting case of nadic predicates : whereas a relation is the semantic value of some polyadic predicate, properties are what monadic predicates are supposed to denote. A typical definition of a relational property, then, is that it is monadic "on the surface" (Armstrong, 1997, p. 92), though it involves, or "harbours" (Kim, 1993, p. 163), a relation. Now, natural languages certainly contain a host of predicates like being Tony Blair's first girl-friend, or being a widow, which contrast with polyadic predicates in that they are meant to be true of a single particular at a time, while explicitly or implicitly relating the individual in question to some further particular. But are there any genuine properties expressed by those monadic-albeit-relational predicates ? Or is a relational property just a « monadic reduction »3 of its purported bearer’s relation to some further object ? In all fairness, I should mention that the phrase « relational property », in a broader sense, could also refer to any feature an object is liable to possess in virtue of its relationship with one or several items in the word. Now it is, of course, notoriously difficult to decide how the words « in virtue of » should be understood in this context. However, the only relational properties I shall consider throughout this paper are the most basic ones : those which simply consist, for a particular object a, in having relation R to some further object b. Although they are sometimes called "impure" relational properties, by contrast with more abstract attributes such as being a sister, it might well be that « particularized » (or, as D. Lewis calls them, 3

A. Newman, 1992, p. 197

168 « haecceitic ») relational properties like being Paul's sister actually enjoy some kind of ontological priority. Moreover, I shall limit my examination to such properties as that of actually having relation R to b. In other words, I shall not consider dispositional properties. Why, then, should we exclude relational properties from the ranks of the respectable, « genuine » properties ? Surely, this bringing together of all relational properties with such gerrymandered attributes as being such as Jacques Derrida was a French philosopher and sugar is sweet or Goodman' s notorious grue should alert us right away. How could reasonably both kinds of properties be thus put in the same boat ? The standard view on this matter can be resisted – and, indeed, it has been resisted, to some extent, by some philosophers, such as Jaegwon Kim or Lawrence Lombard. In a recent paper (Weberman, 1999), David Weberman denies that a change in an object’s relational properties is always a « mere Cambridge change » and provides various counter-examples (to which I shall come back below) to the orthodox view. But, before defending his own position, he first reminds us of what seem to be the two main reasons in favour of the standard view. First, he remarks, there is the «well-entrenched, common-sense intuition » that changes solely in the relational properties of a thing, absent any change in its intrinsic properties, are not genuine changes. A further reason is that, were we to count relational changes among genuine changes, the latter « would seem to abound to the point of absurdity ». Thus, to take one of Kim’s examples, were Xanthippe to undergo a genuine change when she becomes a widow as a consequence of Socrates’ death, this would have to be true also of Xanthippe’s sister (since she becomes the sister of a widow), of her baker (as he becomes the baker of a widow), and so on, ad infinitum. Moreover, since everything bears a relation to anything else, recognizing the genuineness of relational change would mean, for instance, that I have changed, right now, just because a butterfly has landed on a tree halfway around the world, so that I have now acquired a new property : being so many miles from this particular butterfly (ibid). In reply to this, it could be urged that there is, in fact, nothing absurd in Mc Taggart’s claim that « if anything changes, then all other things change with it » (Mc Taggart, 1927, p. 11). Or, in order to make this response look slightly more palatable, one could try to accommodate both mere Cambridge changes and genuine changes by stipulating that things, in the first

169 case, just « change », while, in the second case, they really « alter » (Lombard, 1986, p. 94). But we should certainly agree with Weberman that « it offends our sense of economy and good common-sense » to suppose that any change at all could have taken place in me just because some butterfly has landed on a tree somewhere around the world. Another antiGeachean strategy would be to hold, along with Bradley and the British Idealists, that all relations are internal – the idea, presumably, being that all relational properties would thus qualify as intrinsic. But this suggestion should be opposed as well, both because it is « also saddled with the problem of infinite change » and because it seems to be committed to «a dubious essentialism whereby all of a thing’s properties are essential to it » (p. 142). Surely, then, we should reject the « Cambridge » view that all changes in relational properties are genuine changes. The orthodox (or « Geachean ») view, however, is that no relational change whatsoever is a genuine change. And, while the infinite change argument surely succeeds to refute the former contention, it does not carry, by itself, any weight against Weberman’s much more plausible claim that certain relational changes, at least, are indispensable. Perhaps, then, we ought to inquire further about the reasons which lie behind the « common-sense intuition » that, if a thing changes solely in its relations, it does not really change. The idea, presumably, is that, in such cases, the thing itself has not really changed, but only the things around it (p. 141). But why should it be so ? Or, to put what is basically the same question in somewhat different terms, why should all relational changes be counted as purely extrinsic changes − and all relational properties, therefore, as extrinsic properties ? Now I am, of course, fully aware that this might sound like a very odd question. Is not « extrinsic property », in common philosophical parlance, just another name for a relational property ? Granted, it will be said, the two words are not really synonymous. An extrinsic property, as most philosophers would now define that term, is one that an object could not possess unless one or more distinct objects exist somewhere in the world.4

4

Actually, this standard definition raises its own difficulties (see Kim, 1982; Lewis,1983 ; Lewis & Langton, 1998). But, for our present purpose, we can leave those complications aside. Note, however, that relations themselves may be described as « intrinsic » or « extrinsic » on this account : for instance, one way to describe the

170 But, even though the two words are not mere synonyms, and even though they do not even seem to be strictly coextensive either5, we can nevertheless regard them as being, in practice, roughly equivalent (as long, that is, that we stick to the above definition of « extrinsic »). I do agree and am, therefore, quite willing to accept that, by turning towards extrinsicality so defined, it is quite unlikely that we are going to learn much more about the reasons why we should discard relational properties : obviously, the answer cannot be just that they are merely extrinsic, both because all (or most) relational properties indeed trivially happen to be « extrinsic » by that definition and because, insofar as the two words, for all that, are not synonymous, one might well ask why the fact that a property is such as its instantiation by a particular entails the existence of some further object should imply that it is not a genuine property. However, « intrinsic » and « extrinsic » clearly have further connotations, more en rapport with their etymology, that the standard definition given above does not fully capture. As traditional philosophers would have understood it, the phrase « intrinsic property » conveys the idea (or the metaphor) of a property pertaining, some way or other, to the « inherent nature » of its bearer. An extrinsic property, by contrast, would be one that remains purely « external » − and, as it were, somewhat foreign − to the very nature of the things by which it is instantiated. Maybe this could provide us with a clue as to why relational properties are so widely thought to be mere Cambridge properties, or, failing this, with some basis upon which a principled criterion could be laid down in order to decide which of them, so-called Humean theory of causality is that it makes the causal relation « extrinsic to its pairs » (Lewis) 5

Think of the property of loneliness, introduced by Kim (1982) in the course of his attempt to define intrinsicality vs extrinsicality. Something is lonely, in that sense, if and only if no contingent object wholly distinct from it exists (otherwise, it is accompanied). Kim’s idea is that intrinsic properties are those properties whose exemplification is not incompatible with loneliness, whereas extrinsic properties, on the contrary, imply accompaniment. But then loneliness itself, by this account, is an extrinsic, though obviously not a relational, property. On the other hand, it might be held that some relational properties are not extrinsic according to the standard definition - as, for instance, being self-identical. Now, of course, it is contentious that self-identity is a genuine relation. But then what about being in love with oneself (or, if you believe that intentional relations are not genuine relations either, being self-destructive or having committed suicide) ?

171 at any rate, should be so classified. But then a first difficulty is how we are to understand the notoriously problematic idea of a thing’s « nature ». Is this supposed to refer to the so-called «essence » of that thing - which might explain why an intrinsic property is often confused with an essential property –, or do we intend it to comprise the whole set of its monadic properties, whether essential or accidental ? And then, of course, there is the question of how we should cash out the « internality/externality » metaphor itself. Should we say, for instance, that an extrinsic property is one that something could exemplify solely in virtue of the existence of something in the word exclusive of itself, rather than due to its own nature ? Or is the idea supposed to be, rather, that a property remains extrinsic to whatever item happens to instantiate it, as long as it has no bearing whatsoever on what that very item is « in itself » ? Both interpretations are certainly worth considering. Are all relational properties, then, « extrinsic » in anyone of these readings ? A natural suggestion, at this point, is that this in fact depends on whether the relation involved, in each particular case, is itself an internal or an external relation. III - Internal relations and genuine properties Now, there are, of course, many ways in which a relation might be said to be « internal ». For Russell (1924, p. 335), the idealist « axiom of internal relations » meant « primarily » that every relational proposition is logically equivalent to one or more subject-predicate propositions. But, elsewhere, Russell himself takes the axiom to claim that every relation « is grounded in the nature of the related terms » (1910, p 139). Sometimes, the phrase is also used to refer to those relations holding « within » an object, or a system, taken as whole – either between the whole and its parts, or between its parts, or constituents, themselves. Nonetheless, most philosophers, nowadays, would define an internal relation as one such that the existence of its terms entails that the relation holds6. In Armstrong’s words, a relation is internal if and only if « given just the terms of the relation, the relation between them is necessitated » (2004, p. 9), i.e. « if and only if it is impossible that the terms should exist and the relation not exist" (1997, p. 87). However, this standard definition turns out to be, itself, somewhat ambiguous. From even a brief survey of the literature, it appears that, by an « internal » relation, one could mean : either (i) a relation which is grounded 6

a definition one could find in Moore and Wittgenstein, although Mulligan (1991) traces it back to Höfler and Meinong

172 in, or supervenes upon, the monadic non-relational properties of its terms (Hawley, 1993, p. 213; Lewis & Langton, 1998, p. 129), or (ii) a relation which is essential to the identity of a least one of the terms (Moore, 1922; Campbell, 1990, p. 111). This is not to say, of course, that this first-blush classification is in any way exhaustive. A relation may have foundations in the intrinsic properties of its terms, while having a larger supervenience basis. Or it might supervene upon some further relation(s), which, in turn, will be grounded or not (and, if they are, might themselves supervene upon either relational or non relational properties). A dyadic relation may be internal − in either sense (i) or (ii) − to one of the terms, and external to the other. Moreover, there might well be also internal relations (according to the standard definition given above) which do not supervene upon the intrinsic properties of their terms, while they make no contribution to their identity either : numerical difference, arguably, provides a good example of that third type of internal relation. Still, grounded and constitutive relations appear to be the two main classes of internal relations. Yet, it should be obvious that (i) and (ii) are neither equivalent nor incompatible. As Moore famously remarked (Moore, 1922; Campbell, ibid), that a relation is anchored in the nature of its terms does not entail that it is essential to any one of them : this, in fact, depends on whether the underlying properties belong to its terms, themselves, essentially or contingently (provided, of course, your are willing to acknowledge the validity of this modal distinction). On the other hand, it seems that a relation might be essential at least to one of its relata and, yet, not supervene on any monadic foundation : this last category of strongly internal relations, I propose to call « (directly) constitutive ». (Of course, that there really are internal relations in this sense – which seems to be what the British Idealists had in mind when they claimed that all relations are internal − is open to dispute7). Finally, relations which are neither supervenient upon, nor constitutive of the nature of

7

Many philosophers would probably accept that there might well be relations of that kind – notably « structural relations - holding between such varieties of abstract, formal or intensional entities as space points, numbers, concepts or meanings, phenomenal colours, social institutions, artworks and so on. Whether there are constitutive relations beyond this abstract domain is much more controversial. A widespread argument to the effect that they are no such relations obtaining between concrete particulars is that this would violate Hume’s principle that there cannot be any kind of logical link between « distinct existences ».

173 their terms − nor entailed, in any other way, by their very existence −, I shall call purely external relations8. Now, although the currently standard definition of an internal relation as one that is entailed by its terms is ambiguous between (i) and (ii) insofar it is meant to cover both (as well as other) cases, it certainly makes room for (at least some) of the relevant distinctions. Suppose that a and b are, respectively, F and G, and that R (a, b) supervenes on both states of affairs – as it seems to be the case with so-called « comparative » relations, such as is taller than, is the same colour as, etc. According to Armstrong, such relations are necessitated by their terms. Keith Campbell, by contrast, holds that what he calls « external » (i. e. contingent) founded relations are not entailed by their terms (Campbell, 1990, p.112). But there is no real conflict here, since everything hinges, really, on what one takes the « terms » of the relations to be. Armstrong himself is eager to insist that for such relations "to fall under definition of internal relations, the particulars involved must be taken as having their non-relational properties. Resemblance, for instance, depends upon the properties of the resembling things. If we abstract away from the properties of particulars, then almost no relations between particulars are internal. What is needed is the thick as opposed to the thin particular (...)" (1997, p. 88). For Armstrong, then, "almost no relations" are internal to the relata taken as thin particulars. Why "almost no relations", rather that no relations at all ? Well, presumably, numerical difference - to say nothing of identity, which we should probably regard as a pseudo-relation - is internal to its terms qua thin particulars. The problem, however, is that this would seem to apply to « directly » constitutive relations as well. How are we, then, to account for this particular category of internal relations ? Actually, this might well be the sort of circumstance where raising the truthmaker question can be expected to throw light on some fine ontological distinctions. Given that an internal relation is such as it is necessi8

Compare with Campbell (1990, p. 112). While Campbell, in place of the usual twofold division between internal and external relations, provides a three-fold division (with relations being internal or external, depending on whether they are essential or not to the identity of the terms, and the latter dividing again into founded and unfounded relations), I offer a five-fold classification, making room (at least as a theoretical possibility) for both « constitutive », i.e. essential albeit unfounded, relations and « primitive » internal relations such as numerical diversity.

174 tated by its terms, it seems clear that the mereological sum of a and b, in that case, provides a sufficient truthmaker for the proposition « R (a,b) »9. But, as remarked by Armstrong, it does not always provide a minimal – let alone a unique minimal – truthmaker for that proposition. To quote Armstrong’s own examples, on the plausible assumption that numerical difference is an internal relation, Venus + Mars appear to be a minimal truthmaker − « indeed a unique minimal truthmaker » − for the truth . But consider, now, the truth , assuming that size is a monadic property. As Armstrong remarks, « Venus + Mars seems to be still a truthmaker for this truth, but it is not clear that it is a minimal truthmaker. For this truth, it seems that we do not need all the properties of the objects, or even all their non-relational properties. It is enough that Venus is a certain particular size, and that Mars is a certain particular size. These are states of affairs. The minimal truthmaker appears to be the mereological sum of these two states of affairs. The other properties of Venus and Mars seem irrelevant » ( 2004, p. 50). So far, so good. But what, then, of constitutive relations ? Armstrong’s own foreseeable hostility towards this particular category of relations now-withstanding10, I would suggest that we answer as follows. To say that R (a, b) is strongly internal to a, in that sense, is just to claim that a’s identity, for instance, depends on its relation to b, so that, were this relation not to hold, a would not be what it is (or, equivalently, a as such would not exist). Thus, although the mereological sum of a and b certainly provides a truthmaker for the proposition, it is clearly not a minimal truthmaker. What is a minimal truthmaker (indeed, as its stands, a unique minimal truthmaker) for this truth is just the existence of a : if a exists, then necessarily « R (a, b) » is true.11 Of course, if the holding of R is essential to the identity of both terms, then we have two minimal truthmak-

9

However, see Hochberg (1999, p 50-51) for an objection to this claim, as well as Armstrong recent reply to it in his 2004, p 104-105. 10 But see note 14 below 11 This, at first sight, might look paradoxical, as one would expect the truthmaker for any relational truth to include everyone of the terms involved. Yet, if F is an essential property of a (as, for instance, humanity is arguably an essential property of Socrates), one might presume that a is the truthmaker for « a is F » (cf Smith & Simon, this volume). But then, likewise, if a is essentially, constitutively related to b, though not the reverse, a should be the minimal truthmaker for « R(a,b) ».

175 ers, since the existence of any one of them, in this case, is enough to make « R (a ,b) » true – and so forth for three-terms, four-terms relations, etc12. If this is correct, it seems that the truthmaker requirement can help us to distinguish between the various ways in which so-called « internal » relations can be said to be necessitated by their terms. On the other hand, in the particular case of constitutive relations, one may well wonder what is, in the end, the metaphysical import of the truthmaker principle. For, once we have defined a internal relation, in general, as one the holding of which is « entailed » by its terms, we seem entitled to believe that the terms of any such relation will suffice for the truth that the relation obtains. But, then, there would also seem to be some reason to conclude that the relation is, as Armstrong would put it, no addition of being to the terms. According to Armstrong, « here we have cases where the form of the truth : < a has R to b >, fails to reflect the nature of reality », since in fact the truthmaker is « no more than a + b ». That is, « a somewhat deflationary truthmaker is thus being offered for this sort of truth » (2004, p. 50). Now, there are indeed some grounds for thinking that this deflationary (and, as it were, reductive) conclusion applies to the main varieties of internal relations. But, to a first approximation at least, things seem to be different as far as constitutive relations are concerned. For, whether or not there really are such relations, it remains that the concept of a (directly) constitutive relation would seem to imply some kind of ontological priority over the terms of the relation. One could make parallel remarks about the doctrine that supervenient entities are no addition to the entities upon which they supervene. Suppose that we avail ourselves of a (very broad) definition of supervenience according to which « entity Q supervenes upon entity P if and 12

Note that things are different, though, if R(a, b) is a « strongly internal » relation due to its flowing from some essential monadic properties of the terms. Let us pretend, for instance, that you believe in the existence of sense-data. Suppose, further, that you are currently presented with a brown patch standing next to a yellow patch in your visual field (let us call them B and Y). I take it that it is essential to any visual sense-datum that it is the colour it is. I shall also assume that relations such darker than between phenomenal colours as such are internal, necessary relations. Now, of course, it is wholly contingent that your are presently experiencing just those two sense-data : for example, B could have been there, though not Y. Nevertheless, given they are both present in your visual field, necessarily B is darker than Y. Yet, since B might have existed without Y, and vice-versa, neither the occurrence of B, by itself, nor that of Y entails the truth that one is darker than the other : it is only B + Y which can do the job

176 only if its impossible that P should exist and Q not exist, where P is possible » (Armstrong, 1997, p. 11). From the standard definition of an internal relation, it immediately follows that every such relation « supervenes on the existence of the terms" (ibid) – so that, according to a currently popular claim about supervenience, it enjoys no separate existence indeed, beyond that of the terms. Now, there is no doubt that « directly constitutive » relations, inasmuch as they are formally necessitated by their terms, can be said to supervene, in some sense, on their relata. Still, as far the metaphysics of relations is concerned, this purely formal approach seems to put things upside down. For, clearly, our intuition is that, while founded relations flow from the intrinsic properties of the their terms, the relata of « constitutive relations », on the contrary, have their identity determined by the existence and nature of the relation they have to each other. On the face of it, then, it would seem that the concept of supervenience does not always make the same, purportedly deflationary, contribution to the ontological inquiry that it is commonly supposed to make. (Unless, that is, we choose to see this as a reductio of the very idea of a « constitutive » relation)13. 13

Lack of space prevents me from exploring in full detail the implications, in this respect, of Armstrong’s recent change of mind about the instantion of universals. Indeed, Armstrong now holds with Douglas Baxter (2001) that what is involved in the instantiation of a property-universal by a particular is partial identity, and he argues (while Baxter himself denies) that, as a consequence, instantiation should be regarded as « a necessary connection between contingent beings » (Armstrong, 2004, p. 47). Relations, likewise, would seem to hold of necessity. At first sight, this new account of the « exemplification tie » might be thought to result in some blurring of the internal/external distinction. According to Armstrong, however, we can « still distinguish internal from external relations because the external relations demand states of affairs < that is, distinctive, genuinely relational, states of affairs> while the internal relations do not » (p. 52). Actually, I find it very difficult to see how, on the partial identity view of instantiation, the distinction in question can be sustained in this fashion. For suppose that relation R holds of particulars a and b : both a and b are contingent beings (and, likewise, the relation-universal R might have not existed); yet, according to the partial identity theorist, given that they do exist, R must hold of a and b. So, it looks as if all relations now conform to what Armstrong still takes the definition of internal relations to be. Furthermore, to the extent that a and b themselves would not have existed if they had not been so related (though close counterparts of both particulars might then have existed), all relations might be said to be partially constitutive of their terms (and vice versa). By the same token, it looks as if the terms (or say, the mereological sum of the terms) of any relation provide a sufficient truthmaker for the truth that the relation obtains. Maybe, then, we should say that all relations supervene on the (mereological sum of) their terms – unless we prefer to say that the terms and

177

Armed with these distinctions, we may now return to the question with which we began : are all relational properties extrinsic properties in the narrow, more demanding (though, admittedly, somewhat metaphorical) sense of that word ? At the first blush, it would seem that relational properties generated by purely external relations are, indeed, extrinsic in this sense. By the same token, those which are associated with strongly internal - and, above all, with « directly constitutive » - relations should be counted, on the contrary, as intrinsic : indeed, the latter are cases of what T. L.S. Sprigge (1988) calls « intrinsic connectedness ». Finally, relational properties associated with ordinary (i.e. contingent) founded relations - which seem to be « less rigorously anchored in their terms » (Campbell, 1990, p. 111) - would appear to stand somewhere between these two extremes. At this point, we should recall Weberman’s suggestion that, if all relations were internal, all relational changes would count as intrinsic changes - and all relational properties, therefore, as genuine properties. In the light of the distinctions I have just made, it might indeed look as if there were some sort of parallelism between the intrinsic/extrinsic distinction, as it applies to properties, and the internal/external distinction as it applies to relations. And now we might be tempted to think that this alone provides us with an adequate criterion for the genuineness of such or such class of relational properties. From the foregoing considerations, it should be clear, however, that there are in fact two (main) different senses in which a relation may be said to be « internal » (and presumably, therefore, in which a relational property may be said to be « intrinsic ») : either because it has some foundation in the monadic properties of its terms, or because it is, on the contrary, directly responsible, as it were, for the identity or quiddity of (at least one of) the relata. Now, given that our intuitive idea of a genuine property is that of something that really « makes a difference » to something, it would seem that, by contrast with relational properties corresponding to the latter kind of relation, those which are associated with the former should not be counted, in the end, among genuine properties. For, although the relation-universal involved (partly) supervene on each other : in either case, it is unclear to me how certain relations (deemed « external ») could be said to demand states of affairs of their own, while others would not be in that position. Suppose, however, that Armstrong is right on this score : my point is that this would make things appear even worse as far as the metaphysical bearing of both the theory of truthmakers and the concept of supervenience is concerned.

178 in such cases the fact that the relation obtains, or ceases to hold, certainly implies that some genuine change is taking place in (at least) one of the terms, this relational fact, far from making any difference by itself to any of the relata, appears to be purely consequential upon the underlying nonrelational change. Indeed, consider the main examples of so-called « mere Cambridge changes ». Many of them involve relational properties associated with purely external relations, as in Kim’s example of being fifty miles from a burning farm (Kim, 1993, p. 13) – or, at any rate, with properties which have been traditionally included in that category, like being the widow of Socrates, being married to Camilla Parker-Bowles, etc. (one might also think of Geach’s example of the butter rising in price, as opposed to the butter melting in the pan). Then we find Geach’s other famous example of Socrates who undergoes a mere Cambridge change every time a fresh schoolboy comes to admire him. This is a case of an intentional, unilateral relation with a foundation in one of the terms only – a relation, therefore, which remains purely external to the other term. A similar example, originally put forth by Aristotle, is that of the relation between the knower and the known. On this issue, indeed, the position of the Scholastics - or, say, of Aquinas and a few others - was that, whereas the « relation » (i.e. relational property) of being the knower of x is a « real relation », that of being known is nothing but a « relation of reason ». Finally, we find such cases as that of Socrates who becomes shorter than Thaetetus just because Thaetetus has grown in size : although (or since) the relation, this time, is bilateral, grounded in both relata, it can hold or cease to obtain in virtue of only one of them changing intrinsically, absent any non-relational change in the other relatum. The conclusion, thus far, is that mere Cambridge (relational) changes concern either grounded or purely external relations. On the other hand, consider the sort of examples that are put forward by Weberman in favour of his claim that certain relational changes should qualify as genuine changes. Most of them involve social relations and social objects (including artworks). Indeed, Weberman’s argument relies, to a large extent, upon the assumption that those very social or legal relations that many philosophers, following Locke, have been prone to regard as the paradigm of an external relation, are, in fact, what I call « directly constitutive » relations. No wonder, then, that « much of what the Geachean view regards as bogus change » constitute, according to him, « some kind of real

179 change » (Weberman,1999, p. 141). Thus, although it does not change intrinsically, i.e. physically, just because the Treasury Department has declared such bills obsolete (it is not as if it had a corner torn off), a dollarbill undergoes a genuine change when it becomes worthless. If, on the contrary, its monetary value increases, it is now endowed with causal powers that it did not have previously (it can buy more things). Similarly, given our legal system, becoming a father, a husband or a widow (even unknowingly), being convicted or being sworn in as President of the United States obviously makes a difference – which may, in turn, have important consequences - in how one is likely to regarded by others. Another example is that of a figure in a painting which comes to acquire different aesthetic and representational properties (and therefore, one presumes, may cause a distinctive emotion) as a result of its relations with other figures around it (p. 143-144). Generally speaking, Weberman’s claim is that « while relational change may be bogus in entities defined in terms of their physical properties, it is sometimes genuine in entities identified in terms of their emergent, relational properties » (p. 140). Hence the following « criterion » : a genuine relational change is one which involves relational properties that bear on the way an emergent entity is identified and individuated (p. 147). Now, I am not going to discuss in full detail any one of these examples, as I cannot engage here in the complex and vexed issue of the ontological status of social or cultural objects. Note, however, that there seems to be some degree of dissimilarity between Weberman’s examples, as well as some equivocation in his talk of « emergent entities » (p. 145). My own view is that a distinction should be drawn, somehow, between (i) cases where a thing’s relations to some futher thing(s) may be regarded, with some plausibility, as genuinely constitutive of a new, emergent entity (a « qua object », in Kit Fine’s useful terminology), (ii) cases where they should just be thought to give rise, in the most trivial way, to a new relational property (which might be considered, all the same, as a genuine property on other grounds, e.g. in virtue of bestowing new causal powers to the objects by which it is exemplified), and (iii) cases where they just make a difference in the way we conceive of those objects. As I see it, the dollar bill belongs to the first category (since it is an artefact which was, after all, designed from the start to fulfill a certain social role), whereas the figure in the painting clearly belongs to the second – the tricky issue concerning fatherhood, widowhood and the like. Weberman’s concept of an « emergent relational property » (ibid) it, itself, somewhat confused. This should be particularly obvious in the case of the figure in the painting. For,

180 even if we allow that the interrelations between the various figures in the painting might be constitutive of any one of them14, surely a distinction should be made between those relations, or relational properties, on the one hand, and the «emergent» property the figure acquires thereby (which may well be, in turn, a relational property, albeit of another sort : e.g. a dispositional property), on the other hand. To repeat, I do no wish to discuss these issues further. All what matters to me, in the present context, is that the sort of relations Weberman seems to have in mind are, in fact, strongly internal, indeed constitutive, relations. Actually, Weberman himself is emphatic that his assertion that some changes in relational properties are, in effect, genuine changes does not imply that they involve essential properties (p. 142). And, indeed, the kind of relational properties he considers are not, in general, essential to their terms qua physical objects. But they − or the underlying relations − are obviously essential to the the same items qua social, institutional or artistic « emergent » entities. Clearly, then, they belong to that category of strongly internal relations which properly deserve to be called « directly constitutive » relations. On the face of it, thus, it would seem that, were we to follow Weberman’s suggestion, we might discern some form of correspondence, indeed, between the « internal/external » distinction as applied to relations (or the « intrinsic/extrinsic » distinction, properly conceived and revisited), on the one hand, and the principled division that we would like to effect between genuine and non-genuine relational properties on the other hand. However, this is a result which we could achieve only at the cost of regarding constitutive relations as the only truly « internal » − indeed as the only fully real − relations. But this, surely, would be a most unwelcome conclusion. In the first place, it would be plainly at odds with the modern, post-Russellian, claim that external relations, on the contrary, are (the only) real relations a point to which I shall return at once. Furthermore, from the point of view of someone who, like Weberman, is eager to hold that relational properties are not, as a rule, bogus properties, it seems hardly promising. For, of all internal relations, constitutive relations are those whose actual existence is the most controversial : at best, they would seem to represent no more than a minority. According to Weberman, whereas the « Cambridge view» of change is obviously to broad, the Geachean view of the genuineness of a 14

A more telling example, in that regard, would be that of those institutional, contextual or historical relations that such philosophers as G. Dickie or J. Levinson have claimed to be in part constitutive of artworks qua artworks

181 change is most certainly too narrow. But Weberman’s own criterion for the genuineness of a relational change is, itself, much too restrictive. There is no need to say that « constitutive » relational properties do make a radical difference to their bearer, since they are supposed to be critical to their very identity. But why we should we require from every « real change » that is turns out to be that radical ? Here we should remember Weberman’s own remark (right or wrong) that, in the various examples he gives of a genuine relational change, the thing that changes thereby acquires new causal powers. The most plausible way of cashing the « genuine change » intuition, then, would seem to claim that a genuine change is one that makes some difference to the causal powers of the object(s) involved15. Indeed, to the extent that a thing’s identity is a matter of that thing’s essential causal powers, « constitutive » change, after all, just amounts to an extreme, limiting, case of a « genuine change » so defined. Yet, it might be objected that Plato’s causal criterion of existence is not, in fact, appropriate to relational properties. According to Stephen Mumford (1998, p 122), for example, it is « a criterion which applies only in the case of intrinsic (…) properties. It is arguable that relational properties, if they are properties at all, need bestow no causal powers on the particular in which they are instantiated ». Mumford’s argument is that there are relational properties – like, for instance, being fifty miles from a burning farm – such as their instantiation amounts to a mere Cambridge change, and that a criterion of property existence « need not rule out such (…) properties on the basis of their possession bestowing no causal power ». The main problem with this objection, in my view, is that it presupposes what is actually at stake and which is obviously not whether relational properties « exist » − if all we mean by that is that there are true propositions expressed (and, to that extent, objective « facts » described) by means of pseudo-monadic predicates such as « being fifty miles from a burning barn » −, but whether they are genuine properties. If so, the next question on our agenda is whether the genuine change criterion, once couched in causal terms, yields the same result when applied to relational properties and when applied to the underlying relations. 15

See, for example, Kim (1993, p. 37) : « ‘real changes’ seem to be just those that make a causal difference »

182 IV – The « mismatch » problem Let us consider relations first. Most philosophers would now agree with Russell that relations do not, as a rule, logically or conceptually reduce to properties. Still, contrary to Russell himself, many of them take it that some classes of relations – including, of course, so-called « comparative relations » - are grounded in the monadic properties of their relata. And they also usually take it for granted that such relations are, for that very reason, no ontic addition to their terms. In this respect, their position remains broadly within the lines of the Scholastic conception of a « real relation » – even though, of course, they do not conceive of relations themselves, as the Scholastic did, qua « relative accidents » inhering in their terms. One major assumption of the Scholastic view is that every « real relation » (as opposed to mere « relations of reason » ) depends on some "absolute accident" of the substance in which it is instantiated. Let us call this the foundation requirement. The main debate, then, focussed on whether real relations, so conceived, should be granted some kind of reality of their own (Henninger, 1989). This is where a second requirement came in, which you might indeed call the genuine change requirement. Though the issue was highly controversial in late Medieval philosophy, the prominent view was that relations enjoy only second-class reality. Relations are no doubt "real" (or, rather, some of them are, while others are only the work of the mind), but they have no reality of their own, over and above that of their foundations. On this issue, to repeat, many contemporary analytic philosophers would seem to be in agreement with the view of the Scholastics as far as founded relations are concerned. This is not to say, of course, that this view could not be resisted. Suppose that Socrates is 1m 80 and Thaetetus 1m 76. Should we say that the (objective) fact that Socrates is taller than Thaetetus reduces to the conjunction of these two separate, supposedly monadic, states of affairs ? It might be objected, in Russellian spirit, that it supervenes, instead, on the « fact » that 1m 80 is greater than 1m 76 (or that 1. 80 is more than 1. 76), and that this relation cannot be further reduced. Moreover, even if we leave this objection aside and accept that comparative relations, for instance, supervene on monadic foundations, to what extent does this imply that they are no ontic addition to those foundations ? Does it suffice to invoke Armstrong’s « ontological free lunch » principle : that the supervenient is no increase of being over the subvenient ? In my

183 view, there are two main reasons why relations, qua universals or types, cannot be reduced to monadic properties. A first reason is that relational propositions, as famously demonstrated by Russell, cannot, as a rule, be paraphrased in monadic terms. A further reason (Campbell, 1990, p. 99) is that many relations are, so to say, "multiply realizable". For Socrates to be taller than Thaetetus, it is sufficient that Socrates is 1m 80 and Thaetetus 1m 76; but the "same" relation would hold as well if Socrates were, say, 1m 78 and Thaetetus 1m 75 , etc. : in fact, the relation could have indefinitely many different instances. As long as we consider types of relations and properties, relations, therefore, do not reduce to monadic properties. Yet, it might still be held that some of them are token/token identical with non relational properties. Perhaps, this is how we should construe the « deflationary » view of internal relations : as claiming that, in every particular case, a founded relation is nothing over and above the monadic property-instances which underlie it in both terms. Again, one good reason for this sort of view is that, although grounded relations may well be possessed with some kind of causal role, they do not seem to exercise any causal role of their own. Certainly, we do appeal either to such relations, or to the corresponding relational properties, everytime we are looking for a causal explanation. Yet, there is every reason to believe that, in this case, those properties wich are, in the end, really efficacious are the underlying monadic properties. In other words, although supervenient relations may well turn out to be, in some sense, causally relevant, they do not, however, enjoy any kind of autonomous causal role – either because they are just taken to « program » the existence of some underlying, causally efficacious, property (Jackson & Pettit, 1988), or because their own causal role is merely supervenient (Kim, 1993). In both cases, the relations involved do not seem to make, just by themselves, any distinctive contribution to the causal powers of the terms, so that their instantiation, whenever it takes place, calls for no ontology beyond the occurrence of the underlying relations. Although I have argued elsewhere for that claim16, I must confess that it now seems to me to raise some difficulties. Here, however, I shall not consider those complications, both because of lack of space and because, even if founded relations turned out not be reducible, it would still be true that the relational property that a has, e.g., of being darker than b (just like b’s property of being clearer than a) is one that a can acquire or loose just in 16

see Clementz (2004 a; 2004 b)

184 virtue of b changing qualitatively, absent any intrinsic change in a itself. And, presumably, a property that is such as its exemplification or loss does not entail any real change « in » its own bearer should not qualify as a genuine property. Indeed, this is why Late Medieval philosophers, who thought of relations in terms of relational properties, held that they enjoy no separate existence. Note, however that, insofar as we do not thus conflate relations with relational properties, this would mean that we are confronted with a first case of asymmetry between the two sorts of entity, as far as genuineness is concerned. Be that as it may , let us, for simplicity, grant that internal (or, any rate, supervenient) relations can, from an ontological - though not from a conceptual - point of view, be regarded as token/token identical with the (unordered) pair of their monadic foundations17. Still, we are only half-way. Contrary to Bradley, on the one hand, and to Russell on the other hand, most contemporary philosophers would contend that there are both internal and external relations. Moreover, they would agree with Russell that only at the cost of being (purely) external a relation can qualify as fully real, i.e. as enjoying some form of distinctive existence. Now, in the present context, this widespread assumption raises two major difficulties. In the first place, it would seem to be at odds with the received opinion that relational properties - or, at any rate, properties generated by such external relations – can, by no means, be counted amongst genuine properties. Yet, one might have presumed that, if a relation is a genuine relation, the associated relational properties should qualify, themselves, as genuine. Second, it is arguably not true that all external relations should be be regarded as « fully real » (think only of such convention-based relations as being x’s godfather, not to mention Kim’s example of standing so many miles from a burning farm). For, even if were to grant that founded relations cannot qualify as fully real relations, so that « failure of supervenience » might indeed be regarded as a necessary condition for a relation to enjoy first-class reality, it obviously does not follow (pace Kim, 1993, p. 17

Note that they would better be, from the point of view of the metaphysical relevance of the search for truthmakers. For, as we have seen, if some relation R between a and b flows from their intrinsic properties F and G, then clearly the mereological sum a + b (or, rather, that of the states of affair that a is F and that b is G) is a minimal truthmaker for the proposition « R (a,b) ». Were the relation turn out not to be reducible to this mereological sum, this would immediately cast a doubt on the capacity of the « truthmaker question » to throw any genuine light on the ontology of relations

185 162) that it provides a sufficient condition in this respect. But what further condition, then, shoud be required? At the first blush, the solution appears to lie with the distinction that most philosophers today (following Leibniz and Hume) would be willing to make between those relations which flow from the nature of their terms – to the extent that they might be said to hold between the properties instantiated on both sides, rather than between the objects instantiating them - and those, on the other hand, which deserve to be called « relations of connexion » insofar as they, on the contrary, do genuinely relate their terms. But now, what could a « genuinely relating » relation be, if not one the exemplification or disappeareance of which constitutes a genuine change ? And, again, unless we question-beggingly define a genuine change as one involving genuine properties or relations, it seems that we are led to the familiar conclusion that this is a matter of some difference made to the causal powers of the objets involved. Now, suppose this criterion can help us to draw the relevant distinction between those external relations which should be regarded as genuine relations and those which cannot. Obviously, we would like to see the same « genuine change » criterion (as interpreted in causal terms) apply to properties – including relational properties - and to relations altogether. Yet, on the prima facie natural assumption that there should be some narrow connection between the genuineness of some given relation and that of the associated relational properties, this supposition seems hardly consistent with our former suggestion that relational properties connected with purely external relations should be regarded as extrinsic properties. This, however, drives us back to the former difficulty. An obvious way out would be to argue that all or most supposedly « external » relations have monadic foundations after all. Traditionally, once we have put aside those relations which are based merely on social conventions, causal and spatio-temporal relations appear to be the prima facie most plausible candidates, among external relations, to be elevated to the rank of genuine relations. According to Campbell (1990), however, even these two apparently refractory classes of relation do, in the end, supervene upon monadic foundations. In my view, the prospects for such an extension of the "foundationist program" to all relations look rather dim. Against Campbell, I have argued (Clementz, 2004 a) that causal relations do not strictly supervene upon the monadic properties of their terms : in Scotist vein, one could say that relations in the category of action and passion are extrinsically, rather than intrinsically, « advenient ». However, I

186 shall not try to defend this claim here. But note that things, this time, are as they should be. Maybe we should deny - indeed, maybe it does not even make sense to say - that causal relations can figure, themselves, in causal relations or have causal power. Nonetheless, they obviously result in genuine changes - changes in causally efficacious properties18. We should have no qualms, therefore, in counting them among genuine relations. But what, say, of spatial relations ? In the first place, I shall take it that at least some such relations between medium-sized material objects, like being fifty miles north from, have no foundation whatsoever in the monadic properties of their terms. Of course, they might supervene on some further relations - like, for instance, the relations between the places they are "at". Now, maybe those underlying relations are internal – either grounded in, or constitutive of, their terms. Or maybe not. And, in any case, we would still have to give an account of the « at » relation along the lines of the foundationalist program (in his 1990, Campbell provided such an account, arguing that the « at » relation is an unilateral grounded relation, with no foundation in the objects or tropes involved. But I understand that he has now renounced this idea19). Spatio-temporal relations, in general, might also supervene upon, and thus reduce to, causal relations. Or they might not. These are difficult questions, the answer to which lies (or so I would argue) to a large extent in the hand of physics. Be that as it may, the problem is this. Suppose that at least certain spatial relations between ordinary individual objects are genuine relations, while having no intrinsic foundation in their terms. Assuming that such relations genuinely relate the individuals in question, one is, prima facie, tempted (pace Weberman, op. cit., p. 147) to count the corresponding relational properties as, themselves, genuine properties. But how could it be so, in view of the genuine change criterion for both relations and properties ? Perhaps we should allow that some spatio-temporal relations are causally efficacious, in the sense that they make a contribution to the causal powers of the objects involved : think, for example, of the role played by distance in Newton's inverse square law. Maybe, then, we should also allow that the associated relational properties are such as their acquisition or loss make a causal difference to their bearers and are, to that extent, genuine properties. However, I doubt that this would apply to Kim' s example of being fifty miles from a burning farm : 18

Without the causal relation « nothing else could have causal power ! It makes a difference » (Armstrong, 1997, p. 42). 19 See K. Campbell, 2004, p 365-366

187 presumably, the intuition behind this kind of example is that such « properties » have no causal import whatever (compare with being just ten feet from a burning farm !). What should we say, then ? That the underlying relations are not genuine relations after all (although they could be real in a weaker, derivative, sense : remember that they might supervene on further relations) ? Or what else ? Let us call this the mismatch problem. At first sight, it might look as if there were only two ways out of this predicament. First, we could drop the genuine change requirement as far as relations themselves are concerned. Or, second, we might renounce the idea that to every genuine relation should correspond one or several genuine relational properties. In other words, perhaps we should be ready to accept that sometimes the relational properties induced by the occurrence of a genuine relation are not themselves genuine properties. Now, the first solution should certainly not be discarded from the outset. After all, it might be alleged, we should not make ourselves guilty of what was, probably, the most damaging error of the whole Aristotelian and Scholastic tradition : namely, that of conceiving of relations in terms of relational properties. Thanks God (or Frege, or Russell), modern logic has rid us from this age-old prejudice ! But why, then, should relations themselves be submitted to a constraint – the genuine change requirement – which, perhaps, only made sense for the Scholastics’ « relative accidents » insofar as they were supposed to inhere « in » some substance ? There is, in my view, something to this suggestion that imposing such a constraint upon relations might involve some sort of categorymistake. On the other hand, were we to forsake the genuine change requirement, we would seem to be left with no clear criterion of whether a given class of relations is the plainly real variety, since mere absence of supervenience, as we have just seen, does not seem to provide a sufficient condition. In the end, then, I would rather favour the second solution. In order to illustrate its plausibility, let us suppose that some spatial relation R holds of two material bodies a and b - a distance relation, say, or a is to the left of b. I have no doubt that R should be regarded as a real, genuine, relation, either in its own right or because it supervenes on the relation between a and b’s respective locations (suppose, for instance, that, the latter relation is partly constitutive of the regions of space involved). Still, it is quite conceivable that, in most cases, the fact that R holds of a and b, or that it

188 ceases to hold, does not induce any real change indeed, as far as a and b themselves are concerned20. But, if so, we should allow that, although R itself is a genuine relation, the property that a, say, « has » of being at such or such distance from b is not a genuine property. This does not mean, of course, that it would not be true to say that a has the « property » of having R to b, but only that this is no more than a convenient – but somewhat misleading and, as Russell would have put it, « cumbrous»21 - way of asserting that R obtains (in that order) between a and b. Surely, there must be something in the world in virtue of which this proposition is true – some state of affairs, or some other kind of entity, whose existence necessitates that the proposition is true. It seems pretty obvious to me, however, that the needed truthmaker is the very same one that necessitates the truth of the proposition that modern logic would symbolize by means of the « R(a, b) » schema : namely the holding of the relation R itself between a and b. But note that this seems to be true of every proposition apparently attributing a relational property to some particular, quite independently of whether the « property » in question is, from an ontological point of view, a genuine property or not. And this, at first sight, would mean that the truthmaker requirement, at least in such cases, is insensitive to – and, therefore, cannot be expected to throw any light upon – the distinction between genuine and non-genuine relational properties. V - A (very moderate) plea for relational properties However, there might be a third, more radical solution to the various difficulties that we have encountered so far. This is, of course, to deny that there are any relational properties The current orthodoxy has it that, by subsuming both relations and (nonrelational) properties under the same generic status of being the semantic value of some n-adic predicate (or « function », or « unsaturated expression ») - so that the latter now appears to be only the limiting case of the former -, modern logic has put an end to the multi-secular temptation of reducing the polyadic to the monadic. Yet, one might ask whether this has not, at the same time, encouraged some confusion. From the perspective of 20

Although it might be objected that, from the point of view of current physics, no spatio-temporal relation could be without some (maybe minimal) causal consequence on the material bodies involved 21 B. Russsell, 1903, § 214, p. 222

189 modern logic’s formalism, one might as well define a relation as a « polyadic property » or a (non-relational) property as a one-place relation. No doubt this will do from a purely formal point of view. But, somehow, it is potentially misleading insofar as it seems to result in blurring the categorial distinction between properties and relations, since, in one case, it takes us back to the Scholastic practice of thinking of relations themselves in terms of extrinsic properties, whereas, in the other case, it would encourage the (in my view illusory) hope that, to the extent that the « combinatorial » essence of (particularized) relations can be expected to solve the problem of how a relation is connected with its terms, it might also solve the « exemplification tie » problem in the case of properties themselves (Mertz 1996; Lowe 2002). To put it otherwise, the Scholastics reduced relations to relational properties (« relative accidents »). As the story goes, post-Fregean logicians and philosophers have rejected this conflation. But why should we retain, then, both relations and relational properties ? Do we need relational properties after all ? Here is how, in his classic paper "External and internal relations", G.E Moore argues for the distinction he proposes to draw between relations and relational properties : « If A is the father of B, then what you assert of A when you say he is so is a relational property - namely the property of being the father of B; and it is quite clear that this property is not itself a relation, in the same fundamental sense in which the relation of fatherhood is so; and also that, if C is a different child from B, the property of being the father of C is a different relational property from that of being the father of B, although there is only one relation, that of fatherhood, from which both are derived » (Moore, 1922, pp. 281-282).

One might find in this passage, it would seem, two different arguments in favour of the distinction. First : to say of A that he has the relational property being the father of B is to make an assertion about A. Second : it is one thing to be B' s father, and it is quite another thing, altogether, to be the father of A, even though the same relation (i.e. fatherhood) is involved in both cases. Now, as far as the first argument is concerned, it is beyond dispute that we use such predicates as « being the father of B » to make an assertion about individuals. But then, of course, the question is whether this involves more than a purely semantic or pragmatic device in order to focus on one of the terms of the relation involved. Just by itself, it does not show that there really are relational properties which can serve as an onto-

190 logical ground for such predicates. If so, the whole burden of Moore's demonstration would seem to rest on the second argument. The idea, now, is that the relation of fatherhood, just by itself, cannot account for the difference between being the father of B and being the father of C. It should be noticed that this second argument is entirely different from the first and, moreover, that they appear to lead to different conclusions. Being a father, for instance, is involved in assertions about A no less than being the father of B - so that, by the first account, it should be considered as a relational property. Yet, it is no less an universal than fathering or fatherhood; so that, by the second account, it should be counted as a relation, rather than as relational property. In fact, among writers who defend universals, it is usual to countenance relational properties both « of the generalized or particularized sorts » (Kim, 1993, p. 165). Moreover, Armstrong (1997, p. 92-93) suggests that we should regard the latter as just « impure relational properties » since, strictly speaking, they are not universals, although they are « predicable of many » (just think of being the brother of B, which might be exemplified by several people). So, not only the first argument does it lead many writers to regard generalized relational predicates as denoting bona fide properties, but some of them would go so far as to regard those properties as the only « pure » relational properties, since they are « pure universals » by contrast with « mixed universals ». But what, now, about the second argument taken by itself ? To be sure, it is one thing to be the father of Cain, and it is quite another thing to be the father of Abel. But does it mean that we really need relational properties in order to account for the difference ? Note first that the problem raised by Moore seems to make sense only on the assumption that relations as such are universals (conceived in a realist way). Thus, the difficulty should not retains us if we adopt a particularist view - that is : a trope theory - of both properties and relations instead. Admittedly, they are different versions of the trope theory. However, in all of them, relations exist only as particularized, so that Moore's problem does not arise. Now, let us see what happens if we countenance universals. Here again we have two versions at least : Platonism and Aristotelian realism (« immanent » universals). Further, and more importantly for our present purpose, among universalists we find those philosophers (like Russell 1911, or Mertz and Lowe) who are willing to countenance both universals and particularized properties or relations, and those who, on the contrary,

191 either reject property instances in general (e.g. Armstrong, 1978, pp. 7071) or hold that relations, at least, « have no instances » (Russell 1903, § 55), so that « there are no such entities at all as particularized relations » (Russell, 1973, p. 48). Clearly, the former philosophers should have no more difficulties than trope theorists to pay justice to the intuition, elicited by Moore, that being A’s father and being B’s father are two distinct circumstances. As for those universalists who consider that the very idea of a relation-instance is inconsistent with the principle according to which a relation is one and the same throughout the different states of affairs in which it happens to be instantiated, they will inded insist that, at best, it is only those (token) states of affairs themselves which might be called « particularized relations ». Nevertheless, it seems to me that, in both versions, the difference between A’s having R to B and A’s having R to C (where R is the same relation simpliciter) is sufficiently accounted for by the difference between B and C (or, equivalenty, in terms of the difference between the two states of affairs) : there is no need to introduce relational properties to this effect. If so, Moore's second argument fails too. Here it might be interjected that this deflationary strategy, even though it could be applied to « impure », haecceitic, relational properties, like being’s A’s father, is wholly ineffective as far as « pure » relational properties such as being the father of a son (or just being a father) are concerned. For the latter, and only the latter, are universals properly speaking - indeed, Kim (1993, p. 163) seems to suggest that they have better credentials to qualify as genuine properties, as opposed to mere relations in disguise and, surely, no universal could be identical with a particularized property or relation. However, I do not take this to be a cause of embarrassment for the universalist. As Armstrong himself puts it (1997, p .92), « if a has R to b, and b is a G, then a has the relational property of having R to a G, with this property supervening upon the two states of affairs ». No doubt, « if R and G are both universals, then this relational property would appear to be an universal itself » (ibid). But, as I see it, this universal supervenes upon, and reduces to, the two state-of-affairs types which happen to be instantiated by the facts that a has R to b and that b is a G respectively. One might also object that this solution could not work for symmetric relations, which are usually taken to be identical with their converse. Or that it does not apply to what Kit Fine (2000) calls « neutral relations », i.e. to those relations for which, according to him, there does not even seem to be

192 a meaningful notion of converse since they cannot be properly said to hold of their relata in a certain order. Or that, were you to stick, rather, to the traditional doctrine according to which every relation has a converse, you might still wish to claim (following Williamson 1985) that, since the holding of a relation always entails that of its converse, and vice-versa, each of them supervenes upon the other and, thus, is identical to it. In all such cases, although « by the use of logicians », we have a relation and its converse, « philosophical commonsense » dictates (Armstrong, 1997, p. 90) that we have, in fact, a single relation, a single relational state of affairs. Indeed, we clearly have a single truthmaker. Yet, in most cases, we seem to have at least two different relational properties. But then, the objection goes, how could those two distinct properties both be identical to one and the same (particularized) relation, even though they jointly supervene upon it ? Now, in reply to this, it won’t do to argue that we only have, in fact, two different modes of presentation of one and the same entity – or, as Armstrong puts it in connection with symmetrical relations, that we have « no more than one state of affairs which language allows us to refer to in two different ways » (ibid). For, in most cases, to stand in a certain relation to b and to have the converse relation to a are really two different conditions, which may well have quite different causal consequences. However, I would maintain that all what we have is a single entity - namely the relation itself, which is identical to its converse and is, therefore, the only (immediate) truthmaker for the propositions expressing those conditions. Admittedly, the holding of that unique relation will, in may cases, make a (qualitatively as well as numerically) distinct difference to the causal powers of a and b. But this, in my view, is all what we mean – and, so to speak, « abbreviate » - when we attribute to a and b two different relational « properties » : there is no need to introduce a new category of entities over and above relations themselves22. 22

This, incidentally, should be read as expressing qualified agreement with a remark famously made by F. Ramsey (1990) in the course of his criticism of the particular/universal distinction. A crucial step in Ramsey’s argument is his attack against « complex universals » (a category of universals he took to include relational properties). Take any proposition of the form « aRb » : do we have, in addition to the proposition that R holds of a and b, a further proposition asserting that a has the « complex property » of having R to b, as well as a third one stating that b is having the property of having R (or its converse) to a ? Rightly enough, Ramsey argues that we have three descriptions of the same fact, so that there is, as he puts it, only one proposition. In that sense, « the theory of complex universals is responsible for an incomprehensible trinity, as senseless as that of theology » (p. 14). That Ramsey is most obviously right on

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There is no question, of course, that we need such predicates as having R to b or having R to a F. We are certainly justified, then, in referring to socalled « relational properties » either when we intend to focus on the consequences, for one of the terms of a given relation in particular, of standing in that relation – or, on the contrary, when we are looking for generality and wish to abstract from the individual nature of the terms of said relation in order to provide some law-like sort of explanation of why items thus related are due, or likely, to behave in a certain way. Relational properties, thus, are neither semantically nor pragmatically dispensable. Still, this does not imply that are more than mere façons de parler - that we should take at face value the apparent commitment to their existence made by ordinary or scientific discourse. Now, there are obviously two different ways in which we could try to dispense with relational properties. On the one hand, it could be held that they just reduce to the corresponding relations. After all, it might be said, we all knew from the start that the holding of any particular relation automatically generates – and, therefore, necessitates - that of two or more « relational properties ». But then those properties somehow trivially supervene upon the holding of the relation, so that, given the doctrine of « the ontological insignificance of the supervenient » (Armstrong, op.cit., p. 122), they do not amount to any real increase in being. This is not to say that they do not really exist. All what it means is that their existence is parasitic upon that of the underlying relations. This is why, although « there is a quite important distinction (…) to be made between relations and relational properties » -, the distinction is « not so important ontologically » (Armstrong, 1997, p. 91)23. On the other hand, it might also be argued that the latter should be eliminated straight away in favour of relations, on the ground that the notion of « relational property » is, in itthis score does not mean, however, that we should endorse his rejection of complex universals in general (or, a fortiori, his denial of the asymmetry between subject and predicate). 23

Note that the claim that relational properties reduce to relations should not raise any difficulty for a friend of particularism. Within an universalist framework, on the other hand, it cannot be literally true that relational properties supervene on relations themselves, i.e. qua universals, since distinct « impure » relational properties, at any rate, do not entail different relations (as illustrated by Moore’s example). The most we could say is that they supervene either on relation-instances or on particular states of affairs (see Armstrong, 1997, pp. 92-93; if the relation is internal, it will itself supervene on certain monadic properties, so that «a sort of double supervenience occurs »).

194 self, metaphysically incoherent and in danger of taking us back to the Scholastics’ more or less insuperable difficulty of having to reconcile the esse-in of the so-called « relative accidents » with their esse-ad. I shall not try to adjudicate between these alternatives, both because it is well-known that the distinction between reduction and elimination is, to a large extent, a matter of degree, and because the question whether the notion of a relational property should indeed be condemned as incoherent is clearly one the answer to which would require a thorough discussion of the very concept of a property, in general, which obviously lies far beyond the scope of this paper. In both cases, anyway, the conclusion is that we do need to countenance anything as a distinctive ontological category of relational properties, in addition to relations properly so called. This, however, is not quite the end of the story. For the question from which we started remains : whether, and to what extent, all relational properties are bogus properties. Two possibilities, again, seem to be on offer. First, we might argue that, since no relational property whatsoever enjoys any existence of its own, no such property is a genuine property. But this would be at odds with our former admission that some changes in relational properties - even though they are not exactly those that Weberman has in mind - are genuine changes, while others do not make any substantial difference to the objects involved. On the other hand, it might be held that whether or not relational properties are « genuine » properties depends, in fact, upon whether the underlying relations are, themselves, genuine relations. But then we face what I have called the « mismatch » problem : namely, that some relational properties, although they supervene on genuine relations, do not appear to be genuine properties. It should by now be clear that the familiar claim that relational properties are not genuine properties is in danger of conflating two widely different theses. A first thesis is that no relational change whatever should count as a genuine change. The second thesis is that so-called « relational properties » are not properties in their own right, either because they reduce to the underlying relations or because the very idea of a relational property is intrinsically incoherent. As I see it, the first claim is plainly false : as it happens, it just amounts to the old Aristotelian or Scholastic ontological prejudice towards relations. The second claim, on the contrary, is largely true – indeed, it can be interpreted as expressing some form of intuition that the

195 Scholastic notion of « relative accident » does not really make sense in the end. The solution, or so it seems to me, is to acknowledge both that relational properties, as a matter of fact, either reduce to, or can be dispensed in favour of, the relations which trivially give rise to them, and that certain changes in relational properties are indeed genuine changes (so that we may say that, in one good sense, some relational properties are « genuine » properties). For all what the latter means is that some relational changes i.e. changes in relations - are genuine changes. However, in view of the « mismatch » problem, it does not seem to be true that, in order to count as a genuine change in relational properties, a relational change is merely to be such as it involves a genuine relation. This, as we have seen, is a necessary, but not a sufficient condition. What is further needed is that this change in a relation makes some genuine difference to at least one of the terms of the relation. This, arguably, is all what we (should) mean when we claim that some relational property is a genuine property. Again, it in no way implies that there really are relational properties, over and above relations themselves. To put it in a nutshell : the problem is not that relational properties are not genuine properties – since this depends, for the most part (although not entirely) on the nature of the relation involved -, but, rather, that they are not genuine properties.

REFERENCES Armstrong, D. 1978, Nominalism and Realism, Cambridge : Cambridge University Press ——1992, "Properties", in K. Mulligan (éd.), Language, Truth and Ontology, Dordrecht : Kluwer; reprinted in Mellor & Oliver 1997 ——1997, A World of States of Affairs, Cambridge : Cambridge University Press. ——2004, Truth and Truthmakers, Cambridge : Cambridge University Press. Baxter, D. 2001, «Instantiation as partial identity », Australasian Journal of

196 Philosophy, 79, p. 449-64 Campbell, K. 1990, Abstract Particulars, Oxford : Blackwell. ——2004, « La place des relations dans une théorie des tropes », in J.M. Monnoyer (ed.), La structure du monde : objets, propriétés, états de choses, Paris : Vrin Clementz, F. 2004 a, « Réalité des relations et relations causales », in J.M. Monnoyer (ed.), La structure du monde : objets, propriétés, états de choses, Paris : Vrin ——2004 b, « Remarques sur l’irréalité de l’art et la réalité des propriétés esthétiques », in J.P. Cometti (ed.), Les définitions de l’art, Bruxelles : La lettre volée Fine, K. 2000, « Neutral Relations », The Philosophical Review, vol. 109, n°1 Geach, P. 1969, God and the Soul, Ithaca : Cornell University Press Hawley, K. 1998, « Why Temporary Properties are not Relations Between Physical Objects and Times», Proceedings of the Aristotelian Society, vol. XCVIII Henninger, M. 1989, Relations : Medieval Theories 1250-1325, Oxford : Clarendon Press Hochberg, H. 1999, Complexes and Consciousness, Stockhom : Thales Kim, J. 1993, Supervenience and Mind, Cambridge : Cambridge University Press Lewis, D. & Langton, R. 1998, « How to Define ‘Intrinsic’ », Philosophy and Phenomenological Research, 58 ; reprinted in Lewis, D. 1999 Lewis D. 1999, Papers in Metaphysics and Epistemology, Cambridge : Cambridge University Press Lombard, L. 1986, Events : A Metaphysical Study, London : Routledge and Kegan Paul Lowe, J. 2002, « Properties, Modes and Universals », The Modern Schoolman, LXXIX McTaggart, J.M.E. 1927, The Nature of Existence, vol.II, Cambridge : Cambridge University Press

197 Mellor, D.H. & Oliver, A. 1997, Properties, Oxford : Oxford University Press Mertz, D. 1996, Moderate Realism and its Logic, New Haven and London : Yale University Press Moore, G.E. 1922, "External and Internal Relations", in Philosophical Studies, London : Routledge & Kegan Paul Mulligan, K. 1991 , « Colour, corners and complexity : Meinong and Wittgenstein on some internal relations », in W. Spohn & B. van Fraassen (eds), Existence and Explanation. Essays presented in Honor of Karel Lambert, Dordrecht : Kluwer ——1993, "Internal Relations", 1992 ANU Metaphysics Conference, Working Papers in Philosophy, Australian National University Mulligan, K, Simons, P. &. Smith, B. 1984, « Truth-Makers », Philosophy and Phenomenogical Research, vol. XLIV, n° 3 Mulligan, K. 2003, « From Truth to Truth-Making and Beyond» (draft) Mumford, S. 1998, Dispositions, Oxford : Clarendon Press Newman, A. 1992, The Physical Basis of Predication, Cambridge : Cambridge University Press Ramsey, F. 1925 « Universals », in Philosophical Papers, D.H. Mellor (ed.), Cambridge : Cambridge University Press Russell, B. 1903, The Principles of Mathematics, Cambridge : Cambridge University Press; ——1910, Philosophical Essays, London : Allen & Unwin ——1924, « Logical Atomism », in R. C. Marsh, Logic and Knowledge (1956), London : Allen & Unwin ——1973, Essays in Analysis (ed. D. Lackey), London : Allen & Unwin Shoemaker, S. 1979, « Identity, Properties and Causality », Midwest Studies in Philosophy, vol. IV, ——1980, "Causality and Properties", in Identity, Cause and Mind : Philosophical Essays, Cambridge : Cambridge University Press, 1984

198 Sprigge, T. L. S. 1998, « Intrinsic Connectedness », Proceedings of the Aristotelian Society, vol. LXXXVIII Weberman, D. 1999, «Cambridge Changes Revisited : Why Certain Relational Changes Are Indispensable », Dialectica, vol. 53, n° 2 Williamson, T., 1985, « Converse Relations », Philosophical Review, 94, pp. 249262

‘Is True’ and ‘Makes-True’: Two Predicates Without Properties HERBERT HOCHBERG University of Texas at Austin

Russell introduced the notion of an entity that “makes” a proposition or belief true into English speaking philosophy. He did so in connection with his early discussions of atomic facts and he also employed a variant of the phrasing by speaking of a truth ground as a “verifier.” The further variant, “truth-maker,” has become the phrase of choice, largely due to the paper by Mulligan, Simons and Smith. Recently Smith has sought to use the modal notion of 'necessity' to arrive at a definition of 'x makes p true' and, like D. M. Armstrong, at a “theory of truth-makers.” Such a theory is one that addresses the variety of questions that Russell took up explicitly in the first decades of the century — what entities are required as the ontological grounds for various kinds of truths. Leaving open the question of what truth “bearers” are — propositions, judgments, statements, mental contents, etc. — and simply speaking of propositions — the various kinds include atomic, negative, general, existential, identities, and so forth. Thus Russell’s arguments for negative and general facts and Plato’s discussion of negation in the Sophist come readily to mind. Smith, like Armstrong, seeks to avoid negative facts and, in so doing, rejects a so-called “maximalist” account of truth-makers: every truth requires a truth-maker. That statement itself has given rise to a further issue separating maximalist from minimalist theories of truth-makers. That issue, which divides Armstrong from Smith, is not of concern here. This paper focuses on three problems: (I) whether “makes true” and “is true” represent, respectively, a relation and a property’ (II) the complexity of facts and the so-called “Bradley problem”; (III) the recent resurrection of a supposedly formidable problem facing those who recognize facts.

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I

Truth-making

In setting out his view, Smith (1) takes there to be a “real tie” of necessitation — “Necessitation is to be conceived as a real tie spanning the divide between ontology and logic.” ; (2) defines a predicate —“necessitates”— in terms of a modal arrow — “DN

xNp := E!x & (E!x⇒ p)”;

(3) construes the arrow in terms of the familiar diamond—“where p ⇒ q abbreviates ¬ ◊(p &¬q)”; (4) understands the necessitation relation to hold between truth-bearers and truth-makers—“where p, q, …, are schematic letters standing in for particular judgments ...and other candidate bearers of truth.” (Smith, 1999, 276) These claims raise several problems. One concerns taking the existence of a and b to necessitate the diversity of a from b. And that, in turn, points to a problem regarding talk of necessitation. For (S1) '(a exists & b exists)’ does not logically entail (S2) ‘a ≠ b'—yet a’s existence and b’s existence supposedly necessitate the truth of both. Thus, in a familiar sense of “necessitates,” (S1) does not “necessitate”— logically entail—(S2), while the truth-maker for (S1) is the truth-maker for (S2). This points to a question concerning whether two logically independent statements can viably be said to have the same truth maker—a question we shall return to. Since Smith speaks of a necessitation relation, while treating 'necessitates' as a defined predicate, he problematically assumes that defined predicates stand for properties and relations. That general problem need not detain us here. What should, and will, detain us is Smith’s use of a primitive modal notion (be it expressed by the diamond or the arrow) as a key element of his ontological analysis of the grounds of truth. Moreover, as his use of 'entails' is not that of 'logically entails', Smith’s statement that “the relation of necessitation, which holds between an object x and a judgment p when the existence of x entails the truth of p” (1999, 274) is unclear. What is clear is that his purported definition of “necessitates” makes critical use of an unexplicated use of “entails” along with an unexplicated use of a modal operator— the diamond operator—and implicit “principles” of necessitation. Applied to the particular case of (S1) and (S2), he can only insist that

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the existence of “a and of b” necessitate the truth of both. Or, perhaps, that their existence necessitates the truth of (S1), which, in a special sense of “entails,” entails the truth, in turn, of (S2). The claim that a and b suffice to furnish the truth ground for 'a ≠ b’ or that their mereological sum a + b does will not do since one then presupposes that a is a proper part of the sum or, to put it differently, that a + b ≠ a. And, hence, that a≠b. There is no escaping the need to appeal to the diversity of a and b —as a basic fact.1 Armstrong has rejected this argument by suggesting that I mistakenly think that every predicate represents an attribute or relation. Hence, given (S2), we have the predicate ‘≠’ and, consequently, the relation of diversity. (S2) is then true in that a and b stand in the relation ≠. (Armstrong, 2004, 104105) But that is not what is at issue. Rather, what is at issue is the use of a primitive relational predicate—diversity (or identity). It is a matter of the need to account for one’s use of primitive terms, or aspects of the schema one employs for philosophical purposes. That is an old theme—running through the empiricist distinction between simple and complex ideas back to Plato’s concern with the five basic forms. This has nothing to do with the obviously weak claim that every predicate stands for a property. All one need do is note that, speaking in terms of a logically perspicuous symbolism, defined signs need not occur and, trivially, need not be taken as indicating or representing anything. Suppose, for example, in Tractarian fashion, one takes diversity to be indicated by the use of diverse names for diverse things and dispenses (or attempts to dispense) with both ‘≠’ and ‘=’. The point is not avoided. For it is then obvious that the semantic rule that diverse names are interpreted into diverse objects reflects the recognition of diversity. There is a more general point about mereological sums that is worth a brief digression. One basis for the rejection of facts is the idea that only mereological compounds or complexes are intelligible. Facts, seemingly requiring some non-mereological combinatory connection among constituents, are thus problematic, and, to some, unintelligible as entities. It is ironic is 1

This is not to say that ‘a=a’ expresses a fact—though it can be taken to show that a exists, since, given a semantic rule that requires that names name, and hence ‘(∃x)(x=a)’ —where ‘a’ is a name, ‘a=a’ is a consequence of ‘(x)(x=x)’, which is a logical truth. In terms of Kant’s distinction between pure and impure analytic a priori truths, the former would be an impure analytic a priori truth and the latter a pure one.

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that one who restricts complex entities to mereological sums implicitly distinguishes collections — lists if you will—of entities from mereological sums while, in effect, identifying the two. For such a one holds that for any collection (group, list, etc.) of entities there is a complex entity—the sum of the elements of the collection. Whether such a one then arbitrarily declares that the sum is “really” no more than, or is “supervenient on” the elements is irrelevant. Simply put such a “mereologist” has collections, that are not entities, and mereological wholes that are—be they “supervenient” or “no additions to being” or whatever. Such a view also fails to recognize the need to declare that elements form a further entity—a sum—that is not to be identified with a “list” of entities in that it is, itself, a further entity. For if it is not, the mereologist simply plays a game with complex signs. Taking '(E!x ⇒ p)' to be true in a relevant case, and thus employing some unexplicated modal concept, Smith takes a modal truth to connect x, or x's existence (that x exists), with p, a truth bearer of some kind—sentence, judgment, proposition, etc. Hence, Smith’s modal, "real tie spanning the divide" between ontology and logic, ties, not ontology and logic, but objects and facts to judgments, propositions, etc. and introduces modal facts of necessitation. He might not think so since he has introduced the arrow in terms of the diamond. Thus he might hold that all he does is make a negative claim involving a modality. Since, for him, true negations are not ontologically grounded but are true in virtue of the “absence” of facts, such problems are brushed aside. We will return to this theme. In any case, whether he recognizes such modal facts or not, he simply invokes definitional stipulations or axioms, following the lines of some modal calculus, governing his use of 'necessitates’ (whether in terms of the arrow or the diamond), since he cannot appeal to logical entailment. As this merely codifies his terminology, no real explication of 'necessitates' or 'makes-true' is offered, in spite of the chain of definitions he introduces linking the two expressions that reflect the “real tie” of necessitation. In some cases the truth-maker that necessitates a judgment (proposition, statement) being true will be a fact. Thus the appropriate sign replacing the variable 'x' in ‘E!x & E!x ⇒ p' will be a sign for a fact. This forces Smith to use a definite description of a fact or introduce purported "names" of facts and the possibilities that go along with them, as on Carnap's early

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1940s discussion (Hochberg, 2001, 4-12). What sort of definite description is open to him? Consider the case of 'Fa'. However he takes the definite description, which, assume, is the expression '∂', it must be such that 'E!∂ ⇒ p' holds. Thus, even with an unexplicated modal notion, where he does not have to show that 'E!∂' entails 'Fa', (which is reason enough to reject his view), he must at least make it plausible that he can speak of the relevant modal conditional being true. Thus he will have to “connect” ∂ to 'p'. But, then, for atomic sentences, and their negations, any viable connection he specifies will show that his notions of 'makes true' and 'necessitation' become irrelevant — all that is needed will fall out from the way one connects an atomic sentence to an atomic fact. This will become clear when such a connection is spelled out later. Questions about whether objects like a as well as F are "truth-makers" — for existential claims — in addition to “facts,” are of no real import, as '(∃x)(x=a)' will either be used to define 'E!', as it is used with names, or the latter will be taken as a primitive predicate of existence. The problems involved in the latter I ignore, for, in either case, the statements will be trivially true in a perspicuous schema where all primitive predicates and logically proper names (primitive zero level signs of the schema : 'a', 'b', etc.) will refer to or "name" properties (relations) and particulars, respectively. (Thus, as indicated earlier, if we limit ourselves to the primitive terms of a perspicuous schema, Armstrong is right to hold that I take every such predicate to represent a property or relation.) Smith’s sign 'p' will then simply be a place marker for an existential statement 'E!a' or '(∃x)(x=a)'. So the entailment will hold, and a will necessitate 'p' since the existential statement will be trivially true, being a consequence of the interpretation rules of the schema. Whether one then says that it is a, or a's existing, that is the relevant ground of truth, to shift from talk of truth-makers and necessitation, is of no import. In the case of 'a ≠ b' I have already argued that 'a + b' does not suffice. But, one should recall how Smith's and Armstrong's notions of necessitation permit them to speak of the existence of a and of b necessitating the truth of 'a ≠ b' without '(∃x)(x=a) & (∃x)(x=b)' entailing 'a ≠ b'. Of course, just as one rules out names that do not name one can rule out diverse names for the same object. Then, as “a exists” is a consequence of the interpretation rules, so will ‘a ≠ b’ be. The first rule does not force the use of the second and, in both cases, one must be aware of what is “pa-

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cked into” the rules. One does not escape ontological consequences by replacing axiomatic claims by semantic rules. Smith requires a conjunction of claims involving the existential operator so that in cases where 'E!∂' is false and we nevertheless have 'E!∂ ⇒ p' as true we will not be able to conclude '∂ necessitates p', a condition for taking ∂ as a truth-maker. Note one oddity of Smith's presentation. 'p' is a schematic letter standing in for a particular judgment, but the appropriate expressions it stands in for are not of the kind 'the judgment that Fa', but, rather, 'Fa'. If it were otherwise the modal apparatus he employs would be inappropriate. But then it seems we deal more with propositions than with judgments, where the latter are taken in the sense of a judgment actually made by someone : Smith judging that a is diverse from b. And surely, the existence of a and of b, or even the diversity a ≠ b, is not such that the statement that they, or "it," exist necessitates Smith's judgment that a is diverse from b — as the latter, however construed, would “entail” that Smith made such a judgment and, apparently, that there are judgments, while the existence of a and b or of the fact of a being diverse from b do not. Thus it is not just the existence of a and of b that should be involved in his talk of necessitation but of judgments as well. Moreover, the same point arises if one thinks in terms of propositions rather than actual judgments. For, however, one uses 'necessary', since 'E!a’ follows from 'E!a', the conditional holding between "them" is necessary. Given the existence of a, the proposition that a exists is trivially "necessitated" by the existence of a. But then the proposition exists, whether anyone has explicitly made such a judgment or not. So what one should have is something on the order of a description of what will play the role of a truth-maker and another description of what will play the role of a truth-bearer. But then given both an entity, a potential “truth-maker,” (ι∏), and a truth, a “truth-bearer,” (ι Ø), we can capture the idea of truth-making and of what others have spoken of as an ontological ground of truth, by taking the former to be the truth-maker for the latter in the following sense, with 'is true' as a suitably introduced truth predicate: (TM) IF ‘E! (ι∏) & (ιØ) is true, THEN (ι ∏) makes (ιØ) true IFF ‘E! (ι∏)’ entails ‘(ιØ) is true’.

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Such a statement simply specifies or stipulates the use of the phrase '...makes ___true' in context. Smith defines such a relational predicate in a far more complex way, using the notion of necessitates. Yet (TM) captures, simply and less problematically, the idea involved by employing the standard use of 'entails' rather than 'necessitates' and modal concepts. (TM) is reminiscent of Carnap's attempt to use of reduction sentences to avoid the problems posed by dispositional predicates for the use of the standard conditional. Here it not only avoids problematic uses of 'necessitation', as that is used by Smith and Armstrong, but the need to recognize either propositional entities that are not apprehended or judgments that are never made as correlates of facts. For one can only speak of something making something else true if we have both "things" to start with — whether the truth bearers are sentences, propositions, thoughts, or judgments. The simple point is that if 'necessitates', as Smith uses it, is to have the force the term should have, the existence of something along with a conditional being necessary will necessitate the existence of something else — an appropriate truthbearer. The same is true for Armstrong's simpler use of 'necessitates'. Smith speaks of judgments in connection with the variable 'p' in 'x necessitates p', but he clearly requires a sentence to replace 'p' in a specific instance of 'E!x ⇒ p' and thus takes a sentence to represent a specific “judgment-content." Otherwise, as noted, the use of “⇒' is not straight-forward. But then he uses 'specific judgment' in the sense of 'specific proposition', and not, as he apparently intends, in the sense of a judgment actually made by someone. By contrast with Smith’s pattern, the use of (TM) does not force the acceptance of 'E! (ιØ)' — i.e. of propositional contents as entities — given 'E! (ι∏)’, which is as it should be if one does not accept a propositional entity for every fact that is a potential "truth-maker." Moreover, in his use of variables like 'p', that can be replaced by sentences like 'Fa', Smith implicitly makes use of a pattern that implicitly recognizes possibilities or situations. For he must connect 'Fa' to some "entity", where the latter's existence makes 'Fa' (or the proposition or content of a judgment it expresses) true. To say that it is a's being F is to return to a Carnap-type semantic (designation) rule for such a sentence while to introduce a definite description is to do something along the lines of the pattern :

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‘Fa’ is true ↔ Fa ↔ E! (ιp)(such that F and a are the sole constituents of p) with ‘p’ as a variable ranging over atomic facts. This latter pattern will do, I believe, for the analysis of “truth” in connection with atomic sentences or thoughts with such contents. But it is not Smith’s pattern. That pattern leads Smith to dismiss the issues surrounding true negations —including questions about negative facts as truth-makers. And that dismissal, in turn, has an odd consequence for his analysis. Consider '(∃x) ¬Fx'. It is an existential claim, so one would think it is true in virtue of the existence of something, and that cannot be a negative fact, like a's not being F, for there are no such things according to Smith. Likewise it cannot be the fact that something is not F or "lacks" F, for that would also introduce a negative fact. Yet, it cannot be simply a, or the existence of a or any other particular that is not F, that furnishes a truth-maker. That will not do, unless the particular is "essentially" not F. For, otherwise, one merely plays with words, as it is clearly the object’s not-being-F and not merely the object that is what is appealed to. So Smith has to return to the "lack" or "absence" of a truth-maker for '(∀x)Fx' as the truth ground of '¬(∃x)Fx'. Perhaps he feels the absence or “lack” of such a truth-maker permeates the universe as Pierre’s absence permeates Sartre’s café. Assume there is a fact, p, as a term of a purported truth-making relation, with objects of diverse kinds, π and ∏ as constituents of p. We might describe the fact as: (1) (ι p)(C(π, p) & C(∏, p)), where “C” is read “is a constituent of.” Alternatively, instead of thinking in terms of a constituent relation, we could consider two relations between “constituents” of a fact and the fact — being a term in the fact and being the predicable or attributable element in it. Let “T” and “A” represent, respectively, those relations. The fact might then be described as : the fact such that π is a (the) term in it and ∏ is the predicable in it, (2) (ι p)(T(π, p) & A(∏, p)).

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As they stand, there is no fundamental difference between (1) and (2). We could even make things more explicit be expressing the difference of type between π and ∏ in terms of the fact p being of a certain logical form — Øx. (1*) (ι p)(C(π, p) & C(∏, p) & C(Øx, p)) or (2*) (ιp)(T(π, p) & A(∏, p) & F(Øx, p)), with “F” for “is the logical form of” in (2*), would do that explicitly. Moreover, a significant difference emerges with the use of (1*) and (2*). In (1*) the logical form — of monadic exemplification — is taken as a constituent of the fact, while in (2*) it is taken to be the “form of the fact” and not a constituent term or predicable, along with π and ∏. Thus, (2*) reflects our not taking Øx to be a further constituent — a “connecting tie” or relation combining the two constituents, π and ∏ : it is simply the logical form of the fact. As objects are of a kind (logical form) that can be terms in facts but not attributes (relations) in facts, and attributes (relations) are attributable in facts as well as terms in “higher-order” facts, so facts are of a form. Suppose one objects that the Bradley type question can be raised by asking whether it is not also true that π is the term of the fact described in (2*). That is, consider: (3) T(π, (ι p)(T(π, p) & A(∏, p) & F(Øx, p))). Does not the truth of (3) require a further fact and thus start us on the infamous “regress” ? The answer, quite simply, is “no.” For, by Russell’s theory of descriptions, (3) simply amounts to: (3*) E! (ιp)(T(π, p) & A(∏, p) & F(Øx, p)), which unproblematically and simply states that the original fact exists. Interestingly enough, the same point can be made with the use of (1*), (2) and (1), though I have indicated why I prefer the pattern of (2*). That aside, we recover some basic themes. First, exemplification is not needed

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as a connecting relation in atomic facts. Second, facts are recognized as basic objects even though they have constituents. Third, worries about a predicative tie — leading Bradley to reject predication and Frege to the pattern built on the incompleteness of concepts (functions) — can be avoided without taking the first’s drastic measures or offering the second’s problematic pattern. Suppose we accept one classic solution to the problem of individuation and hold that an ordinary object must have a unique, individuating constituent — a constituent that grounds the individuation of the object and, unlike the predicable attribute, is neither a predicable nor is something that is common to diverse particulars, as characteristics are. One can either think in terms of facts like “Plato is wise” as having Plato, or such an individuating item of Plato, as the term and wisdom as the predicable. Or one can take Plato as a complex of such an item and “his” attributes. In the latter case we can, following Russell’s 1940 pattern, taking ordinary particulars as complexes of qualities, construe “ordinary” particulars as facts. For simplicity, let Plato be one of the red circles we began with, rather than a wise philosopher, and let R and S be the respective color and shape attributes. With π, as above, taken as the individuating haecceitas and “COMP” for Russell’s compresence relation, and not thinking being the term or attribute or form of a fact as logical relations, rather than thinking of a fact as a complex composed of terms or constituent parts, Plato would then be construed as: (4) (ι p)(T(π, p) & T(W, p) & T(S, p) & A(COMP, p) & F(Rµ(x, ∏1, ..., ∏n), p)), where “Rµ(x, ∏1, ..., ∏n)” represents the logical form of a fact whose attribute is a multi-grade relation, which COMP is, that takes an individuating “item” and predicables as terms. Alternatively, if one seeks to work out a view more in line with Russell’s rejection of such “individuators” or rejects the problem of individuation, Plato simply becomes : (5) (ι p)(T(W, p) & T(S, p) & A(COMP, p) & F(Rµ(∏1, ..., ∏n), p)). This fits with recognizing that Russell’s bundles of compresent qualities are really compresence facts, if one works out his view. I spoke of a recon-

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ciliation with Ramsey, since, looking at (4) we see that a traditional particular ground of individuation (a haecceitas) and universal attributes both become terms, while COMP is the only predicable — which fits with Ramsey’s appeal to a constituent of relation between a fact and elements of different types. But this also emphasizes that Ramsey essentially employs the very distinction he purportedly rejects. On either alternative, (4) or (5), standard predications, such as the statement that Plato is wise can now, in a sense, be said to be necessary, since the property can be said to be a constituent Plato. What that means, in terms of (4)), if it is carefully expressed, is that: (6) E ! (ι p) (A(CO, p) & T(W, p) & T(S, p) & T(π, p)) iff W((ι p) (T(W, p) & T(S, p) & A(CO, p) & T(π, p))) is a logical truth. That is, it follows from “the fact” that Plato exists that he is wise, given (4).2 That (4) expresses the analysis of the object Plato, as a fact with certain terms, is, of course, part of the story. In a crucial sense, however, what is stated is clearly not necessary — for standard predications have, in a way, been “replaced” by existential claims like “E ! (ιp) (A(CO, p) & T(W, p) & T(S, p) & T(π, p)).” And those are not, in any sense, “necessary” or logical truths (Hochberg, 2001, pp. 128-132). Actually what this reflects is a feature of “bundle” ontologies, whereby it is, in an imprecise sense, taken to be necessary that the bundle composed of W, S, etc. contains W. [One may also say that the truth ground for a statement of class membership is not a relation between an element and a class, but simply the class itself. That involves a particular ontological analysis of what a class “is.”] Such an analysis of particulars and their connection to properties allows one to dissolve the notorious Bradley-problem. For, suppose one raises that problem by suggesting, for example, that employing (4) forces the acknowledgment of an additional fact, the fact that W is a term of the fact (ι p) (T(W, p) & T(S, p) & A(CO, p) & T(π, p)) —i. e. the fact that grounds the truth of “T(W, (ιp) (T(W, p) & T(S, p) & A(CO, p) & T(π, p))).” The 2

Having noted how (5) and (4) differ, we can simply stay with (4).

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regress is blocked by noting that such a statement, by Russell’s theory of definite descriptions, simply reduces to the claim that the fact (ι p) (T(W, p) & T(S, p) & A(CO, p) & T(π, p)) exists — the fact that is the truth ground for “W(Plato), ” i. e. for “E ! (ι p) (T(W, p) & T(S, p) & A(CO, p) & T(π, p)). ” No further fact is forced upon one, and the same holds for “CO” and “A. ” This is one major point behind the present analysis of atomic facts and the specification of the truth grounds for atomic sentences.3 Taking particulars as facts of compresence, as in (i), we recognize an additional constituent that is compresent to “individuate” the ordinary particular. Such a “pure individuator” could be taken either as a special kind of property, or as Bradley’s “abominable bare particular,” or as a special individuating “item” — neither a property nor a particular. But there is an irony in the recognition of such things that the pattern of (i) brings out. One argues for there being such an item — dialectically as some put it, and, in so doing, employ principles like : diverse complex entities cannot share all constituents. Thus, consider the individuating item in, π. It is clear that while we may construe π as the individuating item in Plato — Plato, not π, was observed in Athens long ago. What one does is refer to π by referring to Plato — the individuating item of Plato. Yet, Plato is analyzed, as in (i), in terms of π. Thus in addition to seeing the utter triviality of the introduction of entities like π — as pure individuators whose task is to individuate — we see an odd feature of such purported entities. They are identified in terms of what they supposedly individuate. This is not a real paradox of identification, since one would have seen Plato, at the proper time, without having to know his “analysis,” as Moore might once have put it. We don’t identify Plato by means of π. Nevertheless, it is odd and there is nothing corresponding to that in the case of taking wisdom to be a universal property. π neither unites the properties of Plato, as a traditional substratum, nor even exemplifies them. It simply plays the role of individuating one ordinary object from another — a mere “marker” as it were or “factor of particularity.” That is why the problem of individuation or particularity becomes trivialized. It does not become that trivial on Armstrong’s view — 3

For the details see (Hochberg, 2001, 123-132).

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for Plato is not reduced to a bundle of properties as he retains a “factor of particularity.” The “factor of particularity” thus involves the use of particularity in a two-fold sense : it grounds the “fact” that Plato is a particular and it individuates Plato from other particulars. The two are suggestive of bundles comprising universals along with a “factor”, like π. On the view employing (i), particulars like Plato explicitly become facts or states of affairs — only “individuators” like π, if needed at all, remain basic particulars — basic entities that are neither facts nor universals.

II.

The Complexity and Simplicity of Facts

What has been arrived at is a somewhat uncomfortable metaphysical view, since facts, in some senses, are taken to be simple but to be entities that have component entities — qualities, relations and, possibly, individuating “markers.” It is often noted, in various contexts, that the notion of simplicity is not itself simple. With respect to facts that becomes clear in a quite precise sense. Facts, atomic facts, are simple in that (1) they do not have other facts as constituent terms ; (2) their analysis does not take them to be mereological compounds of their components ; (3) they are terms of the logical relations A, T and I. Yet, they are not here taken to be simple on the ground that they are not “determined” by the components itemized in their analysis. The latter point requires explanation. It has been argued that facts must be recognized since, given a non-symmetrical relation R and terms a and b, we cannot from the list of items R, a, b and, even adding the logical form ∏xy, distinguish Rab from Rba. But, if we recognize the need for including ordering entities in the analysis of relational facts, we can determine from an appropriate “list”— one that includes the account of order in the fact — whether Rab or Rba is indicated. That issue I cannot take up here, but simply note it and also note that one cannot viably argue, as Armstrong has tried to do, that Rab simply differs from Rba. One must give an account of relational order in such purported facts. Doing so then indicates a sense in which facts can be taken to be complexes. There are clearly other senses in which facts can be said to be complex.

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First, facts, standing as they do in the asymmetrical relations T and A can be said to have components — terms and attributes (relations). Second, the logical forms of facts differs in a significant way from the logical forms of particulars, attributes and relations. The first point is one that requires no elaboration, but the second does. Particulars and universals are of different logical kinds. Forget, for the moment, the present view construing particulars as bundles indicated by definite descriptions and take the familiar view of Russell’s logical atomism phase. That can be seen as employing the familiar notion of a particular as an entity that can only be a term of a fact, and not what is an attribute (where attribute includes relations). An attribute, by contrast, is what can be an attributed in a fact. If one recognizes higher order facts, as Russell did not in the logical atomism essays, then an attribute is what can also be a term of a higher order fact. Thus, particulars and attributes differ logically — in their logical forms. On the present analysis that difference is captured by basic particulars, if such there are, being entities that can only be terms in facts. Atomic facts, as well as ordinary particulars construed as facts, on the present analysis, are clearly “complex” in comparison to attributes and relations in that the latter are components of the former and are of logical forms, like φx and Πxy. They are also perspicuously represented by definite descriptions and not simple labels — predicates or “names.” Yet a category of atomic fact is recognized, and the apparatus of quantification and variables is employed regarding them. In that basic sense one takes there to be a fact of a form standing in the logical relations A and T to terms and attributes — and hence, in that sense, simple. It is as if the traditional notion of substance returns in the case of facts, but not as that which preserves identity through change or individuation. Rather it simply serves as the ground or basis of the unification of the terms, attribute and form into a fact. It thus reflects the basic purported difference from mereological sums, which supposedly are no more than their elements. Facts are clearly entities “over and above” their components. Yet they are completely determined (specified) by the latter. It can be noted that so taking facts reflects Russell’s 1913-14 notion that logical forms of atomic facts were not constituents of facts, as particulars, qualities and relations were taken to be, but the “way” the constituents were “put together.” (Russell, 1952, 52)

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III.

Resurrecting and Reburying the Great Truth-maker

In the last decades a recurrent attack on facts, and thus on truth-makers generally, continues to resurface, like a zombie from a bad film. The latest return of the so-called “great fact” paradox occurs in a recent book, Facing Facts. What is interesting about this most recent recurrence is that, for perhaps, the first time, it makes transparently clear how a trivial error can generate a mountain of pages. Before turning to that it is worth noting how the account of facts set out above simply brushes the purported problem aside.4 On the present view of facts we do not employ a denotation or designation relation for definite descriptions, as there is a reference or designation relation for primitive predicates and logically proper names. Hence there are no semantic (interpretation) rules for descriptions, taken independently. In place of such rules we have the three part biconditionals as semantic rules employing definite descriptions of atomic facts. So, consider two true atomic sentences, “Fa” and “Gb,’ that we can take as premises, aping the Great Fact argument. The argument, recall, with “S” and “T” being any true sentences can be put as: (I)

l. S 2. T 3. “S” designates S (designates the fact that-S, is made true by the fact S — below “S” is used without quotes to represent the fact).

We then supposedly can derive “‘S’ designates T” thus showing that any true sentence designates the same fact as any other true sentence. The argument assumes, first, (P) that we may substitute logically equivalent sentences and, second, (P*) we may substitute “coexten4

The line of argument is often traced back to Frege. It was noted by Gödel and employed by Quine, but the purported problem has become associated with D. Davidson’s name. That is due, in part, to his repeated use of it to support his rejection of facts as truth grounds. His simple rejection of facts, following C. I. Lewis, is based on their not having spatial-temporal location. (Davidson, 2001, 183)

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sive” singular terms. The argument is easily seen to purportedly apply to all candidates for truth-makers, and not just facts. Just consider the statements S and T to be the assertions that a certain truth-maker exists. Hence it is not merely an attack on facts but on the very idea of something being a truth ground for a truth bearer. Take S and T to be the two atomic sentences “Fa” and “Gb.” Consider the argument pattern: (1) Fa (2) Gb (3) “Fa” is true ↔ Fa ↔ the fact having a as a term, F as attribute and φx as form exists (4) “Gb” is true ↔ Gb ↔ the fact having b as a term, G as attribute and φx as form exists with (3) and (4) understood to be semantic rules providing both (I) the interpretation of subject-predicate juxtaposition and (II) the specification of the truth-makers for the sentences. They, in short, parallel what Smith attempts with his definitions and postulates regarding “necessitation.” We then have, simply and trivially, the consequence: (5) “Fa” is true ↔ Gb ↔ the fact having b as a term, G as attribute and φx as form exists, since we have (1) and (2), and hence “Fa ↔ Gb.” But (5) is completely harmless and trivial. We do not, and cannot, arrive at the conclusion that (5) is a semantic rule giving the truth ground for “Fa” or that “the fact having b as a term, G as attribute and φx as form = the fact having a as a term, F as attribute and φx as form.” That can be seen as the way the non-extensionality of contexts involving “designates,” linking sentences and names of sentences, is paralleled. In his book S. Neale (2001) repeats an earlier 1995 discussion, relying on additional rules about description operators, that takes a “proof” of a version of “the Great Fact” argument to be “valid” if descriptions are treated in accordance with Russell’s theory. The purported point of Neale’s book is to show that those who would deal with “facts” have

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work to do to provide an adequate semantics for the use of descriptions. But, it is his claim of validity for variants of the notorious “slingshot” employing Russell’s analysis that is of real interest. He sets out a complex variant and defense of Davidson’s argument that crucially relies on the use of abbreviations in context and which, if simply presented in unabbreviated form, is immediately seen to be absurd: (II)

1*. 2*. 3*. 4*.

S T “S” designates S “S” designates T.

premise premise premise

It is absurd since it uses replacement based on “material equivalence” to derive step (4*). The simplicity of Neale’s version of the argument is disguised by the introduction of “inference” principles and the purported justifications of those principles. The complexity of his presentation is due, in part, to the use of a variant of descriptions like “(ιx)(x = Socrates & S)” to guarantee that the description will be fulfilled, whether “S” is true or not. I will indicate what is involved below. That aspect of his discussion leads Neale to give two versions of the argument (170-74),5 but, at the crucial place in both of them, he replaces “S” by “T,” in a lengthy, roundabout discussion that, ultimately, is based on “S ↔ T” taken as a premise, on one variant, along with what plays the role of (3*). On the other variant the premises are those of (I), (hence the stronger “S & T”) with his version of (3*). I will simply deal with the second argument, which he calls a “complete connective proof.” Using his notation, with “φ” replacing “S”, “ψ” in place of “T” and the sign “ ” in front of a sentence to indicate a context for the sentence — a context like “ ‘S’ designates ...” or “the fact that-ψ = the fact that-...,” we have, with the last reading, “ ψ” and “ φ” read, respectively, as “the fact that-ψ = the fact that-ψ“ and “the fact that-ψ = the fact that-φ.“ Consider then: 5

What they amount to is easily seen in terms of versions that use class abstracts rather than descriptions. If you assume “ψ & φ” (take “ψ” and “φ” as true) then the class {x| x is F and ψ } = {x| x is F and φ } = {x| x is F}; if you assume “ψ ↔ φ” then you have {x| x is F and ψ } = {x| x is F and φ} = {x| x is F} when the materially equivalent statements are true and {x| x is F and ψ } = {x| x is F and φ} = Ø when they are false.

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lN. ψ ↔ φ 2N.  ψ

premise premise.

The premises specify the truth-functional equivalence of the statements and that one of the relevant facts is “self-identical.” We then get: 3N.   (a = (ι x)((x = a & ψ) v (x = b & ¬ψ))) from (2N) by the use of the principle of the substitution of logical equivalences. The more complex definite description (in place of the description in (I)) simply allows for taking the definite description to be uniquely satisfied whether “ψ” is true or false and has no real bearing on the point at issue. It is also understood that the descriptive phrase in the context is “just shorthand” for the expanded Russellian version that results in the apparent identity sentence being an existential statement.6 That existential statement is logically equivalent to “ψ.” Then we get to step (4N): 4N. (ι x)((x = a & ψ) v (x = b & ¬ψ)) = (ι x)((x = a & φ) v (x = b & ¬φ)) (4N) comes from (1N) and the use of the Russellian contextual definition for definite descriptions. Thus (4N) “is shorthand for”: (∃x)[(y)((y=a & ψ) v (y=b & ¬ψ)) ↔ y=x) & (∃z)((w)((w=a & φ) v (w=b & ¬φ)) ↔ w=z) & x=z)]. The next step is the crucial one. It takes us from (4N) and (3N) to 5N.  (a = (ι x)((x = a & φ) v (x = b & ¬ φ))), from which one goes directly, via the principle of substitution of logical equivalences, to 6

There are questions about such identity contexts that we bypass.

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6N.  φ Thus concludes one of Neale’s versions of the Great Fact argument, (Neale, 2001, 173-74). Regarding (5N), which follows by a “principle of substitution” that Neale employs — aping Davidson’s and Quine’s use of such a principle, Neale gives an extended justification of the use of the principle. The justification purportedly shows that an objection that can be raised to the move to step (9) in (I) is not viable. That objection, simply put, is that one gets nowhere if one uses expansions of the definite descriptive phrases. Hence the argument depends on the misleadingly employment of shorthand expressions. (Misleading in that all one really does is to replace one “materially” equivalent statement by another, thus really using a version of (II) that is hidden by the use of descriptions.) The problem is supposedly avoided since it is purportedly the case that the move to step (9) that Davidson employs is mirrored by a sequence of steps employing expansions of the definite descriptions along Russellian lines. But when we look at the principle of substitution Neale employs (2001, 160-61), and the claim that it is justified by there being a corresponding sequence of steps using expansions of the descriptions we find the casual shift into English expositions explaining that the key expressions with descriptions are “just shorthand for” (2001, 171) or “shorthand for” (2001, 173) expansions with existential quantifiers. What this covers over is that he must tacitly assume that the expansion of “(ι x)(x = Socrates & S) = (ι x)(x = Socrates)” in (8) is an “extensional sentence.” That means, simply put, that the expansion of “(ι x)(x = Socrates & S) = (ι x)(x = Socrates)” can be replaced by the expansion of “(ιx)(x = Socrates & T) = (ι x)(x = Socrates)”. It is most amazing, when one thinks about it, that an argument that carries through when one uses “just shorthand” is blocked when one uses “longhand.” Nowhere is a parallel argument in longhand offered (nor can one be without the reliance on replacement justified by material equivalence). All we really have is a version of (II). But what is of some interest is how the trick is performed. What happens is this. Recall the familiar idea that a statement Q is logically entailed by one P if and only if Q is true in every “model” in which P is. Thus, clearly,

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neglecting quotation marks, S and T do not logically entail each other. So, instead of using S ↔ T as a premise to construct a derivation, in a straightforward manner, explicitly appealing to that “equivalence” (or a statement containing T from one containing S), Neale reasons as follows. Given such a premise, S ↔ T, T will hold in every model in which S does. Thus, in any such model, the statement employing the description making use of S will have the same truth-value as the statement involving T. He thus, in his informal reasoning justifying his additional “rules,” shifts from the familiar concept of logical entailment by now appealing to T holding, where S does, in all models of a certain kind. The appropriate kind, we can call them equivalence or E-models, are those where S ↔ T holds (alternatively, where both S and T both do).7 Thus the taking of the biconditional as a premise serves to limit the models that need be considered in his metalinguistic reasoning to justify the introduction of rules governing descriptions, and it allows one to speak of a context, x = Socrates & T — being satisfied by anything, in such a model, that is satisfied by x = Socrates & S. This informal reasoning in the “meta-language” serves to allow him to avoid employing a straightforward and overt derivation, appealing to material equivalence (S ↔ T ), by a slippery use of the phrase “holding in a model.” Thus we find the key phrasings in his “reasoning” about his new rules — “if φ and ψ are both true” (Neale, 2001, 171) and “… whenever line (1) [φ ↔ ψ] is true” (2001, 174). What is additionally misleading is Neale’s reiterating the familiar points that Russell and Whitehead took the contexts of Principia to be truth-functional. (That is basically true and, in fact, was one reason for Russell’s developing his multiple relation analysis of intentional verbs.)8 Neale thinks that not understanding this feature of Principia is 7

The term “E-model,” introduced above, is not used by Neale. The “extensionality” of the first edition of Principia Mathematica raises questions. Given the use of functions and the taking of diverse functions of different order to have identical extensions, there is a sense in which Principia’s functions are not extensional and a sense in which they are, as the term “extensional” is used. There are also questions about functions themselves and the distinction between functions, on the one hand, and properties and relations (as constituents of atomic facts), on the other. Functions, i. e. propositional functions, are clearly not such constituents and, if one considers the ontological foundation on which Prin8

219

what lies behind the objection to the great fact argument that is based on the move from step (8) to (9) in (I). He thus fails to understand that the objection is based on an appeal to extensional contexts that permits the move from (3*) to (5*) in (II). That is, using his notation, what is objected to is the attempt to avoid openly acknowledging that one makes use of material equivalence, and hence basically employs the pattern (N): (N)

lN*. ψ ↔ φ 2N*.  ψ ∴ 3N*. φ

premise premise

For if that is done openly, there is no longer an air of “paradox” surrounding talk about facts. (N) is as pointless as (II). All that Neale does is disguise his appeal to material equivalence by relying on Emodels in his informal “reasoning” justifying the new rules he introduces.9 The issue is not about definite descriptions nor about “positing entities” like facts, nor even about providing a “semantics for definite descriptions” that function “outside the realm of extensional logic.” (Neale, 2001, 223) It is simply about purporting to offer an argument that neither depends on nor implicitly makes use of : p↔q . .⊃ . ƒ(p) ↔ ƒ(q). That was what motivated Davidson’s recourse to depending cipia rests to be composed of particulars, universal properties and universal relations formed into atomic facts, there are grounds for holding that they, along with propositions, disappear as “incomplete symbols.” 9

Neale’s citation, at various places, of Principia theorems involving descriptive phrases is distracting. The key point is that in Principia Whitehead and Russell note (deliberately not using “propositional” quantifiers): All the functions of propositions with which we shall be specially concerned will be truth-functions, i. e. we shall have p↔q . .⊃ . ƒ(p) ↔ ƒ(q). (1950, 115) Noting that, one can only wonder why Neale bothers with a lecture on Principia’s extensionality, emphasizing that it contains: (ι x) φx = (ι x) ψx . .⊃ : χ{(ι x) φx} ↔ χ{(ι x) ψx}.

220

only on logical equivalence and substitution of “identicals.” The simple point is that the purported substitutions and replacements are not what they purport to be.

REFERENCES Armstrong, D. M. 2004: Truth and Truthmakers, Cambridge. Hochberg, H. 2001: The Positivist and the Ontologist: Bergmann, Carnap and Logical Realism, Rodopi, Amsterdam. Neale, S. 2001: Facing Facts, Oxford. Russell, B. A. W. 1952: Our Knowledge of the External World, London. Smith, B. "Truth Maker Realism", Australasian Journal of Philosophy, 77 (3), 1999, 274–291. Whitehead, A. N. and Russell, B. A. W. 1950 : Principia Mathematica, vols. I, II. Cambridge.

Senex erit puer Truthmakers for tensed sentences FRÉDÉRIC NEF EHESS, Paris

According to truthmakers theory, if something is true, it is because it is made true by something else1. Such a theory must not be confused with correspondence theory of truth. The equivalence « A is made true by B iff A corresponds to B » is a way of identifying these two truth theories. We can doubt whether this equivalence is acceptable, because correspondence is compositional and truthmaker theory is not. I see similar difficulties with a singular statement like Emma exists I do not believe that « Emma » is a truthmaker of this statement. The existence of Emma is a fact, and the truthmaker of the statement is that fact. One of the few arguments in favor of the compositionality of truthmaker would be the following. If we accept that atomic elements like tropes constitute the underlying structure of reality, we may try to determine a strict correspondence between semantic and ontological structures (cf. F. Moltmann 2005), but the compositionality principles as applied to tropes is not self evident. Truthmaking is not identical either to the supervenience of the truth of B on the being of A. The very nature of the relation between A and B in truthmaking seems to be an open matter : essential dependance, necessita1

Je remercie Kevin Mulligan pour sa relecture extrêmement précieuse et ses corrections minutieuses. Merci aussi à Mark Sainsbury pour une seconde lecture et des remarques très utiles. J’ai profité plus que je ne saurais dire des remarques des participants, au premier rang desquels je souhaite distinguer David Armstrong. Merci aussi à Francis Wolff et aux membres du séminaire du lundi pour nos longues discussions sur le temps.

222 tion, projection (B. Smith 2004) ? All we can say without much fear of contradiction is that supervenience principle is weaker than truthmaker principle (TMP) : supervenience can be realized in many ways – through correspondence of course, but also probably through the minimal theory of truth. Moreover this idea of the multirelaisability of supervenience must not be confused with supervenience in the case of singular existential statements like « Emma exists ». Identification of truthmaking with supervenience of truth on being also raises a problem where what makes something true does not exist any longer or not yet. Think about so called negative facts. There are well known techniques for doing without them. Or think about modalized and tensed statements. The TMP is neutral : what makes something true is what makes it true – nothing is said about the being or non being of what makes something true. In itself the truthmaker principle rules out saying that the truthmaker of « Emma has not eaten an apple » is a negative fact expressed by this statement. In order to save ontological symmetry Marian David (2004) for example thinks we have in that case « an existing non-fact ». I therefore agree with S. Keller (2004) when he maintains that the TMP does not necessarely imply that a truthmaker exists (in the strong sense of existing). TMP (Simon Keller’s version) : What is true depends upon what exists With the following qualification : « it is important to distinguish Truthmaker (i.e. TMP) from the stronger thesis that for every truth there exists something that makes it true » (p. 85) The supervenience principle ( SP) on the other hand, is allergic to nonbeing : truth cannot supervene on non-being — we exclude the artificial solution of letting supervenience relates being with the being of non being. In that case non-being would be nothing but privation of being. At least at first sight, presentism is not compatible with TMP. If only present does exist, then a past statement is about nothing. Future statements bring their own difficulties, caused by the very nature of the future itself. Not only future things, according to presentism, don’t exist, but we don’t know how to fix the truth conditions of the future statements. Even if we believe we know these correct truth conditions, they don’t throw any light

223 on the nature of the future, because in fact the epistemic and semantic mechanism of truth ascription is somewhat obscure.

I.

Trutmakers predicaments : how to keep together supervenience of truth, ontological symmetry and asymmetry between past and future.

A truthmaker theory for tensed statements has to respect three principles and explain two basic facts : 1. TMP : something true is made true by something else (cf. above Keller’s version). 2. PSTB (principle of the supervenience of truth upon being) : truth supervenes upon being2. 3. POS (principle of ontological symmetry) : A relation has to tie existing beings3. 4. FF1 (first basic fact) : There is a strong epistemic asymmetry4 between past and future ; the past is necessary, whereas the future is possible. 5. FF2 (second basic fact) : What is future is epistemically not accessible. We cannot know with certainty what happen next (we can make suppositions, but it is not genuine knowledge). FF1 and FF2 seem to give some reason to adopt POS and POS is not compatible with the PSTB applied to past and future statements. PSTB is weak form of TMP. 2

J. Bigelow The Reality of Numbers, p. 132-133, cf. Lewis 1998, p. 206-207, for a readmission of the principle. 3 Armstrong implicitly adopts POS when he says : « can we admit such relations (between an existent and a non-existent) ? They are veru ugly additions to our ontology ! » (2004, p. 147). J. Bigelow gave this formulation of the POS : « Take a first supposition that in order to hold between two things, both of the two things will have to exist. Call this the principle that all relations are existence entailing » (1998, p. 37) 4 We admit epistemic asymmetry, because there is a general agreement on it, whereas the ontological nature of this asymmetry is debatable.

224 We have therefore to examine carefully : (i)

the relation between FF1 + FF2 and POS : do these two basic facts give reasons to give up POS ?

(ii)

the non compatibility between POS and PSTB

(iii)

the possible distinction between TMP and PSTB

In fact, only after having examined (i-iii) it is possible to decide if POS is compatible or not with TMP in the contexte of tensed statements (or, in other words, in the frame of temporal truthmaking). POS is explicitly adopted by Armstrong, Bigelow and Lewis. This principle seems obvious for relation of dependance (hence supervenience) and causality : if A depends on B, A and B must exist. Nothing existent depend on anything which is non-existent. If A is a cause of B, A and B must exist – if A does not exist, it cannot cause or be caused by anything existing. Presentists have maintained that POS excludes past and future. Only the present exists. The consequence is evidently that if only present exist there cannot be any truthmakers for past and future statements. But POS does not seem compatible with TMP, because if TMP can be applied only to the present, then it is not certain that it can be applied to anything, because the present is so vanishingly thin, that is, strictly speaking, present has no duration, it is only a border between two non-existents. Let us go back to our example (a) Emma has eaten an apple. The presentist would paraphrase (a) as (a’) : (a’) It was the case that Emma eats an apple (de dicto reading of the temporal operator ‘past’) or (a’’) It is the case that Emma has eaten an apple (de re reading of the operator ‘past’).

225 In both cases (a’) and (a’’) there is a relation between a past operator and a present utterance or between a presnt operator and a past utterance. To admit POS is not to exclude FF1 and FF2 – they have to be taken for granted – but only to refuse introducing contradiction in the language of representation. The presentist pretends to accept POS, but he has to give a specious purely epistemic interpretation of FF1 and FF2. These facts are interpreted as fact relative to our epistemic ability, and not necessarily as fact relative to the ontological structure of time. To apply TMP to tensed statements brings probably more difficulties than we usually think and more than Armstrong himself have supposed in the last chapter of Truth and Truthmakers, even if is favourite solution leads him to envisage that we should “modify the truthmaker theory”, too high an ontological cost, according to him.

II. How to solve the contradiction caused by the application of TMP to tensed statements ?

We have three solutions if we want to keep TMP : (i) to question FF15 and presentism, (ii) to limit the application of POS, (iii) to challenge presentism. A/ To question FF1. To accept four-dimensionalism (4Dism ) is calling in question FF1 and presentism. From the point of view of 4Dism FF1 is an illusion, a systematic error caused by negligence. However we may perhaps question FF1 without giving up presentism : the asymmetry would be then considered as 5

It seems not reasonable to rejetc FF2 : future is epistemically inaccessible and all the counterexamples we can oppose (scientific prediction, prophecy, clairvoyance…) are dubious for different reasons. Even in the strongest case, if I say truly, through second-sight, who is the winner of French 2007 presidential election, I have to wait for May 2007 in order to ascertain the truth of the prevision, and it is not the inaccessibility of future which permits this true prediction, but psychic powers which expand my epistemic abilities. In fact this (purely fictious) example is more naturally interpreted as supporting FF2 and usually friends of psychic powers do not argue for the accessibility of future in general.

226 purely epistemic and we would choose presentism, because it corresponds to our epistemic structure, whithout necessarly being committed to an underlying ontology. It would be an epistemic version of presentism distinct from an ontological one. Epistemic presentism would be defined as follows : we have direct access only to the presentness6 but this not imply an ontological commitment towards past entities. Ontological presentism is a strong thesis, restricting actual existence to present entities. We can guess that the ontologicaly minded presentist would have a strong tendency to adopt the de dicto reading of « Emma has eaten an apple », whereas the epistemically minded presentist would pick the de re reading. Ontological presentism implies epistemic presentism, but not conversely, what is coherent with PSTB. This last principle, we have said, affirms that truth supervenes upon being. If there is a difference in being, there is difference in truth, or in the propositions conveying truth. If ontological presentism is true, then a difference in truth between what is present and what is not present will supervene on this difference on being. We will see later that this difference does not exist between the present and what is now past. FF1 must be taken seriously if we want to be serious tensers. If it has been the case that Fa, the state of affairs Fa does not exist any more, but has existed. Presentists who give up the choice between non-existing things and present past complex complex operator paradoxically blur the difference between past and present. If Fa has existed the truthmaker of Fa is indeed the truthmaker in the past (what presentist call present past). This asymmetry cannot be a reason or the reason for pushing aside the haecceistic solution discussed by M. Rea (2004). He recalls that concerning non present things some philosophers suggest there is still a reference to their haecceity and Rea gives a reason to resist this suggestion : there is no genuine reference to the haecceity of a future thing, in so far as future statements cannot be singular ones.7 Simon Keller prefers a chisholmian

6

It is important to underline that there is no presentation of presentness. As Prior insisted upon, present is categorematic. There is a general presentation of present things, but « present » cannot be dtached of present things. Incidentally this would destroy all the blunders of phenomenology of the presentness. 7 We find this idea already in Richard Gale (1967) and in many places in Prior writings. According to Gale « Professor Carnap will fly to the moon » is not genuily refering to a singular entity. In this sentence « Professor Carnap » is, despite appearances, a definite description. It is an abbreviation of the italicized expression « The Professor Carnap I know now will be the same as the one who will fly to the moon ».

227 ontology of non instantiated haecceities, a solution as debatable of that of Rea. The ontology adopted by the partisans of truthmakers is more secure and contains only moments (Mulligan, Simons et Smith 1983), properties (Bigelow 1998), states of affairs (Armstrong 2004). Regarding the dubious haecceity of future entities, Prior exposed an illuminating thought experiment. Imagine a predicator, a vaticinator who prophecies : « A will do X and B will do Y », and suddenly exclaimed : « A and B will do X and Y, but in fact I do not know who does what ! ». According to Prior, this prophet is a man of good faith – an authentical and honest visionary —. Why ? Because he has had no access to the individual essences of A and B, in vitue of FF2, even if he is or was a true visionary. Now, the asymmetry between future and past is in favour of the solution we are discussing (which is to contest the truth of FF1). If there cannot be reference to an haecceity in the case of future statements, this supports FF1, because this asymetry is basically epistemic, and perhaps even ontological reasons or facts, if we opt for a 4Dist dynamical model of the universe. In that sort of model the ramified structure of the future is progressivly pruned. The more the universe grows in age, the fewer are the possibilities, in so far as we can conceive this pruning as an objective cosmological process. There is another route, by the way of the entropy principle : more disorder, fewer possibilities.

B/ To limit the field of application of POS. We can try to show that POS does not apply to temporal relata, for POS could be considred as flexible, applying more or less, depending on the type of relation. For example it seems possible to compare an existing entity with a non existing one and even to compare two non existing entities : Chirac is taller than Blair Napoleon was smaller than me

Mark Sainsbury however reminds me Kaplan’s examples denying convincingly this. I will postpone the discussion of this point to a future occasion.

228 It works also for fictional entities : Napoleon is smaller than Sherlock Holmes (look at the the Sherlock Holmes Companion) The same concerning partial similarity relations : Chirac looks like Daladier King Lear looks like Job As this principle seems not to apply to comparisons and likenesses, it appears possible to breach it for temporalia. Its validity being apprently not universal, we are prepared to accept also in the case of temporalia that it does not apply either. The nominalist strategy consists in taking partial similarity to be paradigmatic.8 It seems difficult to assume that all relations have the same ontological weight and it is probably false to generalize hastily only on the basis of this distinction between internal and external relations : within each of these two kinds of relations we have different degrees of strentgh. We are undoubtly justified in considering the relation between past and present in a statement as a weak form of relation, in so far as this relation does not possess two fundamental elements of relations : relation itself, having a direction, the ad aliquid of the medieval thinkers considered by them as important as connexion itself, and second the dispositional character. Let us consider a genuine ontological relation, paternity. It is a relation of dependance, for the existence of the father depends upon the existence of the son (or the daughter) : without son (or daughter) there is no father in this relation of paternity9. In the relation of paternity there is an ad aliquid (the relation is oriented toward the son or the daughter). In the relation between past and present there is only an element of unilateral dependency, and there is no ad aliquid element, no dispositional character. From a formal point of view, this kind of relation has no converse and is asymmetrical, whereas the relation of paternity, a paradigm of genuine relation, has a

8 9

Cf. Schönberger (1994) for a precise study of Buridan’s theory of relation. Even if the father, without the son, might have existed.

229 converse. The relation between past and present has only two formal properties : irreflexivity and transitivity.

C/ Call the presentism into question, or at least accept it in a weakened form in order to tolerate PTM. This rejection takes two forms. The first is radical : 4Dism . We have however a priori ruled out this radical solution. The second solution is to weaken presentism, in order to give to POS a form compatible with TMP. A logical and grammatical analysis of past statements (i.e. statements with past inflexion) is needed. We limit ourselves here to past statements, for the consideration of the future adds nothing new but a greater complexity due to the future itself. A. Prior insisted on the necessity of this grammatical analysis as soon as we face questions pertaining to tense and existence10. This above mentioned strategy consists in a paraphrase of past statements, in order to make conspicuous the hidden function of a deep present operator, which dominates syntactically the past operator and semantically modifies it. This strategy is derived from the Prior’s claim : « The past is not the present, but is [A. P. underlining] and the future is not the present but is [ib.] the future present ». (Prior, 1958, p. 8).

The paraphrase delivers the following equivalence : Emma has eaten an apple = it has been the case that Emma eats an apple We could of course prefer the paraphrase : It is the past, Emma eats an apple but the important point is to make visible a present past. More generally and formally : Pp = PPrp

10

See Past, present and Existence (Prior 1967).

230 (Pr : present i.e. « it is the case presently that » ; P : past, i.e. « it has been the case that »). In order to get the symmetry between P and Pr, we should perhaps express the operator in another way, but we have prefered the orthodox paraphrase : « it has been the case that Prp ». This equivalence is not ad hoc, for it is an analogy between it and the one we know already very well in tense logic : Pp ⇒ FPp If it has been the case at least once that p, it will be at least once that it has been at least once that p (or more simply : if it has been the case that p, then it will be the case that it has been the case that it has been the case that p. In order to get an equivalence, we should obtain the converse implication : FPp⇒Pp Is it materially true ? Suppose that it will be the case that Emma has eaten an apple. May we infer that Emma has eaten an apple ? No, because the future past can be not past relativly to the present. We see that through the grammatical expression of the consequence It will be the case that Emma has eaten an apple does not imply that the event in question is past for us. In virtue of FF2 we are not even sure that the event will indeed actually occur. We can notice that the sophism Senex erit puer (the old man will become a boy) rests upon that sort of fact concerning the nature of the future. This sophism is present in the Buridan’s Sophismata : « This [the old man will become a boy] is proved true since it is equivalent of the statement that he who is or will be an old man will be a boy. This is true of Antechrist. The opposite however is clear by induction, since the old man will not be a boy, nor this, neither this one, and so of singulars, because whatever old man is indicated, it is false to say that he will be a boy. » (Buridan, 1966, p. 111).

The meaning of this sophism is that the one who will become an old man will first become a child. It is easier to understand the litteral meaning of the sophism if we consider the case of the child not being born or not being a baby. Conversely : that the old man will become a child is false, because

231 if he is aged, he cannot go back to the past. The two readings are the following : (∃x)F(Ox & Cx) (∃x) (Ox & F(Cx)) (where « O » is « old », and « C » « child ») We can ask ourselves if the translation of the two formulas gives an adequate formal representation of the logical form of the sophism. We can therefore suggest in order to falsifying the sophism : If it will be the case that a has to become an old man, the it will have been the case that a has become a child Another equivalent of the formula, with F instead P, is the following : Fp ⇒ FPp i.e. « if it will be at least once the case that p, then it will be the case at least once that it has been the case at least once that p. » Prior proposed a more complicated paraphrase in order to make explicit present implicit in embedded operators. Following scheme of It was the case that p and it is not now the case that p he proposed of the following sentence Queen Ann died 250 years ago with he paraphrase : It was the case that [it was the case only 250 years ago that] Queen Ann is dying and is not now the case that [it was the case only 250 years ago that] Queen Ann is dying The formal translation of this paraphrase is PP250 yearsp & ¬ (NP250 yearsp)

232 (P250 years is a metric operator of the form Pn where n is a period, meaning « it was the case n times ago », and N is the deictic operator « now »11). This priorian stategy is analogous to Marian David’s (M. David, 2004) in defense (against David Lewis) of the correspondence theory of truth. M. David recalled the possible objection against TMP. If we have a non-fact, the application of TMP would give an absurd (or at least utterly trivial) result : Any non-fact makes the truth that there is a non-fact The answer to this objection is the following, according to Marian David : « It is not the non-fact that makes true the truth taht there is a non-fact ; rather it is the existence of the non-fact that makes true this truth. » (Marian David, 2004, p.47)

There is indeed an analogy between the two strategies. Prior respects POS in respect to past and even future sentences. M. David wants to keep POS for the non-facts. However Prior’s strategy seems more reasonable : it introduces transformations at a relatively unsophisticated level, the grammatical one, whereas M. David, who at firts sight seems very close to priorian transformations, introduces at the contrary an important distortion. If a non-fact can be said to exist, in which sense of « exist » is this non-fact existing ? It is indeed a distortion, because the non-fact of Mary not eating an apple cannot be put on the same footing than the fact of Mary actually eating an apple. It seems more reasonable to hold the old doctrine saying that a state of affairs obtains or not, the state of affairs which obtains being a fact. There is a state of affairs consisting of Emma eating an apple and this state of affairs may obtain or not.

Conclusion

11

Introduced by Hans Kamp (1971), who contrasted for example the two sentences : It was the case that there would be an earthquake/ It was the case that there would be now an earthquake. F. Vlach inroduced the operator K (« Then ») : the first of these two sentences is equivalent to : It was the case that there would be then an earthquacke. The interplay between N and K is an important part of tense logic.

233 TMP does not apply only if we restrict the domain of application to atemporal or detensed sentences. Prior says that « present » is in fact syncategorematical — what is present is a day, a moment, a year — and the present does not exist. We could introduce a present with a variable size (lato sensu present), but this solution brings more problems than it could hope to solve : we should have to determine contextually with a variable present the size of a temporal interval and we introduce then elements foreign to temporal reference. But if we have a stricto sensu present, then as the size of this present is strictly equivalent to the present moment (= 0) and therefore we are obliged in that case to accept abstract truthmakers, because we will not be able to dispose of truthmakers with a temporal extension. How can abstract truthmakers make something true ? We could retort that states of affairs as abstract entities would be fine. But abstract states of affairs if they can be embedded under cognitive verbs, are deprived of causal power, and cannot therefore make true something, for making true is causal relation. We can ask ourselves if the truthmaker is neutral regarding entities playing the function of truthmakers. This problem is distinct from the problem of Kevin Mulligan (2003) and is closer to the Lewis’ problem (2002). Lewis has discerned the consequences of the introduction of truthmakers concerning the overlaping of individuals across possible worlds. There could be a neutrality concerning the types of entities (states of affairs, facts, properties (Bigelow 1998)), but not concerning the nature of these entities, either abstract or concrete. The problems we have examined are perhaps caused by the choice we face between presentism and 4Dism. We have therefore to verify that this is a genuine difficulty and not a pseudo-problem. Our position at the end of this paper, in particular with the help of Prior’s analysis is that it is not a pseudo-problem, elimininable by formal or technical means (restriction of POS, doubt about the relational character of truthmakers…) but on the contrary that is a genuine probelem, caused by the complex and intricated relations between time and existence. We have proved that the absence of quiddity of futuralia supports FF1. The radical choice produces apories, because to have the choice between presentism and 4Dism is very unsatisfactory. Presentism is perhaps close to

234 common sense intuition, but its formal and conceptual representation appears much more difficult as anticipated, if we refuse to fall back into a pseudo theory of truth. 4Dism agrees with science, but contradicts common sense, because it involves an ontology of temporal parts, full of well known predicaments. It is certain that the universe described by relativistic physics is a four-dimensional variety. It is however obvious that tense topology is not identical to time topology.12 It is not natural for example to consider time as a fourth dimension of space, if we look for a time topology closely connected to tense topology. The notion of ontology could employed above may appear ambiguous. We have side by side a formal ontology, defined as a mathesis universalis which is beyond the subjective and anthropocentric prehension of time and space, and a material ontology of spatio-temporal structures, as instants, intervals, histories, locations, paths etc. associated with conceptual schemes at work in this subjective prehension, depending upon limitations of intellectual equipment. Truthmaker theory is located in the heart of this ambiguity of ontology and if this depressing diagnosis is accurate, it is not surprising hat the truthmaking of tensed statements is full of puzzles. We can conclude this relativly frustrating succession of remarks with the rewarding words of Aristotle : « I think that it is not easy matter to dogmatize over such problems without more exhaustive inquiry [ or : without having examined them many times] . To bring up the points in detail [or : to have gone through the various difficulties] is however, not itself wholly useless. » (Cat., VII, 8b, 22-24)

REFERENCES

Armstrong, David, 2004 : Truth and Truthmakers, Cambridge University Press Bigelow, John, 1988 : The Reality of Numbers, Oxford : Clarendon Press

12

Cf Newton Smith (1980) on tense topology and more genrally the two books of H. Mellor on « real time » (1981, 1998)

235 ___ 1996, “Presentism and Properties”, Philosophical perspectives, vol.10, pp. 35-52 Buridan, transl. 1966, Sophims on Meaning and Truth, transl and introd. Kermitt Scott, Century Philosophy Source Books, Appleton-Century-Crofts, New-York (French transl. Sophismes, introd. Joël Biard, Vrin, 1993? Paris). David Marian, 2004, “Don’t Forget about the Correspondance Theory of Truth”, in Lewisian Themes. The philosophy of David Lewis, F. Jackson & G. Priest, eds., Clarendon Press, Oxford, p. 43-48 Gale, Richard 1967 : TheLanguage of Time, Routledge & Kegan paul, London Kamp Hans, 1971 : « The Formal Properties of Now », Theoria, 37, p. 227-273 Keller Simon, 2004 :”Presentism and Truthmaking”,Oxford Studies in Metaphysics I, Oxford University Press, p. 83-106. Lewis, David, 2002 : “A World of Truthmakers”, Papers in Metaphysics and Epistemology, Cambridge University Press, p. 215-220. Mellor, Hugh : 1981, 1998 : Real Time, I, Cambridge University Press, Real Time II, Routledge and Kegan Paul, London. Moltmann Fredericke, 2005 : “Properties and Kinds of Tropes : New Linguistic Factes and Old Philosophical Insights“, Mind, 123, p. 1-41. Mulligan, Kevin, 2003 : “From Truths to Truthmaking and beyond“, ms. Mulligan, Kevin, Simons, Peter, Smith, Barry, 1984 : « Truth-Makers », in that volume Newton-Smith, 1980 : The structure of Time, Routledge and kegan Paul, London Prior Arthur N. 1958 : Papers on time and modality, Oxford University Press ——1967 : Past, present, future, Oxford University Press Rea Mikael, 2003 : « Four-dimensionalism », Oxford Handbook in Metaphysics, Oxford University Press. Schönberger Rolf, 1994 : Die Relationstheorie des Johannes Buridan im Kontext seines Denkens und der Scholastik, E.J. Brill, Leiden.

Truthmaking as Essential Dependence E. J. LOWE University of Durham

1. Truth and truthmaking The idea that all truths need to be made true is an appealing one. This is so whatever one may think the ‘primary’ truthbearers to be—sentences, statements, beliefs, or propositions. To avoid undue complexity, I shall assume that propositions are the primary truthbearers in what follows, but I don’t think that this assumption is crucial to the general thrust of the arguments that I shall be advancing. So, why should I say that it is an appealing idea that all true propositions need to be made true? Note here that I don’t, at this stage, say that they need to be made true by something, and in this sense need to have truthmakers, construed as being existing entities of some sort—although I shall be defending such a position in due course. Well, there is plainly a difference between a proposition’s being true and that same proposition’s being false—and this is a difference that we obviously want to be able to explain. It doesn’t follow that this difference is a difference between a proposition’s possessing one property—the property of being true—and its possessing another property, the property of being false. For we can’t assume without argument that the predicates ‘is true’ and ‘is false’ express properties of the entities to which they are applied. Indeed, although I am no nominalist and believe in the existence of properties—both conceived as universals and conceived as particulars that are instances of those universals—I do not consider that truth and falsity are properties in that sense. More precisely, I do not consider that a true proposition is one that exemplifies the universal truth, nor that it possesses a truth trope or mode, whether or not conceived as a particular instance of such a universal. If a proposition’s being true were indeed a matter of its exemplifying truth or possessing a truth trope, then I think it would not, after all, be clear why a true proposition would need to be made true in the sense in which it intuitively needs to be. For its being true would then just be a matter of how that proposition was ‘in itself’—assuming, at least, that truth so-conceived

238 would be a non-relational property, as the syntax of truth-predication suggests. That is to say, a proposition’s being true would, on this way of conceiving the matter, be analogous to an apple’s being red, or its being round. If an apple is round, it is so because it exemplifies roundness, or possesses a roundness trope. But it does not need to be made round, in anything like the sense in which, intuitively, a true proposition needs to be made true. Of course, there will need to be a cause of the apple’s roundness and so it will need to be ‘made round’ in that sense. But it is surely no part of the intuitive idea of truthmaking that making true is a kind of causing. Rather, when we say that a true proposition needs to be ‘made’ true, we mean that it has to be true ‘in virtue of’ something, where ‘in virtue of’ expresses what I would call a relationship of metaphysical explanation. In other words, a true proposition must have truth conferred upon it in some way which explains how it gets to be true. But may it not now be interjected that, likewise, a round apple needs to have roundness conferred upon it in some way which explains how it gets to be round? And couldn’t it then be said that a round apple is round precisely in virtue of exemplifying the universal roundness, or in virtue of possessing a roundness trope? And then isn’t this precisely a matter of its being ‘made round’, in a non-causal sense analogous to that of a proposition’s being ‘made true’? I think not. I happily acknowledge that a round apple is, in a perfectly good sense, round in virtue of exemplifying the universal roundness or in virtue of possessing a roundness trope. But this is just to say that what it is for a round apple to be round is for it to exemplify the universal roundness or to possess a roundness trope. It is not at all to say that roundness is conferred upon it in either of these ways. For the roundness of a round apple, we are now supposing, simply is either the universal roundness or a roundness trope—and it would just be circular to say that its roundness in either sense is conferred upon the apple by its exemplifying or possessing that very roundness. The only sense in which, as I put it earlier, a round apple ‘needs to have roundness conferred upon it in some way which explains how it gets to be round’—the only sense in which it needs to be ‘made’ round—is the causal sense. To ‘make it round’, in this sense, is just to bring it about that the apple exemplifies the universal roundness or possesses a roundness trope. And we have already rejected the idea that a proposition needs to be ‘made’ true in this sense. So comparison with the case of an apple’s being round in fact helps to undermine, rather than support, the suggestion that the truth predicate ‘is true’

239 expresses a universal, or that there are truth tropes that certain propositions possess. 2. Formal ontological predicates The truth predicate, I consider, is best seen as belonging in the same category of expressions as such predicates as ‘exists’ and ‘is identical with’. They are formal ontological predicates and we can say, if we like, that they express formal ontological properties and relations—truth, existence, and identity—provided that we don’t make the mistake of supposing that such ‘properties and relations’ are elements of being, that is, existing entities in either of the ontological categories of universal or trope. Formal ontological properties and relations are not elements of being, to be included amongst the overall inventory of ‘what there is’: rather, they contribute to the nature of reality as a whole solely by helping to constitute how reality is. In might be thought, of course, that this was precisely the role of universals and tropes, but that would be wrong—for, according to the sort of realist position that I am defending, these are elements of being to be included in the overall inventory of what there is, along with other categories of entity, such as so-called concrete particulars or, to use an older terminology, individual substances. The nominalist will no doubt want to take issue with me here and contend that we no more need to regard roundness and redness as ‘elements of being’, whether as universals or as ‘abstract’ particulars, than I am saying that we need to regard truth, existence and identity in this light. The nominalist will urge that, since I have acknowledged this in the case of what I am calling formal ontological properties and relations, it is gratuitous of me to refuse to acknowledge it in the case of more mundane ‘properties and relations’, such as redness, roundness and betweenness. I will be accused of drawing an arbitrary line and of having started out upon a slippery slope down which I cannot, in any principled way, help sliding into full-blown nominalism. Well, I reject the charge. A principled and non-arbitrary line can be drawn between those predicates that are candidates for expressing real universals and those that are not. Note, I am not implying here that every predicate that is a candidate for expressing a real universal must be taken actually to express one. I am perfectly happy with the contention, favoured by philosophers such as David Armstrong, that it is a largely or perhaps even wholly empirical matter which of these predicates we should regard as ac-

240 tually expressing real universals and, indeed, a largely or perhaps even wholly empirical matter what real universals we should suppose reality as a whole to include. All that I am saying is that it is not an empirical matter, but rather an a priori one, that certain predicates, such as ‘is true’, ‘exists’, and ‘is identical with’, are not candidates for expressing real universals. That is to say, I hold that we can know, purely by reflecting on the matter, that someone could not have grasped properly the meaning of such predicates if he thought that their semantic role was to express certain real universals, conceived as elements of being. No doubt the nominalist will want to reply that a similar thing could be said about all predicates—that, in effect, a realist construal of their semantic role, if taken seriously, could only be taken to reflect an imperfect grasp of their meaning. But I believe that any such charge is certainly open to rebuttal, because I believe that a perfectly coherent account of predication can be supplied by the realist. I don’t, of course, believe that all predication can be understood on this model, because I don’t believe that all meaningful predicates should be taken to express real universals. So why do I ‘draw the line’ in the place I claim to, in distinguishing between those predicates that are candidates for expressing real universals and those that are not? Briefly, my guiding line of thought on this matter is as follows. Reality as a whole must contain what I am calling ‘elements of being’. Moreover, I think that it must contain a plurality of such elements. Although reality is one, it is a one that embraces many. Some mystic philosophers have denied this, of course, holding that reality is one in an absolutely simple and undifferentiated way, but I can make no sense of this. For, in the sense of ‘reality’ now at issue, even ‘appearance’ is to be understood as being included in ‘reality’—and appearance is certainly not, to all appearance, absolutely simple and undifferentiated. Moreover, I cannot make any sense of the view that reality can be cleanly divided into two domains, the domain of appearance and everything else, such that only the domain of appearance contains multiplicity and differentiation of any kind—the view, roughly speaking, that there is on the one side differentiated appearance and on the other side ‘the world’, with the latter being completely undifferentiated ‘stuff’, or ‘the noumenon’. Apart from anything else, I cannot see how reality as a whole can be coherently divided into ‘appearance’ and ‘the world’, nor in any other way analogous to this, such as into ‘mind’ and ‘world’, or into ‘representation’ and ‘reality’ (‘re-

241 ality’ in the latter case being taken, of course, to be less than what I have been calling ‘reality as a whole’). 3. Ontology, categories, and metaphysical realism I am, thus, an ontological pluralist, but not an ontological relativist: I hold that there is just one reality, but that it embraces a multiplicity of elements of being. One of the tasks of ontology, then, is to provide an inventory of those elements of being. However, such an inventory could not intelligibly be nothing more than a gigantic washing list. It would miss the point of ontology altogether to suppose that its task were simply to enumerate all the entities that there putatively are: shoes and ships and sealing wax, cabbages and kings—et cetera, et cetera. Many nominalists, it seems to me, implicitly suppose that, in the last analysis, this is all that we may hope to do by way of characterising the elements of being. They fundamentally agree with Quine when he said that the basic question of ontology is ‘What is there?’, but that it could be answered by the one-word English sentence ‘Everything’.1 He meant, I think—and meant seriously— that this is the best general answer that we can give to that question. To this it may be replied that Quine himself, if not his followers, also held that the best answer to the question of what there is is to be found by determining what it is that the bound variables of our best-supported scientific theories should be taken to quantify over. And it may be added that it seems that he himself thought that the answer might well turn out to be that all that exist are numbers and sets, since all of our best-supported scientific theories can be interpreted most economically as quantifying only over such entities, rather than, say, over spatiotemporally located material objects or materially filled regions of space-time—since any sentence putatively quantifying over entities of the latter sorts can be reinterpreted, consistently with the empirical evidence in support of the theory containing it, as a sentence quantifying over sets of numbers (to wit, numbers specifying the coordinates of what were previously conceived to be space-time locations).2 However, it would not be consistent with the spirit of Quine’s phi1

See W. V. Quine, ‘On What There Is’, in his From a Logical Point of View, 2nd edn (Cambridge, MA: Harvard University Press, 1961).

2

See W. V. Quine, ‘Things and their Place in Theories’, in his Theories and Things (Cambridge, MA: Harvard University Press, 1981).

242 losophy more generally to suppose that he was seriously committed to Pythagoreanism—the view that, in reality, all that exist are mathematical objects. For Quine espoused the doctrine of ontological relativity, which excludes the idea that there is any privileged way of specifying the contents of reality that is wholly independent of one’s means of representing it in language.3 And what language we use is a contingent matter, determined by cultural and psychological factors. This applies quite as much to the language of science as to any other language. It may perhaps be that the language of fundamental physics and the theories expressed in that language can be interpreted, without affecting their empirical content or predictive utility, as quantifying solely over numbers and sets, and so as incurring an ontological commitment only to mathematical objects. But for a Quinean naturalist this fact should not be construed as providing support for any serious endorsement of Pythagoreanism as a contribution to fundamental metaphysics, that is, as a putative account of what the real elements of being are. However, my concern is not to defend Quine nor to try to render his ontological pronouncements more palatable than they might seem to be. I think, in fact, that he ultimately has nothing intelligible to say about ontology and would happily accept that charge, on the grounds that ontology as I conceive of it is an impossible enterprise. By my way of thinking, however, the reason why Quine has nothing intelligible to say about ontology as I conceive of it is that he really does believe that the only perfectly general answer, of the sort that I would acknowledge as being relevant, that can be given to the question ‘What is there?’ is the one-word reply ‘Everything’. On Quine’s view, the most that the doctrine of ontological relativity will allow us to say about the nature of reality ‘as it is in itself’ is that there are things, where the term ‘thing’ is perfectly neutral, denoting no more than a possible value of a variable of quantification. Anything whatever could, of course, be such a value. There is no room, in Quine’s view, for categorial differentiations amongst ‘things’ in any ontologically serious sense. At most he allows that different predicates may be true of different things: perhaps some things are ‘cabbages’, for instance, while others are ‘kings’. But if we were to say that some things are ‘universals’, say, while others 3

See W. V. Quine, ‘Ontological Relativity’, in his Ontological Relativity and Other Essays (New York: Columbia University Press, 1968).

243 are ‘particulars’, he would take this as conveying no more than just another putative difference between the predicates true of different things. It may be instructive to compare Quine’s minimalist ontology with various so-called ‘one-category’ ontologies. One such ontology is the pure trope ontology, according which the only elements of being are tropes or property instances.4 Another is the ontology of classical resemblance nominalism, according to which the only elements of being are concrete particulars, or individual substances.5 Ontologists espousing these views certainly do not think—or ought not to think—that belonging to an ontological category is just a matter of being describable by a predicate: that ‘is a trope’ or ‘is a concrete particular’ is just on a par with ‘is a cabbage’ or ‘is a king’, the former predicates differing from the latter merely in that they are universally applicable. If they thought that, it would simply be unintelligible that there was any dispute between them as to which view was correct. Neither of them thinks that telling whether something is a trope as opposed to a concrete particular is remotely like telling whether something is a cabbage as opposed to a king. The trope theorist holds that what we call cabbages are in fact ‘bundles’ of tropes, whereas the classical resemblance nominalist holds that they are entities—concrete particulars as he conceives of them—which admit of no decomposition into anything other than further concrete particulars. Their difference is a difference concerning the ontological status of the entities to which all of our descriptive predicates apply. Two such ontologists could agree perfectly about how to describe the world—agree, for instance, that it includes shoes and ships and sealing wax, cabbages and kings, along with anything else that one could expect to find on a gigantic ‘washing list’. They differ over the nature of entities to which these descriptions apply—whether or not cabbages, for instance, are ‘bundles of tropes’. But Quine has no serious interest in any such dispute. His is most aptly characterized not as a one-category ontology—the one category being ‘thing’ in the broadest possible sense, or ‘entity’—but rather as a no category ontology. On Quine’s view, all that we can ever do is to disagree about how to describe what there is, not over what there is to be described.

4

See Keith Campbell, Abstract Particulars (Oxford: Blackwell, 1990). See Gonzalo Rodriguez-Pereyra, Resemblance Nominalism: A Solution to the Problem of Universals (Oxford: Clarendon Press, 2002).

5

244 But a no category ontology is an incoherent ontology. For either it maintains that what there is is many, or that what there is is one, or that what there is is neither many nor one. As I have already explained, my own view is that the only coherent position is that although reality is one, it contains multiplicity—so that what there is is many. Quine himself seems to suppose so too, for he holds that ‘to be is to be the value of a variable’ and seems to be committed to the multiplicity of such values. Pythagoreanism would certainly respect the principle that what there is is many—many mathematical objects, including all the numbers. But Quine also espouses the dictum ‘No entity without identity’ and in some sense that must be correct too.6 For how can there be multiplicity where there is neither identity nor distinctness? There can only be many if each of the many is a one that is identical only with itself and distinct from each of the rest. However, a no category ontology leaves no scope for any real difference between one and many nor between identity and distinctness. Given his no category ontology, Quine’s one-word answer to the question ‘What is there?’— ‘Everything’—is misleading to the extent that it suggests that what there is is determinately and objectively either one or many. For the Quinean, all questions concerning ‘how many’ things there are and which things are identical with or distinct from one another have to do with how we describe reality, not with what reality contains prior to or independently of our attempts to describe it. Thus Quine is implicitly quite as committed to the ‘amorphous lump’ conception of reality as Michael Dummett is explicitly committed to it.7 Both of them are anti-realist metaphysicians in the fullest sense of the term, because the distinction between an utterly formless ‘something’ and nothing at all is a distinction without a meaningful difference. Indeed, in the end they are both nihilist metaphysicians, because there is no coherent way for them to exempt us and our descriptions or thoughts about reality from the annihilating acid of their anti-realism. 4. Identity, essence, and essential dependence The preceding discussion may seem to have taken us far from the topic of truthmaking, but the digression has not been an irrelevant one. Its purpose was to defend the view that formal ontological predicates need to be under6

See, for example, W. V. Quine, ‘Speaking of Objects’, in his Ontological Relativity and Other Essays. 7 See Michael Dummett, Frege: Philosophy of Language, 2nd edn (London: Duckworth, 1981), pp. 563ff.

245 stood in a different way from ordinary, empirical or descriptive predicates. These formal ontological predicates include those used to assign entities to certain ontological categories, such as the predicates ‘is a trope’ and ‘is a concrete particular’. They also include, I maintain, such predicates as ‘is true’, ‘exists’ and ‘is identical with’. We should not expect the basis on which these predicates are correctly applied to entities to be at all similar to the basis on which empirical or descriptive predicates are correctly applied to them. It is part of the task of metaphysics to explain how empirical or descriptive predicates may be correctly applied to entities by appealing to formal ontological features of and relationships between those entities. For example, a trope theorist may explain how the descriptive predicate ‘is red’ is correctly applicable to an entity by saying that the entity in question is a bundle of tropes which includes a trope belonging to a certain resemblance class of tropes. A classical resemblance nominalist may explain the same thing by saying that the entity in question is a concrete particular which itself belongs to a certain resemblance class of concrete particulars. Neither of them, of course, would—or coherently could—apply the same explanatory strategy to explain how the predicates ‘is a trope’ or ‘is a concrete particular’ are correctly applicable to entities. How, then, are we to explain how formal ontological predicates are correctly applicable to entities? In some cases, I want to say, such a predicate applies to an entity in virtue of its identity, that is, in virtue of what that entity essentially is. It is for this reason that the predicate ‘is a trope’ or the predicate ‘is a universal’ applies to any entity. The same reason obtains in the case of the identity predicate itself, ‘is identical with’. This predicate is correctly applicable to an entity x and an entity y in virtue of the identity of x and the identity of y—and, of course, if it is correctly applicable to ‘them’, then ‘they’ are one and the same entity, with the same identity. But, equally, the distinctness predicate, ‘is distinct from’, is correctly applicable to entities in virtue of their identities. However, at least some entities, I want to say, depend for their identities on the identities of other entities. What this means, as I understand it, is that it is part of the essence of such an entity that it is the very entity that it is in virtue of a unique relationship in which it stands to one or more other entities. (I use the term ‘essence’ here in precisely the way that Locke recommended, to denote ‘the very being of any thing, whereby it is, what it is’—which, he says, is the

246 ‘proper original signification’ of the word.8) This is my own view about, for instance, tropes—or, as I prefer to call them, modes. I hold that if m is a mode or trope—suppose, for example, that m is a certain roundness mode—then it depends for its identity on the identity of the concrete particular or individual substance that possesses it—a certain apple, say. This is because, in my view, it is part of the essence of m that it is the very entity that it is—this roundness mode as opposed to any other exactly resembling roundness mode—in virtue of being the roundness mode that is possessed by this apple. Pure trope theorists, of course, cannot take the same view of what they call ‘tropes’, since they do not believe in the existence of either universals or individual substances. So although both my ‘modes’ and the pure trope theorist’s ‘tropes’ may loosely be termed ‘property instances’, they are in fact entities belonging to rival and quite distinct ontological categories, because the entities belonging to those putative categories are quite different in respect of ‘what they essentially are’, that is, in respect of their ‘identities’. The pure trope theorist must apparently hold that each trope has its identity underivatively, not that it depends for it on or owes it to other entities of any sort. Identity dependence in the foregoing sense is a species of essential dependence.9 But there are other species as well. Very plausibly, an entity can, for example, depend essentially for its existence on one or more other entities, without necessarily depending essentially for its identity upon those other entities. Immanent universals seem to provide a case in point. Observe that, very plausibly, it is not part of the essence of the universal roundness that it has the roundness of a certain apple as one of its instances, for the simple reason that the universal could have lacked that particular instance. This is because the apple is a contingent being and, moreover, exemplifies roundness only contingently—it could have lacked the 8

See John Locke, An Essay Concerning Human Understanding, ed. P. H. Nidditch (Oxford: Clarendon Press, 1975), Book III, ch. III, sect. 15. 9 For more discussion and a definition of identity dependence, see my The Possibility of Metaphysics: Substance, Identity, and Time (Oxford: Clarendon Press, 1998), ch. 6. My thoughts about these matters have been helped by some of Kit Fine’s work on the subject, but nothing that I say concerning them should be assumed to coincide with his own views. See, in particular, his ‘Essence and Modality’, in James E. Tomberlin (ed.), Philosophical Perspectives, 8: Logic and Language (Atascadero, CA: Ridgeview, 1994) and ‘Ontological Dependence’, Proceedings of the Aristotelian Society 95 (1995), pp. 269-90.

247 roundness mode that it actually possesses. Consequently, it seems, the universal does not depend for its identity upon this or indeed—I should say— any other mode that is an instance of it. Even so, if the universal roundness is an immanent universal—as I hold it and all other universals to be—then it seems that it does, in a perfectly good sense, depend essentially for its actual existence on the roundness modes of all actually existing round individual substances. For, on the immanent conception of such a universal, it is part of the essence of the universal that it actually exists only if it is actually exemplified by certain individual substances, in virtue of those substances possessing modes that are particular instances of the universal. If other substances had exemplified the universal, then the universal would have depended for its existence on the modes of the universal that would in that case have existed—but, again, it seems that it would have depended upon them essentially, again because it is part of the essence of an immanent universal to exist only if it has particular instances. 5. The varieties of metaphysical dependence It is important to recognize that essential dependence is not the only variety of metaphysical dependence. Sometimes, for instance, an entity can, in a perfectly good sense, depend metaphysically for its existence on another entity, even though it does not depend essentially for its existence on that entity. Suppose, for example, that mathematical objects such as the natural numbers exist and are necessary beings—that is to say, that they are beings ‘whose essence includes existence’. What this means is that it is, supposedly, part of the essence of a number, such as the number 7, that it exists. One might suppose, indeed, that the number 7 does not depend essentially for its existence on anything else, not even God or other numbers— although in fact it is, I think, plausible to say that it depends essentially for its existence at least on other numbers, for it is plausibly part of the essence of the number 7 that it stands in certain arithmetical relations to other numbers. Be that as it may, consider now a contingent being, such as a certain apple. This apple plausibly depends essentially for its existence, both actual and possible, upon certain other contingent entities. For instance, it is plausibly part of the essence of this apple that it actually exists only because a certain apple tree actually exists—the apple tree on which it grew—so that the apple depends essentially for its actual existence on that apple tree. However, it is not plausibly part of the essence of this apple that it actually exists only because the number 7 exists. For it is surely no part

248 of what this apple essentially is that is related to an abstract mathematical object like the number 7 in any way. Nonetheless, it is clearly the case that this apple could not have existed without the number 7 existing, simply because—or so we are assuming—the number 7 is a necessary being. But this is just to say that this apple stands in a certain relation of metaphysical dependence to the number 7: the relation in which one thing stands to another when it is metaphysically necessary that the first thing exists only if the second thing does. We can call this species of metaphysical dependence ‘necessary dependence’, to distinguish it from what we have been calling ‘essential dependence’. Elsewhere, I have called it ‘rigid’ existential dependence.10 We have just seen an example of something that depends necessarily for its existence on a certain other thing, even though it does not depend essentially for its existence on that other thing—the things in question being, in this case, a particular apple and the number 7. But it seems that it can also be the case that something depends essentially for its existence—at least, for its actual existence—on some other thing or things, even though it does not depend necessarily for its existence (in the sense just defined) on the other thing or things in question. In effect, we saw an example of this earlier, in the case of the immanent universal roundness and the roundness modes of all actually existing round substances. For I said that the universal roundness depends essentially for its actual existence upon those roundness modes—indeed, that this is what it is for such a universal to be ‘immanent’. And yet it is clearly not the case, as I pointed out earlier, that it is metaphysically necessary that the universal roundness exists only if those roundness modes exist, for that very universal clearly could have existed even if none of those roundness modes had existed, provided that other roundness modes had existed instead.

6. Truthmaking as essential dependence We are now in a position to apply some of these considerations to the case of truth. I said at the outset that it is an appealing idea that all truths need to be made true. We can now try to cash out this idea in terms of the notion that the truth of any proposition is a metaphysically dependent feature of 10

See my ‘Some Formal Ontological Relations’, Dialectica 58 (2004), 297-316.

249 it—remembering that by ‘feature’ here I do not mean a property, either in the sense of a universal or in the sense of a mode or trope. The idea, then, is that any true proposition depends metaphysically for its truth on something. Now, conceivably, a proposition might depend metaphysically for its truth simply on itself. This might be the case, for instance, with logically necessary truths. But most propositions are surely not like that. In any case, in order to proceed further, we need to consider what species of metaphysical dependence is most plausibly involved in truthmaking. I think it is most plausibly essential dependence that is involved, rather than necessary dependence. We can begin to see why by noting that, analogously with the case of existence, we should say that a proposition depends necessarily for its truth on a certain entity just in case it is metaphysically necessary that the proposition is true only if the entity in question exists. However, this means, for instance, that the proposition that this apple is round depends necessarily for its truth on the number 7—for it is, clearly, metaphysically necessary that the proposition that this apple is round is true only if the number 7 exists, simply because (as we are supposing) the number 7 is a necessary being. But it would surely be quite inappropriate to say that the number 7 is a ‘truthmaker’ of the proposition that this apple is round. However, it may be suggested that what is wrong with the foregoing proposal is not that it invokes the notion of metaphysical necessity, but just that it invokes it in the wrong way. The reason why the number 7 cannot be a truthmaker of the proposition that this apple is round, it may be said, is just that that proposition could have been false despite the existence of the number 7 and a truthmaker is not, or not merely, something whose existence is necessary for the truth of a proposition but something whose nonexistence is necessary for its falsehood—in other words, it is something whose existence metaphysically necessitates the truth of the proposition. In the language of possible worlds, it is something that exists not, or not merely, in every possible world in which the proposition in question is true, but in no possible world in which it is false. However, this view of truthmaking presents some serious difficulties. First, it is now being implied that if something is a truthmaker of a certain proposition, then it is something such that it is metaphysically necessary that this thing exists only if that proposition is true—and hence that the existence of a truthmaker is, in that sense, metaphysically dependent on the truth of any proposition that it supposedly ‘makes true’. But this seems to reverse the proper direction of dependence between truthmakers and truth. Secondly, a

250 difficulty arises regarding the truthmakers of necessary truths. For, because any necessary being exists in every possible world and any necessary truth is false in no possible world, it turns out, according to the proposal now under consideration, that any necessary being is a truthmaker of any necessary truth, so that the truthmaking relation becomes utterly indiscriminate where necessary truths are concerned. What we should say, I believe, in order to avoid these difficulties is that truthmaking involves a variety of essential dependence. A truthmaker of a proposition, I am inclined to say, is something such that it is part of the essence of that proposition that it is true if that thing exists. (Notice that I just say ‘if’ here, not ‘if and only if’, for reasons that will become plain in due course; we shall also see later on that there is a certain difficulty attending the proposal that I have just advanced, so that I think that it can only be regarded as a first approximation to what is wanted.) This account of truthmaking enables us to say, as was suggested earlier, that any proposition that is a logically necessary truth is its own truthmaker: for, plausibly, it is indeed part of the essence of, say, the proposition that nothing both is and is not—the law of non-contradiction—that it is true if it exists. And since, plausibly, this proposition is also a necessary being, in whose essence it is to exist, it follows that it is part of the essence of the proposition that nothing both is and is not that it is unconditionally true, as befits a law of logic. (So perhaps the chief difference between purely logical truths and other propositions is that, while it is part of the essence of any proposition that it is either true or false, only in the case of a proposition that is a purely logical truth is it part of the essence of that proposition that it is true.) Metaphysically necessary truths that are not logically necessary should not be seen in the same light: they are not their own truthmakers. Consider, for example, the mathematically necessary truth that 7 plus 5 equals 12. In this case, it seems that the proper thing to say is that it is part of the essence of this proposition that it is true if the natural numbers exist—or, at least, if the numbers 5, 7 and 12 exist. These numbers are truthmakers of the proposition in question. For it is upon these numbers that the truth of that proposition essentially depends, because it is part of the essence of these numbers that they stand in the relevant arithmetical relation. So we can already see that by appealing to the notion of essential dependence to explain the idea of truthmaking, we can avoid the unwanted implication that the truthmaking relation is utterly indiscriminate where necessary truths are

251 concerned—for we have already been able to discriminate between the truthmakers of logically and arithmetically necessary truths. To illustrate this point further, suppose that it is a metaphysically necessary truth that God is omniscient, on the grounds that it is part of God’s essence that he is omniscient. Then we can say that it is, equally, part of the essence of the proposition that God is omniscient that it is true if God exists—and hence that God himself is a truthmaker of this proposition. However, it would seem that he is not its only truthmaker, God’s omniscience being another—where by ‘God’s omniscience’ I mean the particular omniscience of God, which is a mode (and, perhaps, necessarily the only mode) of the universal omniscience. And it would certainly seem to be part of the essence of the proposition that God is omniscient not only that it is true if God himself exists, but also that it is true if God’s omniscience exists. For, after all, it is surely part of the essence of God that he exists if and only if his omniscience exists and, equally, part of the essence of God’s omniscience that it exists if and only if God exists. I am aware that saying this may lay me open to a charge of heresy on some accounts, because I seem to be distinguishing between God and his omniscience in a way which might seem to challenge the doctrine of God’s simplicity! However, I can proceed no further at present in these theologically deep waters, so offer the example only for the purposes of illustration without presuming that anything that I have said about it is ultimately defensible from either a metaphysical or a theological point of view. 7. Why facts are not needed as truthmakers It will be noticed that I have not so far invoked facts as truthmakers of propositions, nor do I desire to do so. It suffices, I believe, to invoke only entities in the ontological categories of universal, individual substance and mode for these purposes. Facts are typically invoked as truthmakers by those philosophers who believe in the existence of universals and individual substances (or ‘concrete particulars’), but not in the existence of modes or tropes.11 They need them for this purpose because in the case of a contingently true predicative proposition of the form ‘a is F’, where ‘a’ denotes an individual substance and ‘F’ expresses a universal, Fness, neither 11

See, especially, David M. Armstrong, A World of States of Affairs (Cambridge: Cambridge University Press, 1997).

252 a nor Fness nor the pair of them can be a truthmaker of the proposition in question, on any remotely acceptable account of truthmaking. Consequently, these philosophers invoke a new kind of entity, a’s being F, or a’s exemplifying Fness, which supposedly has both a and Fness as ‘constituents’ but is in some way more than just the conjunction or sum of a and Fness, and take this to be the truthmaker of the proposition that a is F. But, to my way of thinking, this manner of proceeding is mystery-mongering to no good purpose, brought about simply because the philosophers in question have tried to do without one of the fundamental categories of being. The mysterious element in their account emerges when we ask about the nature of the supposedly contingent ‘connection’ between the constituents of a supposedly contingent fact. Notoriously, it will not do to regard this as being a further ‘constituent’ of the fact, on pain of falling into Bradley’s famous regress. To label the connection a ‘non-relational tie’ is just to give a name to the mystery without solving it. It seems that the only tenable way of proceeding is abandon any idea that facts are somehow ‘composed’ of their alleged ‘constituents’ and hold instead that the ‘constituents’ of facts are mere abstractions from, or invariants across, the totality of facts, identifying that totality with what Wittgenstein called ‘the world’. However, then it is obscure how any fact can really be contingent, because if the constituents of facts are just abstractions from the facts containing them, it would seem that the very identity of any such constituent must be determined by its overall pattern of recurrence in the totality of facts. That is to say, it becomes impossible to see how any given constituent could have been a constituent in a possible totality of facts different from the actual totality. But in that case, the very point of invoking facts in the first place has been undercut, since they were invoked to provide truthmakers of supposedly contingent predicative propositions—and yet now it seems that there can be no such propositions. All predicative propositions turn out to be necessary truths, because the identity of any individual substance is now taken to be determined, in quasi-Leibnizian fashion, by the totality of predicative truths concerning it.12

12

This seems to be the position towards which Armstrong himself has been gravitating: see David M. Armstrong, Truth and Truthmakers (Cambridge: Cambridge University Press, 2004).

253 8. How are contingent truths possible? How, then, can the possibility of contingent predicative truths be preserved according to an ontology which eschews facts as their supposed truthmakers? In the following manner. Consider again the proposition that this apple is round, which would seem to be a contingent one if any proposition is. According to an ontology which includes not only individual substances, such as this apple, and universals, such as the universal roundness, but also modes, such as this apple’s roundness, any roundness mode of this apple would be a truthmaker of the proposition that this apple is round. For any roundness mode of this apple depends essentially for its existence both on this apple and on the universal roundness. Consequently, it is part of the essence of any roundness mode of this apple that it exists only if both this apple and the universal roundness exist. More than that, however, it is clearly part of the essence of any roundness mode of this apple that it exists only if this apple exemplifies the universal roundness, that is, only if the proposition that this apple is round is true. Notice that I say ‘only if’, not ‘if and only if’—for, clearly, it is not part of the essence of any roundness mode of this apple that if the proposition that this apple is round is true, then that roundness mode exists: for this apple could have been round in virtue of possessing a different roundness mode. Nonetheless, it seems clear that what we can say is that it is part of the essence of the proposition that this apple is round that it is true if and only if some roundness mode of this apple exists. However, it is a contingent matter whether or not any roundness mode of this apple exists, because this apple is not a necessary being and, moreover, it is not part of the essence of this apple that it exemplifies the universal roundness—in other words, it is not part of the essence of this apple that it possesses any roundness mode. The relation of essential dependence between this apple and any roundness mode that it may possess is asymmetrical: it is part of the essence of any such roundness mode that it is possessed by this apple, but it is not part of the essence of this apple that it possesses any such roundness mode. What we have found, in effect, is the sort of thing that can provide the ‘contingent link’ between an individual substance, such as this apple, and a universal, such as the universal roundness, which has to exist in order for the proposition that this apple is round to be true. Any roundness mode of this apple can provide such a link, for any such mode is a contingent being whose existence suffices to guarantee that this apple exemplifies the uni-

254 versal roundness. For it is part of the essence of any such roundness mode that it is an instance of the universal roundness, and it is also part of the essence of any such roundness mode that it is possessed by this apple. Consequently, if such a mode exists, the apple possesses it and the mode is an instance of the universal roundness, whence it follows that the apple exemplifies the universal: it does so simply in virtue of possessing a mode that is an instance of that universal. Some philosophers who do not countenance the existence of modes make the mistake of trying to let the relationship of exemplification itself provide the ‘contingent link’ between an individual substance, a, and a universal, Fness, which has to exist (in addition to a and Fness) in order for the proposition that a is F to be true. But this strategy is bound to fail, because the exemplification ‘relation’ is only a formal ontological relation, not a genuine ‘element of being’. Consequently, it is not something that can be said to exist at all. Other philosophers, acknowledging this point, nonetheless assume that the ‘relation’ of exemplification is a direct formal ontological relation between the substance a and the universal Fness. But then the problem is to see how this relationship can obtain merely contingently. For, given that a and Fness do not need to stand in this relationship to one another—given, that is, that it is not part of the essence of either of them that they do so—what could possibly explain whether or not they actually do so? Notice that a causal explanation is not what is being sought at this point, but a metaphysical one. It is hopeless, really, to appeal to a notion like ‘unsaturatedness’ here, quite apart from the fact that it rests on a dubious metaphor. This is the idea that a universal such as Fness is ‘incomplete’ in itself, rather like a chemical ion whose outer electron shell awaits completion by the addition of one or more other electrons—and that the ‘completion’ can be brought about by the ‘union’ of Fness with an individual substance, such as a. The idea is hopeless because it remains utterly obscure how the ‘union’ is achieved. In the case of a chemical ion, what happens is that some free electrons are attracted into the ion’s outer shell by the electrostatic force exerted by the ion’s nucleus—and this force is certainly something real, an ‘element of being’. Nothing analogous is available in the case of a and Fness, when exemplification is conceived of as a direct formal ontological relation between them.

255 Modes provide the answer to the problem. Modes are real beings which stand in non-contingent formal ontological relations both to individual substances and to immanent universals. When an individual substance possesses a certain mode, it is part of the essence of that mode that it is possessed by that substance, although not part of the essence of that substance that it possesses that mode: they stand in a relationship of asymmetrical essential dependence to one another. Similarly, it is part of the essence of any mode that it is an instance of a certain universal, although not part of the essence of that universal that it has that mode as an instance: they too stand in a relationship of asymmetrical essential dependence to one another. An individual substance exemplifies a given universal just in case a mode exists which stands in two such relationships of asymmetrical essential dependence, one to the substance and one to the universal. Thus exemplification is an indirect formal ontological relationship between individual substances and universals and one that can be contingent because it can be a contingent matter whether an appropriate mediating mode actually exists. 9. Propositions and what they are ‘about’ I have been arguing that the intuitively attractive idea of truthmaking is best cashed out in terms of the notion of essential dependence. More specifically, I have been maintaining that a truthmaker of any given proposition is something such that it is part of the essence of that proposition that it is true if that thing exists—although, as we shall shortly see, this account may need to be modified in a certain way. And by the ‘essence’ of any entity I mean that in virtue of which it is the very entity that it is. So, for example, it is part of the essence of any entity that it belongs to a certain ontological category and also part of its essence that it is that member of the category in question as opposed to any other. Thus, assuming that there are such entities as propositions and that they comprise an ontological category—even if only a sub-category of some more fundamental category—it will be part of the essence of any given proposition that it is a proposition and that it is that proposition as opposed to any other. But at least some propositions depend for their identities on entities belonging to other ontological categories. Any proposition that is, as we say, ‘about’ certain other entities depends for its identity on those entities. Thus, the proposition that a certain individual substance, a, exemplifies a certain universal, Fness, depends for its identity on both a and Fness: for the proposition is essentially ‘about’ those other entities and so couldn’t be the very proposition

256 that it is without being ‘about’ them. It may not necessarily follow from this that it is part of the essence of the proposition that a is F that a and Fness both exist. If that were so, it would mean that the proposition depends essentially for its existence on the existence of a and Fness, and so cannot exist unless they exist. However, one might be able to argue that a proposition can exist while depending for its identity on other entities which do not exist. I am by no means convinced that this can be argued successfully, but am prepared to keep an open mind about the matter for present purposes. What is clear, however, is that—at least in certain cases—if a proposition is ‘about’ certain entities and hence depends for its identity on those entities, then it is part of the essence of that proposition that it is true only if those entities exist. I say ‘at least in certain cases’—and the cases that I have centrally in mind are contingent propositions about the entities in question, where these entities are themselves contingent beings. Possible exceptions would be propositions such as ‘Either a is F or a is not F’, which I would not describe as being a ‘pure’ logical truth, because it is ‘about’ certain non-logical entities. Conceivably, it might be held that this proposition is true, in virtue of its logical form, even in circumstances in which a and Fness do not exist. Be that as it may, what we now have to notice about truthmaking is this. A truthmaker of a proposition need not, in general, be something upon which the identity of that proposition depends. Thus, for example, I argued earlier that the proposition that a is F has as a truthmaker any mode of Fness possessed by a. On the view of truthmaking that I have proposed, this commits me to saying that such a mode is something such it is part of the essence of the proposition in question that it is true if that thing exists. This raises a certain difficulty that I shall discuss shortly, but let us go along with the suggestion at least for the time being. So suppose that m is a certain mode of Fness possessed by a. Then, I want to say, m is a truthmaker of the proposition that a is F—and yet the proposition that a is F by no means depends for its identity upon m. For the proposition is not ‘about’ m at all: it is only ‘about’ a and Fness. So this serves to illustrate my point that a truthmaker of a proposition need not, in general, be something upon which the identity of that proposition depends. Incidentally, we can now see clearly why it was important to say that a truthmaker of a proposition is something such that it is part of the essence of that proposition that it is true if—not if and only if—that thing exists.

257 For it simply isn’t the case, for instance, that the proposition that a is F is true only if m exists: it could have been true in virtue of the existence of another mode of Fness possessed by a. At the same time, it is worth emphasising once again why we need to characterize truthmaking in terms of essential dependence rather than merely in terms of what I earlier called necessary dependence: that is, why we should not say that a truthmaker of a proposition is something such that it is metaphysically necessary that that proposition is true if—or, indeed, if only if—that thing exists. For, as we noted earlier, this would make any necessary being a truthmaker of any necessary truth, quite indiscriminately. 10. A sketch of a theory of truthmaking Now, however, I need confront the difficulty that I alluded to a moment ago. I said that if m is a certain mode of Fness possessed by a, then m is a truthmaker of the proposition that a is F—and I certainly don’t want to give up that claim. But I have also been maintaining that a truthmaker of a proposition is something such that it is part of the essence of that proposition that it is true if that thing exists. This means that I must claim that it is part of the essence of the proposition that a is F that it is true if m exists. But this is problematic if one thinks, as one may well do, that no entity can be in any manner essentially dependent on any entity that could fail to exist in circumstances in which that entity itself did exist. It was this thought that motivated the doubt, mentioned earlier, that an entity could depend for its identity on something non-existent. Now, clearly, we must be able to say that the proposition that a is F could be true in circumstances in which m itself failed to exist: but then the constraint on essential dependence that is now being proposed would rule out our saying that it is part of the essence of the proposition in question that it is true if that mode of Fness, m, exists. Perhaps the most that we can say about the essence of the proposition that a is F is that it is part of the essence of that proposition that it is true if some mode of Fness exists. But then how do we define the truthmaking relation in terms of essential dependence, given the constraint being proposed, on the assumption that it is to be defined as a relation between entities—or, more precisely, as a relation between an entity and a proposition? One possibility would be to say that an entity e is a truthmaker of a proposition p if and only if it is part of the essence of p that p is true if some en-

258 tity relevantly similar to e exists—for example, a mode of Fness possessed by a, in the case in which e is such an entity. But the notion of ‘relevant similarity’ invoked here is much too vague for our purposes (though I shall suggest a way of rendering it more precise in a moment). An alternative possibility would be to appeal to the essence of e rather than to the essence of p and say that an entity e is a truthmaker of a proposition p if and only if it is part of the essence of e that p is true if e exists. But this would be implausible, because it is most implausible to say, for example, that it is part of the essence of a certain mode of Fness possessed by a, m, that a certain proposition ‘about’ a and Fness is true if m exists. For it is most implausible to say that an entity such as m has it as part of its essence that it is related in any way whatever to any proposition. What we are looking for is a satisfactory way of completing the following biconditional statement, intended as a definition of the truthmaking relation: ‘An entity e is a truthmaker of the proposition p if and only if ...’. And the problem that has just been raised is a problem for our original proposal that this should be completed by the clause ‘it is part of the essence of p that p is true if e exists’. But it is more specifically only a problem for the right-to-left reading of the biconditional. There is no problem in saying that if it is part of the essence of a proposition p that p is true if e exists, then e is a truthmaker of p. The problem only arises for the claim that if e is a truthmaker of the proposition p, then it is part of the essence of p that p is true if e exists—the problem being that this seems to require us to allow that it can be part of the essence of a proposition that it be related to an entity which might fail to exist in circumstances in which that proposition itself did exist. It is obvious that we shall be required to allow this if we hold that all propositions are necessary beings but that some of their truthmakers are not. But, as we have seen, we shall still be required to allow it if, for example, we hold that a proposition exists only in circumstances in which all of the entities that it is ‘about’ exist—if, for instance, we hold that the proposition that a is F exists only in circumstances in which both a and F exist. For then a certain mode of Fness possessed by a, m, need not exist in every circumstance in which that proposition exists, nor even in every circumstance in which that proposition is true. I suspect that there is no simple and straightforward way to deal with this problem. But rather than leave the issue entirely unresolved, I shall instead tentatively offer a suggestion for an alternative approach. It may be that

259 rather than simply trying to find a way to complete the foregoing biconditional statement in order to specify the relation of truthmaking, we should proceed in a more roundabout manner, allowing a specification of the class of truthmakers to emerge out of a theory of truthmaking. The axioms of the theory might be taken to be something like the following. (1) For any proposition, p, there are one or more types of entity, E1, E2, …. En, such that, for any i between 1 and n, it is part of the essence of p that p is true if some entity of type Ei exists. (2) An entity, e, is a truthmaker of the proposition p if and only if e belongs to one of the entity-types Ei, which, according to axiom (1), is involved in the essence of p. Thus, for example, a mode, m, of the universal Fness that is possessed by the individual substance a would by this account qualify as a truthmaker of the proposition that a is F, for the following reason. Axiom (1) is satisfied in this case by the entity-type mode of Fness possessed by a, because that is an entity-type such that it is part of the essence of the proposition that a is F that that proposition is true if some entity of that type exists. And m is an entity of that type. Hence, by axiom (2), m is a truthmaker of the proposition that a is F. In effect, this is a way of cashing out more rigorously the notion of ‘relevant similarity’ that was toyed with earlier. One final word: it will be noted that nowhere throughout the preceding discussion have I attempted to define truth itself, as opposed to the relation of truthmaking. This is because I take the notion of truth to be primitive and indefinable, alongside the notions of existence and identity. Only some of the family of formal ontological notions are definable and truthmaking plausibly ought to be one of them. But truth itself, I believe, is too fundamental a notion to admit of non-circular definition.

Identity Makers PASCAL ENGEL Université de Paris IV-Sorbonne

“ What, art thou mad? art thou mad? is not the truth the truth ? Henry IV, I, II, 90 The identity theory of truth, according to which a true proposition is identical with a fact, seems to be a reductio ad absurdum not only of correspondence theories of truth in general, but also of the very idea of truthmaking. This is why it has been often invoked as a genuine rival to the truthmaking theory of truth. In this short article, I propose a reductio ad absurdum of the reductio ad absurdum. I hope, from the confrontation, to highlight some of the advantages of thinking of truth in terms of truthmaking, but I do not propose to defend a particular version of it. 1. Truthmaking A theory of truthmaking emerges from taking seriously the common sense idea that Dummett once expressed as the truism that truth, in order to be truth, must be truth in virtue of something. The truth of the truth-bearers must be determined by, or grounded in something which is not truth, (Rodriguez-Pereyra 2002: 31). But what is the relationship of grounding, determining , and of course of making, in which truthmaking consists? Is it a real relation, like causality, or a logical relation, like entailment, or some other relation (Mulligan 2003)? At least, according to friends of truthmaking, it must be a relation of necessitation: one must accept the truthmaker principle: (TM) For every truth there must be something in the world that makes it true Most of the time it is said, using Bigelow’s characterisation, to be minimally the relationship of supervenience of truth upon being :

262 (STB) Every truth supervenes on being or in other words: “If something is true, then it would not be possible for it to be false unless either certain things were to exist which don’t, or else certain things had not existed which do” (Bigelow 1988: 133). But as Rodrigez-Pereyra notes, supervenience is not sufficient, for being also supervenes on truth: if something exists, then it is not possible for it not to exist unless certain truths were false. So the relation of supervenience has to be understood as an asymetrical dependency of truth upon being. Another way of putting the same idea is to say that truth is not, according to the truthmaker idea, primitive (Rodriguez Pereyra 2002: 31). This is a very important point, for in many conceptions of truth (in particular the disquotationalist and minimalist conceptions) truth is primitive. That truth is primitive means that what truth is is exhausted by a set of principles and properties of the predicate or of the property of truth, and not by the existence of entities which are not truths. It can mean also, especially in Davidson’s version of minimalism (Davidson 1996) that truth is a primitive predicate which is implictly defined by a theory of truth applied to the sentences of the language. In either of these senses, what STB and the insistence on the grounding relation mean is that there is no theory of truth without a theory of being, or without an ontology. Tell us what kinds of things there are, and how things are, and you will know what truth is. It is not enough to study the properties of a semantical relation. From here, truthmaker theorists diverge. Some, like Armstrong (2003) accept the principle of truthmaker maximalism: (TMM) Necessarily for every truth , there is a truthmaker for this truth Others accept only that some truth have truthmakers: they reject the idea that negative, disjunctive, general or modal truths have truthmakers. Most of the time, those who reject truthmaker maximalism accept only the view that atomic propositions have truthmakers. Another great divide within theorists of truthmaking is upon the kinds of entities which are to play the role of truthmakers. Many early and late theorists have taken facts to be the basic entities of which the world is made of, hence the basic truthmakers;

263 but among these some take facts to contain universals as well as individuals, whereas others include only tropes, and some others also events (Mellor 1995). And some truthmaking theorists discount facts from the realm of truthmakers, to allow only things and their properties to play this role (Lewis 2003). Here I shall follow the main trend, and assume that the basic truthmakers are entities such as facts and states of affairs. Somewhat misleadingly, I shall talk of the truthmaking conception of truth as a family of conceptions, although there are large differences between the various versions. 2. The identity theory of truth The identity theory of truth is the view that truth and reality are just the same thing, but it is more aptly formulated for our purposes as the view that a proposition is true if and only if it is identical with a fact: (IT)

is true if and only

is identical with a fact According to the early proponents of IT in contemporary philosophy (Bradley, Russell and Moore, see Baldwin 1991, Candlish 1989) this is meant to be a robust or substantial conception, saying that bits of true thoughts, or propositions, are identical to bits of reality. There is, however, another version of IT, hinted at by Frege 1 (see Hornsby 1997) and more recently defended by McDowell (1994, 2004) and Dodd (2002) which says that IT just amounts to the truism that facts are true propositions. Robust identity theories, which say that true propositions are facts in the world, are of two kinds. Identity is a symmetric relation, which can be read from left to right, and from right to left. From left to right the identity theo1

“A correspondence, …, can only be perfect if the corresponding things coincide and are, therefore, not distinct things at all. It is said to be possible to establish the authenticity of a bank note by comparing it stereoscopically with an authentic one. But it would be ridiculous to try to compare a gold piece with a twenty mark piece stereoscopically. It would only be possible to compare an idea with the thing if the thing were an idea too. And then, if the first did correspond perfectly with the second, they would coincide. But this is not at all what is wanted when truth is defined as correspondence of an idea with something real. For it is absolutely essential that the reality be distinct from the idea. But then there can be no complete correspondence, no complete truth. So nothing at all would be true; for what is only half true is untrue.” (Frege 1967: 18-19)

264 rist nudges propositions into facts, the world is made of true propositions and we get a theory on the realist pole (this was famously Moore’s own version towards 1900). From right to left, the identity nudges facts into thoughts, and we get a theory on the idealist pole (Bradley)2. Let us consider only the first type of version, which I shall call the identity theory of facts (ITF). There are two versions of it, depending how one answers the following question: if a true proposition is a fact, how can a false thought be identical with a fact? Will there be facts which are objective falsehoods? Or should we say instead that false thoughts are not really thoughts, and that only true thoughts are? Truth and falsity seem to be contingent properties of thought contents: these can be true or can be false. To take up Wittgenstein’s term, propositions have two “poles”, truth and falsity, and can instantiate whichever property. Hence if they are identical with facts, they seem to be identical with merely possible facts, and not necessarily with actual facts. On this view, facts can obtain or not, and if they don’t they remain only possible. But there is another notion of fact, according to which facts cannot fail to obtain, or are essentially facts. So ITF can be read in two ways, both for truth and falsity : (ITF a) (i) The thought that p is true = the fact that p contingently obtains (ii) The thought that p is false = the merely possible fact that p (ITFb) (i) The thought that p is true = the essentially obtaining fact that p (ii) The thought that p is false ≠ the essentially obtaining fact that p According to (ITF a), facts themselves have two poles : (they are bipolar (Dokic,1998)). In possible world terminology, a true thought could be true at another possible world if it were identical with a possible fact, but truth in the actual world is defined as the actualisation of a possible fact.3 According to (ITFb), facts have only one pole: . Facts which are not actual are not facts, but mere “states of affairs” or “virtual” facts. Truth is identity with what is essentially or neces2

Although it is tempting to represent the fact oriented view as realist and the thought oriented view as idealist, in all rigour the world is, on either view, neither made of facts nor made of thought, as McDowell (2004) reminded me. 3 See e.g Fine 1982,

265 sarily a fact, and could not be a fact in other possible worlds. Hence falsity is simply the absence of fact, non facthood. But we might go further and allow facthood also for false propositions. So there is a reading of (ITFb) on which false thoughts are identical with negative facts. (ii) is replaced by: (ITFb) (iii) The thought that p is false = the essential fact that not p Famously Russell held such a view for some time, until he was too much worried by this consequence of his early identity theory of truth.4 ITFa and ITF b (i)-(ii) do not only rely on two different notions of fact, but also on two different notions of proposition or thought. For ITFa, a single entity, a thought or a proposition, can be true or false, hence identical to an actual or a possible fact. If I think, for instance, that spring has begun, my thought is one thing, and their being true or false are other things. Same thought content, different realisations. This is why ITFa is a bipolar theory of facts. For ITFb (i)-(ii), on the contrary, when I think truly that spring has begun, my thought is a fact, the essential fact that spring has begun, but when I think falsely that spring has begun, my thought is not a fact, since only the fact that spring has begun obtains. Hence it is not a thought, if the identity theory is correct, but a mere representation. It does not have the same content when it is identical to a fact and when it is not. This why ITF b (i)-(ii) is a unipolar theory of facts : only true propositions can be facts. Only when negative facts are introduced with ITFb (i)-(iii) can one reinstate the bipolarity of facts, but also one has to introduce a bipolarity of propositions or thoughts as well. More recently versions of the identity theory have been held by John Mc Dowell (1994, 2004) Jennifer Hornsby (1997) and Julian Dodd (2002) which, while resting upon the basic identity of propositions and facts IT, are meant to reject any ontological commitment to entities such as facts.5 The identity theory then becomes simply the truism that a proposition is true if and only if it is a fact. Thus Mc Dowell writes: 4

One of the familiar reasons why the notion of negative fact is worrying is that, to put it in terms of an identity theory, a single truth would also be identical with an indefinite number of such negative facts. 5 There are differences between these versions, which I do not attend here. see Engel 2001

266 “There is no ontological gap between the sort of thing one can mean, or generally the sort of thing one can think, and the sort of thing that can be the case. When one thinks truly, what one thinks is the case. So since the world is everything that is the case (as [Wittgenstein] once wrote) there is no gap between thought, as such and the world.” […] “But to say that there is no gap between thought, as such, and the world is to dress up a truism in a high flown language. All the point comes to is that one can think, for instance, that spring has begun and the very thing, that spring has begun, can be the case. That is a truism, and it cannot embody something metaphysically contentious, like slighting the independence of reality.” (McDowell 1994: 27.)

This is meant to be no more contentious than the redudancy conception of truth expressed by the familiar biconditional (R) The proposition that P is true iff P Actually the modest version of the identity theory is meant to free us from the difficulties that the ontological talk about facts created, hence to avoid to “dress up a truism in high flown language”. If this is correct, then the identity theory of truth is a fully deflationist view of truth.6 An important consequence of the modest identity theory is that it will reject the ITFb version of IT according to which facts are essentially obtaining entities. Trivially for the modest or minimalist identity theory, just as true propositions are facts, false propositions fail to be facts, which just means that the proposition P is false iff not P. At best, for the modest identity theory, only the version ITFa can be countenanced. Exeunt negative facts. this seems to confirm a verdict that a number of writers have given on the identity theory,. To speak like Armstrong (1997: 228) the identity theory itself has fallen “into the gravitational field” of the redundancy theory. So how can we hope to extract from it a substantive theory of facts ? In so far as we conceive ITF on the model of a correspondence theory of facts as truthmakers, then, it is difficult to resist the thought voiced by Baldwin, that “the identity theory is the result of adding the unnecessary insistence that truth requires a relationship between thought and the world.” (Baldwin 1991: 50)

6

Lewis (2001) considers the identity theory as a version of correspondence theory of truth, which in turn is said to be a version of the redundancy theory.

267

3. Identity theory as a reductio of truthmaking? Consider now the main principles of truthmaking in comparison with the claims of an robust identity theory of truth. First (IT) entails the truthmaker principle TM : the truthmaking relation is simply interpreted as the identity relation between true propositions and facts, in the same manner as an identity theorist interprets the relation of correspondence as a version of the relation of identity. Trivially every truth is grounded in a fact. We can also, given the necessity of identity and in assuming that “the proposition that P” and “the fact that P” are respectively rigid designators for propositions and fact, say that the identity between facts and propositions is necessary. ( the proposition that P = the fact that F ⊃ = the fact that F )

F

the proposition that P

and so for any particular fact. In this sense true propositions are necessitated by facts. IT also entails TMM, truthmaker maximalism : every true proposition has a truth maker, which is identical to it. And trivially IT grounds truth in being and entails the supervenience of truth over being STB, as a case of identity. Truthmakers are identitymakers. But of course this assimilation of truthmaking ot a robust version of identity theory can’t be right. When one says that truths are grounded in facts and entities upon which they depend, one does not say that they are simply identical. Moreover, identity is a reflexive and symmetric relation, but grounding is neither symmetric nor reflexive. In this sense a truthmaker is not an identity maker. A modest identity theorist can retort that since the robust version of IT can’t be assimilated to the truthmaking conception of truth, the modest version has to be adopted. This is the line taken by Dodd (2001, ch.2). But a truthmaking theorist will reject this. At no point, the principles of truth making can be made equivalent to those of an identity theory of truth,

268 for it is an essential feature of truth makers that they are not identical to the truths which they make. In other words, TM entails that If

is true, necessarily there is at least one entity, distinct from

, whose existence entails that

is true For an identity theorist, there are as many facts as there are truths, and a one-one relation between facts and truth bearers. On some versions of truth making, the truthmakers mirror the propositions. But on most interesting versions, the facts are not simply the tautological accusatives, to speak like Armstrong, of propositions. But on a truthmaker theory of facts the truthmaking relation is one-many, or many-one. To take simple examples, if p or q (inclusive or) is true, this truth has two truths makers, p and q. Or for a true existential sentence saying that there is at least a black swan, there are as many truth makers as there are black swans. Conversely, to one truth maker correspond many truths. For instance, if it is true that either p or q is true, then the truth maker for p is also a truth maker for the disjunctive truth, and for innumerably many other truths (Armstrong 1997:129-130). In other words, facts as truth makers are not true propositions. This prevents a correspondence theory of facts from “falling into the gravitational field of a redundancy theory, to their mutual confusion” (ibid. 128). But it also prevents a correspondence theory of facts from falling into the gravitational field of an identity theory of facts, if such there be, since the identity of propositions and facts implies that there is a one-one relation between them. But the truthmaking conception of truth is not only non equivalent to the identity conception of truth; it gives us also an argument against it. According to ITFa and the modest conception of the identity theory, facts are, just like propositions, bipolar: they are be positive or negative, just as propositions can be true or false. But the very idea that fact can be bipolar is incoherent. It was actually the objection which was pressed by Moore when he rejected his earlier identity theory of truth: [Suppose I have the true belief ]that a given tree, which I see, is an oak…The proposition that the tree is an oak is something which is and equally is whether the belief is true or false…But... the fact that the tree is an oak is something which is, only if the belief be true, and hence it is quite plain that…the fact that

269 the tree is an oak is quite a different thing…from what I believe, when I believe that it is one..” (Moore 1953: 308]7

Moore’s notion of a fact is the notion that facts essentially obtain, as opposed to the notion of facts as states of affairs which may or may not obtain. It is in this sense that facts have only one pole : either they obtain, and they exist, or not and they are not facts. This contrasts strongly with thoughts or propositions, which can be true or false, but which keep their contents whether they are true or false. Propositions, unlike facts are “bipolar”. A modest identity theorist can answer in the following way : (Dodd 87-88 ) “Socrates” designates Socrates in every possible world in which he exists, regardless of whether he is married or not. By contrast, “Xanthippe’s husband” designates Socrates only in those possible worlds where he is married. This does not prevent Socrates from being identical with Xanthippe’s husband. Similarly “the proposition that P” designates the proposition that P in all possible worlds, whereas “the fact that P” designates that proposition only in those worlds in which it is true. So why would this observation refute the identity thesis? But the point is precisely that when a proposition is false there is no possible world in which it is true, hence no fact to which it could be identical. But the very idea of fact as having two poles yields an incoherent notion of fact (Fine 1982). This can also be shown through a linguistic argument to the effect that in number of uses facts are not equivalent to true propositions. In The fact that Mary went was a surprise for John the description is not equivalent to a true proposition. Or we cannot argue in the following way Mary ‘s thought was that John would come That John would come would be a surprise Therefore Mary’s thought would be surprise8 7

Quoted by Künne 2003 : 9-10.

270 So the friend of the identity theory of truth cannnot use (IT) as a form of reductio of truthmaking and correspondence truth. He cannot argue that an identity theory of truth provides a reductio of the notion which the friends of truthmakers finds essential. On the identity theory of truth, truth is not grounded or made true by anything. True propositions are facts, and that’s the end of it. But that is not the end of it. 4. Truthmaking and truth aptness Most of the objections against a modest identity theory of truth are the same as those that one can rasie against a redundancy and other deflationist conceptions of truth. This is not the place here to restate them.9 A theory of truth cannot get rid of the truism, upon which the truthmaking conceptions rest, that truth, in order to be truth, has to be grounded in something else. But there is still an important objection to the truthmaking conception, which is, in particular voiced by David Lewis: “Why is the truthmaker conception of truth a conception of truth? It seems instead to be a theory of all manners of things, and not especially of truth, and what we learn about truth does not come from it but rather from the allied redundancy conditionals. Truth is mentioned in the truth maker principle only for the sake of making a long story short. Take for instance the (1) it is true that cat purr iff there exists something such as the existence of that thing implies that cats purr this by the redudancy conditional is equivalent to (2) Cats purr iff there exists something the existence of which implies that cats purr but (2) tells us nothing about truth. It is about the existential grounding of the purring of cats. (Lewis 2002: 278-79)

David (2002) replies to this on behalf of the correspondence theorist that the argument could as well be used against the redudancy conception, since it implies an infinity of biconditionals which are about truth, and the truthmaker principle is not identical with its instances, but offers a generalisation about truth. Lewis, however, has a point, which can be formulated thus. The truthmaker conception of truth implies that a theory of truth cannot be given unless one also provides an ontology of the kinds of things 8 9

Künne 2003 p. 10. I have given some reasons to reject a deflationist conception in Engel 2002.

271 which make truth truth. When these various kinds of makings will have been spelled out, there should be no more to way about truth. But, Lewis’s objection says, we shall have ended up with a whole treatise on ontology, not on truth. The intuition which underlies Lewis’ objection is that a theory of truth should not simply list the kinds of truths there are and tell us a sortal about each, but it should give us a general account of what truth is, independently of the fact that there are such and such kinds of truths : negative, general, modal, temporal, deontic, etc. A theory of truth should have to be about the common core of all such kinds of truths. The idea that there are various kinds of truthmaking relations, specific for the varieties of kinds of truths, should not be confused with what is sometimes referred to as a “pluralist” conception of truth, according to which there are as many truths as there are subject matters : mathematical, ethical, empirical, etc. (Wright 1992). For this pluralistic stance is also congenial to a deflationary or minimalist conception : there are truths, but no property of truth. Truth does not come up to much more that the usual truisms about disquotation, syntactic embeddings, and the ordinary platitudes about it. For a truthmaker conception, on the contrary, there is such a property as truth. It is philosophically interesting. But in order not to make the whole topic of a theory of truth collapse into ontology of metaphysics, what we should accept is the existence of a common property of truth which has the very same formal properties in each domain, but which is realised differently in each domain. We need something like a distinction between the claims of a theory of truth and the properties of our statements of being, in each kind of domain truth apt. Not all domains are truth apt : for instance ethical statements may not be, or statements about universal properties may not be. But a theory of truth contains the main properties of the concept of truth. In this sense, it will include such principles as the truthmaker principle and the principle of supervenience of truth over being. These are sustantial requirements to be added to the usual platitudes that truth is correspondence, objective, that is disquotational, a norm of assertion and belief, and the like. The job of sorting out the various ways in which truths can be truths will be devoted to ontology. 10

10

I have defended such a quasi functionalist conception of truth and the distinction between truth and truth aptness in Engel 2002.

272

REFERENCES Armstrong, D.M. 1997 A World of States of Affairs, Cambridge: Cambridge University Press ——2003 Truth and Truthmakers, Cambridge: Cambridge University Press Baldwin, T. 1991 “The Identity theory of truth”, Mind, 100, 35-52 Bigelow, J. 1988 The Reality of Numbers, Oxford: Oxford University Press Candlish, S. 1989 "The Truth about F.H. Bradley', Mind , 98, 331-48 David, M. “Don’t Forget about the correspondence theory”, Australasian Journal of Philosophy, 82, 1, p.42-47 Davidson, D. 1996 “The Folly of trying to define truth”, Journal of Philosophy, 94, 263-78 Dokic , J.1998 “The Ontology of Perception: Bipolarity and Content”, Erkenntnis Dodd, J. 2000 , An Identity Theory of Truth, London McMillan Engel, P. 2001 “The false modesty of the identity theory of truth”, International Journal of Philosophical Studies, 9(4): 441-58 ——2002 Truth, Acumen, Chesham ——2004 “The unimportance of being modest: A footnote to McDowell’s note, International Journal of philosophical Studies, 13, 1, 89-93 Fine, K. 1982, “First-Order Modal Theories III- Facts”, Synthese, vol. 53, 1, 43-122 Hornsby, J. 1997 "Truth: the Identity Theory", Proceeedings of the Aristotelian Society, XCVII, 1-24 Künne, W. 2003 Conceptions of Truth, Oxford: Oxford University Press Lillehammer, H. & Rodriguez-Pereyra, G. eds 2003 Real metaphysics, Essays in Honor of D.H. Mellor, London: Routeldge. Lewis, D. 2002 “Forget about the correspondence theory”, Analysis, 61, 275-80 ——2003, “Things qua truth makers”, in Lillehammer and Rodriguez Pereyra 2003 25-38

273 McDowell, J. 1994 Mind and World, Harvard: Harvard University Press ——2004, “The true modesty of the identity theory of truth: a note on Pascal Engel’s false modesty of the identity theory of truth, International Journal of philosophical Studies 13, 1, 82- 89 Mellor, D.H. 1995 The Facts about causation , London: Routeldge Mulligan , K. 2003 “The truthmaking tie”, to appear Rodriguez-Pereyra, G. 2002 Resemblance nominalism, Oxford : Oxford University Press Wright, C. 1992 Truth and Objectivity, Oxford : Oxford university Press

Truth-making : What it is not and What it Could be STEFANO CAPUTO

1. Introduction By the end of the seventies the rise and fall of the correspondence theory of truth in contemporary philosophy seemed to be of interest only to historians of philosophy. Having emerged in works by Moore, Russell, Wittgenstein, correspondence theory had already begun to fall out of favour after Frege’s identification of facts and true proposition s; it later met its ruin, first with Wittegenstein’s criticism of the tractarian conception of language, then with Strawson’s questioning of the existence of facts in his attack on Austin’s version of the correspondence theory and finally with the stones launched by Davidson’s slingshot against the distinctness of facts1. Correspondence theory seemed to have been superseded on the one hand by more refined Tarski-style definitions of truth-predicates, and on the other by the growth of the deflationist stance rooted in the work of Ramsey2. This was the state of the art until, in 1984, the seminal article TruthMakers by Mulligan, Simons and Smith appeared3, shedding new light on the question. At about the same time Australian philosophers, such as David Armstrong and John Bigelow, were defending a realist stance in philosophy, considering the question of what makes some true sentences true to be the central one for approaching problems in metaphysics and the philosophy of mathematics4. On both these philosophical sides it was claimed that at least the central intuition of the correspondence theory was still alive and not sufficiently accounted for by more fashionable approaches to the problem of truth, the intuition at stake being that truth is grounded in 1

See: Moore (1953), Russell (1918), Wittgenstein (1921), (1953), Frege (1918), Strawson (1950), Austin (1950), Davidson (1969). 2 As to the first strand: Kripke (1975); as to the second: Ramsey (1927), Field (1994), Horwich (1990). 3 Mulligan, Simons, Smith (1984). 4 Bigelow (1988); Armstrong (1997).

276 being. Perhaps facts are mere shadows of language, perhaps there is no way that is both intelligible and general to analyse the relation of correspondence ; it was nonetheless felt that at least one thing needed be saved in the correspondence theory: that, for any true truth-bearer (or at least any true truth-bearer in a basic class), there must be something making it true, otherwise truth would float in the air; this is what could be called the correspondence intuition. According to those philosophers, the expression “something” in “something making it true” was to be read (given their sympathy for the correspondence conception) as meaning “some thing”, “some entity”. This meant that the last twenty years have seen a revival of the debate, if not on correspondence theory, at least on the correspondence intuition. The debate has centred on questions, such as: 1) How many true truth-bearers have entities making them true? 2) What exactly is making true? As to the first question, some have answered that every true truth-bearer needs some entity making it true, thus advocating what is called truthmaker maximalism5. Others have adopted a form of neo-logical atomism, answering: only for a basic class of true truth-bearers is it the case that there is some entity making them true. Finally there is the most sceptical reply: only in a very limited number of cases is there some entity making truth-bearers true, so there is not even an extensional tie between truths and truth-makers. As to the second question, some began to characterize making true using the modal notion of necessitation ; others tried to refine the modal approach ; while yet others appealed to the notion of internal relation or to the notion of essence6. It seems to me that the second question is the most basic, at least from the methodological point of view: in fact answers to the question about how many things are in the relation R depend partly on the concept of “R” we start with. In what follows I will discuss two kinds of analyses of the notion of making true: modal analyses (in particular those proposed by Barry Smith) and 5

As to the first answer see: Armstrong (1997); Mulligan (2003); for the second, Simons (2000), Smith (2004); for the third, Dodd (2002). 6 For the modal approach see: Fox (1987), Smith (1999); for the internal relation approach, Armstrong (1997); for the essentialist approach, Mulligan (2003), (2004).

277 essentialist analyses (in particular one recently proposed by Kevin Mulligan). I will show what I believe to be the shortcomings of these analyses. Finally I will put forward an analysis I think is immune from those shortcomings and preferable on independent grounds. 2. Two constraints As I am going to claim that two analyses of the notion x makes y true are unsatisfactory, I want to make explicit two constraints I believe any adequate analysis of this notion should satisfy. I think these constraints are overtly or covertly accepted by everyone engaged in the debate concerning truth-makers and making true. The first one is what I call the “becauseconstraint”; its source is a general feature of the notions expressed by instances of the form x makes y F7. Such instances are used to attribute some explanatory power to x being in certain way: x being in a certain way explains why y is F8. For instance if I say, “Carlo makes Maria happy”, I will be willing to think that Carlo’s being in a certain way (for instance, his being so nice to her) explains why Maria is happy: this entitles me to say that Maria is happy because Carlo is nice to her. Sometimes what has explanatory power for something being F is simply the existence of something else. An example of such use is when we say that a given promise makes an action obligatory or that the firing of a certain neuron makes someone sad. In such cases what is claimed is that the mere existence of the promise or of the firing has explanatory power for the action in question being obligatory or the person being sad: only the occurrence of the neuron’s firing and nothing else explains why that person is sad; only the existence of the promise and nothing else explains why the particular action is obligatory. The use of “making” generally involved in the debate on truthmaking is the latter: what supporters of truth-makers are not willing to deny is that there are entities that simply by existing explain truth-bearers’ being true, and are therefore truths’ ontological grounds. (BC) if x makes y F then y is F because x exists.

7

Although both predicates and their nominal parts can be substituted for “F” (so that both “x makes y red” and “x makes y run” count as instances of “x makes y F”), in what follows I will narrow the substitution class for “F” to the class of nominal parts of predicates. 8 This is underlined in Mulligan (2003).

278 The second constraint, which I call the “relevance-constraint”, is a consequence of the instance of the because-constraint which is obtained replacing “F” with “true”. What features an entity should have in order to explain why y is F will depend on what conditions must be satisfied for y to be F. Conditions that must be satisfied for a given truth-bearer to be true are called truth-conditions; therefore whether some entity makes a given truthbearer true will depend on the truth-conditions of the truth-bearer involved. This dependence can occur in two ways: either the truth-conditions are existential or what grounds their satisfaction is the existence of some entity. Truth-conditions are closely linked to semantic content, as is shown by the following principle: if truth-bearer y says that p, then the condition that must be satisfied for y to be true is that p. So whether some entity makes a given truth-bearer true will also depend on the semantic content of the truth-bearer. This does not mean that whatever makes a truth-bearer true must be represented by it9; rather what is needed is the following: (RC) if x makes p true then either p says that x exists or x’s existence grounds the satisfaction of the conditions that, given what p says, must be satisfied for p to be true. This means roughly that if x makes p true then x must have something to do with the subject matter of p; if the subject matter of p is Mary and her being sad, what makes p true must have something to do with Mary and her sadness. 3. Modal analyses The mainstream in the last twenty years’ literature on truth-makers has been to analyse the relation of making true by using modal notions. Making true was initially identified with necessitation10. 1) x makes p true =def E!x & † (E!x → p).

9

Here, and in what follows, I use the verb “to represent” and cognate terms in a non theoretically loaded way: for instance when I say things like “Tom is represented by p” I mean that Tom is one of the several things p can be sensibly said to be about. 10 Fox (1987).

279 The reason for this move may have been that it seems correct to consider necessitation as a necessary condition for being an ontological ground. Necessitation is in fact a constraint for truth-making which is deducible from the because-constraint. If x is such that its mere existence and nothing else explains why y is F, then it should not be possible that x exists without y being F. In fact if this were possible, the world could be different in terms of y being F without being different in terms of x existing and this would be a good reason for believing that something else, in addition to x’s existence, is needed to explain why y is F. Unfortunately, as was first noticed by Restall, necessitation is not a sufficient condition for truth-making: definition (1) satisfies neither the because- nor the relevance-constraint11. In the first place, every existent makes every necessary truth true, although it is not so that necessary truths are true because of the existence of whatever and that they are about whatever. In the second place, for any a and b such that necessarily if a exists so does b, a makes any proposition true that is made true by b; as b makes the proposition that b exists true, a makes this proposition true as well, even though it is not because of the existence of a that it is true that b exists and even though the proposition that b exists cannot be sensibly said to represent either a or the existence of a12. As an instance of this kind of problem, take a to be any contingent being and b any necessary being (me and God): the definition compels us to say that I make the proposition that God exists true, even if it is not because of my existence that it is true that God exists and in no way can the proposition that God exists be said to be about me or my existence. Against counterexamples of this kind it could be argued that they appeal to dubious entities as necessary beings. To this I reply that it is not necessary for the soundness of the counterexamples that such entities exist; what is sufficient is that assuming their existence is not incoherent. If God existed we would not be disposed to say that it is true that God exists because I exist and, as a consequence, we would not be disposed to say that I make true that God exists. So x necessitates p does not entail x makes p true. 11

Restall (1996). Restall (1996) provides a slingshot kind argument to the effect that each existent makes true any true proposition. The argument assumes that instances of “p v ¬ p” are necessary truths: since it is not obvious that such instances are necessary truths I will not assume in what follows that this argument is correct. 12

280 The violation of the because-constraint can be better appreciated if we keep in mind that the truth of “† (E!a → E!b)” is usually at least considered as a necessary condition for a to be ontologically dependent on b. This involves that defining truth-making as necessitation compels us to consider any dependent entity as what makes it true that its depends exists. But this seems to turn things upside down: if a is ontologically dependent on b it seems more correct to say that it is because of the existence of b (perhaps with some further condition) that it is true that a exists and not the other way around. As an instance of such a problem, take the brightness of Carola’s smile and Carola: the definition under discussion compels us to say that the brightness of Carola’s smile makes it true that Carola exists; but the opposite is surely true: it is Carola, perhaps with some further condition, which makes it true that the brightness of her smile exists. After all the brightness of Carola’s smile is the way a dependent part of Carola is: so the existence of such brightness can serve at most as evidence of the existence of Carola, as smoke is evidence of fire, but evidence is not ontological ground13. Barry Smith tries to overcome these problems using only modal notions plus mereology. The first definition proposed is: (2) x makes p true =def E!x & † (E!x → x ≤ σy. yPp)14. “σy. yPp” means “the mereological sum of the entities projected by p”; the relation of projection is defined as the dual of necessitation: (3) xPp =def p & † (p → E!x). Replacing in (2) “yPp” with the definiens in (3) we have: (4) x makes p true =def E!x & † (E!x → x ≤ σy. p & † (p → E!y)). (4) indeed solves some problems of the definition of truth-making as necessitation, but unfortunately not every problem is solved. Contingent beings no longer make necessary truths true: such truths in fact do not entail the existence of any contingent being. The same holds for contingent 13 14

This problem was already raised by Smith (1999). Smith (1999).

281 and necessary beings: the existence of the latter does not entail the existence of the former. Unfortunately, what is still there is the problem of dependent parts and their wholes. The brightness of Carola’s smile satisfies the following condition: it cannot exist except as a part of Carola; Carola is in turn projected by the proposition that Carola exists; so the brightness of Carola’s smile is necessarily part of the merological sum of the things projected by the proposition that Carola exists (it is necessarily a dependent part of Carola, which is in turn part of the sum in question). Therefore the brightness of Carola’s smile makes the proposition that Carola exists true, contrary to what we would expect: in fact it is not because of the existence of the brightness of Carola’s smile that it is true that Carola exists, rather the other way around. Moreover the proposition that Carola exists does not represent Carola’s smile, thus the relevance-constraint is also violated. The second definition proposed by Smith is simpler and more demanding than the first: (5) x makes p true =def E!x & † (E!x ↔ p)15. (5) is more demanding than (4) because it requires that a truthmaker for p be such that its existence is entailed by p; so (5) succeeds in excluding dependent parts from what makes the propositions saying that their substances exist true. (5) has however problems of its own. The main problem is the following: any two necessarily coexistent beings, say a and b, are such, according to (5), that we can say both that a makes the proposition that b exists true and b makes the proposition that a exists true, regardless of either the existence of a having explanatory power for it being true that b exists or the existence of b having explanatory power for it being true that a exists and although the two propositions seem not to share any content (except the concept of existence). Using (5), for instance, we are compelled to say that Number 2 makes the proposition that Justice exists true, provided we have a Platonist view of these entities: if (5) were a correct analysis of “x makes p true” then every Platonist would be a Pythagorean16.

15

Smith, (1999), (2004). Again, as before, the actual existence of any necessary being is not needed for the example to make its case.

16

282 Smith is well aware of problems of this kind, and indeed he has a reply. The reply is that such problems are pseudo problems raised by our finegrained intuitions, cognitively determined, concerning the content of truthbearers. But semantic content in itself is not different from the conditions that must be satisfied for truth-bearers to be true: truth-making specifies the case when such conditions consist in the existence of a particular entity. Therefore if the existence of a is a condition that must be satisfied for p to be true and necessarily b exists if and only if a exists, the existence of b is also a condition that must be satisfied in order for p to be true; thus b makes p true17. My point against this argument is that it presupposes the modal account of truth-conditions and, of course, accepting such an account also involves accepting a modal account of truth-making. However the considerations above are intended precisely to emphasize the shortcomings of modal accounts of truth-making (and, a fortiori, of truth-conditions): they are intended to show that modal accounts violate very strong intuitions about truth-making revealed by the because- and relevance- constraints. It could be countered that because- and relevance- constraints are not important for truth-making; but if they were not important for truth-making, there would not be any reason to reject the definition of truth-making as simple necessitation. Smith himself however puts forward his definitions in order to overcome the problem of malignant necessitators, which the definition of truth-making as necessitation must face. Malignant necessitators are however malignant precisely for the reason that they violate because- and relevance- constraints; so these constraints are important for truth-making and if they are important they are always important and not just up to a certain point. Finally (5) involves a further problem: sentences of the form “E!a iff p” express a symmetric logical relation whereas “because” (and so making F) expresses an asymmetric relation. Pythagoreans believed that Number 2 makes Justice exist and precisely for this reason they would have denied that Justice makes Number 2 exist. For this reason they thought that what makes it true that Justice exists is Number 2, while at the same time they would have denied that Justice makes it true that Number 2 exists. Nonetheless if (5) is a definition of making true our Pythagoreans were wrong: Number 2 makes it true that Justice exists and Justice makes it true that 17

Smith, (2004).

283 Number 2 exists. The moral is that once the question about the truth of a sentence of the form “E!a & † (E!a ↔ p)” has been settled, there is still room for asking whether or not a makes it true that p. So the definition in question does not state a sufficient condition for “x makes p true”. The reason why modal accounts violate both relevance- and because- constraints is that modal notions are too coarse-grained to grasp representational content and explanatory relations: it is not sufficient that † (p ↔ q) for it to be so either that q because p or that what is said by p has something to do with what is said by q. So modal accounts are doomed to failure: while they may define something this is not making true. 4. An essentialist analysis In some well-known papers, Kit Fine has underlined the shortcomings of modal accounts in dealing with the problem of what it is for something to be essentially in a certain way: modal notions are more coarse-grained than the notion of essence. So Fine claims that instead of analysing the latter via the former, it should be realized that modal truths are grounded on the essences of the objects they are about18. In a recent paper Mulligan remarked that the shortcomings of modal accounts of essence are the same as those of modal accounts of making true. This leads him to a natural conclusion: modal accounts of making true are mistaken because making true is a relation that holds between an entity and a proposition in virtue of their essences. The first problem we encounter here is the following: to say that truthmaking is an essence-induced relation does not reveal much about the nature of truth-making; after all many relations can be exemplified by their relata by virtue of the essences of such relata. What we would like to know is not so much what the status of the exemplification of the truth-making relation is, but rather either what the nature of the relation is or, at least, what content the notion of “x makes p true” has19. 18

Fine (1994a) (1994b). This is what Mulligan (2003: 547) says about immediate truth-making: “To say that the fact that p immediately makes true the proposition that p is just to say that the truth-making relation holds in virtue of the essences of each.”. This sentence does not help to clarify what truth-making is, for it only presents a species of truth-making (immediate truth-making) leaving the general kind Truth-making unanalysed. A simi19

284 I will therefore discuss here, as if it had explicitly been proposed by Mulligan, a definition of truth-making according to which truth-making is not simple necessitation but necessitation induced by the essences of the relata. (6) x makes p true =def E!x & x/p †(E!x → true p)20. Here the index “x/p” is an essence operator which can be read “x and p are essentially such that”. The essence of the truth-bearer should, in Mulligan’s proposal, “determine what portion of reality the truth-bearer represents”21, to avoid, together with reference to the essence of the truth-maker, malignant necessitators. For instance, both reference to the essence of Stefano and to the essence of the proposition that 2 + 2 = 4 prevent Stefano from being a truth-maker for such a proposition. In fact the essence of Stefano does not involve numbers, nor can the proposition that 2 + 2 = 4 be sensibly said to be about Stefano. Reference to the essence of the proposition that Carola exists prevents the brightness of Carola’s smile from being a truth-maker for such a proposition. In fact, although such brightness, if things like brightnesses exist, is identity-dependent on Carola (and so it is in virtue of its essence such that it cannot exist without Carola), the proposition that Carola exists does not represent such brightness. The last example allows us to appreciate that, in some critical cases, (6) does its job in virtue only of reference to the essences of truth-bearers, while reference to essences of truth-makers is ineffective. In fact the definitional schema (7) x makes p true =def E!x & x† (E!x → p),

lar problem arises with the characterization of the truth-making relation as an internal relation which was proposed by Armstrong (1997). That a relation is internal means, given Armstrong’s account of being internal, that the relation is such that necessarily if the relata exist then the relation is exemplified by them. But this leaves open the question concerning what being in that relation amounts to. 20 It would be more correct to say that what is defined by the definition is the sense of “making” and not of “making true”: in fact the truth-predicate reappears in the definiens. 21 Mulligan (2003: 547).

285 in which the definiens is not committed to truth bearers (and, a fortiori, to their essences), allows the brightness of Carola’s smile to be a truth-maker for the proposition that Carola exists: essential necessitation (as defined in (7)) turns things upside down no less then simple necessitation does. A stronger version of (7), namely (8) x makes p true =def E!x & x† (E!x ↔ p), which avoids the case of the brightness of Carola’s smile, still has problems. Take the case of a Leibnizian God who, by its very essence (and so necessarily), created the world; it could be claimed (in a Kripkean view of essential properties) that the world essentially involves the existence of its creator. So (8) compels us to say that our world makes the proposition that its creator exists true. And this, again, seems to turn things upside down22. How does (6) manage to avoid such problems? It does so precisely thanks to its reference to the essence of the truth-bearer, which should determine what portion of reality the truth-bearer represents: the proposition that Carola exists does not represent the brightness of Carola’s smile and the proposition that God exists does not represent the world! This, however, raises a problem: if someone tells us that the proposition that Carola exists is true because of the brightness of Carola’s smile and that the proposition that the Leibnizian God exists is true because of the created world, the reason we are astonished seems to be different from the reason for which (7) and (8) are not open to counterexamples. What is wrong with the previous statements is not, at least prima facie, that speaking about Carola’s existence is not speaking about the brightness of her smile, or that speaking about God’s existence is not speaking about the created world: the problem seems to be metaphysical rather than semantic. What is wrong seems to be that it is not in virtue of the existence of the brightness of Carola’s smile that the truth-conditions of the proposition that Carola exists are satisfied (i.e. it is not in virtue of that brightness that Carola exists) and it is not in virtue of the existence of the created world that the truth-conditions of the proposition that God exists are satisfied (i.e. it is not in virtue of the created world that the Creator exists)! 22

This case is made, in a slightly different way, in Correia (2002) against essentialist conceptions of ontological dependence. The suitability of these examples for our topic should be no surprise: ontological dependence is the inverse relation of a particular case of making F: making exist.

286 Of course, people believing in individual essences can object that it is in virtue of their essences that truth-bearers have their truth-conditions. Even accepting this point, a sentence like “The created world makes the proposition that God exists true” should be considered wrong for two reasons: that the proposition that God exists is true if and only if some specific conditions are satisfied; and that the created world is not what grounds the satisfaction of such truth-conditions. As we saw when stating the relevanceconstraint, in order to be what makes a truth-bearer true, an entity should satisfy a disjunctive condition: either the truth-bearer says that it exists or its existence grounds the satisfaction of the conditions that, given what the truth-bearer says, must be satisfied for the truth-bearer to be true. Taking anything whose existence grounds the existence of Carola (for instance the vital processes occurring inside her body), even if the proposition that Carola exists does not represent such entities, it still makes sense to say that these entities are what makes the proposition that Carola exists true. Nevertheless, according to (6), this is false because the vital processes inside Carola are not represented by the proposition that Carola exists. Therefore (6) does not provide necessary conditions for truth-making. A similar case is provided by logically simple propositions ascribing things their contingent properties, like the proposition that this rose (on my table) is red. There are philosophers who claim that there are entities like tropes, whose mere existence grounds things’ having their contingent properties: this rose being red is grounded in the existence of the particular redness of this rose. If these philosophers were right it would seem correct to say that the redness of this rose makes it true that this rose is red. Nonetheless, according to (6), even in such a situation, this would be false. In fact, the predicate “is red” (or the concept of being red) does not represent any particular redness, otherwise the proposition that another (red) rose is red would be false simply because there is a different trope involved in grounding the rose’s being red. The point is that (6) can allow the rejection of sentences like “The brightness of her smile makes it true that Carola exists” merely by invoking the fact that the brightness in question is not represented by the proposition. In fact, as far as the metaphysical aspect of the question is concerned, (6) cannot appeal to ontological grounding but only to essence-induced necessitation which, as we saw, is the opposite of grounding. So (6) avoids counterexamples for the wrong reasons: it misses the metaphysical reason (ontological grounding) and lets essences of truthbearers play a mistaken role, the appropriate role being that of determining

287 the truth-conditions of the truth-bearer and not that of preventing what falls outside the representational content from playing the role of truth-maker. The fact that (6) does not provide necessary conditions for truth-making is also shown by the following case. The case is interesting because it shows that not even being an essence induced necessitator of p is a necessary condition for being a truth-maker of p. Take any singular existential true proposition, for instance the proposition that I exist; the proposition is about me and it seems perfectly sound to say that it is true that I exist because I exist. So the proposition that I exist - and I - satisfy both becauseand relevance- constraints; we would thus be allowed to say that it is me that makes the proposition that I exist true: things themselves make truthbearers saying that those things exist true. Unfortunately I am not such that in virtue of my essence it is true that I exist! Otherwise I would be something essentially existent : the ontological argument would apply to me and I would be a necessary existent. But I am not a necessary existent, so essence-induced necessitation is not a necessary condition for truth-making: an entity can make a proposition true even if it is not in virtue of its essence that the proposition is true. Therefore truth-making is not essenceinduced necessitation23. 23

Some might object that this argument depends on the false premise that there are singular existential propositions. This premise is false because singular existential sentences, like “Andrea exists”, actually express general propositions like “Something is identical to Andrea”. My answer is that I think that the Russellian idea that the logical form of singular existential sentences is that of quantified identity sentences is mistaken; as to the arguments for such a claim I basically agree with McGinn (2002). Moreover, if someone agrees that “Andrea exists” expresses the proposition that there is something identical to Andrea, then that person cannot accept both (1) and (2): (1) Andrea makes true that there is something identical to Andrea; (2) truth-making is essence-induced. In fact even though self-identity is usually considered an essential property of everything, this can happen in two ways: either accepting or denying that a sentence like “Andrea = Andrea” entails the sentence “There is something identical to Andrea”. The Russellian must of course choose the first option. But, in the first option, an existence claim is already either presupposed or semantically contained by ascriptions of self-identity (as it is by property ascription in general). The intuition behind the inference rule of existential generalization is in fact that nothing can be in some way (not even self-identical) without existing. From this perspective, that an entity is self-identical has as a metaphysical condition the existence of such an entity. But if the entity in question, Andrea, is a contingent being, then it is not in virtue of its essence that it is in the domain and therefore it is not in virtue of its essence that something in the domain is identical to Andrea. Therefore someone accepting a Russellian analysis

288 The supporter of (6) might react to this point simply taking a revisionary stance toward our intuitions: in spite of our willingness to assert things like “It is true that Stefano exists because Stefano exists”, Stefano does not make that Stefano exists true; namely for the reason that, even if he is at least one of the things represented by the proposition, he is not such that in virtue of his essence if he exists it is true that Stefano exists24. This strategy has, however, the discouraging result that nothing except the state of affairs that Stefano exists can make the proposition that Stefano exists true. Nothing except the state of affairs that Stefano exists can in fact be thought to have both of the following features : a) being what is represented by the proposition that Stefano exists; b) being essentially such that if it exists (obtains) it is true that Stefano exists25. (a) is in fact satisfied by states of of singular existential sentences and an essence-induced conception of making true cannot have things themselves as truth-makers of singular existential sentences (quantified identity propositions): it is not in virtue of its essence that Andrea makes it true that there is in the domain something which is Andrea but in virtue, instead, of having that essence, and he has an essence because he is in the domain. 24 The sentence “Stefano exists if and only if it is true that Stefano exists” seems to be true only by virtue of the denominalizing property of the truth predicate; moreover, if we exploit the denominalizing property of the truth predicate in “Stefano exists if and only if it is true that Stefano exists”, we are left with “Stefano exists if and only if Stefano exists”, which is an instance of the form “p → p” which, again, seems not to be true in virtue of what Stefano is, but by logic only. 25 Here, and in what follows, obtaining is conceived as the way in which states of affairs exist, so that there are no non-obtaining states of affairs (as there are no nonexistent entities in general). Talk of obtaining can be turned into talk of existence if one thinks that the existence of facts is nothing but the obtaining of states of affairs, thus if one thinks of facts as obtaining states of affairs. This seems to be the conception endorsed by Mulligan: “To say that a state of affairs obtains is to predicate a mode of being of it. This mode of being, like such other modes of being as being alive, enduring, perduring entails but is distinct from existence in the sense of the quantifier. Thus if a state of affairs obtains, a fact exists”, (Mulligan 2003: 549). It could be argued that, given the conception of facts as obtaining states of affairs and the conception of obtaining as the way states of affairs exist, it is a mistake both to say that a fact exists and to say that it does not exist: in fact to say of a fact that it exists is to say of an obtaining state of affairs that it exists, and this is redundant because obtaining is merely the way entities such as states of affairs exist; therefore to say of a fact that it does not exist is to say of an existing thing (an obtaining state of affairs) that it does not exist and this is to state an inconsistency. To this it could be replied that after all redundancy does not create logical problems; against the inconsistency claim it could be argued that the sentence “The fact that p does not exist” means no more than the

289 affairs if one believes that they are what propositions represent; (b) is satisfied by states of affairs (or by facts) because it can be claimed that biconditionals of the form the state of affairs that p obtains iff it is true that p or the fact that p exists iff it is true that p (if you are content with talk of the existence or non existence of facts) are true in virtue of what facts or states of affairs are, and thus in virtue of their essence. Why is this discouraging? Because one of the reasons (I suspect the main one) why the notion of making true appeared to be philosophically interesting was that it left open the possibility of defending a correspondence conception of truth without being committed to its most controversial points, such as commitment to facts or states of affairs. We now discover that we were wrong: there are some prima facie logically simple propositions, such as singular existential ones, which can be made true only by states of affairs. It should be noted that this problem cannot be avoided by relaxing the relevance-constraint and being content with some entity which is essentially such that if it exists Stefano exists although it is not represented by the truth-bearer: this in fact would involve accepting a definitional schema like (7) for x makes p true. Unfortunately, as we saw, every individual quality of Stefano satisfies (7) without satisfying the because-constraint. To avoid counterexamples of this kind one could choose a more demanding definitional schema, such as (8). But apart from the fact that, as we have just seen, (8) has its own problems as a definitional schema of x makes p true, (8) brings us back to the realm of states of affairs. What other than the state of affairs that Stefano exists could be such that in virtue of its essence (and perhaps in virtue of the essence of Stefano) it is true that it exists (obtains) iff Stefano exists? Well, it could be replied, you do not need a state of affairs if you have a metaphysics of substances according to which: a) substances are individuated through their origins; b) there are not only originating substances (such as Stefano’s parents), but even originatsentence “The state of affairs that p does not obtain”; alternatively one could resort to a neo-Meinongian distinction between two modes of predication (such as Zalta’s (1983) encoding and exemplifying), so that saying of a fact that it does not exist would amount to denying the exemplification of existence to an object which encodes such a property. Even if, following Mulligan, in what follows I say of facts that they exist (or do not exist), I do not take a stance on the question concerning the soundness of such statements: my argument would still be in place even if only talk of states of affairs which obtain were allowed.

290 ing events which are essentially the originating events of their originated substances (for instance the birth of Stefano). In such a metaphysics the birth of Stefano and Stefano are such that in virtue of their essences it is true that the birth exists iff Stefano exists. This proposal has several problems. First of all it shares with (5) the problem of symmetry: it is both true that the existence of Stefano essentially entails the existence of his birth and that the existence of the latter essentially entails the existence of the former; therefore we can say not only that the birth of Stefano grounds Stefano’s existence but even that Stefano grounds the existence of Stefano’s birth. But ontological grounding is an asymmetrical relation. The second problem is that the proposal is not generalizable to every singular existential proposition: even granting that essentiality of origins is true for complex substances such as me or the chair I am sitting on, it seems to me that it cannot be true for every existent. First of all, this would start a metaphysical regress in the identity of entities. Second, it is a convincing metaphysical thesis that there are primitive entities whose identity and existence is not grounded on the identity or existence of other entities: examples of such entities are, according to some metaphysicians, primitive substances such as selves or the basic constituents of matter or both26, according to others, primitive tropes whose combination grounds the existence of all other entities. And if Platonism is right, there are entities, such as abstract entities, for which it makes no sense to speak of origins. Take any of those entities, call it a: it seems that there can be nothing which satisfies the formula “E!x & x/a † (E!x iff E!a)”, except, of course, the state of affairs that a exists or the fact that a exists, provided you have such entities in your ontology and you believe that exemplifications of schemas such as the state of affairs that p obtains iff p and the fact that p exists iff p are true in virtue of what states of affairs and facts are. To summarize, my point against (6) is that, in the first place it forces its advocates to take a revisionist stance toward our intuitions concerning what makes what true (and this is a good reason to reject it if you do not wish to be revisionist toward the intuitions that Stefano makes it true that Stefano exists and that it is true that Stefano exists because Stefano exists). In the second place, once this stance is taken, the advocates of (6) are forced into the following dilemma: either there are many logically simple 26

See Lowe (1998).

291 true propositions that are such that there is no entity making them true (so both truth-maker maximalism and truth-maker neo-logical atomism are false), or things like states of affairs (or facts) are truth-makers and we are back to the old problems of the correspondence conception of truth. It would be nice to have a notion of truth-making which does not a priori force us to buy states of affairs just to ensure that every true singular existential proposition has a truth-maker. This could be done through a notion of truth-making according to which any entity makes the proposition that it exists true: unfortunately the essentialist notion of truth-making is not such. 5. Pleonastic states of affairs as truth-makers and non-immediate truth-making. Mulligan adopts a three-step strategy in order to overcome such problems. The first step is to buy states of affairs as truth-makers. The second step is to defend a conception of states of affairs which promise to escape all the sceptical worries the enemies of facts and states of affairs have, namely the conception of states of affairs, in the words of Stephen Schiffer, as pleonastic entities27: ontological commitment to such entities is guaranteed by trivial linguistic transformations expressed by biconditionals of the form the state of affairs that p obtains iff p. The third step consists in introducing the notions of non-immediate truth-making and making obtain: nonpleonastic entities make pleonastic states of affairs obtain and so make true, non-immediately, the propositions which those states of affairs make immediately true28. The most obvious way to criticise such a proposal would be to question the very notion of a pleonastic entity, particularly the idea defended by Schiffer and Mulligan that pleonastic entities are both language-created and language-independent. The idea to pursue here would be to show that such a notion is either incoherent or confused, so that there are no pleonastic entities. But to make this criticism explicit would require a paper dedicated to this topic alone and I will therefore not deal with the question here. The point I want to put forward here is a different one: even granted that there 27

Schiffer (1996), (2003). Another source of Mulligan’s theory is the notion of ontological free lunch which was used in Armstrong (1997) in order to explain the ontological status of the relation of making true. 28 For the three-step strategy see Mulligan (2003), (2004).

292 is something such as a pleonastic state of affairs, pleonastic states of affairs are not suitable as truth-makers, for they do not survive the becauseconstraint. Pleonastic states of affairs are “introduced” in the ontology by biconditionals of the form 9) The state of affairs that p obtains iff p or 10) The state of affairs that p obtains iff it is true that p. The problem is the following: what entitles us, starting from (9) or (10), to say that it is true that p because the state of affairs that p obtains ? Let us start with (10). In the first place (10) is a biconditional which in itself says nothing about the direction of the explanatory relation between the proposition that the state of affairs that p obtains and the proposition that it is true that p. In the second place if one thinks that the notion of a state of affairs is introduced by instances of (10) one should in principle accept that there is a conceptual priority of the notion of truth over the notion of a state of affairs which obtains. But conceptual priority of the notion expressed by a formula α over the notion expressed by a formula β is a reason to assert “β* because α*”29, as in the sentence, “Pietro is a bachelor because he is an unmarried man”. So if one considers (10) as a schema of biconditionals which introduce the notion of a state of affairs, one should be willing to say that the state of affairs that p obtains because it is true that p, and this means conceding that states of affairs do not satisfy the because-constraint. Of course the move of the advocate of states of affairs as truth-makers is to deny that states of affairs are introduced by biconditionals of form (10) and to claim that they are introduced by biconditionals like (9). But here the problem is that if states of affairs are introduced by biconditionals like (9), how is the connection between the concept of an obtaining state of affairs and the concept of truth made? The most natural answer (for an advocate of pleonastic transformations) would seem to be: using “Tarskian” biconditionals of the form 29

β* and α* are the relevant closed formulas obtained from β and α. For instance, if β is “x is an obtaining state of affairs”, β* is “That p is an obtaining states of affairs” and if α is “x is true”, α∗ is “That p is true”.

293 11) It is true that p iff p. What links states of affairs and truth are thus the right-hand sides of (11) and (9). Given what we said about conceptual priority, (9) and (11) should entitle us to say both 12)

It is true that p because p30

and 13)

The state of affairs that p obtains because p.

The question is now what entitles us to infer from (12) and (13) 14) It is true that p because the state of affairs that p obtains. Nothing, I believe. “It is true that p” and “The state of affairs that p obtains” are in fact both explained by p, but the simple fact that there is an explanatory relation between both sentences p and q and a third sentence r, is no more a reason to say p because q than to say q because p. What would be needed is some independent reason to assert one explanationsentence rather than its converse and neither (9) nor (10) nor (11) provides such a reason, at least as far as I can see. A way out for the advocate of pleonastic states of affairs as truth-makers is to claim that in (10) the explanation flows from “The state of affairs that p obtains” to “It is true that p” because the concept of truth is introduced by instances of (10), starting from the concept of the obtaining of a state of affairs, a concept which is in turn introduced by instances of (9). So we can say both that it is true that p because the state of affairs that p obtains and that the state of affairs that p obtains because p. The problem with this proposal is that it seems ad hoc. Why should we grant that the concept of truth is introduced through biconditionals like (10) and not through biconditionals like (11)? In the first place, it does not seem that the former bi30

(11) entitles us to (12) because there is a conceptual priority of p over “It is true that p”. I think there are good reasons for this claim, not least the fact that it is reasonable to suppose that we learn to use the truth-predicate through sentences like “If the cat is on the mat, it is true that the cat is on the mat and if it is not on the mat, it is not true that it is on the mat”.

294 conditionals are more adequate than the latter to account for our use of the truth-predicate (of course anyone who does not believe deflationism will think that neither biconditional gives a satisfactory account of the concept of truth). In the second place, instances of (9) make use, on their right-hand sides, of the same sentences which are used on the right-hand sides of (11); therefore it seems that before introducing the notion of an obtaining state of affairs through instances of (9), we already have the material to introduce the concept of truth through instances of (11). Another way out for an advocate of pleonastic facts as truth-makers, which is at the same time against deflationism in the theory of truth, is to claim that the relation between the concept of truth and the concept of state of affairs is not given by a list of biconditionals but by a finite definition of truth which involves the concept of a (pleonastic) obtaining state of affairs. This philosopher would defend a pleonastic correspondence conception of truth31. The problem with pleonastic correspondence is however that it misses the main (and perhaps only) good point of correspondence theory against deflationism: that correspondence theory (unlike deflationism) provides us with a finite definition of truth. The problem here is that the pleonastic correspondence definition of truth is only seemingly finite: in fact it makes use of a concept of state of affairs which is a concept of a pleonastic entity, so a concept introduced via an infinite list of biconditionals like (10). The pleonastic correspondence definition of truth is like a house whose foundations lay on shifting soil. We can conclude, therefore, that pleonastic states of affairs are not truthmakers. What an advocate of obtaining states of affairs as truth-makers should do is precisely the opposite of defending a pleonastic conception of obtaining states of affairs: this philosopher should argue for a conception of states of affairs as metaphysically fundamental entities, a conception which justifies asserting exemplifications of the schema

31

This conception has been defended by Volpe (2004). Ideas of this kind were defended for the first time, as far as I know, by Hill (1999), (2001) in the spirit of reconciling correspondence intuitions with deflationist approaches to truth; aiming at such an ecumenical goal, Hill does not claim, as Volpe does, that the notions of correspondence and of state of affairs enter in a definition of truth. He claims only that there are principles connecting a priori our concept of truth with these notions.

295 15) p because the state of affairs that p obtains. From (15) and (12) we can infer (14), and thus satisfy the becauseconstraint. Arguing for (15) means, in fact, claiming that obtaining states of affairs are the entities grounding the satisfaction of the truth-conditions of propositions and this seems a very sensible reason to claim that obtaining states of affairs are what make propositions true. Surely if something grounds the satisfaction of the conditions for something else to be F, then it grounds the being F of such a thing and so makes such a thing F. Thus, if one wants to have obtaining states of affairs as truth-makers, one should do what, in different ways, Wittgenstein in Tractatus Logico-Philosophicus, Russell in The Philosophy of Logical Atomism, and, more recently, Gustav Bergmann in Realism and David Armstrong in A World of States of Affairs, have done: claim that the world is a world of facts, so that this red rose is nothing but a fact32. This metaphysics is plagued with well-known difficulties, but at any rate this is the price that must be paid for having states of affairs as truth-makers; otherwise the because-constraint will remain unsatisfied33. From what has been said, two conclusions can be drawn which go against the essentialist conception of truth-making. First of all, the case against pleonastic states of affairs is one more example of the fact that the truth of sentences of the form “a/b (E!a iff Fb)” is not a sufficient condition for a to make b F. In fact if there are pleonastic obtaining states of affairs and essences, they are the very kind of things of which sentences of the form “a/b (E!a iff Fb)” are true34. Secondly, if pleonastic obtaining states of affairs are not truth-makers, the advocate of essential truth-making is still left without truth-makers for true singular existentials, for, as we saw, only an obtaining state of affairs can be, given the essentialist definition of truthmaking, what makes it true that Stefano exists. So even the essentialist about truth-making, who is at the same time an advocate of pleonastic facts, can save neither truth-maker maximalism nor truth-maker neological atomism. 32

This robust fact can be conceived either as one (or more) obtaining states of affairs, as in Wittgenstein, or as merely a state of affairs: in this case a state of affairs is the exemplification of a property by a particular, as in Armstrong and Bergmann (1967). 33 For a battery of such difficulties see: Dodd (1999). 34 Replacing “a” with “the obtaining state of affairs that p” “b” with “the proposition that p” and “F” with “true”.

296 What has been said concerns the first two steps in Mulligan’s argument. I want now briefly to say something about the notion of making obtain a state of affairs: this notion is supposed to ground pleonastic truth-making in more worldly entities, which make pleonastic states of affairs obtain. This is Mulligan’s conception of states of affairs as tips of icebergs: If states of affairs are truth-makers, there will be other entities of which such states of affairs are the tips which will also make these states of affairs obtain and, in some cases, make true (non-immediately) what these states of affairs make true35. How should the notion of making obtain be understood? From some examples of making obtain given by Mulligan it appears that the following could be a schema of axioms for making obtain 16) a makes obtain the state of affairs that Rn t1...tn if a makes t1…tn Rn 36. (16) seems to presuppose (13) which grounds the obtaining of a state of affairs in the way the world is: since a state of affairs obtains because things are in a certain way, whatever makes things be in that way makes the state of affairs obtain. Schema (16) raises two problems. The first is that since the notion of making obtain is clarified via the schematic notion of making Rn and making true is merely an instance of such a form, it is likely that all the problems we encountered in the proposed analyses of the notion of making true will still be there with the notion of making obtain. Take the case of the obtaining state of affairs that the fundamental and contingent entity a exists. If making Rn is analyzed in an essentialist way, it is difficult to find an entity that makes obtain in virtue of its essence the state of affairs that a exists. It could be said that a makes obtain, but not in virtue of its essence, the state of affairs at stake37. This move creates several problems, however. It must be explained how, given schema (16), a can make a exist, even though not 35

Mulligan (2003). This schema seems to be implicitly accepted in Mulligan (2003: 552): “A complex of processes including conception and parturition makes a the father of b and so makes the state of affairs that a is the father of b obtain”. 37 Mulligan (2003: 551). 36

297 in virtue of its essence; and it seems to me that there is no sense of “making” in which it is true that a contingent entity makes itself exist. The only way out is to consider a sentence like “a makes obtain the state of affair that a exists” as a primitive truth about making obtain. But this seems to be an ad hoc solution which has the disadvantage of missing what there is in common between different exemplifications of making Rn; after all such exemplifications are not primitive expressions but composite ones : what they have in common is “making”. A last thing should be noted. We saw that schema (16) presupposes (13); but we have a twin of (13) with the truth-predicate, namely (12). This fact should entitle us to write a twin of (16) with the truth-predicate 17) a makes that Rn t1...tn true if a makes t1…tn Rn. But once we accept (17), whatever makes obtain, in whichever way (essential or not), a state of affairs will make true, in the same way, the proposition made true by the state of affairs. So the notion of making obtain seems to be superfluous as a way of grounding truth-making in more worldly entities than states of affairs. 6. A sketch of a different proposal. Modal and essentialist accounts are unable, in different ways, to satisfy the because-constraint. This fact suggests a simple move: identifying making F, and specifically making true, with the because-constraint and so with a kind of explanation. This can be done starting from a general claim about making F, put forward, in slightly different ways, by Wolfgang Kuenne and Jennifer Hornsby, which is expressed by the following schema: 18) nom(p) makes b F iff b is F because p38. where “nom(p)” is a schematic expression for which a nominalization of p must be substituted in order to obtain an exemplification of the schema. 38

Although neither Kuenne (2003) nor Hornsby (2005) explicitly endorse (18), (18) seems to capture their general idea about making F. Hornsby for instance put forward the following equivalence: nom(q) is explained by nom(p) ╬ q because p; but the lefthand side of the equivalence is in turn intended as a possible clarification (in more general terms) of the form x’s being G makes y F.

298 There is an instance of (18) whose right-hand side properly amounts to the because-constraint. Such an instance is obtained replacing p with a sentence of the form “a exists”: 19) nom (a exists) makes b F iff b is F because a exists. Ontological ground, or objectual making F, can be characterized through the right-hand side of (19): 20) x makes y F =def y is F because x exists Truth-making is an instance of (18) and (20) obtained by replacing F with “true”: 21) nom(p) makes b true iff b is true because p and 22) x makes y true =def y is true because x exists39. What it is crucial to notice here is the difference between (18) and (21), on the one hand, and (20) and (22), on the other. While in fact (20) and (22) deserve the title of definitions respectively of making F (a schematic notion indeed) and making true, this is not true of (18) and (21) whose schematic character deprives them of generality. In other words: (18) and (21) characterize making F and making true only insofar as, in talking about something making something else F, we use nominalizations as noun phrases. What is interesting here is that while assuming (18) and a sentence of the form “b is F because p” we can infer the correlative sentence of the form “nom(p) makes b F”, the same sentence cannot be inferred assuming “b is F because p” and (20). For instance, given (18), if Carola is happy because Gilda is nice to her it is trivially true that Gilda’ s being nice to her makes Carola happy; this however is not a reason to believe that Carola is happy because Gilda’s being nice to her exists. It would not be inconsistent to believe that Carola is happy because Gilda is nice to her (and therefore that Gilda’s being nice to her makes Carola happy) and also not believe that there is an entity which is Gilda’s being nice to Carola and that the existence of such an entity explains why Carola is happy. This means that it is not obvious that there is any intersection between the extensions of the 39

This definition of “x makes y true” is also defended by Schnieder (in print).

299 notion characterized by (18) and the notion defined by (20). The same is true of the notions characterized respectively by (21) and (22). This is perhaps what leads Mulligan to isolate a special kind of truth-making, immediate truth-making, as truth-making which holds in virtue of both the essences of the truth-bearer and the truth-maker. But, in the first place, what has been said about the intersection between the extensions of the predicates characterized respectively by (18), (20) and (21), (22) amounts to saying that it is not a trivial matter whether something which immediately makes y F (true) is also the ontological ground of y’s being F40. In the second place (18) and (21) show that what Mulligan calls “immediate truthmaking” is part of a much more general phenomenon, which is not linked in any specific way to essentiality. For instance, there seems not to be any essential connection between Gilda’s being nice to Carola and Carola’s being happy, but rather a mere causal one. Nonetheless, provided that Carola is happy because Gilda is nice to her, that Gilda’s being nice to her makes Carola happy is as trivially true as that the fact that snow is white makes it true that snow is white (provided that it is true that snow is white because snow is white). The systematic phenomenon enlightened by (18) and (21) is rather that when a complex predicate of the form “x makes y F” appears in contexts of the form “nom(p) makes b F”, we are in presence of trivial transformations of sentences of the form “b is F because p”. This of course leaves open the question concerning how trivially true the explanatory sentences in question are: for instance, “it is true that snow is white because snow is white” is trivially true, while “Carola is happy because Gilda is nice to her” is not so. What kind of explanation must be involved in the definientia of (20) and (22) in order to ensure necessitation? The connective “because” can in fact convey different kinds of explanations: when I say that Maria is happy because Carlo is so nice to her, “because” expresses a causal explanation; on the contrary when I say that it is true that 2 + 2 = 4 because 2 + 2 = 4 or that this surface is red because it reflects light in such and such a way, what is at stake is not a causal explanation. This is clear with the truth-case but it should be also clear with the red-case: someone saying that this surface is red because it reflects light in such and such a way can believe that being red is nothing but reflecting light in such and such a way, but causal relations involve that the relata are different! While causal explanations do not involve necessitation non causal explanations do. “Involving necessitation” 40

In §5 this general claim is applied to pleonastic states of affairs.

300 here is intended in this sense: “p because q” involves necessitation iff “p because q” entails “† (q → p)”. This, given the definitions (20) and (22), amounts to saying that if a is an ontological ground of b being F, “b is F because a exists” cannot be a causal explanation; in fact if “b is F because a exists” were a causal explanation, “† (a exists → b is F)” would be false and therefore a would not necessitate (in the canonical sense) b being F, which is a necessary condition for a being the ontological ground of b being F. So it is up to the advocate of the because-analysis of making F to explain the difference between the causal and the non causal because, since only the latter is involved in the definientia of (20) and (22) if they are to capture the notion of ontological ground. According to Kuenne the particular kind of explanation involved in the non causal making F is either conceptual analysis or theoretical reduction41. I partially agree. It is certainly true that paradigmatic uses of “x makes y F” and “x’s G-ing makes y F”, where “makes” is understood in the non causal sense, are particularisations of claims concerning what it is for something to be F. If I say that its reflecting light in a certain way makes this surface red, my claim is an answer to the question: What is it for that thing to be red? And the answer to this question is an instance of the answer to the general questions: What makes things red? What is it for something to be red? Answers to these questions are sometimes given by providing a conceptual analysis and at other times by providing a theoretical reduction: philosophers, for instance, aim to answer questions such as “What makes an action right?” by providing a conceptual a priori analysis of what it is for something to be right; scientists more often aim to answer questions such as “What makes something red?” by giving theoretical, a posteriori, reductions, saying for example that what it is for something to be red is for it to reflect light in such and such a way. So there are certainly cases of making F which must be accounted for in the model of theoretical reduction or conceptual analysis. But there are also cases for which it seems difficult to give such an account. One of these cases is put forward by Mulligan: 23) a particular promise makes, by its very essence, a particular action obligatory.

41

Kuenne (2003).

301 One could try to give an account of this case in the model of what it is for something to be F, by claiming that we assert (23) because commitment to the existence of things such as promises is part of our theory of what it is for actions to be obligatory. This can happen either, so to speak, directly or indirectly: directly, for instance, if we have a contractualist theory of what being obligatory is; indirectly, for instance, when we have a deontological theory which sees keeping promises, as one of our primitives duties. But, it could be objected, no particular conception of moral obligatoriness is required to believe that promises make the actions promised obligatory. What is required is simply the mastery of the concept of “being a promise”: everyone mastering such a concept knows that if a promise occurs then a particular action (the action promised) is obligatory, merely because of the existence of the promise. This is a conceptual and necessary truth concerning promises and not a necessary truth concerning what it is for something to be obligatory. Therefore, although “your promise makes your action obligatory” is analyzable with “your action is obligatory because there was your promise (concerning it)”, in asserting the latter we are not asserting a claim concerning the nature of moral obligatoriness, i.e. a claim concerning what it is for an action to be obligatory. What we are doing instead is asserting a primitive truth given the concept of being a promise: given such a concept, the existence of a promise is sufficient to explain why a particular action (the action promised) is obligatory. What is important in the analysis proposed is that the right hand sides of (18) and (21) and the definiens of (20) and (22) are explanatory formulas which do not say that a relation holds between two entities: “because” is a sentential connective, not a two-place predicate. This allows us to understand the plainly objectual and relational making expressed by (20) and (22) as merely a particular case of a non-objectual and non-relational making which amounts simply to explanation. What is primarily at stake in making F are explanations and not objects ! Such objects enter the scene only when and because explanations call them into play. Ian McFetridge was the first to underline the relation between truth-makers and explanations42. There is however an important difference between his account and the one put forward here. According to McFetridge “x makes p true” means “x (a fact) explains the fact that p is true”; therefore according to him the notion of truth-making is the notion of a particular relation, namely 42

McFetridge (1990). On McFetridge and truth-making see Liggins (2005).

302 the relation of explanation. On the contrary, I do not think that the notion of explanation is involved in the analysis of the notion of truth-making. The reason is that understanding the sentence “a makes it true that p” does not require grasping the concept of a particular fact or proposition (different from the proposition that p); therefore the sentences “a makes it true that p” and “that q explains that it is true that p” have different ontological commitments. By using instances of “x makes it true that p” we are providing explanations; but providing an explanation is not speaking about such an explanation (or about the entities which are in the explanatory relation)43. Let me stress some advantages of the because-analysis of making F and making true. In the first place the because-account does not suffer from the shortcomings of modal and essentialist accounts, both unable to satisfy the because-constraint. But the because-account of “x makes y true” is identical to the because-constraint! Therefore the shortcomings of the rival accounts are by definition overcome. In the second the because-analysis provides a general account of expressions of the form x makes y F. In addition we have a simple explanation of how each entity can be said to make the proposition that says that it exists true. It is sufficient, for instance, to agree that it is true that Andrea exists because Andrea exists and that the kind of explanation involved here is either theoretical reduction or conceptual analysis. An argument for this claim is that the sentence “if it is true that Andrea exists this is true because Andres exists” is a conceptual truth44. Therefore this account does not force us into the dilemma of having 43

Peter Simons has emphasized that there is a relation between truth-makers and reasons: “The idea that truths require truth-makers is an ontological rendering of the principle of sufficient reason, that there needs to be a reason why a truth is true.” (Simons, 2000: 17). Nonetheless he wants the sense of “reason” in which truth-makers are reasons to be sharply distinguished from the sense of “reason” as “explanation”: “Disambiguating ‘reason’ in one of two possible ways, truth-makers are entities in the world which ground truths rather than other truths which explain or entail truths.” (Simons, 2000: 17-18). Moreover he seems to identify with entailment the way in which the existence of an object is a reason for a proposition being true: “The objects A make the proposition that p true iff the existence of A is sufficient for the truth of the proposition that p” (Simons, 2003: 557). I think that this proposal, in addition to sharing the shortcomings of modal characterizations of truth-making has a particular problem: it compels us to consider ambiguous the word “reason”, when there is no reason to do so. 44 I have more substantive arguments for defending the claim that p counts as a partial conceptual analysis of “It is true that p”; they are based upon comparison, in different contexts, between “It is true that p” and “p” on the one hand, and typical cases of syn-

303 to choose between the denial of truth-maker principles and the commitment to facts or obtaining states of affairs as truth-makers. What is more, the last point allows us to appreciate that the because-analysis explains how we can consistently assert that something makes y F and still deny that some thing makes y F: when we do so we are simply asserting an exemplification of (18) and denying the correspondent exemplification of (20). This idea is important if we are to face an argument which is often put forward by advocates of truth-makers and more generally of the correspondence conception of truth, the argument being that if there is no thing making propositions true then there is nothing making propositions true and so truth will be ungrounded45. The reply to this argument is that someone who does not believe that there is an entity whose existence explains why it is true that snow is white, may be willing to assert that there is something making it true that snow is white: namely that snow is white. Such a person believes that it is true that snow is white because snow is white and therefore he is implicitly or explicitly convinced that the proposition that snow is white can count as an explanation of the proposition that it is true that snow is white. So there is a modest reading of the correspondence intuition that truth is grounded which can be easily taken for granted: if something is true there is an explanation of its being true; these explanations are provided by the (true) instances of the schema it is true that p because p46. onymy (such as “a is a bachelor”/”a is an unmarried man”) on the other hand, (with particular attention to because contexts). I am aware that this involves a deflationist stance toward truth. See Caputo (2005). 45 This argument is explicitly stated in Rodriguez-Pereyra (2005). 46 This reading of the correspondence intuition was originally put forward by McFetridge (1990: 42). There is however an important difference between my position and McFetridge’s on this point. Given his analysis of truth-making as explanation, the modest reading of the correspondence intuition can be formulated as a truth-maker principle (if something is true there must be something making it true) preserving the meaning of “makes” which is involved in the analysis (“makes” as “explains”). On the contrary, this cannot be done, given the because-analysis of truth-making. Such an analysis, in fact, does not involve the notion of explanation. What I think is that by formulating the modest reading of the correspondence intuition as a truth-maker principle we are moving from the basic use of “making”, which is analysed by means of because-sentences, to a metalinguistic use which is committed to explanations (which are linguistic or propositional objects). How are these different uses of “making” connected? The answer is that the metalinguistic generalization involved in the modest truth-maker principle is reached through semantic ascent starting from the instances of it is true that p because p.

304 Finally the proposal makes clear what should be done to argue for fullblooded truth-maker principles. Only true singular existential propositions are such that we know, merely on the basis of our concept of truth, that there are entities making them true. But if we assume, as seems plausible, that explanation is transitive, then all that we have to do in order to argue that a given proposition, if true, has some entity making it true is to show that a singular existential sentence can count as an explanation (of one of the relevant kinds) of the sentence expressing the truth-conditions of the proposition; or equivalently to show that what it is for the truth-conditions of the proposition in question to be satisfied is for some entity to exist. Let us take, for instance, the true proposition that this ink is black. The proposition is true because this ink is black. If one manages to show either that what it is for this ink to be black is for a particular entity to exist, or that there is some entity which is for the ink’s being black what a promise is for a particular action’s being obligatory, then one has, eo ipso, shown that the entity in question makes the proposition that this ink is black true. Lewis was basically right when he said that the question concerning the existence of some entity making the proposition that cats purr true is actually a question concerning the existential ground of purring cats47. This is true except for singular existential propositions. Given the analysis here proposed of “x makes y true” what makes it true that Andrea exists is Andrea himself (and in a mediated way the existential grounds of Andrea’s existence, if there are any). A different way to express in general terms what is really at stake in full-blooded truth-maker principles is the following: the supporter of one of these principles claims that what it is for a n-tuple of individuals to exemplify an n-ary property is for some entity to exist. This entails, I think, arguing that at least for each fundamental property one of the following holds: either its exemplification consists in the existence of entities of some kind, or it is a primitive essential feature of what exemplifies it, or it is an internal relation. A difficult task indeed.

47

See Lewis (2001). It seems to me that the identification of truth-makers with difference-makers does not do justice to the correct intuition of Lewis to the effect that truth-makers are what existentially ground how the world is: number 2 is a differencemaker for the proposition that God exists (if God exists and is a necessary being) but it is not the existential ground of God’s existence.

305 I want finally to discuss some objections to the because-account of making F and making true. The first objection, put forward by Mulligan, is that there are cases of relational-objectual making which do not seem to be treatable in the model of because-sentences. These are cases involving objects and propositions stating their essential properties or internal relations as in 24) Orange, yellow and red make the proposition that orange lies between yellow and red true. 25) Stefano makes the proposition that Stefano is a man true. (24) and (25) make trouble for the because-account because they are not equivalent respectively to “It is true that Stefano is a man because Stefano exists” and “It is true that orange lies between yellow and red because orange, yellow and red exist”: these latter sentences are in fact clearly false while (24) and (25) are both true. The reason why they are true, the objection goes, is that we have here two cases of essence-induced making: Stefano, for instance, makes it true that Stefano is a man not in virtue of its existence but rather in virtue of its individual essence. A supporter like me of the because-account can react to this objection in two ways. The first one is to deny that (24) and (25) are true (or obviously so): they are theoretically loaded statements which only someone who already believes in something like essence-induced making would be willing to accept. What is intuitively true is rather something like the following: that orange, yellow and red are such and such makes it true that orange lies between red and yellow; that Stefano has DNA of a certain kind (or that he is a rational being, or something else) makes it true that Stefano is a man. The second one is to slightly modify the because-account of making F and making true so that it can account for the truth of (24) and (25). This can be done with the following two definitions: 26) x makes y F =def y is F either because x exists or because x is what it is 27) x makes y true =def y is true either because x exists or because x is what it is48 48

Of course also the because-constraint must be modified in similar way.

306 With (26) and (27) the advocate of the because-account simply acknowledges that sometimes what explains that something is F is not that something exists but rather that something has a certain nature, that something is what it is, and that these can also count as instances of making F. An advocate of essence-induced making can object to this proposal that the modified because-account is actually a covert essentialist account. In fact “what it is” in (26) and (27) means “what it essentially is”, so that reference to the individual essence of a thing is covertly made. To this it can be replied that it is not necessary to understand talk of the nature of something as ontological committing to individual essences : as Fabrice Correia has convincingly argued, such a talk can be understood in terms of talk concerning what it is for a thing to be that thing, what being that particular thing is49. Given (26) and (27) it can be said that (24) is true because what it is for three colours to be in the relation lie between (x, y, z) is for those colours to be in a given order on a scale of wavelengths; but to be in a given order on a scale of wavelengths is part of what it is for a given colour to be itself. Thus, that each colour of an n-tuple of colours is what it is, is taken as a theoretical reduction of the fact that the n-tuple exemplifies the relation lie between (x, y, z). Something similar can be said about (25): what it is for something to be a man is to be a certain way (for instance to be a rational being); but part of what it is for Stefano to be himself is for him to be a rational being, so to be a man belongs to what it is for Stefano to be himself. The second objection is the following: what is at stake in theoretical reductions and conceptual analyses is what being such and such consists in. In fact what makes the difference between theoretical reduction and conceptual analysis, on the one hand, and other kinds of explanations (for example causal explanations) on the other, is precisely that the former and not the latter aim to answer questions such as, “What does being such and such consist in?” This suggests a different way of defining making F which does not make use of because-sentences and which, the opponent claims, is conceptually prior to because-analysis:

49

Correia (2004). Correia also provides some good reasons not to believe that expressions of the form “F-ing” (in which “F” must be replaced by a predicate) denote properties; when one comes to expressions of the form “being a” (being that particular thing) these are also reasons not to believe that such expressions refer to a property which is the individual essence of a.

307 28) x’s G-ing makes y F =def y’s being F consists in x’s G-ing. 29) x makes y F =def y’s being F consists in x’s existing (or in x’s being what it is). 30) x’s G-ing makes y true =def y’s being true consists in x’s G-ing. 31) x makes y true =def y’s being true consists in x’s existing (or in x’s being what it is)50. The consisting-in analysis, the objection goes, is not only conceptually prior in respect to the because-analysis but also metaphysically more revealing: “to consist in” is in fact a relational notion and therefore making F and making true are basically relational notions, contrary to what the advocate of the because-analysis claims! Two things should be said concerning this proposal. In the first place this analysis is equivalent to the because-analysis only insofar as cases like those of promises are excluded: if we also want to account for these cases we must reject the consisting-in account: a promise can make an action obligatory even if it is not true that the promise being obligatory consists in the existence of promises. Therefore that something being F consists in the existence of something else is not a necessary condition for the latter thing making the former one F. In the second place it is an open question whether or not consisting-in sentences indeed have any conceptual priority over because-sentences and are in any way metaphysically more revealing51. Here much depends on the answer one gives to the following ques50

This is basically an application of the analysis of the notion of grounding put forward by Fine (2001). I part company with Fine when he wants grounding to be sharply distinguished from reduction; in fact he claims reduction involves the non-reality of what is reduced and this is not the case with “to consist in nothing more than”. This point seems to me not so compelling. At least in ordinary cases, reduction is not taken to involve elimination of what is reduced: to claim that water reduces to H20 does not involve the claim that water is unreal and that only H2O is real; the contrary seems in fact to be true: since water reduces to H20 and H2O is real, water is real as well. Vision (2005) has put forward a similar analysis using the notion of constitution. 51 It should be noted that answering this question is also relevant for what has been said concerning promises. The explanation involved in the analysis of this case has been considered as a conceptual truth concerning promises; therefore the supporter of the consisting-in analysis could claim that even this case shows that this kind of analy-

308 tion: Are expressions such as “x’s G-ing” ontologically committed to non pleonastic entities?52 If they are, the consisting-in analysis reintroduces a genuine commitment to objectual and relational truth-making. If they are not, understanding such expressions is parasitic on understanding sentences of the form “x Gs” and therefore the consisting-in analysis will turn out to be a nominalized variant of the because-analysis. These are however questions which I will leave open here: there is still much work to be done to make a proposal out of what is just a sketch of a proposal53.

REFERENCES Armstrong, D. M. (1997), A World of States of Affairs, Cambridge, UK, Cambridge University Press. Austin, J. L. (1950), “Truth”, Proceedings of the Aristotelian Society, 24 (suppl. vol.): 111-129, reprinted in: Austin, J. L., Philosophical Papers, 2nd edition, Oxford, Oxford University Press, 1970: 117-33. Bergmann, G. (1967), Realism. A Critique of Brentano and Meinong, Madison, The University of Wisconsin Press. Bigelow, J.C. (1988), The Reality of Numbers: A Physicalist’s Philosophy of Mathematics, Oxford, Clarendon Press. Caputo, S. (2005), Fattori di verità, Milan, Albo Versorio. Correia, F. (2002), Existential Dependence and Cognate Notions, PhD Dissertation, (in print). sis is more basic then the because-analysis of truth-making: a conceptual truth concerning being a promise is after all a proposition concerning what being a promise consists in. 52 Pleonastic entities must be excluded from the range of putative referents since the argument against pleonastic states of affairs as truth-makers put forward in §5 can be extended to cover any pleonastic entity. 53 I am grateful to Andrea Iacona, Philipp Keller, Diego Marconi, Kevin Mulligan and Barry Smith for their helpful comments both on this paper and on my PhD dissertation on Truth-Makers. Kevin Mulligan deserves particular thanks for having encouraged me to write this paper…despite the fact that one of its main concerns is arguing against what he thinks about truth-making!

309 Correia, F. (2004), “Generic Essence”, talk at the workshop Relations, Geneva, June 7 2004, (in print in Noũs). Davidson, D. (1969), “True to the Facts”, Journal of Philosophy, 66: 748-764. Dodd, J. (1999), “Farewell to States of Affairs”, Australasian Journal of Philosophy, 77 (2): 146-160. —— (2002), “Is Truth Supervenient on Being?”, Proceedings of the Aristotelian Society, 102: 69-86. Field, H. (1994), “Deflationary Views of Meaning and Content”, in: Field H., Truth and the Absence of Fact, Oxford, Oxford University Press, 2001: 104-140. Fine, K. (1994a), “Essence and Modality”, Philosophical Perspectives, 8: 1-16. ——1994b, “Senses of Essence”, in: Sinnott-Armstrong W. (ed.), Modality, Morality and Belief, New York, Cambridge University Press: 53-73. ——2001, “The Question of Realism”, Philosophers’ Imprint, 1: 1-30. Fox, J. F. (1987), “Truthmaker”, Australasian Journal of Philosophy, 65: 188-207. Frege, G. (1918), “Logische Untersuchungen, Erster Teil: Der Gedanke”, Beiträge zur Philosophie des deutschen Idealismus, I: 58-77; Engl. Transl.: “The Thought” in: Frege, G., Collected Papers in Mathematics, Logic and Philosophy, Oxford, Blackwell, 1984. Hill, C. (1999), “Truth in the Realm of Thoughts”, Philosophical Studies, 96: 87-121. ——2001, “The Marriage of Heaven and Hell: Reconciling Deflationary Semantics with Correspondence Intuitions”, Philosophical Studies, 104: 291-321. Hornsby, J. (2005) “Truthmaking Without Truthmaker Entities”, in: Beebee, H., Dodd, J. (eds.), Truthmakers. The Contemporary Debate, Oxford, Oxford University Press. Horwich, P. (1990), Truth, Oxford, Basil Blackwell. Kripke, S. (1975), “Outline of a Theory of Truth”, Journal of Philosophy, 72: 690716. Künne, W. (2003), Conceptions of Truth, Oxford, Oxford University Press.

310 Lewis, D. K. (2001), “Truthmaking and Difference-Making”, Noũs, 35 (4): 602-615. Liggins, D. (2005), “Truthmakers and Explanation”, in: Beebee, H., Dodd, J. (eds.), Truthmakers. The Contemporary Debate, Oxford, Oxford University Press. Lowe, E. J. (1998), The Possibility of Metaphysics, Oxford, Clarendon Press. McFetridge, I.G. (1990), “Truth, Correspondence, Explanation and Knowledge”, in: McFetridge, I.G., Logical Necessity and other essays, edited by J. Haldane, R. Scruton, London, Aristotelian Society. McGinn, C. (2003), Logical Properties, Oxford, Clarendon Press. Moore, G. E. (1953) [1910], Some Main Problems in Philosophy, London, Allen & Unwin. Mulligan, K. (2003), “Stati di cose, verità e fattori di verità”, Sistemi Intelligenti, XV, 3: 539-556. ——2004, “Truth-Making Trivialised and Fact-Making”, Talk at the Conference Truths and Truthmakers. 20 Years After, Aix-en-Provence, December 9-11 2004 (now in this volume : “Two Dogmas of Truthmaking”). Mulligan, K., Simons, P. M, Smith, B. (1984), “Truth-Makers”, Philosophy and Phenomelogical Research, 44: 287-321. Ramsey, F. P. (1927), “Facts and Propositions”, Aristotelian Society, 7 (suppl. vol.): 153-170. Restall, G. (1996), “Truthmakers, Entailment and Necessity”, Australasian Journal of Philosophy, 72: 331-340. Rodriguez-Pereyra, G. (2005) “Why Truthmakers”, in: Beebee, H., Dodd, J. (eds.), Truthmakers. The Contemporary Debate, Oxford, Oxford University Press. Russell, B. (1918-19), “The Philosophy of Logical Atomism”, The Monist, XXVIIIXIX, reprinted in: Russell, B., Logic and Knowledge, London, Allen & Unwin, 1956. Schiffer, S. (1996), “Language-Created, Language-Independent Entities”, Philosophical Topics, 24: 149-167. Schnieder, B., “Truth-Making Without Truth-makers”, Synthese (in print).

311 Schiffer, S. (2003), The Things We Mean, Oxford, Clarendon Press. Simons, P. M. (2000), “Truth-Maker Optimalism”, Logique et Analyse, 169-170: 1741. Simons, P. M. (2003), “Fattori di verità e impegno ontologico: due facce della stessa medaglia?”, Sistemi Intelligenti, XV (3): 557-569. Smith, B. (1999), “Truthmaker Realism”, Australasian Journal of Philosophy, 77 (3): 274-291 . Smith, B., Simon, J (2004), “True Stories”, Talk at the Conference Truths and Truthmakers. 20 Years After, Aix-en-Provence, December 10-12 (now in this volume : “Truthmakers Explanations” ). Strawson, P. F. (1950), “Truth”, Proceedings of the Aristotelian Society, 24 (suppl. vol.): 129-156, reprinted in: Strawson, P. F., Logico Linguistic Papers, London, Methuen, 1971. Vision, G. (2005), “Deflationary Truthmaking”, European Journal of Philosophy, 3: 364-380. Volpe, G. (2004), “Corrispondenza pleonastica”, talk at the 6 th National Conference of Italian Society of Analytic Philosophy (SIFA), Genoa, September 24-27 2004. Wittgenstein, L. (1921), “Logisch-philosophische Abhandlung”, Annalen der Naturphilosophie, 14; english translation: Tractatus Logico-Philosophicus, London, Routledge, 1961. Wittgenstein, L. (1953), Philosophische Untersuchungen. Philosophical Investigations, Oxford, Blackwell. Zalta, E. (1983), Abstract Objects, Dordrecht, Reidel.

A New Solution to the Problem of Negative Truth STEPHEN MUMFORD University of Nottingham

1. The problem of negative truth Aristotle famously distinguished truths of two kinds. Truth was either ‘to say of what is that it is, or of what is not that it is not’ (Metaphysics Γ, 7, 1011b, 26). Analytic philosophy in the last century, and truthmaking theory in particular, has had a difficulty with the second case. There is a strong intuition that truth is supervenes on being. According to truthmaker theory, what this means more accurately is that truths are determined or necessitated by truthmakers, which are states of affairs or facts in the world (Armstrong 2004). The proposition 1, when true, has its truth necessitated by the state of affairs of there being a hippopotamus in the room. Those with an attraction to a correspondence theory of truth will see virtue in this account. Truthmaker theory has a number of elements that are often regarded as prerequisites for an acceptable theory of truth. Truth is a property of propositions, or some such linguistic entities, but is a property held in virtue of having the right sort of relation to non-linguistic entities in the world. As Armstrong has spelled it out recently, the appropriate relation is one of cross-categorial necessitation from facts to propositions (2004: 5). There may be worries about whether necessitation can be cross categorial (Mumford 2005) but these are not taken up here. Truthmaker theory has prima facie plausibility in many cases, which are cases of the first kind mentioned in Aristotle’s account of truth. The problem addressed in this paper concerns the second kind of purported truth: where we say that something is not. For example, the following are apparent truths: , , and Russell’s own example, 1

I adopt the now widespread convention of isolating a proposition with angled brackets.

314 (1918: 189). If this is a variety of truth, then it creates obvious problems for truthmaker theory and any correspondence theory of truth. These propositions appear to be saying something about how the world is not, as Aristotle’s account makes clear. But if they say something about how the world is not, then how can they be made true by how the world is? In other words, how can there be a fact or state of affairs in the world that makes such propositions true when the propositions themselves say only that something is not the case? This suggests a twofold division corresponding to Aristotle’s distinction. First there are the positive truths, which state that some fact is the case. Where there is indeed such a fact in the world, this type of proposition is true. Second, there are the putative negative truths, which state that something is not the case. The problem which faces us, and to which there has never yet been a satisfactory solution, is what are the truthmakers for these negative truths? Solutions to this problem have been offered before but I agree with Molnar (2000) that none of them are a success. I will not examine any of these other ‘solutions’ in great detail but I will state briefly what they are and why they are problematic. First, a natural response to the problem is to say that there are many facts that are relevant to our negative proposition and that they can together make it true because they are together inconsistent with its contradiction.2 This is the so-called incompatibility solution. Hence, the room contains a table, a chair a group of human beings and other objects. Being a human being is incompatible with being a hippopotamus, as is being a table. The positive facts are thereby incompatible with there being a hippopotamus in the room so they make it true that . The basic structure of this approach is to say that when we assert some proposition , we are effectively asserting some other proposition (or set of propositions S = {, , }), where q is incompatible with p (or a set S of propositions is incompatible with p). Therefore ¬p. The weakness of this as a solution to the problem of negative truth is that an assertion that p is incompatible with q, or p/q, itself appears to be a negative truth, as p/q is equivalent to ¬(p & q). At best, therefore, we will have replaced one negative truth with another and will have made no progress in saying what are the truthmakers of negative truths. 2

Russell discussed this ‘solution’ in 1918: 188-90.

315 A second ‘solution’, and the one for which Russell ultimately opted (1918: 189-91), is that as well as the facts that make positive truths true, there are also negative facts that make negative truths true. Russell accepted that there was something deeply counterintuitive about negative facts (1919: 287), which is why this remains unsatisfactory as a solution to the problem. There would have to be, presumably, non-beings. When we say it is true that there is not a hippopotamus in the room that is because there really is in the room a negative entity which is a non-hippopotamus. There would have to be, according to this account, a world of negative facts or objects that mirrored the world of positive existents. The room would presumably be crowded with such negative existents because as well as containing a non-hippopotamus, the room it seems also contains a non-giraffe, a nonunicorn, a non-Jacques Chirac and all sorts of other non-things. This is not an ontology that many have found attractive. Armstrong has proposed another solution recently that makes use of some of the same devices as the first two. Armstrong suggests that negative truths are made true by a conjunction of all the relevant first-order positive facts plus the addition of a higher-order totality fact. The positive facts themselves do not entail the required negative truth, as Armstrong requires in his truthmaker necessitarianism. But they will entail the negative truth if they are accompanied by a totality fact: a higher-order fact that says that these are all the first-order facts. The problem here is that the totality fact is a fact that these are all the (first-order) facts ; in other words, ‘no more facts’. The totality fact is, therefore, a negative fact. Armstrong’s solution is thus the same as Russell’s but for the advantage Armstrong claims in economy. Armstrong will need fewer negative facts than Russell as the same totality fact, together with a collection of first-order positive facts, may entail not just that there is no hippopotamus in the room but also that there is no giraffe, no unicorn, and so on. This shows, however, that Armstrong’s solution works in the same way as the incompatibility solution. It has to assume a negative in order to get from the totality of what is to a truth about what is not. Again, therefore, we may wonder whether we have made real progress or merely displaced the problem. A final available option can be noted. Some truthmaker theorists are prepared to say that negative truths are true but do not have truthmakers.3 Perhaps they are true primitively or by default. It should be noted about 3

I understand this to be the position of Barry Smith and of Peter Simons in his 2005.

316 this ‘solution’, however, that it essentially jettisons the truthmaker project in the light of the problem. It gives up on truthmaker maximalism, which is the view that every truth has a truthmaker. It is plausible to think, however, that there are more negative truths than positive truths. If that is the case, then the ‘primitivist’ response looks like a strategic withdrawal to a relatively modest claim. It means that truthmaker theory no longer offers a unified theory of truth. I do not claim that these four previous solutions are irredeemable. Indeed they are all tenable if one is prepared to accept certain consequences, though I suggest that these are unpalatable. Sometimes we have no choice but to accept such things. I am, however, going to offer a different way out for the truthmaker theorist that, I claim, should be accepted as the most sensible solution available. 2. The solution The solution requires one major move at the start, after which everything else falls into place. There may be some resistance to this initial move because it requires us to reject Aristotle’s second class of truth, effectively abandoning the T-schema in this case. However, for a truthmaker theorist, this move should not be regarded as counterintuitive. It should be seen as perfectly in line with their theory of truth and, more importantly, their most intuitive theory of falsehood. The theory of truth, in the minimal truthmaker theory I describe, is that a proposition

is true if and only if

has a truthmaker T.4 This is the intended meaning of df. 1: df .1 t

iff Tp I accept Armstrong’s view that there need not be a one-to-one correspondence between truths and truthmakers. Some truths have many truthmakers and some truthmakers make many truths true. Some may have a unique minimal truthmaker. df. 1 is intended to remain neutral on this issue. 4

There are, of course, many other aspects to truthmaker theory than the simple statement of df. 1, which is why I call this a minimal truthmaker theory. I wish to remain neutral on these many other issues in this paper.

317

The first step in understanding the new solution is to have a theory of falsehood that complements the theory of truth in df. 1. It is, however, surprising how elusive a theory of falsehood is in truthmaker theory. Perhaps the definition of falsehood is considered too obvious to state. What theory of falsehood should a truthmaker theorist adopt? I suggest the following: df. 2 f

iff ¬Tp That is,

is false if and only if p has no truthmaker. Thus it is false that there are unicorns if there is no truthmaker for . This is a rational theory of falsehood for a truthmaker theorist to hold, I maintain, because it respects the intuitions that motivate truthmaker theory. Truths are made true by something in the world, falsehoods are not. Truths correspond to some fact or facts in non-linguistic reality. Falsehoods do not: there is nothing in the world to which they correspond. Armed with a basic theory of falsehood, we are now in a position to make a very simple move, which effectively solves, through avoidance, the problem of truthmakers for negative truth. One way of stating this solution is to say simply that there are no negative truths. This dissents from Aristotle’s view that to say of what is not, that it is not, is a truth. Truthmaker theorists have, I claim, a principled reason to reject this. Stating that something is not can never produce a truth because there cannot be a truthmaker for a statement that something is not. To say that ¬p is, on the account I offer, to say that p has no truthmaker. It is to say, therefore, in accordance with df. 2, that p is a falsehood. Truthmaker theorists, or at least truthmaker maximalists, accept that there is an existential commitment in saying that p is true. If one accepts that p is true one is existentially committed to the truthmaker of p. I have argued, however, that ¬p has no existential commitment. It is not, therefore, a truth at all. It is effectively to state that p is false (f

) or, in other words, to deny p. This gives us a principled reason, based in a metaphysics of truth that the truthmaker theorist should accept, to recast negative truths as falsehoods. The step that is to be taken might be thought bold, but it is solidly based in an understanding of truth. It is to say that all putative negative truths are philosophically best understood as disguised

318 falsehoods. Hence, an ordinary assertion of truth that should instead be understood as meaning that it is false that . In general, I maintain that wherever we have a putative case of t, we should instead understand it as f

. t, if we are maximalists, presents us with the problem of negative truth because, by df. 1, it existentially commits us to the existence of a truthmaker. Despite the best efforts of our best philosophers, we have not found the truthmakers for negative truths, which was Molnar’s (2000) conclusion. We can, however, say that f

without any existential commitment, without requiring a truthmaker, and thus avoid the problem of finding truthmakers for a negative truth. A virtue of this account is that it leaves truthmaker theory intact as a unified theory of the metaphysics of truth. Truth is metaphysically univocal in that every truth is true in virtue of the same feature: having a truthmaker. Truthmaker maximalism is preserved. The price for this is that the domain of truth is restricted. The current theory allows falsehood, and possibly more falsehood than truth. But this restriction may be as it should be. Truthmaker theorists may have managed without a theory of falsehood because they could treat any putative falsehood as a negative truth. Thus, where it is false that there is a hippo in the room, they can say it is true that there is not a hippo in the room. This strategy, however, could lead to the position that truth is ubiquitous, which is not a desirable consequence. Surely there must be at least some falsehoods. But the truthmaker theorist cannot allow as equivalents t and f while also accepting df. 1 and df. 2. That would tell us that something with existential commitment was equivalent to something without it. Given the plausibility of

being false when p has no truthmaker, that would mean that t, if it is equivalent to f

, also has no truthmaker. Then how can t be a truth, in truthmaker theory, if it has no truthmaker? That would violate df. 1. If we have to decide, therefore, we have rational grounds within the theory, to accept the falsehood of and not attempt to convert it into a putative negative truth. However, we have just rejected the equivalence of t and f

. Can logic, and indeed thought, get by without that equivalence? I propose in its place something that looks similar but which, I maintain, is significantly different, namely: f

iff ¬t

. p is false when, and only when, it is not

319 true. The significant difference is that this does not commit us to anything ‘negative’ being true. ¬t

is acceptable while t is not because ¬t

is exactly the same, with the same ontological commitment (none) as f

. ¬t

does not purport to be a truth – it is actually a falsehood – so does not require a truthmaker. t does purport to be a truth so, if truthmaker maximalism is to be held, does require a truthmaker. We cannot find such a truthmaker so we are left with a problem of negative truth. On my proposal, there are no negative truths, hence no problem of finding truthmakers for them. This is the very simple solution to the problem of negative truth. The proposal raises some concerns, however, and I must now show that it is false that they are serious. 3. The T-schema, assertion and denial The T-schema is usually regarded as a central platitude that any theory of truth must respect (see Engel 2002: ch. 2):

is true if and only if p. The proposed solution is, however, inconsistent with the T-schema. I allow f

without allowing that t. Application of the T-schema would, of course, oblige us to permit that f

if and only if t. I cannot allow this because, on the proposal, f

has no truthmaker, thus no ontological commitment. I cannot allow, therefore, that it be equivalent to, nor even entail, a truth. All truths entail ontological commitment to their truthmakers, as I am understanding truthmaker maximalism. In denying f

iff t, I am therefore denying the applicability of the T-schema for at least these cases. Is it correct to do so? I would argue that we have good reason to reject the T-schema if we are committed truthmaker theorists. To see this, we can adopt a principle that Armstrong himself employs in dealing with another problem. Recall, first, that we allowed that the relation between truths and truthmakers is not necessarily one-to-one. Some truthmakers can make many truths true. Armstrong utilises this point when he responds to the so-called regress of truth (2004: 78-9). Where it is true that p, it is true that it is true that p: t

→ t. And so on indefinitely: t → t. Armstrong tells us, however, that not every truth requires its own unique truthmaker. Indeed the truthmaker for t

can and will be the same truthmaker as that which is the truthmaker for

. The regress of truth is

320 not vicious, therefore, because each further truth requires no extra truthmaker, hence there is no ontological inflation that requires ever more entities infinitely. The extra truths are gained for no increase of being. I find this diagnosis of the regress of truth appealing. I would want to generalise from it and allow that f

entails t only if t involves no increase of being over f

. However, we have seen that, being a falsehood, f

has no existential commitment. Being a truth, t would have existential commitment. t would, therefore, require an increase in being over f

. For this reason, I say that a truthmaker theorist should not allow that f

entails t. For this very reason, they must deny the universal applicability of the T-schema. A further inference can be drawn from this result. We can never permit t as a truth. We must never allow that a falsehood is a truth; that is, we can never allow that it true that something is false. Where something is false, we say that it has no truthmaker. This also means that there is no truthmaker for it being true that it is false. We never permit true that p is false, therefore. Similar reasoning explains why we cannot allow it to be a truth that

has no truthmaker, or ¬Tp as it appears in df. 2. There may be a temptation to say that

is itself a proposition and is true: t. If so, we would fall foul of the no increase of being principle. Our analysis of f

is that ¬Tp:

has no truthmaker. But then ¬Tp tells us what a falsehood is. It cannot, therefore, be both a truth and a correct account of falsehood as, again, that would have a falsehood entailing a truth. It would also be a further negative truth, so we would have merely swapped one negative truth, t, for another, t

. Instead, I understand

to mean that f

. More schematically,

has no truthmaker should be understood as ¬t; hence f by df. 2. One source of resistance to the proposal, and which tempts us to retain the T-schema, is a logic that permits assertion only, rather than both assertion and denial. A statement that f

is most frequently understood by philosophers to be an assertion. Hence, if I say f

, I am usually understood to be asserting that f

, and what does an assertion mean other than an assertion of truth? Hence, an assertion that f

will be taken to be an

321 assertion that it is true that f

: t. I do not permit this so I must offer an alternative explanation. I allow simply f

, without t because I take it that a statement of f

is not an assertion at all; rather, f

is a denial (of p). In stating that f

, I am not saying that anything is true. On the current proposal, f

has no existential commitment to a truthmaker so it cannot be regarded as an assertion of truth. I can, however, deny that p, which is exactly what I am doing when I say that p has no truthmaker. It is clear, therefore, that I should permit both assertion and denial. To do so seems naturally to reflect two cognitive attitudes that we may take to a proposition. Analytic philosophy, however, will typically allow a logic with only one. Note that Frege (1879) allowed only an assertion stroke and not a complementary denial stroke. Instead of denying that p, Frege’s logic offered us instead an assertion that ¬p. This creates no difficulty for purely logical purposes. Our theory of truth, however, has to be both logically and metaphysically adequate. I would suggest that the problem of negative truth has arisen through attempting a metaphysical analysis of all truth that has restricted itself to a logic of assertion. This diagnosis is largely speculative, but certainly I see the admission of denial both helpful and natural with regard to the problem of negative truth. 4. Eliminability The proposal works only if all putative negative truths are eliminable. The proposal is that such negative truths are metaphysically to be understood as falsehoods. Because the proposal has universal scope, it is of course in danger of defeat by a single counterexample. Just one ineliminable negative truth shows that not all negative truths are falsehoods, hence the problem of truthmakers for negative truths remains. In most cases, recasting a putative negative truth as a falsehood is a simple matter. t becomes f. t becomes f. t becomes f. For the reasons that have been given above, I think all these cases are best understood to be falsehoods rather than truths because it is clear that they contain no existential commitment. There is one problem area, however, where one might at first fear defeat. This concerns the distinction between internal and external negation and

322 how both could be recast as falsehood without loss of meaning. The problem is illustrated by noting the difference between the internally negated: (1) and the externally negated: (2) . Both (1) and (2) appear to be negative, hence I want to treat them as falsehoods. If I convert both to f, however, it seems I lose the distinct meanings of the internal and external negation. This seems to be important because, adapting and applying Russell’s (1905) reasoning, (2) is true while (1) is false. If I treat both as f, I would be guilty of ignoring Russell’s important point about the hidden existential commitment of certain forms of statement. The internal negation in (1) contains an existential commitment to there being a present King of France, and this is false because there is no present King of France. (1) as a whole is therefore false: a negative falsehood, if you like. (2), however, is true on Russell’s reasoning: it is a negative truth. Because its negation is external, it contains no existential commitment to there being a present King of France. External negations are a standard case of negative truth and for them, I would argue that f suffices as an adequate recasting in terms of the proposal. A bit more work is required for internal negations, however. I follow Russell in accepting that a sentence with relatively simple grammatical structure may hide a greater logical complexity. In this case, we need to understand an internal negation in a similar way to Russell as involving a conjunction. Specifically, we have a conjunction of an existential commitment to some object and then an ascription of some predicate or property to that object. The structure can be seen below: (3)

&

In (3), we need to make it clear that the object to which we predicate G is that same object of which we assert existence in the first conjunct, hence we ascribe to it an arbitrary name a, though the reference here may carry

323 over anaphorically. If this is the structure of an internal negation then it presents us with two cases of internal negations: (3a) f & f (3b) t & f In (3a), it is false that a exists, as in the case of the present King of France. It is therefore false automatically, on the current theory, that a is G: because there is no a, there will be no truthmaker for Ga, which means that Ga is false. (3b) is a case where a does exist but where it is false that Ga. Suppose, for example, that I say “this pen is not blue”, apparently truly because it is a red pen. This would be a negative truth, which would then have to be recast as a falsehood. In such a case, the first conjunct – the existential commitment – is true, the pen exists, but the second conjunct is a negative truth (t