Universals, Concepts and Qualities - New Essays on the Meaning of Predicates

There is something which Plato was but Pericles was not.

In (9) it appears that the position occupied by the predicative expression in (8) is generalized upon and replaced by a quantifier-phrase. If 'a philosopher' may be interpreted as a first-level predicate in (8), it follows that (9) represents quantification over predicate-position. By such a line of reasoning Dummett concludes : 'we have reduced the assertion that a given predicate has reference to a banality exactly parallel to that which the ascription of reference to a proper name amounts ' ( 1 97 3 , p . 222). In his second argument Sen endeavours to confound this line of reasoning by maintaining that predicative expressions cannot occur in predicate-position ( 1 9 82, pp. 1 00-1 0 1 ) . In support of the claim S en makes a point that has continued to resonate through ensuing debate. 14 Predicates ( 'x is a philosopher' ) are incomplete expressions that go together with a name ( , Plato ' ) to produce a sentence. B ut predicative expressions are not incomplete; they cannot be combined with a name to produce a sentence ( ,Plato a philosopher ' ) . Therefore predicates and the predicative expressions derived from them are not interchangeable. S o even if it is granted that we are able to refer to the bearers of predicative expressions and quantify over the positions they occupy, it does not follow.that the.same is true of predicates . I S In his third and final argument S en seeks to reduce to absurdity the assumption that predicative expressions - conceived as logical even though not grammatical predicates - have reference ( 1 982, pp. 1 02-5 ; 2000, pp . 5 5 8-9). He begins by scrutinizing the transformational process that purportedly allows us to derive (8) from (6) and (7) . In order to perform this derivation the predicate 'is a philosopher' must first be replaced by the predicative 'a philosopher' before being moved into grammatical subj ect position. (6) is then reparsed in the form ( 1 0)

A philosopher is what Plato was .

B ut exactly what is the role of 'what' in this sentence ? Sen asks us to compare ( 1 0) to (11)

S ocrates i s whom Plato admired the most.

In this sentence ' Socrates ' occurs as logical subj ect (as a purely referring expression) and the relative pronoun ' whom' is used to pick out the reference of 'Socrates ' . In

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( 1 0) 'what' appears to perform the same role as 'whom' in ( 1 1 ) : it functions as a relative pronoun that picks out the referent of ' a philosopher' . But in order for 'whom' in ( 1 1 ) or ' what' in ( 1 0) to pick up on a reference already made, ' Socrates' and ' a philosopher' must already have succeeded in so referring. It follows that the predicative expressions must - like proper names - be conceived as genuine referring devices (logical subj ects). With this intermediate conclusion established, Sen proceeds to argue that predicative expressions cannot be regarded as merely grammatical transformations of predicates . If the differences between predicative expressions and predicates are merely grammatical - without logical significance - then predicates will perform whatever logical role predicative expressions perform. Since the latter expressions are logical subjects (merely referring devices), it follows that predicates are also logical subjects . B ut then (6), from which ( 1 0) was transformed, consists in the juxtaposition of two referring expressions ( ,Plato ' , ' x was a philosopher ' ) of the same sort. This is evidently absurd. The proposal that predicates are mere referring expressions reduces the genuinely truth-evaluable sentence (6) to a mere list of subj ects . So Sen draws the final conclusion: predicates cannot refer (on pain of absurdity) but must perform some other logical role that dovetails with the referring function of names to yield genuine sentences. In this way Sen seeks to remedy a purported defect of Frege's view. Frege was also keenly aware that a sentence could not be reduced to a list of referring expressions. And sometimes Frege seemed to suggest that the difference between a sentence and a mere list can be explained by attributing different kinds of referents - saturated obj ects and unsaturated concepts respectively - to names and predicates (Frege, 1 952) . But for S en it is clear that this suggestion - whether or not it is Frege's - promises no advance . Instead of distinguishing sentences from lists of names, this suggestion merely distinguishes between different styles of lists, lists that mention only one kind of thing and lists that mention both saturated and unsaturated things. An illuminating description of the difference between lists (of whatever kind) and genuine sentences 'remains obscured from sight Sen writes however radical the difference between the entities which they introduce might be, s o long a s they are introduced a s referents o f subj ects, or predicates . . . there is no difference between what the subject does and what the predicate does . ( 1 982, p. 1 04)

If a sentence is to be distinguished from a list, Sen insists, it is vital to keep clearly in view the intuitively different functions that names and predicates perform. Whereas names are used to refer to things, predicates 'describe ' them. It is doubtful whether the semantic functions of names and predicates can be elucidated in terms more basic than these - Sen certainly displays no inclination to do so. But if this difference in semantic function is to be kept in view, then - S en also insists - it must be recognized that names and predicates introduce the entities associated with them in different ways. Whereas names 'refer to ' or ' denote ' their bearers, predicates ' connote' or 'imply ' the properties they express (ibid . ) . It is because names and predicates introduce entities in the contrasting styles characteristic of referring and descriptive expressions that the juxtaposition of a name and a predicate results in a genuine sentence. If we fail to keep in sight the intuitively different ways in which

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names and predicates introduce the entities associated with them - ways that can ultimately be elucidated by no other means than the use of names and predic ates to display the contrasting styles in which these entities are introduced - then we will be unable to see that a list of referring (or connoting) expressions is different from a sentence proper. 1 6

v

What are we to make of Sen's arguments that predicates do not refer to properties? There can be no doubt that with this final argument S en brings us to a perspective upon predication and quantification that is broad and deep. And it is from the perspective lately developed - the perspective from which it is recognized that names and predicates perform irreducibly distinct functions - that some of Sen's other arguments appear at their most persuasive. Recall his argument that predicates do not refer because they lack a feature of prototypical referring devices, a criterion of identity that enables us to identify the bearer of an expression as the same again. To this it might be obj ected - as Strawson has done - that the criterion of application associated with a predicate itself serves as a criterion of identity for the property it introduces : by learning how to apply a predicate we learn how to identify the property it introduces (Strawson, 1 976, p. 1 95 ) . Contra S en there appears then to be a significant sense in which predicates may be said to refer to properties . But it is now apparent that S en may respond to this reply with equanimity. He may s ay: there is indeed a signiiicant sense in which the criterion of application associated with a predicate introduces us to the property it connotes. But what must be kept in view is that the way in which a predicate introduces us to this property - call it 'identiiication' if you will - is quite different in kind from the way in which a name introduces its bearer. Only so will a sentence be distinguished from a list. Despite the undoubted force of this reply, it is nevertheless difficuiHo avoid the suspicion that such considerations reach only so far, that recognizing that sentences are by necessity composed of expressions that perform distinct functions establishes only so much. Let it be first conceded that in the most simple and fundamental cases a sentence must consist of one expression (a name) that refers to an obj ect and another (a predicate) that describes the obj ect so picked out. But it still does not follow that a predicate in such a case might not - in addition to its primary descriptive function - also incorporate a reference to a property. After all, we are familiar enough with the thought that names or definite descriptions can perform the semantic function of referring while also incorporating a descriptive element (a mode of presentation) . Just because a predicate must perform a descriptive function in order to conjoin with a proper name to produce a sentence, it does not immediately follow that it cannot also refer. Let it also be conceded that natural language lacks the grammatical resources (propredicates) to replace the predicate expression in such a sentence with a bound variable. But this is liable to seem nothing more than an idiosyncratic shortcoming of language, a shortcoming that c an be overcome - as indeed Frege thought he had done in his Begriffsschrift - by introducing an artificial notation that permits

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quantification over the predicate-position. I f the predicate variables introduced generalize upon the descriptive function of predicates - rather than the referring function of names - there is nothing in this suggestion that conflicts with the insight that lies behind our first concession, the insight that a sentence cannot consist of a list of purely referring expressions . This is because a sentence construction of the envisaged form consists of a name and a bound descriptive variable. It is yet to be established that this form - artificial though it may be - is tantamount to the nonsense combination of two merely referring expressions . Hence it also remains to be established that our neglect of this form in natun il language is anything other than a consequence of the shortcomings rather than the wisdom of our linguistic forebears. The first concern raised - that predicates may incorporate reference while still discharging a descriptive function - may be developed in two different directions . On . the one hand, it may be maintained that the whole of a predicate performs a referential as well as a descriptive function (much as the entire proper name 'Hesperus ' provides a sense and a reference simultaneously). On the other hand, it may be claimed that it is only a proper part of a predicate that incorporates a reference. In effect this is the proposal adumbrated by Wiggins, according to whom it is the predicative stem of the predicate that refers - the part that remains once the copula or the inflections that yield a finite form of the verb are subtracted ( ' wise' , ' a philosopher' , ' run' , 'laugh ' ) . !7 This latter proposal is a plausible one - which is not to dismiss the earlier proposal - not least because the very examples that S en deploys to show the illegitimacy of predicate quantification appear to show that natural language permits quantification into the positions occupied by predicate stems (recall (6) , (7) and (9)). However, S en offers a number of considerations intended to undermine this proposal. A review of these considerations will bring us closer to an understanding of the driving animus behind Sen's views and the prospects of developing a coherent conception of predicate-reference and quantification into predicate-position. The .first consideration that S en off.ers· is · this·. If it is already admitted. that the. property wisdom exists qua meaning of the predicate 'x is wise' , there is no necessity to admit the additional property wise as the referent of ' wise ' , a proper part of this predicate. For to say that Socrates is wise is just to say that Socrates exemplifies wisdom; wise as a further item simply is not needed ( 1 9 82, p. 1 05). But, contra S en, this does not show that ' wise' or any other predicative stem lacks reference. It only shows - if it shows anything - that predicate-stems share a reference with certain abstract nouns. ! 8 The second consideration apparently conflicts with the first: it denies that predicate-stems enjoy any reference whatsoever - this because predicate-stems , like predicates, lack a feature of prototypical devices of reference, a criterion of identity associated with the use of a name ( 1 982, pp . 1 06-7 ) . But - for all that has been established so far - possession of such a criterion may be a sufficient but not a necessary condition of an expression's having reference. In that case a failure to come equipped with a criterion of identity is hardly sufficient reason to deny predicate stems the status of referring expressions . Of course this reply carries a question in its wake: if predicate-stems do not refer in the manner of prototypical devices of reference, what other reason is there to suppose they refer?

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One other reason to suppose that predicate-stems refer is that the positions they occupy appear to be open to quantification. It is intended to be a consequence of the third consideration that S en raises that these p ositions are not open to quantification. Consider the transition between

( 1 2)

Bucephalus is a horse.

and

( 1 3)

There is something that Bucephalus is.

Prima facie ( 1 3) is the result of replacing the predicate stem ' a horse' with a bound vmiable. But, as we earlier saw, Sen argues this is only possible if ( 1 2) is first rendered in the form ( 1 4)

A horse is what Bucephalus is.

Now, in response to Wiggins's suggestion that predicate stems refer, S en adds the further contention that 'a horse' cannot play the role of logical subj ect. He writes in a footnote appended to the 1 9 9 1 reprint of 'Universals and Concepts ' ; Whatever may be the superficial grammatical form of the above construction ( 1 4) , ' a horse' c annot really b e divested o f its essential predicative character. Look a t the double occurrence of the copula 'is ' in the sentence 'A horse is what Bucephalus is' . If the construction is not to be meaningless altogether, we cannot have a dangling copula at the end of the sentence in the second ' is ' . It must be attached to a predicate, and what could that predicate be but 'a horse' itself? The seemingly dangling copula must refer back to 'a horse' and recapture it as a predicate. (Sen, 1 99 1 , p . 1 1 0)

To where do these remarks lead us? And what is the argument supposed to be? The apposition of 'a horse' to the 'dangling copula' in ( 1 4) shows us that 'a hors e ' is essentially predicative in the following sense. Whereas 'Bucephalus ' is a subj ect expression essentially suited to combine with a predicate to form a sentence, the predicate-stem 'a horse' is essentially suited to combine with the copula to yield a predicate. Hence the copula left dangling at the end of ( 1 4) to remind us that ' a horse' i s merely the stem o f a predicate and subj ect only i n grammar. O f course quantification into the position 'a horse' occupies is only possible if 'a hors e ' is capable of performing the role of a subject (cf. 1 982, pp. 1 02-3) . Since 'a horse' is essentially predicative, this cannot be done - this expression cannot combine with a predicate to make a sentence. Therefore it is illegitimate to quantify into the position of ' a horse' or any other predicative stem. What is taken for granted in this whole way of looking at things is that only subj ect-expressions can properly be subjected to the rigours of quantification. It will help us get clear about this if we trace out the route Quine takes when he provides his own argument against the possibility of predicate-quantification. Quine

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begins from the premiss that predicates are not names of any s ort; they are not the names of their intensions (properties) or their extensions (sets) . He ends up at the conclusion that predicate-positions are not eligible for quantification. Quine employs the following argumen,t to guide us from premiss to conclusion: Consider fIrst s ome ordinary quantifIcations : ' (3x)(x walks) " ' (x) (x walks ) ' , ' (3x)(x is a prime number) " The open sentence after the quantifIer shows 'x' in a positi o n where a name could stand; a name of a walker, for instance, or of a prime number. The quantifIcations do not mean that names walk or are prime ; what are s aid to walk or be prime are things that could be named by names in thos e positions , To put the predicate letter 'F' in a quantifIer, then, is to treat predicate-po sitions suddenly as name positions, and hence to treat predicates as names of entities of some s ort. (Quine, 1 970, pp. 66-7)

In this passage Quine moves from the restricted claim that some bound variables those that appear in a variety of ' ordinary quantifications ' - occur in name position to the unrestricted claim that all bound variables occur in name p osition. But to assume the legitimacy of this move is just to assume what Quine purports to show, namely that predicate-positions are not eligible for quantification. It is plausible that there is a subtext to QUine 's argument which when taken into account may be thought to show the charge of circularity unfounded. The subtext goes something like this. It is ' ordinary quantifications ' that provide us with a grasp of what quantification is . And what these ' ordinary quantifications ' show is that quantification is a device for doing generally what names do individually: what names do individually is pick out obj ects ; what quantifiers do generally is range over all the obj ects that names pick out. If this is the subtext to Quine's argument, then the case for circularity is strengthened rather than weakened. The story it tells over-interprets what ' ordinary quantifications ' teach so as to ensure that all and only bound variables occur in name position. It is true enough that ' ordinary quantifications ' show that quantifiers are devices of generalization. But it does not follow from this that generalization can only occur in one style, the style' iii. which bound variables ' of ' ordinary quantifications ' generalize upon the semantic function of the names they replace. It remains an open possibility that there are other styles of quantification that generalize in different ways upon the different semantic functions of other kinds of expressions , 19 A related charge of circularity may be levelled at Sen's account of these matters . On the one hand Sen argues - as we saw in the previous section - that predicate­ quantification c annot be legitimate because it is only by (per impossibile) treating predicates as subjects that predicate-positions can be laid open to quantification. On the other hand he also argues - as outlined in the present section - that quantification into the position of predicate-stems c annot be legitimate because predicate-stems aren ' t subject expressions . The master assumption that drives b oth arguments is this. Quantification cannot be allowed into the position of expressions that are not subj ects . It follows from this assumption that the only way to gain the effect of quantification into the positions of different kinds of expressions that are not subject-expressions is to transform them into subject-expressions . It is then short work for S en to show that any purported transformation of this kind results in

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absurd consequences (reducing a sentence to a list) or palpably fails to yield an expression of subj ect form (because of a dangling copula) . B ut it is only necessary to undertake these discreditable convolutions in the defence of quantification into the positions of expressions other than subj ects if the master assumption is made that only quantification into subject-position is permissible. Without the master assumption in place there is no need to interpret alternative forms of quantification as anything other than direct generalizations upon the different kinds of positions they occupy rather_than indirect generalizations that come about by first (absurdly) attempting to transform non-subjects into subj ects and applying the rigours of quantification only to the subj ect-expressions that result. Since it is precisely the master assumption that is questioned when the p o ssibility is advanced of quantification in the positions of expressions other than subj ects, Sen's arguments presuppose what they are intended to establish. Quantification became a pressing concern for us because of the purported link between quantification and reference. S en argued from the inaccessibility of predicate-positions to quantification to the failure of predicates to embody any kind of referential function. Do the doubts raised concerning the inaccessibility of predicate-positions to quantification show that S en was mistaken in his conclusion that it is not the function of predicates to refer? It is important to realize that nothing of this sort is established by what has gone before. The main line of resistance to Sen's argument developed in this section has made appeal to a general conception of quantification. According to this general conception, quantification and semantic role swing together: quantifiers that bind variables in the positions of different kinds of expressions generalize different semantic role s . For this reason there i s no necessity t o interpret predicate-quantification a s thinly disguised subject-quantification. It follows from this general conception that quantification is a sure-fire sign of reference when the positions quantified upon are occupied by names . This is because it is the semantic function of names to refer, and quantifiers that bind the variables that occur in the name-position generalize upon tIlls &emantic function. Now we have agreed with Sen that the primary semantic function of predicates is descriptive. S o it also follows - given the general conception of quantification in play - that predicate-quantification must generalize upon the descriptive function of predicates. In response to Sen's concern that a sentence cannot be composed solely of expressions whose only semantic role is to refer, a further suggestion has been made: that predicates may discharge descriptive and referential functions at once. But unless there is independent reason to think that predicates perform a referential function - in addition to their descriptive one the fact that quantification into predicate-position may be permitted provides no signal that predicates refer. Since no independent reason has been given to think that predicates refer, the line of resistance we have built up in response to Sen's arguments leaves us still without reason to reject his conclusion, the conclusion that predicates do not discharge a referential function. We have simply outlined a case for the view that the accessibility of a predicate-position to quantification does nothing to guarantee the referential status of predicates that occupy that position. Rather than undermining Sen's conclusion, this case (partially) supports it.

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VI

If predicates do . not refer, what is the relationship between predicates and the properti e s that c9nstitute their meanings ? Following Carnap, Sen suggests that predicates lie in the rei ation of ' intension' to the properties they express ( 1 97 8 , pp. 206-7 ; 1 982, pp. 86-7 ) . According to Carnap, predicates 'F' and ' G' are logically equivalent iff all sentences of the form 'Fx' are logically equivalent with all sentences of the form ' Gx' , and vice versa. Predicates may then be said to have the same intension (express the same property) iff they are logically equivalent (Carnap, 1 947, p. 1 9) . It is a consequence of this proposal that predicates that express the same property are intersubstitutable salva veritate in all truth-functional and modal contexts. Sen identifies two shortcomings with Carnap ' s proposal. First, it assigns properties to predicates regardless of their complexity - regardle ss of whether they are conjunctive, disjunctive or the result of some other more complex operation. But prima facie there is only a necessity to assign properties to the simple predicates from which complex predicates are built up. Second, properties are intended to be the mean ings o f predicates . Predicates that h ave the s ame meaning are interchangeable salva veritate in all the contexts in which they occur. However, Carnap ' s proposal fails to ensure that predicates that have the same intension are systematically interchangeable in this way. This is because a sentence of the form 'Fx' may be logically equivalent to a sentence of the form ' Gx' - so by Carnap 's lights 'F' and ' G ' are logically equivalent and have the same intension - even though there are contexts involving propositional attitude reports in which these sentences fail to be interchangeable salva veritate. 'F' and ' G ' may fail to be interchangeable salva veritate in these contexts because the subj ect of such a report may be ignorant of the logical liaisons that obtain between the sentences in which 'F' and ' G' occur. Sen seeks to overcome both shortcomings in Carnap ' s proposal by denying that complex predicates correspond to properties . Complex predicates correspond to eitherl ogic.al or contradictory compounds of simple predicates . In either case, . Sen claims, complex predicates - and so the properties they express - are 'eliminable by definition' in favour of the simple atoms from which these compounds are built up ( 1 9 82, pp. 94-6). But if only simple predicates express properties, then predicates that have the same intension are systematically interchangeable salva veritate after all. This is because, Sen maintains, simple predicates that are logically equivalent are also synonymous (in the case of simple predicates ' the difference between L­ equivalence and synonym no longer holds ' ) . Since synonymous predicates are interchangeable salva veritate even in propositional attitude reports, it follows that (simple) predicates that are logically equivalent also have the same meaning. Famously Quine was sceptical about properties and attributes because (he claimed) they lack a clear criterion of identity. According to Sen, recognition that properties are the intensions of simple predicates reveals Quine's scepticism to have been unfounded ( 1 982, pp. 8 3-4) . For properties do have a clear criterion of identity: they areidentical iff they are expressed by logically equivalent (simple) predicates . How compelling i s this account o f the relationship between predicates and properties ? To begin with it is awkward (at least) to deny that complex predicates correspond to properties when properties are intended to be the meanings of

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predicates . For how can it be denied that complex predicates have meanings when they are evidently meaningful? Perhaps this awkwardness could be dealt with in the case of complex predicates that correspond to complements, products or sums of simple predicates by saying that they have ' derived' or ' second-class' meanings inherited from the original meanings of their constituent simples. In the case of complex predicates that give rise to contradiction or paradox (e.g. 'x is impredicable ' ) S en suggests that these predicates might fail even t o be well formed ( 1 97 8 , p . 2 1 2 ; 1 9 82, p . 9 6 ) . The latter suggestion i s perhaps less plausible than the former. A s the troubled history of the theory of types has taught, it is far from straightforward to construct rules that show paradoxical predicates to be ill formed without the same rules also j eopardizing the status of many other meaningful constructions. Yet even if both suggestions are granted, there are further, more serious objections waiting to be heard. The reason Sen gives for denying that complex predicates express properties is this : 'complex predicates . . . are e lirninable by definition and, if they are really so eliminable, it is not necessary to countenance properties answering to them' ( 1 9 82, p. 25 8). However, it is far from clear in what sense (if any) complex predicates are eliminable. For example, the disjunctive predicate 'F or G' makes a contribution to ( 1 5)

Most philosophers are F or G.

How is this contribution to be reduced or eliminated? The only strategy that suggests itself is to reduce or eliminate the contribution of 'F or G' to, or in favour of, the contribution its disjuncts 'F' and ' G' make to the disjunctive sentence ( 1 6)

Most philosophers are F or most philosophers are G.

B ut ( 1 6) evidently fails to be equivalent to ( 1 5) most philosophers may be F or G even though most philosophers are not F and most philosophers are not G. Hence the purported elimination (or reduction) fails . The point is a generaJ. one: in a quantified language complex predicates (disjunctive, conjunctive, and so on) play an indispensable role in characterizing how some, most or all things are. So complex predicates fail to be eliminable by definition and so it remains to be established that predicates of this kind fail to express properties . It i s also doubtful whether Sen has provided a clear criterion o f identity for even the properties expressed by simple predicates. S en may be correct in his observation that logical equivalence among simple predicates is a sufficient condition for their synonymy. However, even simple predicates that are synonymous may fail to be everywhere interchangeable. For example, 'is a Hellene' and 'is a Greek' are synonymous · simple predicates. But there are still contexts involving propositional attitude reports where interchange of 'is a Hellene' and 'is a Greek' may result in a change of truth-value. Consider -

( 1 7)

and

Nobody doubts that whoever believes that anyone who is a Greek is a Greek believes that anyone who is a Greek is a Greek.

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( 1 8)

85

Nobody doubts that whoever believes that anyone who is a Greek is a Greek believes that anyone who is a Greek is a Hellene.

Despite the fact ,that there is only the exchange of a synonymous expression between them, ( 1 7) is likely true whereas ( 1 8) is probably false (Putnam, 1 954) . According to S en, properties are the meanings of predicates. S en therefore holds that predicates with the same meaning express the same property whereas predicates with different meanings express different properties . He sets a standard for two predicates to have the same meaning: that they should be everywhere interchangeable salva veritate . The failure of even simple synonymous predicates to meet this standard shows that even logically equivalent simple predicates may fail to have the same meaning. They may therefore also fail to express the same property. The conclusion appears inescapable that logical equivalence among predicates fails to supply a criterion of identity for properties. The difficulty that arises here results from the interplay of two assumptions S en makes: the standard he sets for two predicates to have the same meaning and the assumption that logically equivalent simple predicates have the same meaning. S en may respond to the difficulty raised by modifying one or other assumption. If S en lowers the standard for predicates to have the same meaning, then it may be granted that logically equivalent (or synonymous) predicates may have the same meaning even though they fail to be everywhere interchangeable salva veritate. If it is denied that logically equivalent simple predicates need have the same meaning, then the observation that logically equivalent (or synonymous) predicates fail to be systematically interchangeable need occasion no alarm. But unless he alters the commitments of his theory, neither way out appears to be open to Sen. If he lowers the standard for two predicates to have the same meaning - for example, to mere logical equivalence - then some explanation will be required of the failure of substitutivity in psychological attitude reports of co-meaningful predicates that express the s ame property. The obvious explanation to give is that substitutions fail. because the subjects. oJ. these reports hold differen.t Rojnts of view. towards the meanings of the predicates they refuse to substitute. But this seems just to reinstate a version of the sense-reference distinction for predicates . If, however, Sen denies that logically equivalent predicates need have the same meaning, then we are left without a criterion of identity for properties. The former course - that of readmitting the sense-reference distinction for predicates - runs quite against the grain of Sen's thinking about properties. By contrast, the latter course is one that at least one passage in 'Universals and Concepts ' points us towards ( 1 982, p. 94) . Quine expresses a preference for sets over properties because he claims that sets , unlike properties , enj oy a clear criterion of identity, that is, the Axiom of Extensionality. This axiom says that two sets are identical iff they have all their members in common. Sen notes a difficulty with this view. Extensionality will only serve as a criterion of identity for sets if the axiom is used in tandem with a criterion of identity for set-membership . In the case of a ' closed' set it is easy enough to settle which items belong to it: we can simply enumerate its members . However, in the case of an ' open ' set whose members cannot be enumerated - because the set is infinite or at any rate too large for us to count or because we do not know which things belong to it - membership of the set

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is settled by satisfaction of an open sentence associated with it. For example, whether something belongs to the set of red things or the set of persons is settled by whether it satisfies the predicate 'x is red' or the predicate 'x is a person ' . But this means that the criterion of identity for open sets is only as clear as the criteria of application for the open sentences associated with them. Since it may not be at all clear whether the predicates 'x is red: or 'x is a person' apply to an individual, it may not be at all clear which things belong to the set of red things or the set of persons. But without clear membership conditions Extensionality cannot deliver a clear criterion of identity for sets . The point that Sen is making here may be reinforced. Extensionality makes no mention of times or possible worlds . It says that sets are identical iff they have the same members in common but is silent about whether the members of a set S belong to S at the same time or world. Because Extensionality is silent about the temporal and modal dimensions of membership, it cannot be invoked to settle whether sets could have had different members at different times or worlds . Extensionality cannot therefore be employed to determine whether sets that are composed of different members at different times or worlds are the same or different. Sen's point may be reinforced in another way. Let us step back and reflect: what is a criterion of identity good for? Frege introduced the notion of a criterion of identity in connection with the use of recognition statements (see his 1 950, § 62). According to Frege, a criterion of identity is what enables us to recognize the same obj ect when it appears again in different guises. However, as we have just seen, Extensionality - the archetypical example of a criterion of identity - fails to provide a mechanism for recognizing sets in different guises (temporal or modal) . Moreover - as Strawson has insisted - we have adequate means for recognizing many kinds of thing as the same again even in the absence of identity criteria.2o For example, we reliably recognize persons, languages and architectural styles even though we are unable to formulate informative identity criteria for them. This suggests that the significance of criteria of identity to ontology has been overplayed. And if w e follow the direction in 'Nhich Sen's remarks lead, we should rej ect as misguided the demand made by Quine and others that properties be supplied with criteria of identity or else excluded from our ontology. The proper perspective upon criteria of identity is rather this: that they are to be welcomed but not expected. But once the demand of Quine and others is rej ected, there is no longer reason to insist that simple predicates that are logically equivalent express the same property. Nor is there reason to insist that complex predicates - even though they are meaningful - express no properties . Sen's theory admits only properties that correspond to simple predicates. The internal demands of his theory of universals lead us, however, to a far more abundant conception .

VII

There are many aspects of Sen's theory of universals that remain to be examined. His account of relations, his remarks on the relative priority of tropes and facts , his distinctive conception of the tertium quid, these and other topics have still to be touched upon. Nevertheless, it is already clear that Sen's investigation into the

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relationship between properties and predicates is an important one that continues to repay reflection. It is only by continuing to pursue the issues that he raised - issues centrally concerning the significance of quantificational constructions and the availability of criteria of identity - that we will be able to fathom the nature of predication and the extent to which natural, scientific and mathematical languages are committed to the existence of universals .2 1

Notes

2

3

4

5

6

7 8 9 10

The statement that knowledge of universals is a priori should not be taken to preclude the possibility of perceptual access to universals . See S en (this volume, Chapter 2). See S en ( 1 974, 1 9 7 8 and 1 9 82 ) . I will refer throughout to the versions of these papers that appear in two collections of Sen's work, Logic, Induction and Ontology ( 1 9 8 0) and Reference and Truth ( 1 9 9 1 ) . See Chaterjee (2000) for an alternative perspective on Sen's theory of universals that raises different themes to prominence and arrives at different c onclusions from the present chapter. Sen does not explain in any detail how this account of predication may be extended to quantified contexts, contexts that involve no specification of the predicate by the name of an individual. However, he does offer the suggestion that there is a sense in which both names and quantifiers specify predicates : 'we can say, perhaps, that all predication, general as well as singular, consists in fixing the (range of) application of the predicate' ( 1 97 8 , p. 2 1 5 ) . Of course this does not undermine the correctness of Sen's observation that determiners combine with common nouns to yield quantifier phrases in natural language CAll Indians' , for instance) . What is questionable is the use that Sen makes of this observation. Two further difficulties are noteworthy. First, as we have seen, S en uses this observation to suggest 'x' is a common noun equivalent in force to ' thing' or 'individual' . By Sen ' s lights this observation licenses the transformation o f ( a ) 'For all x, x i s human ' into (b) ' For all x, if x is an individual, then x is human' ( 1 974, p. 90) . But this transformation merely. signals the fact that a common !lOU)J. cannot subsume the role of 'x' as a bOU.n d variable. For as (b) shows, the role of 'x' is not obviated by the introduction of 'x is an individual' ; in (b) 'x' continues to operate as a b ound variable signalling that the open positions in the predicates 'x is an individual' and 'x is a human ' are simultaneously bound by the s ame universal quantifier. Second, instead of showing that variables are common nouns, Sen's observation arguably provides evidence for the proposal that quantifiers in natural language are binary quantifiers (see Wiggins , 1 9 80) . Sen earlier wrote : 'We can perhaps set aside the first view, advocated by traditional logicians, as one which has been effectively demolished by logicians of our time ' ( 1 978, p. 200) . I remain unclear as to just what point S en intends to convey with this remark. S trawson dismisses (i) for the same reason: 'No one at all fastidious would allow ' ' 'swims ' is true of S ocrates" as tolerable English ' (see his 1 974, p. 9 ) . S ee Frege ( 1 979), p. 1 1 9 and Geach ( 1 974) , p. 149. See Dummett ( 1 973), pp. 55, 8 9-90, 1 8 1-3 and Sen ( 1 97 8 ) , pp. 205-6 and ( 1 9 82), pp. 1 06-8 . The differences between objectual and substitutional treatments of quantification are shown in the contrasting truth-conditions they provide for existentially quantified sentences . An existential objectual quantification is true iff there is at least one entity

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Universals, Concepts and Qualities within the range of the quantifier that .satisfies the open sentence after the quantifier. By contrast, an existential substitutional quantification is true iff there is an expression which when substituted for the variable in the open sentence after the quantifier yields a true sentence . Sen als o offers a further argument that relies upon his conception of predication as specification. Specification involves a 'transformation' of the predicate (open s entence) in which its free variables are replaced by names. It is a consequence of this that predicates are not isolable sentence-parts ( 1 97 8 , p. 206; 1 9 82, p. 1 00). S en does not elaborate upon the next step in the argument but he appears to assume that b ound variables are isolable expressions. With this assumption in place it then follows that predicates cannot be replaced by bound variables. Yet since it may be doubted whether bound variables are isolable parts of a sentence - isolable in the sense in which the predicate common to ' S o crates is wise ' and 'B acon is wise' fails to be so - it remains to be established that predicates do not occur in positions open to quantification. See also Sellars ( 1 963), pp. 248-9 . There are several interesting points of contact here between Sen and S ellars ' s treatment of quantification, not least in virtue of the fact that despite these points of contact Sen is a realist whereas S ellars is a nominalist. See Geach ( 1 9 5 1 ) , pp. 1 3 3-4, Strawson ( 1 96 1 ) and Dummett ( 1 97 3 ) , pp. 2 1 5-22 for different developments of this idea. See Dudman ( 1 976), pp. 8 0-8 1 , Wiggins ( 1 984), p. 3 17 , Russinoff ( 1 992), pp. 8 1-2 and Wright ( 1 99 8 ) , pp. 248-50. In fact Sen would not grant so much to his opponent. For, as we will shortly see, Sen als o denies that ' a philosopher' has reference. See Searle ( 1 969), pp. 97-1 03 and Wright ( 1 998),- pp . 254-60 for attempts - closely related to Sen's account - to distinguish a sentence from a list by distinguishing the way in which predicates introduce (or to use their favoured expression ' attribute ' ) properties from the way in which names refer t o their bearers. See Wiggins ( 1 9 84) . Note that in cases where a predicate consists of a copula plus an adjective, or an article and a common noun, the predicative stem is none other than the kind of predicative expression that Dummett introduced to us in the previous section. However, it would be wrong to conclude, as Wright does , that predicate-stems are ' the kind of expression which Dummett called "predicative expressions'" (Wright, 1 99 8 , p . 252). The differences between predicatecstems and predicative expressionscemerges in connection with predicates that consist of a main verb other than the copula: to obtain the corresponding predicative expression the verb is converted into its participial form whereas to obtain the predicate-stem the inflections that convert the verb into its finite form are simply dropped (contrast 'running' and 'run ' ) . See Wiggins ( 1 9 84) , pp. 320-2 1 and Strawson ( 1 9 87) for further discussion of this issue. B ecause 'wise' and 'wisdom' fail to be intersubstitutable, Wiggins denies that predicate stems and abstract nouns cross-refer. Strawson argues, however, that thes e failures o f intersubstitutivity have a merely 'formal, syntactical' significance . S e e Prior ( 1 97 1 ), p p . 34-9, who develops this strategy i n such a way a s to allow not only for quantification into predicate- but also adverb- and sentence-positions . See S trawson ( 1 976), pp. 1 93-207. Referring to this paper S en notes that ' some kinds of Criteria of identity are inappropriate for properties - for at least some properties has been argued at length by P.P. Strawson in his excellent paper' ( 1 9 8 2 , p. 94) . But unfortunately Sen does not elaborate upon the extent of his agreement or disagreement with Strawson upon this point. Thanks t o Keith Hossack, Mike Martin, Alex Oliver, Stephen Read and Madhucchanda Sen for discussion. I would especially like to thank Arindam Chakrabarti for his careful reading of a penultimate draft that led to several improvements being made. I

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gratefully acknowledge the support o f the Leverhulme Trust, whose award o f a Philip Leverhulme Prize provided the opportunity to research the writings of P.K. Sen and to write this commentary on 'Universals and Concepts ' .

References Armstrong, D.M. ( 1 997), A World of States of Affairs. Cambridge: Cambridge University Press. Camap, R. ( 1 947), Meaning and Necessity: A study in semantics and modal logic. Chicago University of Chicago Press. Chatterj ee, A. (2000), 'Universals and Concepts Reviewed' , in Chattopadhyaya et al. (2000) , pp. 265-8 1 . Chattopadhyaya, D . P. , S . B asu, M.N. Mitra and R . Mukhopadhyay (eds) (2000) , Realism: Responses and Reactions. Essays in Honour of Pranab Kumar Sen. New Delhi: Indian Council of Philosophical Research. Dudman, VH. ( 1 976), 'Bedeutung for Predicates ' , in M. Schirn (ed. ) , Studies on Frege III. S tuttgart-B ad Cannstatt: Frommann-Holzboog, pp. 7 1 -84. Dummett, M. ( 1 97 3 ) , Frege: Philosophy of Language. London: Duckworth. Frege, G. ( 1 950), The Foundations of Arithmetic. Translated by J.L. Austin. Oxford: B asil Blackwell. Frege, G. ( 1 952), ' On Concept and Object ' , in P. Geach and M. Black (eds), Translations from the Philosophical Writings of Gottlob Frege. Oxford: B asil Blackwell, pp. 42-5 5 . Frege, G. ( 1 979), ' Comments on S ense and Meaning' , i n his Posthumous Writings. Oxford: Blackwell, pp. 1 1 8-25 . Geach, P.T. ( 1 95 1 ) , 'On What There Is ' , Proceedings of the Aristotelian Society Supplementary Volume XXV, pp. 1 25-3 6 . Geach, P.T. ( 1 974) , 'Names and Identity' , i n S . Guttenplan (ed.) , Mind and Language. Oxford: Oxford University Press, pp. 1 39-5 8 . Levinson, J . ( 1 97 8 ) , 'Properties and Related Entities ' , Philosophy and Phenomenological Research, 39, 1 -22. Motilal, S. (2000), ' ''Sense'' and "Reference" of Predicate Expressions ' , in Chattopadhyaya et al. (2000) , pp. 1 53-69 . Prior, A.N. ( 1 97 1 ) , Objects of Thought. Edited by P.T. Geach and A. Kenny. Oxford: Oxford University Press . Putnam, H. ( 1 954) , ' S ynonymy and the Analysis of B elief S entences ' , Analysis, 14, 1 1 4-22 . Quine, W.V O . ( 1 939), 'Designation And Existence' , Journal of Philosophy, XXXVI, 7019. Quine, W.V O . ( 1 970), Philosophy ofLogic. Englewood Cliffs, NJ: Prentice-Hall. Russinoff, S. ( 1 992), 'Frege and Dummett on the Problem with the Concept Horse' , Nou.s, 26, 63-7 8 . Searle, l . R . ( 1 969), Speech Acts: A n Essay i n the Philosophy of Language . Cambridge : Cambridge University Press. Sellars, W. ( 1 963), ' Grammar and Existence: A Preface to Ontology ' , Mind, 69, 499-5 3 3 ; reprinted i n his Science, Perception and Reality. London: Routledge & Kegan Paul, 1 96 3 , pp. 247-8 1 . S en, P.K. ( 1 974) , 'Variables and Quantification' , in M . Chatterjee (ed. ) , Contemporary Indian Philosophy, S eries II. London: George Allen & Unwin; reprinted in Sen ( 1 980), pp. 5 9-6 1 . S en, P.K. ( 1 97 8 ) , ' A Sketch O f A Theory o f Properties and Relations ' , in J.N. Mohanty and

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S .P. B anerjee (eds), Self, Knowledge and Freedom: Essays for Kalidas Bhattacharya. Calcutta: World Press; reprinted in Sen ( 1 980), pp. 1 9 8-2 1 7 . Sen, P.K. ( 1 980), Logic, Induction and Ontology: Essays i n Philosophical Analysis. Delhi: Macmillan. Sen, P.K. ( 1 982), 'Universals and Concepts ' , in P.K. Sen (ed.) , Logical Form, Predication and Identity, Jadvapur S tudies in Philosophy, vol. 4. Delhi: Macmillan; reprinted in S en ( 1 9 9 1 ) , pp. 82-1 1 0 . S en, P.K. ( 1 99 1 ) , Reference and Truth. Delhi: Indian Council o f Philosophical Research. Sen, P.K. ' S trawson on Universals ' , this volume, Chapter 2. S traws on, P.P. ( 1 96 1 ) , 'Singular Terms and Predication ' , Journal of Philosophy, 58, 393412. S trawson, P.P. ( 1 974) , Subject and Predicate in Logic and Grammar. London: Methuen. S trawson, P.P. ( 1 976), 'Entity and Identity' , in H.D. Lewis (ed.) , Contemporary B ritish Philosophy, Fourth Series. London: George Allen & Unwin, pp. 1 93-2 1 9 . S trawson, P.P. ( 1 987), ' Concepts and Properties ' , Philosophical Quarterly, 37, 402-6 . Wiggins, D. ( 1 9 80), ' ''Most'' and "All": S ome Comments on a Familiar Programme and on the Logical Form of Quantified S entences ' , in M. Platts (ed.), Reference, Truth, and Reality. London: Routledge & Kegan Paul, pp. 3 1 8-46. Wiggins, D . ( 1 9 84), 'The Sense and Reference of Predicates : A Running Repair to Frege ' s Doctrine and a Plea for the Copula' , Philosophical Quarterly, 3 4 , 1 26-42. Wright, C . ( 1 99 8 ) , 'Why Frege Did Not Deserve His Granum Salis: A Note on the Paradox of "The Concept Horse" and the Ascription of B edeutungen to Predicates ' , Grazer Philosophische Studien, 55, 239-6 3 .

Chapter 6

Buddhist Nominalism and Desert Ornithology Mark Siderits

Armstrong once described certain proponents of nominalism as Ostrich Nominalists . These were to be so called because they simply ignored the realist's one-over-many argument for universals, claiming that our application of a single predicate to many individuals is devoid of ontological significance. Other nominalists in Armstrong's taxonomy recognize the force of the one-over-many argument and attempt to respond to it, for example, by appealing to resemblances, or to classes. Ostrich Nominalists simply stick their heads in the sand. Devitt ( 1 9 80) took Quine to be the target of Armstrong's attack, and replied that Quine is not an Ostrich Nominalist. He also adde<;l a new category to Armstrong 's taxonomy, that of Mirage Realist. While the Ostrich Nominalist fails to see what is really there in the desert landscape, the Mirage Realist sees what is not there. This creature is, on Devitt's account, overly impressed by the one-over-many argument, seeing a need for ontological commitment where there is none. I wish to defend not so much nominalism as ostriches . It is a piece of urban myth that the ostrich sticks its head in the sand. Ostriches may lack the colourful plumage of birds living in more bountiful settings. But like many other inhabitants of the barren desert landscape, the ostrich has vision that is clear and sharp. Thus the ostrich does not fail to see the one-over-many argument. Moreover, what it sees is not a mirage. It sees that this argument places the burden on the nominalist to give some account of our disposition to apply the same predicate to many individuals when (as the nominalist claims) the individuals in question do not share a real common nature. Certain B uddhist philosophers developed a form of nominalism that sought to do just this. Like all nominalists, they began with the intuition that the real is particular. But unlike many others, they took this to mean that each particular is unique, that no particular possesses a nature that it shares with any other. They then sought to explain how it is none the less possible to apply a common predicate to many such particulars . They sought to do this using the meagre resources available in a desert. For this reason I shall claim that the Buddhist Nominalists , as I shall call them, are properly referred to as Ostrich Nominalists . The realist opponents with whom the Buddhist Nominalists engaged were eminently sensible. These Indian Realists, as we shall call them, saw commitment to universals as a necessary component of any rational reconstruction and defence of common sense . 1 In addition to universals, their ontology contains the categories

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of substance, quality, inherence and individuator. Substances are the enduring substrates of universals, qualities and individuators . The simple substances include various kinds of fundamental particles as well as selves , space and time . B eing simple or partless , these are eternal. Compound substances are composed of simple substances, and are not eternal. Related to each substance through inherence are one or more universals and certain qualities. The universal determines the substance's membership in a natural kind. The qualities account for the substance's sensible characteristics, but each quality is itself a non-repeatable individual that occurs in no other substance. The qualities of distinct substances do fall naturally into classes, however, and this is accounted for through the inherence of a quality-universal in many distinct qualities . Thus a given substance, for instance a crow, will have inhering in it a universal, crowness, that determines its being of the crow kind, as well as a variety of quality-particulars. Among these will be one colour-particular in which inheres the universal blackness. Our judgements of sameness are thus all reducible to a single kind of identity, numerical identity. To say that this is the s ame crow as the one I saw yesterday is to say that one and the same persisting substance is the obj ect of both sightings . To say that two birds are the same kind is to say that one universal, s ay crowness, inheres in both. And to say that both crows are the same colour is to say that there inheres a single colour-universal in the colour-particulars inhering in each. Now two distinct crows might agree not only in kind but also in all the quality-universals that inhere in their respective qualities, in which case they would be qualitatively indiscernible. They are none the less distinct substances. Why? B ecause the atoms of which they are composed are distinct. Two atoms might also be qualitatively indiscernible, and they have no parts . What then accounts for their distinctness ? Each atom, a s well a s every other simple substance, has its own individuator, something that accounts for its being distinct from every other substance. Indian Realists claim that universals are required to account for our judgements of sameness, and individuators to account for our judgements of distinctness. B ut the last point in the preceding paragraph shows that they use this sort of appea 1 with some discretion. Individuators are not invoked to account for all cases of distinctness . The distinctness o f compound substances can be explained b y appealing to the distinctness of their parts. The distinctness of quality-particulars sharing the same quality-universal (e.g . , two black colour-particulars) can be explained by appealing to the distinctness of the substances in which they inhere. It is only simple substances whose distinctness is said to require individuators . Indian Realists are equally parsimonious in their positing of universals . It is not the case that for every predicate expression there is a corresponding universal. For any pair of expressions having the same extension there is at most one universal. In the case of two expressions whose extensions partially overlap, for neither one is there a corresponding universal. There are no universals for mere aggregates of simple substances, even where there is a single predicate, for example 'mud' . The system of universals is meant to carve nature at its j oints . The universals of the Indian Realist are natural kinds . The difficulties that beset realism and have fuelled nominalist obj ections in the West were well known to the Indian Realist. If the concrete particular consists of (among other things) a substance plus a universal, how are the two related? The category of inherence is invoked to answer this question. But there is just a single

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inherence that ties all universals t o their respective instances. There being just one inherence, there is no scope for the question how the many inherences all fall under the same predicate. Now inherence is said to be that which ties crowness to individual crows, and blackness to individual black-particulars. How is inherence itself tied to crowness and to individual crows? It is self-linking. That is, inherence is just the sort of thing whose nature it is to link other things . The so-called Bradley regress is stopped. The universal does not exist apart from its instances . There are no uninstantiated universals. To the question how the universal is then apprehended, the answer is that it is perceived. When we see a crow we see its crowness as well. When we see a black colour-particular we see its blackness as well. This sounds odd because we think of perception as an eminently causal process, and it is difficult to see how we could causally interact with something that is located not only in the crow in front of me but wherever there are crows. The answer is that I am in contact with crowness by virtue of my perceptual contact with the crow in front of me, which is one of its loci. In fact the universal is s aid to be everywhere, though that may be just a polite way of saying that it is not the sort of thing to have determinate spatial location. To the question how something seemingly eternal and unchanging could enter into causal relations, the Indian Realist replies that not every factor in the total cause of some event need be active. Moreover, they claim, causal relations are relations among universals . The Buddhist Nominalist holds that to tell whether a putative entity is genuinely real we should determine if it is causally efficacious. The Indian Realist will claim that the Buddhist Nominalist is not in a good position to use this test against universals, since Buddhist Nominalists will themselves need universals to explain causal relations. (We return to this point below.) The Buddhist Nominalist has other obj ections to realism, however. There are several different formulations of the Third Man argument. One involves the claim that the many scattered locations of the universal require yet another universal to collect them together into one. Of greater interest, though, is the formulation put as the question : W1J.at collects together the different categories. such as substance, quality and universal? With respect to the category of universals, the Indian Realist denies that there is such a universal as universal-hood, and perhaps this denial is a principled one, and not merely an ad hoc way of trying to prevent the regress that threatens . But in the case of the purported universal category-hood it is difficult to see how the regress is to be stopped. What is most remarkable about the Buddhist Nominalist as an opponent, however, is the utter seriousness with which they take the Indian Realist's one-aver-many argument. This is what earns them the proper title of Ostrich Nominalist. The Buddhist Nominalist agrees that the two birds we spoke of earlier are both correctly called crows. This, they agree, is prima facie evidence for the existence of some one nature that they share. Our judgement cannot be explained solely in terms of the two things resembling one another. For there are many ways in which any two things might resemble one another, so the explanation will need to go by way of respects in which our birds resemble one another. In this case the relevant respect will turn out to be crowness, so the resemblance relation has not helped us avoid commitment to universals . What this is taken to show is that if we are to be consistent nominalists we must take the constituents of the world to each be unique

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and lacking in any shared character whatever. The nominalis t then owes us an account of what it is in virtue of which these two particulars are correctly called crows. It is not enough just to say that because of our linguistic training, we are disposed to apply the predicate 'is a crow ' to both. In virtue of what is this disposition triggered? If we agree that both particulars are correctly c alled crows , it seems there must be some objective feature of each that explains this. And what could this objective feature be if it is not some one thing they share, crowness ? The nominalist is sometimes described as one who holds that the universal is a ' mere name ' . But this cannot mean that what explains our calling b oth birds crows is that they share the same name (i.e . , predicate) . For then what explained our speech disposition would be that we have this speech disposition. This would indeed be sticking one's head in the sand. The true Ostrich Nominalist would not do this . The ontological resources of the Buddhist Nominalist are spartan. Of the five categories accepted by the Indian Realist, the Buddhist Nominalist recognizes only one, that of quality-particulars . Since each quality-particular is distinct from all others, one might have thought that they also accept the category of individuator. But this is rendered superfluous by the fact that there are no shared properties ; individuators were posited by the Indian Realist t o explain the distinctness o f what is otherwise identical. One might think of the quality-particular of the Buddhist Nominalist as self-individuating, in that its nature is to be distinct from all other entities . Like the trope theorist, the Buddhist Nominalist reduces the substances of common sense to bundles of quality-particulars.2 But since the basic problem for the nominalist is the same whether the predicates in question apply to substances or to quality-particulars, and the discussion must be carried out in a common language, the Buddhist Nominalist presents their theory using examples of terms for substances, such as 'cow' and ' crow ' . We shall follow them in that practice, though it should be kept in mind that the resulting analyses will be somewhat artificial, since they are meant to be further reducible. B efore the development of Buddhist Nominalism, Buddhist philosophers had already taken what might be ci1Jled, s.omewhat loosely, a nominalistic stance towMds complex substances such as chariots and forests. According to their thoroughgoing mereological reductionism, our belief in the existence of such things is the result of our using such convenient designators as 'chariot' and ' forest' . Chariots and forests are ' mere names ' . The intuition at work here may be put as : all aggregation is mental construction. Since the universal is explicitly introduced as a one-over­ many, it will also look to the Buddhist as a mental construction, an artefact of the cognitive economies that must be taken if we are to have a language that is usable for creatures like us. But there is an important dis analogy between the case of the aggregate entity and the case of the universal. The goal of constructing a 'reductionist language ' , one free of commitment to wholes such as forests , seems achievable in principle, If mereological reductionism is true, then it should be possible to give a complete description of reality without asserting or presupposing the existence of complex entities . Such a description would employ only those referring expressions that denoted the impartite entities that are the fundamental constituents of complex entities . A complete description along these lines, by stating the properties of these entities and the relations into which they enter, would enable us to see how we might believe there are forests and chariots when there really aren't. B ut, as the

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Buddhist Nominalist explicitly recognizes , the notion of a strictly nominalistic language is an oxymoron. Such a language could contain only names for particulars. It would thus be incapable of expressing facts concerning the relations into which the particulars enter. S)lch a 'language' could therefore not even be used to assert the existence of elementary states of affairs . So while the mereological reductionist approach of terming the complex entity a 'mere name ' was suggestive to the Buddhist Nominalist, that approach does not yield a way to avoid corn.rnl.tment to universals . According to Buddhist Nominalism, the meaning of a kind-term is the ' exclusion of the other' (anyapoha) . This builds on the idea that since a given predicate determines a bipartition of the world, mastery of that predicate may be expressed as either the ability to tell when the expression does apply or the ability to tell when it does not. So according to apoha semantics, the meaning of ' crow ' may be given as : not non-crow. What all the things that are called crows have in common, then, is that they are not in the class of the non-crows. This is clearly meant to avoid commitment to crowness, but will it succeed? Of course we are not tempted to posit a universal to account for the shared character of all the things that are not crows. For we don ' t believe there is a single shared character here. The class of the non­ crows strikes us as a pretty disparate assortment, including as it does ostriches, teapots , the number 7 and the wizard Gandalf. But then we must wonder how we could learn to tell when something is in that class. That we call this the class of non-crows suggests that our ability to determine its membership is parasitic on our ability to determine which are the crows. As the double negation in 'not non-crow ' might have suggested, we seem to be back where we started. This is so, however, only if both negations in 'not non-crow ' are classical. And they are not. The Buddhist Nominalist follows the Indian Grammarian school in distinguishing between two kinds of negation, for which B .K. Matilal coined the terms 'verbally bound' and 'nominally bound' negation. As these names suggest, the former is associated with the verb in a sentence, while the latter is associated with a common 'noun or adjectivec B oth occur in the sentence, 'That is not imp.olite' . This illustrates another difference between the two forms as welL The verbally bound 'not' behaves classically, like exclusion negation, but the nominally bound negative prefix 'im-' behaves non-classically, like choice negation. As the Grammarians pointed out, nominally bound negation is implicative in nature: to say of some act that it is impolite is to proffer what will be taken to be a positive characterization of the action, that it is rude. But the pair 'polite' and 'rude' does not effect a genuine bipartition of the universe. There are those things to which standards of etiquette simply do not apply, such as those that are not human actions. Thus the application of verbally bound negation to a predicate formed through the nominally bound negation of some predicate P does not yield a straightforward assertion of P. To say of something that it is not impolite is not to assert that it is polite, for it may be the sort of thing to which questions of politeness do not apply. To say of something that it is not non-P is just to refuse the characterization of the thing in question as non-P without col11ItIii ment to any positive characterization. It is this feature of the 'not non- ' construction that the Buddhist Nominalist hopes to exploit. Suppose that S/l is one among the many pure particulars making up the universe. To each particular we assign a name. By attaching the nominally bound negative

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particle 'non- ' to our name for Sm we form an expression that may be asserted of everything else in the universe : ' non-sn' . This is guaranteed by the fact that Sn is utterly unique. What may then be said to not be non-sn? Just Sn itself. So this manoeuvre has not succeeded in enhancing our linguistic resources. We started with just names, and what we wanted were usable predicates. The source of the difficulty is that 'non-sn ' effects a bipartition on the universe, dividing it up into Sn and everything else. Suppose though that we could learn to form the class 'ncin-s,,' in such a way as not to include everything else in the universe. This is done by learning to associate with Sn a certain paradigm image Pn which is formed so as to be manifestly incompatible with some but not all of the remaining particulars in the universe. Suppose for instance that Sn were the partiCUlar that was ostended when we were taught to use the word ' crow' . To learn to use this word we must learn to form Pn so that it is evidently incompatible with the perceptual images caused by ostriches, tumbleweeds and asteroid impact craters - but not with those caused by other crows. We would then correctly judge that ostriches, tumbleweeds and asteroid impact craters are non-crows. B ut in addition to Sn, there would be other particulars as well belonging to the class of things that are not non-sll" These may all be said to be crows. We have now mastered a useful predicate expression. How, though, does one learn to form Pn? The Buddhist Nominalist texts actually give two different answers : through the activation of dispositions acquired in the beginningless series of past lives , and through conformity to social convention. The first answer may be immediately dismissed, since it is no more helpful than Plato's myth of recollection in the Meno. 3 The second appears equally unresponsive to the question, since it too seems to presuppose rather than explain the ability. What we want to know is how one can learn to see ostriches but not other crows as distinct from a particular crow if the distinctness in question is not qualitative distinctness lacking a shared nature, or dissimilarity in some respect - but just numerical distinctness. How can one learn to conform one 's linguistic behaviour to that of others if there are no objective features to form the basis of this discriminative capacity? . Still the appeal to social convention does bring out the- point - that the ability in question depends on practices that are responsive to human wants and interests . And this is a crucial point. For it turns out that there is something all the non-sn may be said to share, when 'non-sn' is formed in accordance with the relevant convention, namely that they fail to satisfy a certain desire, say the desire to eat crow. Obtaining an ostrich or a tumbleweed will fail to satisfy that desire; the desire persists in their presence. Obtaining Sn satisfies the desire . B ut the same holds for Sn+ 1 > Sn+2 , and Sn+3 , so these also belong to the class of things correctly asserted to be not non-pn- This is why all four things are said to be crows . To say that there is a social convention at work here is to draw attention to the p oint that it is in virtue of facts about humans that these four things are said to belong to a single class. To this it will be objected that these four particulars could not all equally serve to satisfy the desire in question if they did not have a shared nature. To this the Buddhist Nominalist responds with a pharmaceutical analogy. Aspirin, ibuprofen and Tylenol are anti-pyretics: each has the capacity to abate fever. Yet these are acknowledged to be three quite distinct compounds . It is our interest in fever abatement that makes us see them as having a shared nature. (And it is the

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commercial interests of the pharmaceutical fIrms that make us none the less see them as distinct.) The functional property of being anti-pyretic is multiply realized. In each case it supervenes on distinct base properties . It is our interests and not the world that make us see resemblance, a shared causal power, here. By the same token, the Buddhist Nominalist claims, it is our interest in s atisfying a certain desire that makes us see s'" Sn+b Sn+2 and Sn+3 as forming a natural kind. Each has the causal capacity to satisfy that desire. Obtaining any one of them will do. Considerations of cognitive economy malce it in our interest to see them as alike. And in a social species , the practice of doing so will spread. This is w hy they are all correctly said to be crows . The Buddhist Nominalist thus reduces shared properties t o the causal c apacities of particulars. In doing so they follow a well-worn path in the Buddhist tradition. The Buddha claimed that the proper understanding of c ausation is at the heart of his prescription for overcoming suffering. Buddhist reductionism defends the B uddhist doctrine of non-self by seeking to show that the properties of persons supervene on the causal c apacities of thoroughly impersonal psychophysical elements . Indeed so central is the notion of causation to Buddhist metaphysics that causal efficacy is taken as the criterion of existence: to exist is to make a difference to how things are by bringing about some effect. In the hands of the B uddhist Nominalist this becomes the basis for an argument against the existence of universals. As something permanent and unchanging, the universal could only produce effects unceasingly, which is absurd. Hence the universal could produce no effects, and thus it does not exist.4 But as we saw above, the Indian Realist replies that causation must itself be understood as a relation among universals . This view, which has recently been advanced by Armstrong ( 1 97 8 ) and defended by Fales ( 1 990), was used by the Indian Realist to answer Humean concerns about the causal relation. But it may also be employed as a response to the Buddhist Nominalist causal efficacy argument against universals. For if the causal relation is itself a relation among universals, then any argument that uses facts about causation to show that universal; do not exist must be invalid. One cannot use something requiring real universals to prove that universals are unreal. The Buddhist Nominalist has an interesting response to this obj ection. They will certainly agree that any statement of causal laws necessarily involves appeal to shared properties . Buddhists in general agree with Hume that causal laws are of the form, 'Things of this sort are always followed by things of that sort' . B ut, the Buddhist Nominalist will say, this is hardly surprising given that a usable language must contain predicate expressions . And it does not follow that the facts that make a statement of causal law true involve shared natures, one for all the particulars counting as causes covered by the law, another for all the particulars counting as effects. All that is required of the world is that particulars be succeeded by particulars. Our interests and cognitive limitations will make it the case that patterns in this succession become apparent to creatures like us. Our three compounds will come to seem to us to possess the shared nature of lowering fever. There is still an important question to be raised concerning this pharmaceutical example, however. It depends on our being able to recognize distinct instances of fever as relevantly similar. For the claim is that we come to see our three compounds as having a shared nature because each functions to suppress fever. For us to know

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this, however, we must be able to compare distinct occurrences of fever abatement. And why should this present desire for relief from an unpleasant sensation b e classed with the one last month (when I had the flu) and n o t with the o n e last week (when I stubbed my toe) ? The Buddhist Nominalist would be hard pressed to defend the answer that this is also due to having learned the relevant social convention. Learning of this sort seems to require at least some rudimentary similarity space, some set of basic dispositions to see certain presentations as similar. So it seems the Buddhist Nominalist must fall back on their version of the innateness hypothesis : dispositions are retained from a beginningless series of past lives . And distinct humans have shared similarity spaces because we also have sufficiently similar past lives as to have been born as humans and not, say, as ostriches (who presumably have their own shared similarity space) . At this point the B uddhist Nominalist seems to have reverted to the moderate realism of their unwitting realist predecessors in the Buddhist tradition. Is this the best we can hope for from the B uddhist Nominalist? Perhaps a disposition to find certain presentations similar might be innate without its being . the case that those presentations all share a common nature. For this might be the result not of beginningless karma but of processes of natural selection. The underlying idea in the pharmaceutical case is that when it is to our advantage to do so we may see similarity where there is actually difference - namely difference in the underlying causal mechanisms whereby the three compounds succeed in abating fever. In the pharmaceutical case the judgement of similarity is mediated by learning a social convention. The objection was that such learning cannot take place in the absence of some rudimentary similarity space that is innate. The reply would be that natural selection can play the same role as social convention, providing the organism with useful shortcuts around the overwhelming complexities of the actual causal facts . The facts that obtain in the world are just that this particular is succeeded by that, and this other one by that other. Reproductive success is enhanced for creatures that can master this complexity by working out useful cognitive shortcuts and exploiting the seeming regularities thatresult. This means the capacity to learn, which requires a rudimentary similarity space. Due to natural selection, the organism will thus come equipped with those basic dispositions that make social learning possible . The rest is accomplished through mastery o f a shared language. As creatures of the desert, ostriches must be able to make do with meagre resources . Those necessities that other birds inhabiting more bountiful lands might find ready to hand in the environment, the ostrich must often construct. We have seen how apoha semantics is meant to enable the Buddhist Nominalist to construct universals . The Buddhist Nominalist concedes that the nature of any usable language will appear to make commitment to universals unavoidable. The avoidance of such commitment through paraphrase is not an option. The B uddhist Nominalist thus concedes that universals must be given a certain ontological status. B ut the status they are accorded is that of conceptual fiction - something we take to exist because of requirements on a language that is to be useful for us. This seems to be quite different from the case of the chariot or the forest, where paraphrases are available to show why we need not take the commitments of our language completely seriously. Though the strategy of fictionalism through paraphrase is not available in the case of universals, apoha semantics gives the Buddhist Nominalist an alternative

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strategy. I t is meant t o show how a language containing expressions requiring commitment to class characters might usefully mesh with a world consisting of nothing but unique particulars with causal connections . What other apparent avian necessities are not readily available in the desert? Some of the same considerations that make nominalists suspicious about universals apply with equal force to other purported denizens of the mysteriously lush 'third realm' . These have been said to include such things as numbers and sets �md other mathematical obj ects, as well as propositions and perhaps Fregean senses. Since inhabitants of the third realm are thought to be eternal and changeless, it is difficult to see how they might be accommodated within a naturalistic framework. So there is an apparent difficulty if it should turn out that our descriptions of the world require us to talk of such things . For instance, our best accounts of the nature of the physical world employ numbers, yet considerations stemming from the causal closure principle make it difficult to see how numbers might enter into the constitution of physical facts . The desire to resolve this difficulty is what motivates such 'nominalistic ' treatments of mathematics as that of Field ( 1 9 89) . Much more attention has been paid recently to the case of propositions . It is widely believed that if a non-eliminativist programme is to succeed in psychology, we need some way to individuate beliefs by way of their contents . And here the most promising approach seems to involve commitment to propositions. Now this need not introduce any special difficulties if the propositions in question are Russellian. Russellian propositions are composed of obj ects and properties, so the only difficulty facing the theorist of a naturalistic bent is that of explaining how properties, as universals, enter into concrete states of affairs . But there is some reason to believe that the propositions that are called for here must be Fregean. Now Fregean propositions are decomposable into Fregean senses.s But the latter are just as mysterious as the former, and of a decidedly third-realm cast. Fregean senses are more fine-grained than are objects and properties, so a naturalistic treatment of properties is unlikely to have straightforward application to the case of sens-es. Senses are in any event irl'voked precisely to solve the ,problem ofcognitive significance (the ' informativeness ' puzzle) that arises when w e identify the meanings of terms with their referents (i. e . , objects and properties). So the case for including senses in our ontology seems fairly strong. Yet it is difficult to see what it would mean for a cognizer to ' grasp' a sense if this is truly a third-realm entity. Likewise if beliefs acquire their content through Fregean propositions, it is difficult to see how such mysterious entities could contribute to the differences in action that beliefs are typically meant to explain. Peacocke ( 1 992) addresses these concerns. His approach to what he calls concepts (which are in fact Fregean senses) is meant to show just how mention of these abstract obj ects, which lack spatio-temporal location, can 'play a significant part in the description of the empirical mental states of thinkers ' ( 1 992, p . 99). His strategy of 'legitimation by application' involves showing how the possession conditions for concepts can contribute in a systematic way to the characterization of the belief states of cognizers . Attribution of the belief that p to some cognizer is understood as asserting that the cognizer is in s ome state S with the relational property R. Here R is characterized as the relational property such that any state S having that property is a belief that p. And R may be specified by considering the contribution

. .

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of the concepts of which p is composed to the belief content that p. A given 'concept is in tum to be specified in terms of its possession conditions, those conditions that must be fulfilled for a cognizer to be said to possess the concept. Since possession conditions for concepts involve dispositions to hold propositional attitudes toward propositions involving the concept, and propositional attitudes are systematically tied to action (including linguistic behaviour), there are genuine empirical constraints on the content that p. Does this approach commit one to the existence of concepts ? This depends on whether it is possible to identify the states over which S ranges without employing the notion of conceptual content. If such states could be said to be, for instance, type- or token-identical with non-mental states, then such characterization is possible. If, on the other hand, there is no relation, whether it be identity or constitution or realization, holding between non-mental states and propositional attitudes that would allow one to specify the S-states independently of attribution of conceptual content, then commitment to the existence of concepts as third-realm entities would prove difficult to avoid. If there is some such relation, then the way is open to treating these as fictions . Suppose then that propositions are an avian necessity. This might be because, for instance, a belief-desire model of their psychology represents our last best hope for making sense of their behaviour. Since there are no abstract objects in the desert, the existence of ostriches would require that there be a relation of the requisite sort. But on Peacocke's account there is another requirement as well. As he understands it, the possession conditions for perceptual concepts of a relatively observational s ort (roughly the sorts of concepts that the classical empiricists sought to account for under the rubric of ' simple ideas of sensation' ) require that perceptual representations have non-conceptual perceptual content. And this is spelled out in terms of dispositions to respond to a representation ' s possessing certain observational properties . S o even i f there i s no commitment t o propositions o r t o senses, universals may still be called for. S ince there are n o universals i n the desert, the ostrich i s endangered. C an the Buddhist Nmninalist do any better? The first·point ro mak.e here ig, Hlat the BuddhistNominalist also used their apoha semantics to solve the informativeness puzzle, for both predicate expressions and proper names. 6 Buddhist Nominalism ' thus gives a unified treatment of both concepts (senses) and properties (universals) . This might seem puzzling given that concepts are supposed to be more fine-grained than properties. But what the Buddhist Nominalist has done is give the mechanism of apoha a dual role, exploiting the product-process ambiguity of the term ' exclusion' . The universal represents the reified form of the 'not non-Pn' mechanism. It is the fiction that we construct and project onto the world to account for the objective character of reference . The sense represents our manner of grasping this mechanism. To cognize some particular as a crow is to see it as not excluded by the paradigm image we have learned to associate with ' crow ' . To master the term is to learn to overlook differences between the paradigm and other partiCUlars . It is thus not surprising that two different terms might denote the same prop erty through distinct modes of presentation. It is not surprising that identity statements might be informative. The second point is that this unified fictionalist account of concepts and properties suggests a useful diagnosis of sorites puzzles . As Priest (200 3 ) points

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out, what makes sorites paradoxes so difficult is that they force u s t o recognize cut-off points where there shouldn ' t be any. The B uddhist Nominalist can s ay that this stems from the role that the universal plays in our cognitive economy. The world itself, being a world of just pure particulars, is of course digital in nature . But the linguistically mediated world will be analogue in nature . A usable language will contain observation predicates with a fair degree of tolerance: predicates such that the typical speaker can tell whether or not the term applies 'just by looking ' . This will result in a degree of indeterminacy in their applicability. At the same time, the requirements of a public language make compelling the idea that there is an objective basis to the application of our observation predicates . The latter demand has the universal a s its reified expression. Construed a s a component of the mind-independent nature of reality, the universal must lack indeterminacy in its identity conditions ; for the notion of reality at work here is precisely the one behind the intuition that the real is particular. Hence the appearance that there must be sharp cut-off points in the application of the c orresponding predicate. At the same time, the manner in which we grasp the meaning of the expression tells us there should be no cut-off points . The result is the sorites paradox : the intolerable sense that there must be a precise p oint at which a vague predicate first fails to apply. A third point is that this fictionalist approach to senses might give the B uddhist Nominalist some needed resources for their desert existence. Buddhist Nominalism, like all of classical Indian philosophy, is familiar with only two realms , the physical and the mental. It knows nothing of a third realm, hence of propositions .? This creates the following difficulty for the Buddhist Nominalist. I earlier attributed to the Buddhist Nominalist, as well as to the B uddhist reductionist, views involving a supervenience relation. Now .supervenience is ordinarily understood to involve necessity of some sort or other. It might be held that there are varieties of supervenience relation that do not involve the alethic modalities, and that the various dependencies discussed by Buddhist philosophers were of this sort. But suppose that no supel'venience relation can be specified. without bri.nging in modal notions . In that case, the Buddhist Nominalist will need such notions to expres s their view. If w e agree that alethic necessity i s truth i n all possible worlds, what could a possible world be for a Buddhist Nominalist? Clearly not a concrete non­ actual world, after the fashion of what David Lewis calls actualism. It would then have to be an ersatz world, that is, a maximally consistent set of propositions. S o perhaps the Buddhist Nominalist will have a need for propositions . We have seen how the Buddhist Nominalist can make a place for senses in their fictionalist ontology. And propositions can be thought of as entities that are constructed out of senses. One maj or question here is whether the Buddhist Nominalist has sufficient resources to construct maximally consistent sets of propositions. If so, then they might be able to deploy a concept of necessity in explaining the role of supervenience in their theory. But the resources might be lacking, perhaps due to difficulties having to do with the notion of a bounded totality. This is a question that I shall not here try to resolve. The plumage of the ostrich is not colourful, but it does have its attractions. At one time not so very long ago, when the ostrich plume was in fashion, ostriches were nearly hunted to extinction. We have since lost our taste for their feathers , and

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the o strich population has recovered somewhat, but it has grown shy. Perhaps that is why a b ody of myths has grown up around it. The Ostrich Nominalist deserves to be better known. Perhaps there are lessons to be learned from its spartan but clear­ sighted ways.

Notes

2 3

4 5

6 7

S trictly speaking it is just one school of Indian Realists whom I shall be discussing, the Nyaya school. Several of the other so-called orthodox schools of classical Indian philo sophy posited universals . Moreover, while all schools of B uddhist philosophy deny the existence of universals , not all are equally consistent in their denials. Certain Buddhist schools fail to explain how, in the absence of universals, the s ame predicate c an be applicable to many particulars . Instead they take it as unproblematic that the ultimately real particulars should fall naturally into classes . For a useful presentation of a forerunner of B uddhist Nominalism as a form of trope theory see Goodman (forthcoming) . It does earn an advantage over the Platonic doctrine by explicitly maklng the series of past lives beginningles s . For this means there can be no question of when the disposition was flrst acquired. B ut this in tum means that the account fails to explain the disposition. Armstrong ( 1 978), pp. 1 2 8-32 discusses a similar argument, though in the context of a defence of a variety of realism akin to that of the Indian Realist. S trictly speaking this is true only if s ome way can be found to accommodate the context principle within a compositionalist approach. For a classical Indian treatment of this problem see Siderits ( 1 9 9 1 ) . For the former see Siderits ( 1 9 8 6 ) ; for the latter see Tillemans ( 1 9 8 6 ) . An interesting exploration of this is to be found in Krishna et al. ( 1 9 9 1 ) , which is the result of a dialogue b etween analytically trained philos ophers and the current representatives of the classical Indian realist tradition.

References Armstrong, D.M. ( 1 97 8 ) , Nominalism and Realism: Universals and Scientific Realism, Vol . 1 . Cambridge: Cambridge University Press. Devitt, Michael ( 1 9 80), "'Ostrich Nominalism" or "Mirage Realism" ? ' Pacific Philosophical Quarterly, 6 1 , 433-9. Fales, Evan ( 1 990), Causation and Universals. London: Routledge. Goodman, Charles (forthcoming) , 'The Treasury of Metaphysics and the Physical World' ,

Philosophical Quarterly.

Krishna, Daya et al. (eds) ( 1 9 9 1 ) , Samvada: A Dialogue between Two Philosophical Traditions. Edited by Daya Krishna, M.P. Rege, R.C. Dwivedi and Mukund Lath. D elhi: Motilal B anarsidass . Peacocke, Christopher ( 1 992) , A Study of Concepts. Cambridge, MA: MIT Press . Priest, Graham (2003) , 'A Site for S orites ' , in Liars and Heaps: new essays on paradox. Edited by J.e. Beall. Oxford: Clarendon Press, pp. 9-23. Siderits, Mark ( 1 9 86), ' The sense-reference distinction in Indian philosophy of language' , Synthese, 69, 8 1-1 06. Siderits, Mark ( 1 9 9 1 ) , Indian Philosophy of Language: studies in selected issues. Studies in Linguistics and Philosophy monograph 46. Dordrecht, The Netherlands : Kluwer.

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Tillernans, Tom ( 1 986), 'Identity and referential opacity in Tibetan Buddhist apoha theory' , in Buddhist Logic and Epistemology: studies in the Buddhist analysis of inference and language. Edited by B . K. Matilal and R.D. Evans. Dordrecht, The Netherlands: Kluwer, pp. 207-27 .

Chapter 7

Universals Transformed : The First Thousand Years After Plato Richard Sorabji

The idea of universals underwent surprising changes during the 1 000 years of ancient Greek philosophy. This applies both to universal concepts in the mind and to universals as things . I shall deal with universals as things first and concepts second, but it will turn out that the two subj ects are connected, and that both , underwent big changes }

Plato's Forms and Aristotle's Deflation

In the fourth century BC, Aristotle gave a definition of universals at de Interpretatione 1 7 a 39-40 as 'what is of a nature to be predicated of several things ' . At Metaphysics 1 .6, 987 b l- l O, he describes his teacher, Plato, as having introduced universals as Forms or Ideas . At Phaedo 77-9 Plato spoke of a restricted class of relative UIiiversals like equal, double and beautiful, in which things participate only relatively, that is in certain relations , respects and comparisons . But eventually, he recognized a much wider class of universals as Forms or Ideas, even though there were still qualifi,cations to the t:xtreme principle mentioned in Republic 5 96A that there is a FOn:ll corresponding to each coiimion name . · Perhaps , he suggests In Staiesma,n 262A-263E, we should not recognize Forms for negatives like non-Greek, or numbers other than 1 0,000. There were hesitations reported by Aristotle, Metaph. 1 070a 9-2 1 , about the recognition in two texts, Cratylus 3 89A-C and Rep ublic 596A-B ; 597C, of Forms for artefacts such as bed, shuttle and table, and there were questions in Parmenides 1 30 about Forms for such disgusting things as mud, hair and dirt. That there are universals is not a very startling thesis on its own. But in calling , these universals Forms .or Ideas , Plato had a whole series of very controversial claims to make, of which I shall mention two in particular. The first is that Forms are more real than their instances, in that they exist whether instances do or not. Plato may go further. His denial at Timaeus 37C-3 8B that we can say ' was ' and 'will be' of the Forms was taken by Plotinus to mean that Forms are outside of time altogether. Aristotle's whole scheme of categories in Categories, chs 2 and 5, can be seen as presenting a rival view. Universals depend for their existence on primary substances, which for Aristotle in the Categories means, above all, naturally existing individuals

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such as Socrates. For the universal Man to exist is merely for there to be individual men and for the universal Wisdom to exist is for there to be instances of wisdom in individual men. This is the implication of Aristotle's distinction in the Categories between things such as S ocrates, which are neither present in nor said of anything, and other items in the categories, which are present in or said of something, Cat. 1 a 20-b9 ; 2 a I 1-b6. It fits with Aristotle 's rival view o f the order o f priority that i n his work on scientific method, the Posterior Analytics, he is ready to rewrite definitions of univers al terms, such as the definition of man as a rational animal, into syllogistic premisses about all individual men being rational animals . To get some sense o f the truth in both rival views, one may consider the difference between a perfect answer to a Mathematics examination and to a Philosophy examination. The second idea does not seem even to make sense ; the first does. And someone might say that there is such a thing as a perfect answer to a Mathematics exam, even if he does not mean that there has ever been an actual instance. Part of what Plato wants to do is to treat Justice like this. It is both a coherent idea and an ideal to be striven for, whether or not it has ever been achieved. This too could be put by saying that there is such a thing as Justice. But Aristotle, equally reasonably, thinks that to ask about the existence of justice is to ask about whether it has been achieved in actual instances at one or another time and place. Plato, however, goes much further with his second controversial thesis, that Forms explain how instances come into being, e.g. Phaedo 1 00B-1 02A. Aristotle complains, in Metaph. l . 9 , 992a 24-6, that coming into being requires a triggering cause of the type he calls ' efficient cause' , and that the Forms , being changeless, are not qualified to act as triggers . The history of the subj ect after Plato is for a long time a history of deflation of the status of universals . We have already seen that in Aristotle for a universal to exist is for there to be instances and that it fits with this that in his syllogistic he is willing to rewrite 'Man is a rational animal' as 'All men are rational animals ' , with which we may compare B oethius below. But in Posterior Analytics [hereafter An. Post. ] 2 . 1 9 , he speaks of universals (here ta katholou) in a different sense, but again a deflationary one, to mean universal concepts . An example would be the universal concept of an ox. This further helped to encourage the variety of interpretations later given to universals. A summary of interpretations given to Platonic Forms and to universals (the two subjects can become muddled) is provided by Syrianus in Metaph. [ Commentary on Aristotle 's Metaphysics] 1 05 , 1 9-106, 1 3 .

Stoic Deflation

The S toics in the century after Aristotle, the third century Be, are more deflationary than Aristotle and deny that universals are beings . On the interpretation of Long and Sedley, 2 they thought that universals did not have the characteristics that Plato ascribed to Forms , but were mere concepts, in the sense of things conceived (ennoemata), and that concepts were neither beings (only particulars, for the S toics, have being, according to Syrianus in Metaph. 1 04,20-2 1 ) , nor yet somethings, but escaped Stoic classification into a metaphysical limbo, and could only be called 'not-somethings (outina)' .

Universals TransfOlwed: After Plato

1 07

An alternative argued by Victor Caston3 is that what is being discussed is Platonic Fonus , and that they are being dismissed as nothings (outina), not merely as unclassified, since outina are said by the Stoics not even to subsist as obj ects of thought: S extus Math. [adversus mathematicus] 1 . 1 7 . It is common ground that the Platonic Forms are dismissed as unreal (anuparktoi) in S tobaeus 1 . 1 3 6 , 2 1 - 1 37 , 6 (Wachsmuth). By contrast, universals i n general are not being so dismissed, 1llthough, according to Caston, they are "denied being in two successive ways. For the early S toics starting with Zeno, universals are mental concepts (ennoemata), since mental concepts can play the role of universals in so far as things fall under them (hupopiptein, Stobaeus, ed. Wachsmuth, 1 . 137, 1 ) . Concepts therefore replace Fonus in this role. But the third head of the S toic school, Chrysippus, on Caston's view, treats universals, genera and species not as mental concepts , but as s ayables (lekta), that is as predicates , which serve as the contents of thoughts . B oth earlier and later Stoic accounts of universals come out deflationary, for neither concepts nor sayables have being for the Stoics, although they are not nothings, but ' somethings ' , a classification intenuediate between beings and nothings . One reason for the difference of interpretation is that it is hard to tell what the Stoics described as 'nothings ' or 'not-somethings ' . One text says that it was 'common features ' (ta koina), Simplicius in Cat. [ Commentary on A ristotle 's Categories] 1 05 , 8- 1 6 . Three texts seem to say it was concepts (ennoemata),4 as in Long and Sedley 's report, although the reference to not-somethings is disputed in one text. There is another ambiguity, when one of these three texts , S tobaeus 1 . 1 36 , 2 1 1 37,6, goes o n t o say that the concepts postulated by Zeno are what the ancient (Platonist) philosophers once called 'Forms ' . Similarly, two other texts5 speak: as if it were Fonus themselves that the early Stoics treated as concepts (ennoemata), rather than replacing Forms by concepts. But Caston points out that the S tobaeus passage goes on to talk in tenus of replacement, when it attacks Fonus, saying that they are unreal (anuparktoi), and adds that according to the S toic s , what we participate in, to use the Platonist tenu, are concepts . Common features and Fonus are also replaced, when Simplicius in Cat. 222,30-3 3 says that the common (to koinon) feature of quality in bodies boils down for the Stoics to a concept (ennoema), and to a distinctively individual quality (idiotes), rather than a common (or universal) one. S implicius emphasizes that the resulting entity does not have causal power, or eternity, like the Fonus . Caston further p oints out that Chrysippus discusses genera and species under the heading of s ayables , to j udge from Diogenes Laertius classing them under things signified, Lives 7 ,43. And Caston finds a clue in the S yrianus passage, when it treats Chtysippus, the third Stoic head, differently from his predecessors . Chrysippus is said to take it that Plato 's Forms were introduced for use in conventions about names . The reference to names fits with Chrysippu s ' analysing away the name 'Man' in 'Man is a mortal, rational animal ' , so that it does not name a Fonu, or function as a name at all. Instead, Chrysippus is credited, judging from S extus Math. 1 1 . 8 and 1 1 , with an analysis of general tenus under which 'Man is a mortal, rational animal ' is analysed as 'If anything is a man , it is a mortal, rational animal ' . When ' man ' appears in this analysis, it introduces, on Caston 's interpretation, a predicate, or sayable, in 'if anything is a man ' , and does not function as a name.

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On either interpretation of the S toics, their treatment of universals is deflationary. Universals are not merely, as in Aristotle's Categories, secondary beings or substances. They are not beings at all. The S toics also gave a deflationary treatment of Man, when they analysed ' Man is a rational animal' as 'If anything is a man, it is a rational animal' . 6

Alexander's Deflation

If it is possible, the Aristotelian Alexander, around AD 200, is even more deflationary than the Stoics. But to see how he is so, we must first recognize several apparently different things he says about universals. S ometimes he treats universals as depending on thought, sometimes as forms or natures which have the merely contingent property that they are shared by at least two instances . In the latter, he goes beyond Aristotle, who required only that universals be shareable by more than one particular. They do not have in fact to be actually shared. It is not clear whether, as with Aristotle, Alexander' s criteria apply to two different kinds of universal, or whether, as I am inclined to think, he is combining his criteria to say that there are universals only when our minds recognize the contingent feature of presence in at least two instances. Alexander makes some statements which, at least at first sight, appear to turn universals into mere concepts . That would correspond to one of the w ays in which Aristotle uses the term 'universal ' (katholou) , for example An. Post. 2 . 1 9 , 1 00 a6b5, and to the conception of at least the early S toics. Thus, at de Anima 90,2-1 1 , Alexander says either (the more natural reading) that when universals are not thought of, they cease to exist, or, more modestly, that they then cease to be intellect. At Quaestio 2.28, 79, 1 6- 1 8 , he says that they are constructed (suntithenai) by a conceptual separation ( tei epinoitii khOrismos) . At Quaest. 2 . 2 8 , 7 8 , 1 8-20, he says the genus taken as a genus is a mere name, not a thing that underlies (pragma ti hupokeimenOl,), and it has the property of being common (koinon) only. in thought (noeisthai), not in reality (hupostasis). (Cf. Philoponus in de Anima 3 07 , 3 5 . ) Marwan Rashed has identified some Arabic paraphrases which corroborate the idea that the genus and the universal exist only in the mind.? Although it might seem s o far that the universal is a mere mental construct, it turns out that it is also treated as depending on at least two particulars sharing it. For Alexander thinks (and this is where he goes beyond Aristotle) that for animal, or any other form to be universal (katholou, Quaest. l . 1 1 , 23 ,25-3 1 ) , or a genus ( in Top. 3 5 5 , 1 8-24), is for it to be so shared by at least two particulars , and it is merely accidental to the form whether or not it is so shared. When in Quaest. 1 . l 1 , 23 , 2531 Alexander says that the universal is not a thing in itself (pragma ti kath ' hauto), his point is that the form which 'animal' signifies (i.e. animate being with sensation) is not in its own nature universal in the sense that it has to be shared. The same point is made at Quaest. 1 . 1 1 , 24, 1 1- 1 6 ; in Top. 3 5 5 , 1 8-24, that the form of animal could still exist, even if there were no animal as genus, in the sense that there was not more than one specimen. Alexander drew the conclusion that the definition of human being would be the same, even if there were only one human being, so that definitions are not of things that are common as common, but of

'

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things whose nature may happen to be shared, Quaest. 1 . 3 , 8 , 1 2- 1 7 . Alexander is said to have argued ap. Simplicium in Cat. 8 5 , 1 3- 1 7 , that the sun, the moon and the universe are individuals without a corresponding common nature. Simplicius disagreed. More faithful to Aristotle, he took it, in Cael. 275,5-8 ; in Cat. 8 5 , 1 3-17, that what is common need only have such a nature that it could apply to more than one individual. But in his view, in Cat. 82,30-35 , what is common does the j ob of completing (sumpleroun) an individual, so that the dependence is the other way round from what Alexander said. The requirement of being shared by at least two particulars not only goes beyond Aristotle,. but also has nothing to do with the mind, since the accidental fact of being so shared does not depend on our recognition, although at de Anima 85,20; Quaest. 1.3, 8 , 3-5 , there is an emphasis on s omeone's taking (lambanein) the form in separation from the matter, as if our thought were at least in s ome way relevant. I think it is likely that Alexander does not, like Aristotle, have two different notions of universal, one existing in things and the other as a concept in the mind, but that instead he intends his two criteria of thought-dependence and being shared by at least two particulars to be combined into one. In that case, he will believe that our mind can only construct universals as existing in particulars. We might compare how the equator or the boundary of a country is created by the mind, but applied to the surface of the earth. But he will add that a form will be a universal only if it is correctly understood as being shared by at least two particulars. This interpretation may be supported by his giving a parallel treatment to obj ects of mathematics at in Metaph. 52, 1 5-2 1 . Objects of mathematics are said to exist by thought (epinoiai), but in sensibles, which would make them mind-dependent entities, but ones existing in the world, like the equator. There is further support in Boethius, in Isag. [Commentary on Porphyry's Isagoge] . B oethius claims in 1 64,4 8 to be giving Alexander's view, and it is the combined view that he presents in 1 66 , 1 2-23 . There he says that a species is a thought (cogitatio) gathered from the individuals. But none the less he says in the very same breath- that the species is a hkenes-s and cannot exist exc:.opt in the individuals . . If he means to talk of likeness among humans, and not (as Tweedale suggests) likeness to a Platonic Form, this suggests that he thinks at least two similar individuals must be involved.9 I think it is clear that the form is neither intrinsically particular nor intrinsically universal. For when, for example, Quaest. 1 . 1 1 once again downgrades the universal at 2 1 , 22-3 1 as the mere accident of existing in many things differing in species, it says that this accident attaches to the real thing (pragma) . The real thing can hardly then be a particular form or nature, because that does not possess, even as an accident, the characteristic of existing in many things . The real thing seems therefore to be the form or nature, animal, viewed neither as universal nor as particular, because it remains the same regardless of the accident of being or not being shared by things in more than one species. None the less, I take it that Alexander's view so far is that the Form qua particular has more reality, because the form qua universal is dependent both on the mind and on the accident of being actually shared. The universal genus is not accorded more reality when Alexander says that the destruction of the genus implies the destruction of the species and particulars that fall under it ( Quaest. 1 . 1 1 , 23 , 1 1-1 3 ; 24, 1 6-22; in Top. 4 . 5 , 3 5 5 , 1 8ff. ; D4 Dietrich,

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Refutation of Xenocrates.!O For here Alexander is talking not so much about the genus as about its members. The point is that if all the members of the genus perish, no individual member can survive. Aristotle is equally according reality to the members of species, rather than to species themselves, as B ob Sharples p oints out, II when he says that Providence is more concerned to preserve universal species than individuals. For Providence preserves species only by preserving a sufficient number of individual members. There is only one passage, I believe, which takes a different view of the universal genus as having the greater share of reality. This passage has been stressed by Tweedale (see note 9) and it comes in the now familiar Quaest. l . 1 1 , which discusses Aristotle's remark, 'For the universal animal is either nothing or posterior' , de Anima 1 . 1 , 402 b7. The passage comes at 24,22, and it has been regarded as inauthentic by Paul Moraux, and A.C. Lloydl2 regards at least the end of the last passage as inauthentic. But it fits with Tweedale' s account of the rest of the Quaestio, and the same point is made in a text of Alexander surviving in Arabic and translated by Pines. ! 3 If Tweedale 's text is authentic, a disdavantage is that it becomes hard to see how the genus, or any common item whatever, can depend on the mind for its existence. The text says that the reason why the members would all perish, if the genus did, is that their being consists in possessing the common genus in themselves . I think it unlikely that Alexander himself said this. It is incompatible with the genus being a mental construct and accident, and it sounds close to the very thing that Simplicius accuses Alexander of ignoring, in Cat. 8 2 , 3 0-35 , that an individual cannot exist independently of what is c ommon, because the latter completes it (sumpleroun) . In general, later authors understood Alexander to be deflating universals.

Deflated Universals in Neoplatonism: Proclus and Simplicius

Universals have been. more and more deflated by- Aristotle, the S toics and Alexander. It might have been expected that the Neoplatonists would spring to their defence. But here we come to a big surprise. For several reasons, that is not what happened. Rather, while insisting on Platonic Forms, they treat universals differently. For one thing, Aristotle, we s aw, taking the Forms as universals , complained that they could not serve as causes . The tension between these two roles for Forms came to be settled in favour of their being cause s . Middle Platonism of the first century Be had already found one way to make them causes by putting Forms into the mind of Plato ' s Creator-Demiurge , 1 4 where they c ould exercise creative p ower in the formation of the physical world and of the soul that is said in the Timaeus to animate it. The Neoplatonists are able to take it for granted that the Forms are causes, without even stressing their now even closer relation with the mind of God. By the time of Simplicius in the sixth century AD , their causal role can be presented as mote obvious than their role as universals . Simplicius in Cat. 82,358 3 ,20 does recognize them as one of three kinds of common feature (koinon), alongside the common feature residing in species of the same genus and the concept in the mind gained by Aristotelian abstraction. But Simplicius no longer

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thinks that Platonic Form gives us as clear a case of commonness as does the concept in the mind, because the Form is transcendent and therefore common only as a cause, not as a common nature resident in things (83 , 1 0- 1 2) . Even the common nature may be so diff�rent as between mortal and immortal substance as not to provide a clear case of commonness (8 , 1 2-14), so that only the concept in the mind is fully common. Proclus in the fifth century had supplied a related reason why Forms are not just shared or common properties, in Parm. [ Commentary on Plato 's Parmenides] 8 80,31 1 . For it is not exactly the same property that is shared by the transcendent Form and the common natures distributed among particulars. The common natures p ossess the properties of the Form only derivatively, pros hen or aph ' henos, whereas the Forms bear these properties in a primary way. The discussions of Simplicius and Proclus deserve to be quoted. Simplicius in Cat. 82,35-83,20 Perhaps one should take 'common feature' (koinon) in three ways, [1] The first, the one that transcends the individuals, being the cause of the common nature (koinotes) in them in virtue of its single nature, as it is also the cause of the difference [between them] in virtue of its pre-encompassing many specie s . For example, in virtue of the single nature of animal the first animal, viz. the Animal-Itself, endows all animals qua animals with the common nature they share, and in virtue of its pre­ encompassing the different species it establishes the different species of animals. [2] [83 ,6] The second common feature is the one that the different species are endowed with by their common cause and which resides in them, like the one in each animal. [3] [83,8] The third is the common feature established in our thoughts by means of abstraction, which is later-generated and most of all admits of the notion of the non­ differentiated common feature. [ad 1] [83 , 1 0] For the common cause transcends its effects and is something different from them in all respects . It is common as a cause, but not as a common nature (koine

phusis) . [ad 2] [83 , 1 2] The common nature (koinotes) which completes the individuals has

. differenc e together with the c6mffi6n· featili·e: For there is nothing merely cbiJimdn in mortal and immortal substance, but the common feature is differentiated and the difference is shared in common. [ad 3 ] [ 83 , 1 4] Thus only the result of abstraction which we leave behind when we strip away the differences contains the notion of the common feature qua common. Perhaps Alexander has this in mind when he thinks that it is posterior to individuals . Nevertheless, he does not preserve consistency with his own account, when he s ays that the individuals are constituted out of the common feature and the differences, unless perhaps he considers their constitution, too, according to the manner of thought which yields the definition and exposes the common feature. (Based on the translation by Frans de Haas.) Proclus in Parm. 880,3-1 1 Cousin From this we should infer that the community between the one Form and its many instances should not be in name only [sc. with no common meaning] , lest we should have to seek next, because of the common name, for some single element common to the one and the many, as unity is the common element in plurality; but that the single Form must not be synonymous with those of the particulars coming under it, or we shall have to ask what is the common element present in both kinds of being that are covered by the same term. B ut rather, as has often been said, the common element in the many instances

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is that of being derived from (aph ' henos) and having reference to a single s ource (pros hen) . (Based on the translation by Glenn Morrow and John Dillon.)

Deflated Universals in Neoplatonism: Porphyry

Something else also distracts the Neoplatonists from attempting a reinflation of universals . The Neoplatonist Porphyry in the late third century AD wrote an introduction, Isagoge, to Aristotelian philosophy, whose purpose was to give elementary explanations to beginning students, before they embarked on reading Aristotle's logic . Certain subjects are therefore simplified, or, like universals , avoided. That is why Porphyry leaves it open in Isagoge 1 , 9-1 6 , whether universals exist in reality as too profound for his Introduction. He repeats at in Cat. 7 5 ,24-9 that the question of universals is too profound for a beginning student even to appreciate that talk of universals is talk not of reality (huparxis), but of how things are conceived (epinoia) . It is not universals as Forms that is said to be the thing which is too hard to understand and some, for example S ten Ebbesen, 15 have concluded that he thought of universals just as concepts, and Ammonius in Isag. 69,2- 1 1 , describes him as discussing only mentalistic universals. I think he may rather, like Alexander, be saying that there are universals only when our minds recognize the contingent feature of presence in at least two instances . Admittedly Porphyry, like Alexander, sometimes seems to attach a certain priority to genera (gene), since at Isag. 14, 1 0-12; 1 5 , 1 2-1 3 ; 1 5 , 1 6-20 ; 1 7 , 3-4, he makes species depend for their existence on genera (gene) . But this proves little. For one thing, we have seen that Alexander may have meant no more than that no species in the genus will survive, if all the species perish. For another thing, at in Cat. 90, 1 426 Porphyry introduces a puzzle which similarly makes Socrates depend for his existence on genera, but none the less identifies genera with what is predicated in common (to koinei kategorownenon) , which he treats as if it were merely something thought-dependent. Porphyry' s p�zzle is that what Aristotle calls 'primary substance' , for example S o crates, depends for its existence on the human and animal that are predicated in common, that is, so the puzzle says, on species and genus. So why is S ocrates primary? In reply Porphyry says at 90,32-9 1 ,7 (cf. Simplicius in Cat. 84,20-23 and 24-8) that, if we talce not just S ocrates but all the members of the species or genus, and consider those common features (koina) which are predicated in common (to koinei kategoroumenon) , ontological dependence is reversed, because we conceive (noein, epinoein) animal or horse only through particulars. The genus is here again closely connected with our thoughts. Similarly, at in Cat. 75,24-9, Porphyry mentions that to call something a universal (katholou) is to refer to how it is conceived (ep inoia) . But even this hint that universals may be thought-dependent he characterizes as too profound for beginners . If Porphyry is, for the purposes of beginners, merely following Alexander's treatment of universals, he will have given Alexander more influence on posterity than perhaps he would have intended. We have seen that Alexander thinks of a universal as something the mind constructs, and that he also or alternatively requires that two or more suitable particulars should share the form. Porphyry seems to echo

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this reference to universality as an accidental feature at in Cat. 8 1 , 1 6-20 . But perhaps Porphyry gives a view related to Alexander's because he already doubts the . strict universality of Platonic Forms .

Deflated Universals in Boethius

There is a further surprise because Porphyry 's concessions to Alexander's deflation of universals were transmitted to the Latin West by B oethius, writing in Latin in the early sixth century. B oethius ' second commentary on Porphyry ' s Isagoge takes up Porphyry 1 ,9-1 6, where Porphyry avoids comment, and offers to s ay a little more, but not too much. 16 He expounds the case against the reality of universals, and, like Porphyry and Alexander, refers to the role of thought. Species exist in singulars ; it is only as thought that they are universal or coIDmon. B oethius says he is following Alexander ( 1 64,4), not giving his own view ( 1 67 , 1 7-20) . B oethius i s especially close t o Alexander i n 1 66 , 1 6-23 . There B o ethius s ays that a species is a thought (cogitatio, 1 66, 1 8) gathered from the individuals. But in the same breath he says that the species is a likeness, meaning perhaps a likeness among humans rather than to a Platonic Form, and that the species cannot exist except in the individuals, thereby suggesting that the mind constructs the universal outside itself in the individuals, not unlike the way in which, I suggested, one might mentally construct a boundary line outside the mind on the earth' s surface . If the talk is about likeness among humans, this further suggests that B oethius accepts Alexander's view that at least two individuals must be involved. B oethius states a similar sounding view in Against Eutyches. Admittedly, in On the Trinity (see 2, line 5 1 in the revised Loeb edition) , B oethius may express a belief in Platonic Forms. But this will not represent a different view, if, like Proclus and Simplicius, he did not see Forms as strictly universaL . Writi ng in Latin, B oethius had a particular influence on the Latin Middle Ages . Consequently, it was Alexander's deflationary account of universals that had more influence than the theory of qualifiedly universal Forms on the subsequent understanding of universals in the West. In de Divisione 8 , 9- 1 6 ; 3 8 ,22-5 , ed. John Magee, B oethius deflates universal Man in a different way as being composed of individual men as its parts . 1 7

Deflated Universals in Plotinus

After I had finished writing this chapter, I was very interested to find Riccardo Chiaradonna 1 8 pointing out that Plotinus does not treat the intelligibles in the world of Forms as universals , except in so far as he wants to connect up with Aristotle's way of seeing things, when commenting on him, as at 1 . 8 [5 1 ] 6 (3 1 ) . Chiaradonna adds that Plotinus ' pupil, Porphyry, also omits to speak of intelligibles as universals . O n the other hand, Chiaradonna sees Simplicius a s speaking o f intelligibles as universals in Cat. at 82, 14-22 and suggests that this derives from Porphyry' s pupil

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Iamblichus. However, the passage just quoted in which I see Simplicius as denying that intelligibles are universals starts on the s ame page. Chiaradonna sees it as allowing that they are universals with important qualifications . B ut if I am right that it is better to see it as denying that they are universals in any but an extraneous sense, then Chiaradonna's finding about Plotinus and Porphyry comes even more into its own. For it will mean that it was Neoplatonists of every period, and not only the late Neoplatonists, who abandoned the idea of intelligibles, and hence of Forms, as universals.

Aristotle 's Universal C oncepts : The Shifting B alance of Empiricism and Rationalism

I shall now turn from universals to Aristotle' s universal concepts, although the distinction is not sharp after Aristotle, partly because of the view we have b een tracing that concepts are the only universals there are, and partly because Aristotle ' s universal concepts are often mentioned i n contrast with other types o f universal. Aristotle 's universal concepts feature in a threefold contrast with Platonic Forms and Aristotelian universals distributed among sensible particulars . 19 They are als o mentioned elsewhere,2o and are contrasted, for example, with Platonic c oncepts stored in the mind from birth or from a previous life. These two contrasts require us to recognize four kinds of universal, although 'universal' (katholou) is not necessarily the word used. The threefold contrast tends to speak of what is ' common ' (koinon) , while Platonic universal concepts are often called logoi, a term which is more literally rendered ' [rational] principles ' , since it is sometimes compared with [rational] principles in nature which are not concepts , and is sometimes contrasted with Aristotelian epinoiai, which are concepts . But I shall use whichever translation is clearer in the c ontext. Aristotle offers his account of how we form universal concepts in Posterior Analytics 2 . 1 9 , in opposition to the idea expounded by Plato, notably in Ehaedo . 72E-7 8 B , that certain universal concepts .are recollected from a previous life. Aristotle by contrast holds that rudimentary universal concepts can be acquired through sense-perception. B ut there is disagreement about what role Aristotle gives to sense-perception, and the ancient commentators take views quite different from mine. 2 1 Aristotle Posterior Analytics 2. 1 9 , 100 a3-b 1 2 Now memory (mnhne) results from perception (aisthesis), a s we say, and experience (empeiria) [results] from many memories of the same thing, since memories that are many in number constitute a single experience. From experience, or (e) from the whole universal (katholou) when it has become stable in the s oul - the one beside the many, whatever is one identical thing in them all - [results] a first principle (arkhe) of art (tekhne) and scientific understanding (episteme) ; of art if [the subject in question] is in the realm of coming to be, and of scientific understanding if it is in the realm of what is. S o the states are not [innate] in (enuparkhein) [animals] in a determinate form nor do they come from higher cognitive states (gnostikoteros), but from perception, as happens when a rout has occurred in a battle, and when one man has stopped, another stops and then another, until it reaches the original position (arkhe) . The soul is the kind of thing

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that can undergo this. [ 1 00 a 1 4] But let u s say again what was just s aid, but not said clearly. When one of the indiscriminables (adiaphoros) has stood still, the first universal is in the soul. (For to be sure one perceives the particular, but the perception is of the universal, for instance of man and not of Callias the man.) Again, a stand is made in these until the things that are without parts (amel'es) and universal stand still : for example, first such and such an animal, and then animal, and also similarly here . So it is clear that we must corne to know (gnol'izein) the primary things by induction (epagoge) ; for that is how perception plants the universal in us too. Since s ome of the cognitive states (hai peri ten dianoian hexeis) with which we apprehend the truth are always true while others, like opinion (doxa) and calculation (logismos), admit falsity - while scientific understanding (episteme) and intellect (noLls) are always true; and since no other kind is truer than scientific understanding except for intellect; and since first principles have higher cognitive status (gnorimoteros) than demonstrations ; and since all scientific understanding depends on a rational account (logos) there cannot be scientific understanding of first principles . And since nothing except intellect can be truer than scientific understanding, it follows that the state that knows first principles is intellect. -

In Aristotle 's expression at 1 00 a6-7 , 'from experience or from the whole universal' , I take Aristotle' s word ' or' to mean 'i.e.' , not ' or rather' , a conclusion whose implications Eustratius and 'Philoponus ' avoid in different ways 22 In that case, Aristotle is very reasonably identifying the fIrst rudimentary universal concept in the soul, in an empiricist way, with experience, that is, with many memories . In other words, the rudimentary concept of a lunar eclipse (his example in An. Post. 2.8) just is many memories of lunar eclipses, so no Platonic recollection of lunar eclipse from a previous life is needed. The ' or rather' alternative would leave a gap in the discussion. Aristotle has offered to tell us how concepts are formed, and he tells us how we reach the stage of experience, which is many memories. He would, on the ' or rather' interpretation, then leap to saying ' or rather we reach the fIrst universal' , while omitting to explain how we do so. Of course, Aristotle wants to go beyond the rudimentary universal, and tell us how we reach scientific concepts , and for this memories are not enough: he is not an empL.'1cist about that. The scientific concept of lunar eclipse recognizes,that it is due to the earth's shadow, and later in our chapter Aristotle implies that a scientific concept can only be acquired by nous, which I understand as meaning by spotting it intellectually. This too seems to me true to life. Admittedly, it does not tell us how we do the spotting, but then I think there is no answer to that question. It is sometimes asked whether Aristotle is discussing universal concepts in this chapter, or universal propositions, but I think that here the contrast is a false one?3 For to grasp the concept of lunar eclipse is to grasp the proposition that it is a certain kind of lunar loss of light. The commentators on Aristotle use a number of words for describing how these rudimentary universal concepts of Aristotle are empirically conglomerated

- sunageirein, s unage in, ep isunage in, athro izein, sunathroizein, su llegein, kephalaiousthai24 - from the perception of a number of particulars . In the threefold distinction documented in notes 20 and 2 1 above b etween Platonic Forms, Aristotelian universals in sensible particulars and Aristotelian universal concepts in the mind, some technical terminology is used by Ammonius and in part traced back to Porphyry. Forms are before (p ro) the many, Aristotelian universals in (en)

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the many and Aristotelian concepts after (epi, meta) the many. This terminology got translated into Latin and persisted into the Latin Middle Ages . Aristotle explains the contribution of perception to concept formation in a different way, when he restarts his account all over again at 1 00 a 1 4, translated above. The ancient commentators concentrate on this second account when explaining the way in which Aristotle is being empiricist. Here Aristotle seems to bring in universal concepts at an even earlier stage of human development, saying that perception is already of the universal, 1 00 a 1 7 , in the same breath as repeating his usual view that one perceives the particular. The commentators on the passage regard this as a dim or confused universal, not fully separated from the particular, and Themistius and Eustratius compare Aristotle 's account of how children at fIrst have a confused concept and call all men 'daddy' , Physics l . 1 , 1 84 a22-b I 4 . 'Philoponus ' explains that it is not only the individual's distinctive characteristics that leave a mark in our sense image (aisthema), but also, in a dim way, such universal characteristics as being a human and a mortal, rational animal, 437, 1 5-43 8 , 2 . Reason is, however, given a role soon after this by the ancient commentators . Perception transmits the information to the imagination, and onwards, Eustratius adds, to reason (logos) as a prerequisite of the process of conglomerating a separated universal concept, in An. Post. 266 , 1 4-29 . Hermeias in Phaedr. 1 7 1 , 8-25 , and PhiIoponus in Phys. 1 2 , 24-8 , make our reason responsible for the conglomerating . Aristotle himself implies that reasoning plays a role, when h e says at 1 00 b2-4 that in concept formation we pass by induction (epagoge) from a type of animal to animal in general. Reason was thought of by the Neoplatonists as a faculty for step-by-step reasoning, different from intellect (nous), which contemplates without moving step by step. What happens when Aristotle gives a role in concept formation to intellect (no us) at 1 00 b I 2- 1 5 ? Themistius says that an (unconfused) grasp of the universal is a function of intellect (nous), at in An. Post. 65 , 1 5-2 1 . I took Aristotle to be referring merely to an intellectual spotting. But some ancient commentators , using slightly different nomenc1ature from each other, built up a theory of three types of intellect on the basis of Aristotle 's de Anima, B ook 3, Chapter 5. This intellectualization of Aristotle 's process of concept formation is qualifIed only in so far as the lowest of the three types of intellect is identifIed with the imagination, in contrast to Aristotle' s view that imagination i s a function o f perception, not intellect. Thus Themistius , at in de Anima 9 8 , 3 5-99, 1 0, identifIes what he calls potential intellect with imagination as a storehouse of imprints that can be turned into concepts . And Philoponus at in de Anima 5 , 3 8-6,4, 1 1 ,7-1 1 , s ays that passive intellect, being the s ame as imagination, takes imprints from perceptible objects and possesses them within itself. The idea that Aristotle distinguishes three types of intellect is already found before any of these Neoplatonist commentators in de Anima by Alexander, head of Aristotle's school around AD 200, and in Alexander(?) Mantissa, much of which is likely to be by him. According to Alexander's de Anima, there are three intellects (cf. also Mantissa 1 07 , 2 1-34). We are born with a material intellect; the active intellect gives (de Anima 8 8 , 23-4; Mantissa 1 07,3 1-4; 1 1 1 , 29-32) the material intellect its proper disposition (hexis), so producing, third, the dispositional intellect and enabling us to form concepts which we store (apokeisthai, de Anima 86,5) in

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the dispositional intellect. But there are different accounts in Alexander de Anima and in Alexander(?) Mantissa Ch. 2 (= de Intellectu). According to de Anima 84, 1 9-2 1 ; 85 ,20-8 6 , 6 ; 87,24-5 , the material intellect can already separate concepts (noemata) from enmattered objects presented in sense-perception, although only the dispositional intellect, produced by active intellect, can deploy concepts in the absence of sense perception. In Mantissa 1 0 8 , 1 9-24, it is only active intellect that enables our material intellect to separate forms from matter, and it does so by constituting an example of matterless form to refer to (anaphora). Alexander(?) applies to active intellect the term from Aristotle, GA [de Generatione Animalium1 736 b28, 'intellect from outside' , which, unlike Philoponus, he takes to be a non­ human intellect. Themistius and the so-called 'Philoponus ' give a role in concept formation to active intellect, but regard it as human. For Themistius in de Anima 9 8 , 3 3 -9 9 , 1 0, active ( = productive) intellect turns into universal concepts the imprints derived from perception which are stored in potential intellect. 'Philoponus ' in de Anima 5 3 8 ,4-1 0 makes active intellect inscribe imprints like the painter of Plato 's Philebus. A further role in concept formation is given by some commentators to the imagination (phantasia) . Pseudo-Philoponus, we s aw, s ays that the sensory information is sent in the first instance to the imagination, and Themistius in de Anima 98,35-99, 1 0, that the potential intellect receives imprints from perception and imagination. And Pseudo-Philoponus, as just mentioned, likens actual intellect to Plato 's painter in the soul. Still earlier, as Jonathan B arnes has pointed out, Sextus Empiricus ascribes a role to imagination in the Aristotelian school's account of concept formation at Math. 7 .220-22. But Porphyry has a much more detailed account in his Commentary on Ptolemy 's Harmonics, giving a still bigger role to imagination. Porphyry's account starts off in 1 3 ,2 1-14, 1 4, echoing Aristotelian ideas to a considerable extent, but finishes up with Platonist ones. First, using sense­ perception, the s oul tears forms in an Aristotelian way off external matter and draws them into itself. Second, a faculty connected with opinion gives a name to the sensory datum and inscribes it in worcls on the writing tablet of the soul, in the manner of Plato 's PhilebLis. Third comes imagination (phantasia), which performs a new role of correcting the form received, working out an accurate version and storing it in the soul. This is already a concept (ennoia) . But the universality of the concept is due to the form received being stored in a non-material way. And it seems that imagination performs this function too , of separating the form from matter. When that has been done, one has scientific knowledge (episteme), but not yet nous. Nous arises like a light kindled by leaping fire and the scientific knowledge is made firm by epibole, a kind of mental concentration. Neither the spark nor the mental concentration is further explained, any more than Aristotle explains his intellectual spotting, which is also nOLlS, and which indeed cannot be further explained. Then after a digression, Porphyry reverts at 1 5 , 1-5 to a much more Platonist account of how the reason (logos) within us has a preconception of the form received from matter, and uses its previously possessed conception to supplement and correct the received form. This appears to be a second corrective process quite distinct from that carried out by imagination, and based on the possession by reason of concepts recollected from before birth in a Platonic manner.

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The role of imagination here might seem to be in competition with the enormous role given by other commentators to nOLis. But we have seen that some commentators reported by Proclus and also Philoponus eliminate competition by allowing a very un-Aristotelian overlap between nOLis and imagination, since they identify passive intellect with imagination. There is one more idea that needs explaining, the ambiguous idea of separating from matter. It means one thing with geometrical concepts, and something else in connection with concepts in general. Universal concepts in geometry, for Aristotle, have to undergo an extra process of separation or abstraction from matter, for we think of geometrical curves, for example, without thinking of the matter in which they reside. With natural concepts , by contrast, such as the snubness of a nose, we cannot think of snubness without thinking of the nose in which it resides, for example Physics 2.2. With all concepts, however, even with natural ones, another kind of separation has to take place. For although in thinking of a stone, we think of its matter, the matter of a stone is not actually received into the soul, but only its form, de Anima 3 . 8 , 43 1 b28-432a l . Alexander thinks that the second type of separation is performed by Aristotle 's active intellect, de Anima 87,24-5 , and if the passage is by him, Mantissa 1 08 , 1 9-24 . B oth curves and snubness alike are incapable o f existing separately from physical objects, e.g. de Anima 3 .7 , 43 1 b 1 5- 1 6 . And yet their fonus can be transferred to the mind. Objects of thought, or thinkable forms, reside within sensible forms, and we receive those sensible fonus during perception, and after perception is over, the objects of thought reside within images, de Anima 3 . 8 , 432 a4-1O. We think them, rather than thinldng of them, and we think them within images, de Anima 3 .7 , 43 1 b2, and the thinking part of the soul is the place of thinkable forms in which they are received, de Anima 3 .4, 429 a 1 5 ; a27 . We might compare once again how the equator is located on the surface of the earth, and yet in a sense is something in the mind.

Platonist Concepts: Rl:ld Aristotelian Concepts: How Combined

Platonist concepts are entirely different. They take their start from a selected group of concepts discused in Plato 's Phaedo 72E-77A. Plato argues that these concepts are recollected from before birth. His theory of recollection is here developed from its first mention in his Meno, and is to be developed again later in his Phaedrus. The theory is the opposite of Aristotle 's view that concepts are derived from perceptual experience. Later Platonists tend to refer to Platonic concepts as logoi, although that, as I have said, is a wide term that can refer to all sorts of rational principles and not only to concepts in the mind. There were at least three approaches among later Platonists to the sharp contrast between Aristotelian and Platonist concepts . Some considered that both types of concept co-existed in us. S ome, though listing Aristotelian concepts as one type of universal, argued that Aristotelian concepts could not do the work required of them and we needed only Platonic ones. Some argued that Aristotle himself had accepted Plato 's recollected concepts alongside his own empirically gained ones. The acceptance of both types of concept is found in the Middle Platonist handbook of the mid-second century AD, the Didaskalikos of Alcinous .25 In chapter 4, Alcinous

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reflects the Stoic idea that reason (logos) is a collection of concepts . But we have two types of reason, since concepts empirically gained in Aristotle ' s manner constitute opiniative reason (doxastikos logos), whereas Platonic recollected concepts constitute scientific reason (epistemonikos logos) . I have p ointed out above that Porphyry, in his Comm entary on Ptolemy 's Harmonics, combines the idea that concepts are gained empirically in Aristotle's manner through sense-perception with the idea of reason correcting these concepts , by using concepts recollected in Plato 's manner from before birth. The idea of opiniative reason recurs in the late Neoplatonist Priscian, Metaphrasis on Theophrastus 1 9 , 9- 1 3 . Amorig other late Neoplatonists, Hermeias seems to endorse both kinds of concept at in Phaedr. 1 7 1 , 8-25 (Couvreur) . Not all Neoplatonists who list Aristotle's concepts as a type of logos, or of universals, endorse them. Concentrating on geometrical concepts, Syrianus and his pupil Produs attack Aristotle' s empirically gained concepts as inadequate for the job, and some of their criticisms are repeated later by Simplicius and Olympiodorus.2 6 Sense-perception has never encountered all the figures and numbers . What it encounters is imprecise. It does not encounter lines witho.ut breadth or depth, nor radii that are equal, nor angles that are right, nor sides in fixed ratios. Perceptible quantities are counted as equal regardless of the addition of a grain to one of them. Everything it encounters is changeable and mixed with its opposite. What standard of truth could unaided sense-perception apply to mathematics ? How can we supply deficiencies in what we learn from sense-perception? How can we form concepts from an infinity of particulars, or reach inductive conclusions without examining all instances? How can we compare sensibles in respect of beauty without reference to a standard? All these problems can be met, if we have within us concepts of the Platonist sort. The idea that the Platonic concepts within us can be used in sense-perception to correct sensory information is found in Porphyry On Ptolemy 'S Harmonics, p . 14,32- 1 5 ,6, Diiring. And they would also be needed for correcting empirically gained concepts,jf we did acquire concepts in Aristotle '.s way, Syrianus in Metaph 95,29-3 8 ; Proclus in Eucl. 1 1 2,9-1 3 ,27 ; Olympiodorus on Phaedo, Lecture 1 2. 1 , lines 9-25. The criticisms were extended to the formation of concepts generally outside the realm of mathematics . The problem of inductive inference was a major one. Philoponus canvasses the idea that induction from a limited number of instances is possible only because we have the Platonic concepts in us, in de Anima 4,4-32, and Produs thinks that this is what makes possible the discovery of definitions, in Parm. 9 8 1 ,5-9 ; 244 1 . The point about induction is hinted also by Olympiodorus on Phaedo , Lecture 1 2 . 1 , who talks about the need for forms within, if one is to pass from one thing to another, and by Simplicius in Phys. 1 075 ,4-20, who speaks of the difficulty of assembling universals, given that particulars are infinitely many. Philoponus does, however, attempt a partial defence of Aristotle. At in de Anima 4,20-26, he offers the idea that natural kinds have essences, and whatever feature can be proved (dedeiktai) to belong to one specimen, is thereby shown to belong to all . But presumably this is only acceptable if the feature is shown to follow necessarily from the essence. S o far we have seen the Neoplatonists embrace Platonic concepts as well as, or instead of, Aristotelian ones . But a third permutation I have mentioned was to .

.

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ascribe belief in recollected Platonic concepts as well as empirically gained ones to Aristotle himself. This ascription is made by Iamblichus, according to ' Philoponus ' in de Anima 3 , 5 3 3 , 25-35 , and probably by Plutarch of Athens, j udging from the report of 'Philoponu s ' in de Anima 3 , 520, 1-12. It was also made by Philoponus in de Intellectu 3 8 ,99-40,43 , Verbeke (CLCAG), as is clear from his s aying that knowledge in the child's potential intellect has been suppressed by the process of birth. This is a distortion of Aristotle, but before we finish, we shall see Plato being distorted as well with a theory about the imagination and about the proj ection of concepts into the imagination.

Neoplatonist Concept-Projection and Universals in Imagination

As regards the obj ects of geometrical thought, we find very different theories in Plato, Aristotle and the Neoplatonists, who borrowed a Pythagorean theory of concept-proj ection. Plato himself did not speak of proj ection, not even in this context of the imagination. His Republic at 509D-5 1 1E gives the impression that the obj ects studied by geometry exist outside the mind, like the Platonic Forms, but a little below them. But Syrianus ascribes to Plato the theory that the obj ects of geometry reside in the imagination, in Metaph. 1 86 , 1 7- 1 9 ; 5 0,6-7 . S yrianus ' reinterpretation also makes Plato differ from Aristotle, whose theory we s aw above was that the objects of geometry cannot exist separately from physical obj ects , even though in a sense they enter the mind when they are thought. The theory of proj ection is more complex. Platonist geometrical concepts (logo i) in the intellect are indivisible, but they are spread out, when proj ected (proballein) from the mind into the imagination, where they are exhibited as geometrical figures. Proclus in EucZ. 1 treats the proj ection like projection in a modern cinema. He compares the screen of imagination with a mirror, 1 2 1 ,2-7 ; 1 4 1 ,2-1 9 , and he contrasts the indivisible concepts in the projector with the extended representations on the scre.en, 5 3 , 1 8-55 , 13 . The geometrical figures in the imagination are s aid by S yrianus, in Metaph. 9 1 ,29-34, to be parasitic (paruphistasthai) on the concepts in the mind. Geometers, in his view, would prefer to study the undivided concepts themselves, but through weakness are forced to study the concepts in their images . The p oint is further developed by ' Simplicius ' in de Anima 233 ,7- 1 9 and in Proclus in Eucl. 1 54, 1 455, 1 3 . The geometer, says Proclus, theorizes about the concepts in the mind, but makes his proofs about the circles in imagination. The proj ected geometrical figures are described as universals distributed (katatetagmena) in the imagination by Proclus in EucZ. 1 54,22-5 5 , 1 3 . Normally the imagination is thought of as entertaining particulars, but here we have universals in the imagination, Proc1us in EucZ. 1 5 1 , 1 3-20 ; 53 , 1 8-55 , 1 3 . The theory o f projection in geometry i s ascribed t o the Pythagoreans by ' Simplicius' in de Anima 233 , 1 2 and 277 , 1-6, so one might think it had been introduced by Iamblichus, who s ought in the third to fourth centuries to integrate Pythagorean philosophy with Platonic. But ideas about projection and the imagination are found already in Iamblichus' probable teacher, Porphyry, Sentences 1 5 , p. 7 , 1 -2 and 29, pp. 1 8 , 9 ; 1 9 , 8 , Lamberz. They bring us a long way away from Plato.

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Transformations i n Retrospect

We can see two opposite movements in the treatinent of universals and universal concepts� On universals, the Platonists seem to have bowed, partly through rethinking the Forms, and partly thTough the influence of their texts for beginners, to Alexander's Aristotelian deflation. On universal concepts, however, some of them at least required the Aristotelians to bow to Platonism. In the Aristotelian school itself, Alexander had given a role to three kinds of intellect in concept formation. The Neoplatonists either put Aristotle ' s universal concepts alongside Plato ' s recollected ones as somehow inferior, or rej ected Aristotle' s , or ascribed to Aristotle himself belief in Plato 's recollected ones .

Who was Right?

I have discussed universals and universal concepts , and have pointed out that these were interconnected, because some thinkers made universals into concepts . Who, in my view, was right?27 Plato, I believe, was wrong that universals are causes in the way he supposed. Admittedly, there is a sense in which universals are causes, since heating water is a cause of its boiling. But this is because particular heatings are causes of particular boilings . Even here, admittedly, the universal plays a role in causal explanation, since it is because those heatings are heatings , and not for example because they are noisy, that they are causes of boilings. The universal, then, has some role to play at least in causal explanation. But Plato wanted universals to be causes in their own right, not because of the interrelation of particulars and universals , and this is wrong. S o it is not surprising that his causally efficacious universals got deflated. But did the deflation go too far? I sympathize with Aristotle' s view in the Categories that for a universal to exist .is for it to be exemplified in. at least one .particular instance. B ut! also found.;reasQR. to support Plato, who has a rather radical version of the view that a universal need only be exemplifiable, not exemplified. I tried to show the sense in Plato ' s view by talking about there being a perfect answer to a mathematical examination, in contrast to a philosophical examination, or there being such a thing as justice, even if there were no instances of perfect answers or of justice. This was not to bring back Plato ' s idea that such justice might be a c ause. It might at best be an ideal. Nor was it more than a verbal concession, in that it sought to make sense of a form of words, but it did not offer the most perspicuous way of talking. It would have been clearer to say that justice is a coherent notion and a valuable ideal. In the clearest sense of the terms, then, I think Aristotle is right that universals owe their existence to at least one actually existing instance . More problematic is Aristotle's requirement that a universal be of a nature to b e predicated of more than one thing, and Alexander' s that i t be actually predicated o f more than one . Aristotle would prevent our counting a s universal being the o n e and only winner of a given competition. Alexander would rule out such examples as being a moon of the earth. As it happens , Aristotle himself prefers to treat ' sun' as a proper name in Metaphysics 7 . 1 5 . He there argues that the sun cannot have a

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Universals, Concepts and Qualities

definition, because a definition is a common (koinos) description, so that another thing could come into existence answering that description. But by ' the sun' we mean something unique, like S ocrates , and we should not allow for another sun ' s coming into existence, 1040 a3 0-b2. Two groups went further than Aristotle in the opposite direction from Plato. The first two heads of the Stoic school, · on Caston 's account, made universals into concepts (ennoemata), and their Aristotelian counterpart, Alexander, as I have interpreted him, made universals depend on thought. Alexander betrays the weakness in his view rather clearly, because, talking of a ' form' such as human, he concedes that it c an be shared by more than one particular, even if its being shared makes no difference to its definition. It is hard to see why, if the 'form' is shared (and most people, Aristotle included, would say ' if it is shareable ' ) , anything stops it from being a universal. Why should it also need to be thought? The flIst two Stoics try to avoid conceding that anything is shareable other than the concept, which is shared when two things 'fall under' the concept. Presumably, in order to fall under the same concept, the things do not have to be thought of as doing so. In that case, their falling under the s ame concept is not a consequence of our thoughts , but is a fact independent of our thought. What has happened is that these S toics have avoided admitting a universal property independent of the mind, at the cost of admitting a relation of 'falling under' which is independent of the mind. This relation, being independent of the mind, is not a concept, so the question arises whether it itself is a universal relation with instances 'falling under' it, in which case a non-conceptual universal will have been admitted after alL As so often, the Stoic Chrysippus, if Caston is right, is cleverer than his two predecessors . He identifies universals with sayables (lekta). A sayable is what is signified by an utterance and is not understood by a foreigner.28 A complete one is, roughly speaking, a proposition, which may correspond to an assertion, a question, an oath or a command.29 An incomplete one is a predicate.3o The sayable, like an intentional obj ect, does not have full being. It has an intermediate status, and merely subsists (huphistasth.ai) and is . a something (ti), rather tl:13n a being (o n) 3 1 Its lack of being is connected with its inability to act or be acted on.32 Universals thus have a status far from the being and causal power that Plato gives them. But as predicates , are universals mind-dependent, like the concepts of the first two Stoics ? I think not, because, as others have pointed out, the effects of causes are all s ayables, as, for example, being cut is the effect of the action of a knife on bread)3 Now, many effects have never been the obj ects of thought. Evidently, then, s ayables are things that can be s aid and thought, but do not have to have been. The definition of them as corresponding to rational appearance34 tells us that they can serve as obj ects of the rational mind, not that they have to . Thus the third Stoic head, Chrysippus , cleverly avoids the problems of those who turn universals into something mental. None the less , I think that his treatment of universals as having this special status is a needless elaboration. I believe that Aristotle, subj ect to the qualifications I have mentioned, did enough to deflate Plato 's causally efficacious universals. A further question about universal concepts is the one discussed by those who commented on Aristotle's unexpected statement in An. Post. 2. 1 9 , 1 00 a 1 7 , that although one perceives a particular, perception is of the universal. I think there is .

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something right about the commentators ' idea that, at least at first in a child's life, this could only be a confused universal, not yet separated out. Perceiving the universal red, for example, ought surely to involve perceiving something as red. The infant may not be able to separate out red in this way, until it has perceived red things a number of times . Perception is of rednes s at this early stage only in the very weak s ense that it provides data from which redness can later be recognized. The point about recognition arises also in the account of perception given by the Middle Platonist, Alcinous, in his handbook on Platonic philosophy, Didaskalikos, ch. 4. It sounds strange when he says that we perceive honey only with the help of concepts acquired from earlier perceptions of honey. But the point is, as David Sedley has argued, that one has perceptual recognition of honey, only on the basis of earlier non-recognitional perceptions. I do not obj ect to saying that at a later stage redness can be perceived, in the sense that things c an be perceived as red. B ut I think this is once again a verbal point. I do not see that new information is added by saying that we perceive redness . Even concerning the verbal point, there is, if I am right, an asymmetry. The infant can be s aid to perceive red particulars without perceiving their redness , but one cannot be s aid to perceive their redness without perceiving the particulars.

Notes

2 3 4

5 6 7 8 9

For translations of the texts referred to, see Richard S orabji, The Philosophy of the Commentators, 200-600 AD, A Sourcebook, London, Duckworth and Ithaca, NY, Cornell University Press, 2004, vol. 1, Psychology, 3 (g)(4)-( l 3), 3 (j)(3), 5( a) -( d) ; vol. 3, Logic and Metaphysics, 5 ( a) , (c), (d) , (e) , (f), (g) , 1 2 ( a ) , (b). Long and Sedley, The Hellenistic Philosophers, vol. 1, Cambridge, Cambridge University Press, 1 987, ch. 30. Victor Caston, ' S omething and nothing: the S toics on concepts and universals ' , Oxford

Studies in Ancient Philosophy, 17, 1 999, 1 45-2 1 3 . Besides S tobacus (mete tina), Diogenes Laertius, Lives 7,60 (oute ii ' un); Alexander in Top. [ Commentary on Aristotle 's Topics] 359, 1 2- 1 6 (neither type of ti) (SVF 2 . 3 29). Aetius 1 . 10.5 (SVF 1 .65); Syrianus in Metaph. 1 05 , 1 9-30. Sextus, Math. 1 1 . 8 , with reference to Chrysippus, 1 1 . 1 1 .

Marwan Rashed, 'Priorite de l ' EIDO S ou du GENOS entre Andronicos et Alexandre: vestiges arabes et grecs inedits ' , Arabic Sciences and Philosophy, 14, 2004, 9-6 3 . B oethius i n Isag. 1 64,4, CSEL 48, e d . Brandt s e c . 23 i n the translation o f Paul Vincent Spade, Five Texts on the Mediaeval Problem of Universals, Indianapolis, Hackett, 1 994. M.M. Tweeda1e, 'Alexander of Aphrodisias ' views on universals ' , Phronesis, 29, 1 984, =

279-303. 10 11 12

Trans. S . Pines , Transactions of the American Philosophical Society 51, 1 96 1 , repr. in his Collected Works, vol. 2, Jerusalem and Leiden, 1 986, pp. 9-1 0, Rashed T l . R.W. Sharples, 'Alexander of Aprodisias ' , Aufstieg und Niedergang der romischen Welt, 2.36.2, 1 987, sec. 8. A.C. Lloyd, Form and Universal in Aristotle, Liverpool, Liverpool University Press, 1 9 8 1 , p . 5 1 ; Paul Moraux, Alexandre d 'Aphrodise:exegete de la noitique d 'A ristote, Liege, Faculte de Philosophie et Lettres, Universite de Liege, and Paris, Les B elles Lettres, 1 942.

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1 24 13 14

15

16 17 18 19 20

21 22

Pines , Collected Works, vol. 2, pp. 9-1 0. Atticus frag. 9, [Baudry] , from Eusebius PE Mras GCS 8 , 1 5 . 1 3 ,4-5 ( 8 1 5C-D Viger) ; Alcinous Didaskalikos ch. 9, 1 63 , 1 1-3 8 ; S eneca, Letter 65.7 . The idea continues in the Neoplatonists, Syrianus in Metaph. 1 06,26-107, 1 ; Hermeias in Phaedr. [ Commentary on Plato 's Phaedo] 1 7 1 , 8-25 ; Ammonius in Isag. 42, 1 6-1 7 ; Asclepius fr o m the voice of Ammonius in Metaph. 69, 1 7-2 l . S ten Ebbesen, 'Porphyry 's legacy t o logic ' , i n Aristotle Transformed, edited by R. ' S orabji, taken from Ebbesen's Commentators and Commentaries on Aristotle 's Sop histici Elenchi, vol. 1 , pp. 1 3 8-5 8 . Corpus Latinum Commentariorwn in A ristotelem Graecorum, Leiden, Brill (hereafter CLCAG) . Boethius ' comments are at Book 1 , chapter 1 1 , 1 6 1 ,8-1 1 ; 1 66, 1 4-1 67,20, in CSEL vol. 48, ed. Brandt. Richard Cross, ' Gregory of Nyss a on universals ' , Vigiliae Christianae, 56, 2002, 3 724 1 0, referring to Magee' s interpretation. 'Plotino e l a teoria degli universali ' , in Celluprica, D ' Ancona, eds, with Chiaradonna, A ristotele e i suoi esegeti neoplatonici, Naples, Bibliopolis, 2004, 3-35 . Proclus i n Eucl. 1 , 50, 1 6-5 1 ,9; Arnmonius i n Isag. 4 1 , 1 7-20; 42, 1 0-2 1 (citing Porphyry) ; 1 04,27-3 1 ; Philoponus(?) in An. Post. 2, 435,28-30; Simplicius in Cat. 82,35-83,20 (translated above) ; 69, 1 9-7 1 ,2. Aristotle's universal concepts are referred to n o t only i n the Neoplatonist threefold distinction of universals, cited above, but also by Hermeias in Phaedr. 1 7 1 , 8-25 (Couvreur), and Philoponus in Phys. 1 2,24-8, in the commentaries on Aristotle Posterior Analytics 2 . 1 9 by Themistius, ' Philoponus ' and Eustratius, and they are reflected in the commentaries on Aristotle On the Soul by Themistius at in de Anima 9 8 , 3 5-99, 1 0 and 'Philoponu s ' at in de Anima 3, 520, 1-12. My view is sketched in my Animal Minds and Human Morals, London, Duckworth and Ithaca, NY, Cornell University Press, 1993, pp. 30-3 5 . The following translation of Aristotle is by Richard McKirahan. Eustratius in An. Post. 264, 1 2 , interprets it as ' or rather' . 'Philoponu s ' in An. Post. 436,2, drops reference to the universal and interprets ' experience and the sense-image

(aisthema) 23 24

,

.

There is a real contrast when Themistius in An. Post. 6 3 , 1 5 , takes Aristotle to be discussing all scientific generalizations . I take him to be discussing only definitional ones. Themistius in An. Post. 64,24-65,2; Hermeias in Phaedr. 1 7 1 , 8-25 , Couvreur; Philoponus in Phys. [Commentary on Aristotle 's Physics] 1 2,24-8 ; 'Philoponus ' in An. Post. 436,2- 1 2 ; Simplicius in Phys. 1 075,4-20; Eustratius in An. Post. 266, 1 4-1 9 . I owe to Christoph Helmig the references to kephalaiousthai, which is in Themistius in

An. Post. 64, 1 6 . 25

Charles Brittain has compared other Middle Platonist texts for acceptance of b oth types of concept, the Anonymous Commentary on Plato 's Theaetetus, cols 23 and 468, and Plutarch Platonic Questions 1 .4, 1 000 D-E, and for opiniative reason Plutarch

26

Syrianus in Metaph. 1 2 .28-1 3 , 3 ; 95, 1 3- 1 7 ; and 29-3 6 ; Proclus in Eucl. 1 1 2,9-1 3,27; Simplicius in Phys. 1 075 ,4-20; Olympiodorus in Phaed. Lecture 1 2 , sec. 1 , lines 9-25 (Westerink) . The fullest references are in Proclus in Parm. , and these have been assembled by Christoph Helmig, 'Proclus ' interpretation of Aristotle 's theory of concept formation in An. Post. 11. 1 9 ' , forthcoming. Several of Proclu s ' arguments here are anticipated by Syrianus or repeated by his successors, e.g. the argument from induction at in Parm. 9 8 1 ,5-9 ; 24-4 1 . B ut Helmig cites the following additional argument from in Parm. 896,22-3 3 ; 986,37-9 8 7 , 8 : universal concepts are not postulated for all

On the Generation of the Soul in the Timaeus 1 024.

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27

28 29 30 31 32 33 34

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perceptibles, not for parts , artefacts, or evil things, and that is because we have within us only the concepts of good and natural entities . I am very grateful to Arindam Chakrabarti for asking me to explain my views on this, and for discussing it with me. He himself has argued for the perceptibility of universals in his 'Non-particular individuals ' , with a reply by Strawson, in PK. Sen and Rooprakha Verma (eds ) , The Philosophy of PF Strawson, New Delhi: Indian Council of Philosophical Research, Allied Publishers, 1 994. S extus, Against the Professo rs 8 . 1 1-12. Diogenes Laertius, Lives 7 .66-7 . Diogenes Laertius, Lives 7 . 6 3 . Diogenes Laertius, Lives 7 . 6 3 ; S extus, Against the Professors 8 .70; 10.2 1 8 ; Plutarch, Against Colotes 1 1 1 6 B-C ; On Common Notions 1 074 D . Plutarch, O n Common Notions 1 073 E; Proclus, O n the TimaeLls 3 .95, 1 0-14. S extus, Against the Professors 9 . 2 1 1 . Diogenes Laertius, Lives 7 . 6 3 ; S extus, Against the Professors 8 .70.

Chapter 8

Conceptualism Chris Swoyer

S omewhere in the twentieth century philosophy took the linguistic turn and conceptualism fell off the map . Not that it was flourishing before. Indeed, it has been dormant so long it's surprising it continues to receive even the perfunctory nod it often gets as one of the three maj or accounts of universals . There are various reasons , some good, why conceptualism withered. B ut with the demise of behaviourism, philosophy' s linguistic turn growing a bit long in the tooth, and the ris e of cognitive science, conceptualism deserves a new hearing. My aim here is to begin building a case that concepts can solve some of the problems of universals, both traditional and recent, and that when they are supplemented by in re properties (ones that exist in the spatio-temporal c ausal order) they can solve even more. C oncepts and in re properties may seem a peculiar twosome, but it bears exploring because it would allow us to avoid abstract entities - creatures that lie outside the spatio-temporal causal order - and the severe epistemological problems they generate. My goal is not to present a definitive version of conceptualism, but to open a space where it can be discussed and evaluated. In Section 1 I explain why conceptualism should be of interest now. In Section 2 I note some central features of concepts and in Section 3 I sketch the maj or empirical theories designed to explain them. In Section 4 I examine ways in which . conceptualism could help solve some of the problems of universals . 1

1.

Reopening t h e Case for Conceptualism

Conceptualism, along with nominalism and realism, is one of three traditional families of views about universals. There are many species of each family, but the basic story line goes like this. Realists hold that there are universal properties and that these solve the problems of universals . Conceptualists deny this, arguing that concepts can do most of the work realists invoke properties to do. And nominalists, at least traditional ones, spurn both universals and concepts , arguing that words alone can do all the legitimate aspects of this work. We will return to these three views, but it will be useful to begin by noting the reasons for the demise of conceptualism, and the reasons for reopening the enquiry on it now. Much twentieth-century philosophy took what has been called the linguistic turn, which brought with it a tendency to replace questions about properties and concepts with questions about linguistic expressions and their use. During this period universals were off limits because claims about them lay beyond the reach

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of verification, because they seemed only to exist due to systematically misleading linguistic expressions, or because they were the subj ect matter of the imaginary discipline of metaphysics. People did talk about concepts during this period, even referring to their own work as conceptual analysis , but the concepts involved were not much like the mental entities of traditional conceptualists . Indeed, during this period the posses sion of a concept was often assimilated to the mastery of a word. Concepts (and related mental entities) were also shunned because the Zeitgeist included a general sympathy, sometimes even an enthusiasm, for a behaviourism that had little patience for mentalistic notions. B ut times have changed. No one now could seriously maintain that most philosophical problems are at root problems about language, and metaphysics has been respectable for several decades. Moreover, behaviourism is dead, and concepts are now one of the half-dozen most central concerns in the flourishing field of cognitive science. S o the time is auspicious for reconsidering conceptualism. In the mid- 1 950s the work of several psychologists, linguists and computer scientists came together to launch the new discipline of cognitive science. The field contains quite varied approaches to the study of cognition, but the unifying idea is that human cognition - perception, concept-formation, decision-making, and the like - is a species of info rmation processing. If information is to make anything happen in the real world, it must be embodied in something physical, and the dominant view is that it is embodied in mental representations that are realized, somehow, in the brain. Concepts are quintessential mental representations that figure in all the higher mental processes . Even embodied information is useless unless we can do something with it, so we also need mental ­ computational - operations that process the information encoded in mental representations . Cognitive operations include mechanisms for drawing inferences, retrieving items from memory, and calculating the patterns of movement of our bodies needed to perform the actions we decide to perform. The key here .is that mental operations ·are both causal mechanisms that make · things happen and that the way that they work is sensitive to the content of information encoded in the representations they process . For a simple example, suppose that Ann believes that Max is a dog and that all dogs are animals. This may well cause her to infer that Max is an animal. Nothing guarantees this. Like most dispositions, the activation of information-processing dispositions can be thwarted . in a variety of ways. Ann may fail to notice the entailment, or the original beliefs may not matter enough to explore their consequences. But if she does conclude that Max is an animal, it illustrates how causal relations among mental representations can march along in step with their meaning or content.

_

1.1

Why Concepts ?

There are several reasons why concepts might be useful in dealing with the phenomena that make up the problem of universals.

Generality One hallmark of universals is that many of them apply to more than one thing. The concept dog applies to many different animals, the concept love

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1 29

applies to many pairs of people (who love one another), and so on. Generality is central to perception, thought, communication and action. Among other things , it allows us to bring the known to bear on the unknown. I had to get a shot in the past when I had a strep infection, and so since I have a strep infection now, I'd better get a shot now. The generality of concepts lets us apply lessons we have learned about certain kinds of things to newly encountered things of the same kind .

Thought without language A good deal of thought is independent o f language. This means that nominalists will have a much harder time explaini.ng cognitive phenomena than those conceptualists who countenance, as conceptualists should, concepts that are not expressed by words or phrases. Developmental psychologists have devised ingenious techniques for studying the cognitive lives of human infants, and there is growing evidence that human neonates engage in conceptual thinking soon after entering the world. Indeed, it is difficult to see how they could learn language, or many of the other things that they learn, if they didn't. For example, they employ some concepts, for instance , the object concept, before they have any words like ' object' and before they have any words for any particular objects like mama . (e.g. Carey and Xu, 200 1 ; Morgan and Demuth, 1 996). We sometimes have a thought and then search for the right words to express it. We can also reason with mental images in ways that are difficult to put into words. And we often categorize other people, virtually automatically (often with stereotypes) right off the bat (e.g. B argh and Ferguson, 2000; Kihlstrom, 1 996). There is also little room for doubt that some non-human animals, for example, chimpanzees and dolphins , are capable of reasonably s ophisticated thought. Indeed, animal cognition is now a thriving field within cognitive science (e.g. Allen and B ekoff, 1 997) . Meaning without abstract entities Words, phrases and sentences of natural languages have meanings or, in the j argon, semantic values. There are variOlls accounts· of what these are, but at least for fragments of English that include intensional constmctions like 'believes that' , they are often taken to be properties (or some set-theoretic surrogate for them) . Many words and phrases do not apply to anything in the real world (e.g. 'balding, superannuated witch' ) and some could not (e.g. 'round square' ) . If the semantic values o f these phrases are properties, then they must be uninstantiated properties, and where could they be? The standard answer is that they are ante rem properties, abstract properties that lie outside the spatio-temporal causal order. Such properties pose acute epistemological problems, because it is a mystery how we ever come to know anything about them or get our words to latch onto them (Swoyer, forthcoming, contains an overview; the classic source is B enacerraf, 1 973). In re properties, by contrast, exist in the spatio-temporal causal order, where their instances are, and they often dispose their instances to affect our sensory apparatus or our instmments for detecting and measuring. Such properties thus avoid the epistemic problems that plague ante rem properties , but unlike ante rem properties , they are too sparse, even if we throw in properties definable in terms of them, to supply enough semantic values for all the meaningful expressions of a natural language.

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If concepts don' t themselves require the existence of abstract entities, they might provide a useful middle ground between the two sorts of properties . A person could possess concepts (e.g. round square) that have no instances, and the hope would be that these could provide semantic values for their associated linguistic expressions . A hope is not an argument, of course, and much work would be needed to make good on this , but it does strengthen the motivation for re-examining conceptualism.

Intrinsic interest Finally, conceptualism is a venerable view that has fallen by the wayside, and it should be of interest to see how it fares in a contemporary setting. We may find that it is more promising than we thought, but we may also find that the great advances in the study of concepts and cognition leave it just as implausible as many philosophers have supposed. It is worth knowing, either way. If words alone (and hence nominalism) are not enough to s olve many of the problems of universals , and if ante rem universals are too much (because of their epistemological baggage), what's left? There are two obvious possibilities in between: in re properties and concepts . As we will see, these complement one another, with each being strongest where the other is weakest. So we have two main questions . First, to what extent can concepts solve the problems of universals ? Second, to what extent can concepts plus in re properties solve these problems ? A pure conceptualism would be of more interest and deserves a run for its money. But the second view is more likely to succeed, and the problems facing it are still formidable enough that it would be of considerable interest if it did. 1.2

Conceptualism

The guiding metaphor for realism is discovery. Properties structure the world, carving nature at its j oints , and it is up to us to detect where those joints are. By contrast, a guiding metaphor for conceptualism (as for nominalism) is that we impose order or boundaries on things in the world from ' outside ' ; for the conceptualist, through the application of·our concepts, S ome thinkers of a conceptualist bent argue that it is a matter of choice or convention which basic concepts we employ. Thus Carnap ( 1 950, §2) urges that we can choose to use a 'thing language ' , in which physical obj ects are central, or a 'phenomenalistic language' , in which sense data are. Conceptualism and conceptual relativism overlap here in an interesting way. Others argue that although alternative concepts are possible in some abstract sense, they are not live options for us. The nature-nurture pendulum has swung back to the nature pole (though there are stirrings of an empiricist, nurture-friendly backlash) , and it now seems quite possible that we are biologically wired to use some concepts (the obj ect concept, causation, person) rather than others. Still other thinkers urge that we can modify our framework of concepts, but only gradually, bit by bit (like sailors on a ship at sea) . Conceptualism goes back to the Middle Ages. Porphyry, a third-century student of Plotinus, wrote an introduction (Isag6ge) to Aristotle 's Categories . B oethius later translated it into Latin, and it set the agenda for debates about universals until reasonably late in the Middle Ages. In a highly influential passage Porphyry tells us that he will 'beg off saying anything about whether [Aristotle's] genera and species are real or are situated in bare thoughts alone ' (Porphyry, 1 994, p . 1 ) . Porphyry

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speaks of genus and species (and, some lines later, of Aristotle's other three predicables : differences, properties and accidents), but these are clearly viewed as universals. Conceptualism is the view that the features of generality and universality ' are situated in bare thoughts alone ' . When it comes to properties, esse is concipi. I won't try to follow conceptualism's historical twists and turns , but will mention two enduring conceptualist themes, both evident in Locke and some later empiricists . The first theme is that complex general concepts (Locke calls them ideas) are the 'workmanship of the mind' , 'creations of ours ' , and that 'we draw the boundaries ' o f things i n thought. There i s the clear metaphor o f imposing order o n experience from the outside. Second, although we have some latitude in our construction of complex concepts , they are sensitive to ' similitudes ' among things, guided and constrained by resemblances in various respects, for example, resemblance in colour or shape. Conceptualist themes, or near relatives, sometimes turn up in views that go by other names. On a mid-twentieth-century inventory of the chief options in the philosophy of mathematics we find realism (either as logicism or a set-theoretic reduction of numbers), nominalism (Hilbert' s formalism), and conceptualism (Brouwer's intuitionism) . Similarly in syntactic theory we find realists (e.g. Katz's view that languages are abstract entities) , nominalism (e.g. Quine) , and conceptualism (Chomsky 's mentalism) . And in logic we can view Frege and the turn-of-the­ century Russell as realists about logic (it mirrors a timeless realm of reality), Goodman and Quine ( 1 947) as nominalists , and B oole as a conceptualist (it's not for nothing that B oole entitled his great work On the Laws of Thought; there are definite psychologistic and conceptualistic strains in it). 1.3

Conceptualist metaphysics

There are a few pure conceptualists (and nominalists), but not many. Almost every conceptualist acknowledges the role of some structure in the world as it is independently of how we talk and thiDk about it Without something outside the mind to provide clues and cues and gentle nudges , there is nothing to support language acquisition, classification, or intersubj ectivity of any kind. For example, there needs to be something in the perceptual input that allows a child to discriminate sounds into phonemes of her ambient language. But even with this dollop of realism, conceptualism can still be of interest as long as this mind-independent reality greatly underdetermines the concepts we deploy. The question is how little realism we can get by with. There are two primary models for this. .

Selection models Classificatory mechanisms of some sort are needed to divide the world up into individuals . Our sorta! mechanisms (to use Strawson's 1 959 term) mark out the sorts of things that (we think) are out there waiting to be sorted; they are essential to the individuation and demarcation of things . Whether we have the same thing or something new, one thing or more, depends on which sort of thing we have in mind: this is the same song, but a different verse; same type, different token. On the selection approach there are j oints everywhere: there is too much structure out in the world for us to discern or describe or worry about all of it. Our attention,

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working memory and computational capacities (like thos e of any finite creature) simply aren' t up to it. We do seem to find j oints out in the world, but they are simply a result of the way that we use our concepts to carve things up. On this approach the conceptualist might hold that the world 'in-itself' contains general properties analogous to mass properties (water, mud) , along with many, many different resemblances among the properties. We focus on some of thes e similarities and u s e our sortal concepts t o divide all this u p into particulars. Alternatively one might hold that there are too many sorts of things in the outside world for us to notice all of them, that any collection of things corresponds to some sortal or kind concept, and so that the mind privileges some possible concepts over others. Predispositions to carve in some ways rather than others may be innate, but that ' s j u s t a fact about our evolutionary history. And some ways of carving are simpler and more natural than others, but simplicity and naturalnes s are our values, not nature' s .

Kantian models On Kantian models w e can ' t s ay much about the world a s i t i s apart from our concepts and thought. All our experience and thought requires us t o u s e our concepts, and w e cannot step outside them to some neutral platform from which we can compare some pure, unmediated reality with our concepts to see how well they match up. There is a world-in-itself (we aren't idealists), but it is impossible to separate its contributions to experience from our own. This line of thought must be handled with care, lest it lead to a rather appalling relativism or idealism. It is all to easy for a conceptualist to avoid abstract entities (like ante rem properties) in one place, only to have them bulge up somewhere else. For example, it is easy to find oneself working with types of concepts , rather than with their tokens (or with particular conceptual episodes). But types certainly seem to be abstract. When a philosopher purges commitments to abstracta from her object language, it is als o easy t o hav e oth�r abstracta creep i n through the back, metahnguistic doocFor example, the conceptualist, like most philosophers, needs notions like logical consequence. B ut the most common metatheoretic pictures we have for these, courtesy of model theory, are up to their necks in sets.

2.

What Concepts Do : Features and Roles of Concepts

In this section I will note several, mostly uncontroversial, features of concepts , explore s ome of their roles in cognition, then examine several additional features they have. To a large extent concepts are as concepts do, and the phenomena I ' ll discuss constitute targets for any theory of concepts to explain. Psychologists often posit the existence of various concept-like mental representations, including schemas, scripts, frames, and larger units like semantic networks and B ayesian networks. Most of my discussion will apply to all of these, but I will focus on concepts here.

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Concepts Are (Partly) Mental

Concepts are mental entities S ome philosophers have used the term (or its equivalent, e.g., Frege 's Begriffe) to stand for abstract entities . The issue here is mostly a matter of terminology, and nowadays the more common usage, especially among empirical researchers , is that concepts are mental or psychological entities . It is important to think of them this way here if we are to engage the philosophical tradition of conceptualism, and I will treat concepts as mental representations . (Many) concepts have instances Many concepts are invaluable because they are general; for example, the concepts dog, red and tolerably honest can apply to more than one thing at a time. Psychologists often call the group of things that fall under a concept a category ; philosophers often call it the concept's extension, and I will follow suit. Concepts play many roles in cognition Concepts are constituents of beliefs, desires, intentions and many other thoughts . My thought that red is a colour involves my concepts of red and colour. And we see that concepts play vital roles in all our higher mental processes . Vagueness As concepts like red and tolerably honest and loves show, many concepts are vague or open-textured. If a . concept is vague, there can be things that are clearly in its extension, things that clearly are not in its extension, and borderline cases. Concepts may also lack extensions, either as a matter of fact (professional basketball players under five feet tall) , or of necessity (round square). 2.2

Concepts A ren 't (Purely) Mental

Many of our concepts link up with reality. If they didn' t, we would just live inside om ne;lJs This anchming role of concepts is important in grounding truth values. of our beliefs (and through this some of their other semantic properties) . The belief that some dogs are brown is true because of the way some dogs are, out there in the world beyond my concepts . As we ' ll see, mind-world linkages also ground intersubjectivity, and· they play an important role in concept combination. ..

Symbol grounding: features and bottoming out Many accounts of concepts help themselves , rather casually, to the notion of a feature and, indeed, to the even more loaded notion of a psychologically relevant feature. For example, theorists who believe that concepts have definitions believe that they must (ultimately) be defined in terms of concepts, call them features, that are not themselves defined. Other theorists see concepts as involving similarity to a profrle of features . Features fi t nicely with a conceptual foundationalism that bottoms out with basic, primitive, simple, unanalysable concepts, namely features . One of the j obs for features is to latch on to bits of reality in a way that solves what Harnad ( 1 990) calls the symbol-grounding problem. Unfortunately what counts as a basic feature varies from account to account, and from context to context. The notion of features involves a large promissory note that must eventually be redeemed.

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Are there basic features ? Numerous philosophers have argued that there are no simple properties in the world or atomic concepts in thought. There are several points here. First, perception is sufficiently theory-laden (p. 1 3 8) that we can ' t expect t o find instances o f neutral feature concepts there. Moreover, what i s taken as simple, or as relevant, depends greatly on context (see Wisniewski and Medin, 1 994 for a discussion from a psychologist's perspective) . This means that we can ' t devise simple accounts of how complex concepts latch on to the world in virtue of their having features that latch on (not that the latter was ever very clear) . But there is another important account of how concepts are hooked to the world. 2.3

Direct Reference v s Descriptive Content

S everal central themes in current debates about the nature of concepts are variations on themes that occurred in debates beginning around 1 970 over how much (if any) descriptive content or meaning linguistic expressions have. Does the name 'Roscelin' have a meaning over and above the individual that it denotes, for example, 'the medieval nominalist who fIrst said that universals are just words ' ? Many philosophers thought it did, until Kripke c ame along to argue that from a semantic point of view names are mere labels or tags without descriptive content. To move closer to our topic of concepts, Kripke (e.g. 1 972, pp . 1 34ff. ; cf. 95, l l 8) and others argued that similar points hold for many general terms, including natural kinds of words ( ' dog' , 'elm tree ' ) , mass terms ( ,water') and adjectives ( 'red' , 'square ' ) . And these points and arguments are easily transferred to concepts . Let's recall two of the arguments Kripke and others employed. First, you don ' t need t o know a lot t o b e able t o use a name. B efore I looked i t up, all I knew about Roscelin was that he was a medieval philosopher, but I could none the less talk about him and check to see whether he was a nominalist. Similarly, as in Putnam' s example, I know that elms and beeches are trees , but I have no idea h o w they differ. And the only thing I knew about artlu::itis before I read Tyler Burge was that it could· cause aching pain. S econd, we can use a linguistic expression to stand for s omething even if much, s ometimes virtually all, of our beliefs about it are false. It is possible that s ome medieval scribe made a mistake and that Roscelin was in fact a late Hellenistic physician who never heard of universals . And these points are just as true of the concepts red, e lm and arthritis as they are of the words that expres s them. Although direct reference accounts of denotation are now dominant among theories of reference, they do face problems . For example, they cannot easily explain the failures of substitutivity of co-referential expressions in intensional contexts. Moreover, new possibilities open up once we allow concepts to have ' descriptive content' that doesn' t add up to a definition of necessary and sufficient conditions for its application. And we will see, several accounts of concepts do just this. Still, an account of concepts will have to account for the phenomena Kripke noted, even if it departs from his explanation of them.

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Naturalness

As we s.aw in Section 1 . 3 , properties or concepts or words are needed to mark out individual things. Onc� this has been done, the 'resulting' individuals can still be sorted in a great many ways, but only a tiny fraction of these seem at all natural to human beings (cf. Osherson and Smith, 1 982). S ome aspects of naturalness lie in the eye of the beholder; dolphins and whales probably have concepts rather different from ours because of their rather different environment, interests and needs . But even allowing for such things, many concepts, for example, being green when in France and having a mass of 3 . 2 8kg when in Northern Germany, strike most people as perverse (philosophers get paid for this ?). With time and ingenuity it is possible to devise far more outre concepts, and there are surely many possible concepts we could never formulate or understand because they are far too complicated for us (and for our computers) . There are probably various sources o f naturalness. Among others things , human beings enter the world with strong dispositions to learn some sorts of languages (these include all natural languages ) but not languages of many other sorts (some of which we can specify). And more generally, we enter the world with strong dispositions to use some concepts (e.g. physical object) rather than others (e.g. mereological sum of temporal stages). 2.5

Conceptual A lignment

Many of our concepts are relatively stable across differences in beliefs . When I got a Labrador Retriever I was quickly disabused of many of my oId beliefs about dogs and acquired many new ones . But we think of this as a change in my beliefs about one and the same thing, dogs, rather than the replacement of one concept by another (both expressed by the word ' dog ' ) . Such stability is necessary if we are to change our minds or retain old memories about dogs . My concept is also stable . . across -many counterfactual .situatioI;ls: . ii: .degs ·caught mice; I . wouldn',t-have a mouse problem. . .

Culture and stability Many of our concepts ate public, shared, stable throughout our culture. If they weren' t pretty much the same from one person to the next, it would be very difficult to learn them, and we would often be unable to agree or disagree with one another. It is only because the jurors have much the same concept of murder that they can legitimately agree the defendant is innocent. Concepts are part of our cultural legacy; they often have long and varied histories, play essential roles in our soCial practices and institutions, and many will live on long after we do. Sperber's ( 1 996) epidemiological model of the spread of mental representations from person to person is one account of the way concepts come to be shared. Finally, there are some fundamental concepts (e.g. object, causation) that are relatively stable across cultures (e.g. Brown, 1 9 9 1 ) . Mastery o f a concept caD. come i n degrees, and many concepts may involve (to adapt a point from Hilary Putnam) a division of cognitive labour, with some people deferring to others about just what a concept means . In a heterogeneous society there will also be some basic differences in concepts and beliefs , so that when

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ethnographers report on the Trobriand concept of causation or the Samoan concept of shame, they are often providing a sketch of a cultural average or central tendency. 2. 6

Centrality and Degree

The next point is more controversial. We can employ some concepts without knowing much about them, but in other cases we, or specialists, need a good deal of information to correctly classify instances of a concept or to reason with them ( ,Is the dark spot on the X-ray a malignant tumour? ' ) . Two key questions for any theorist of concepts are how much of this information should be built into the concept, and how much of it two people must share to have the same concept. At one end of the spectrum we find holistic theories that make the content of a concept depend on all of our other concepts and all of our beliefs . Views of this sort occur in some accounts of the incommensurability of concepts (e.g. mass, gene) before and after a scientific revolution and in comparisons of different cultures (e.g. the Ancient Greeks ' concept of rights) . At the other extreme we have atomistic views that treat concepts as directly referential mental representations with no descriptive content. These pictures have an all-or-(almost)-nothing flavour, but in a moment we ' ll see that there are a number of options in between. It is important that on some accounts of concepts (e.g. prototype theories and conceptual role theories) concepts can have descriptive content without any sharp analytic or synthetic distinction and without any claim that some of a concept' s content is essential t o i t while other content is not. As with many other things, for example, ships (like Theseus ' ) , there is often no precise point in our concepts where one more change in belief would rub out the old concept and give rise to a new one . On this view there is no useful distinction between change in concept and change in belief. Indeed, whether we regard a given case as one or the other can sometimes even depend on social and political factors that have little to do with meaning or metaphysics (Stich, 1 996, ch. 1 ) . These views require defence, but my-reasons for holding them are similar to .those of Sellars (e.g. 1 954; 1 974, p. 3 84) and Harman (e.g. 1 987; 1 999), so I won't defend them here. The key point, though, is that some bits of content and some inferential roles can be more central than others. It is more central to my concept of a dog that it is an animal and barks than that all dogs have fewer than six million spots . Furthermore, two people (or one person in different contexts) can agree and disagree about many things even if their concepts are not completely identical. We cannot profitably discuss fruits if you insist, in the face of all the things anyone can say, that they are a species of algebraic numbers and I think of them in a normal way. But we can discuss many things about fruit without talking past each other even if we disagree about whether tomatoes are fruits or vegetables . Stability requires similarity in concepts, but not total similarity. Furthermore, what beliefs or inferential roles are central to a concept can depend somewhat on context. 2. 7

Context

Almost every psychological phenomenon is highly sensItIve to context. Our perceptions in a given situation are influenced by our perceptual set. What we

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retrieve from memory is influenced by the context in which we retrieve it, including expectations , priming, retrieval cues . Our preferences between two options are influenced, sometimes even reversed, by the way the options are framed or described (e.g. Kahneman and Tversky, 2000) . There is also a great deal of evidence that context can affect the way we apply a concept, where we draw its borders of application (e.g. B arsalou, 1 987) . 2.8

Indefiniteness of Content

The contents of our memories, beliefs, desires, values and attitudes are often indefinite, protean, and partially constructed in a given context in ways that depend heavily on that context, for example, expectations , priming, framing effects, the way questions are worded, emotional state and mood (e.g. Kahneman and Tversky, 2000; Slovic, 1 9 9 5 ) . It seems possible that the concepts and beliefs stored in memory are more abstract than we might suppose. If so, there may sometimes be no simple answer to questions about the content of our concepts and beliefs, though there may be in particular contexts . 2.9

Kinds of Concepts

Empirical work has largely focused on concepts of various sorts of obj ects (e.g. birds, fruit, furniture) and (especially in cross-cultural research� colours. But there are many other sorts of concepts, and the differences among them may be of philosophical or psychological or linguistic interest. We can classify concepts by their content: moral concepts (duty, justice, individual rights) ; social concepts (love triangle, bureaucracy) ; logical concepts (some, not, and, only ij); concepts involving the self (e.g. the self), concepts of abstract things (Euclidean triangle, vector space over the reals) ; aesthetic concepts (beautiful, kitsch) , and so on. We also classify concepts by their structHre- (or the stmcture ·of their instances ) ; sortal concepts (concepts of sorts o f things , e.g. dog, chair) ; quality concepts (associated with adj ectives, e . g . , white, square); relational concepts (loves, lies in between) ; compound concepts (axis of evil, pet fish) , and so on. Different families of concepts may also be structured in different ways. For example, there are hierarchies of concepts connected by relations like is a kind of; dogs are a kind of mammal and mammals are in turn a kind of animal. The organization here is a descendant of Aristotle 's hierarchy of genera and species. The nature of a concept may even depend on how it was learned, say by learning a definition versus being exposed to examples and receiving feedback about the accuracy of one ' s classifications . A popular current distinction is between concepts based on similarity, for example, red, and those based on rules , for example, prime number (Smith and Sloman, 1 994; Nosofsky et aI. , 1 994; Erickson and Kruschke, 1 9 9 8 ; Patalano et aI. , 200 1 ; cf. Tenenbaum, 2000) . As w e will see, this i s part of a more general tendency to see cognition as involving both rule-based constructs and similarity-based constructs .

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Cognitive Functions of Concepts .

Concepts play essential roles in all our higher mental processes, including perception, learning, memory, inference, problem-solving, decision-making and action. I will touch on some of these here.

Classification We emp loy concepts constantly to sort the world into types of things (people, lakes), events (explosions, bank robberies), stuff (water, mud), qualities (redness, having a mass of 3kg), and more. Proper classification is often vital; the psychiatrist needs the correct psychodiagnosis to decide what drugs to prescribe for her suicidal patient, and she may use devices (like the Minnesota Multiphasic Personality Inventory) designed to help with classification. Nosology and taxonomy are important areas of study in their own right (e.g. Waller and Meehl, 1 997) , and classification systems like Mendeleev' s periodic chart play an essential role in organizing knowledge . There can even be deep divisions about how things in a given field should be classified, as illustrated by the debates among pheneticists , cladists and others in evolutionary biology. Perception Perception, along with action, is one of the two interfaces between the mind and the rest of the world, and it depends on concepts in various ways. For example, most vision is to some degree 'theory-laden' ; we see things as things of a given sort. I don ' t see a medium-size brown shape in the comer. I see a dog. This involves 'top-down processing ' , which depends on our concepts (e.g. dog, in, corner) and our perceptual set. Or consider speech perception: it is very difficult for a person to hear mere sounds when she hears her native language spoken (as she may when listening to a language she doesn't know) . She virtually has to hear it as meaningful words and sentences. There is disagreement about how much top-down processing (if any) there is, but most vision scientists endorse some sophisticated descendant of Helmholtz 's view of perception as 'unconscious inference' . Inference Concepts mediate inference. When I see that the creature under the rock is a rattlesnake, I immediately infer that it is dangerous and best avoided. Indeed, many concepts contain mini- (usually defeasible) predictions about what will happen under various circumstances . If that liquid is water, it will quench my thirst, dissolve sugar, extinguish fire, clean the dishes . And many concepts als o contain mini-postdictions . To be legally drunk you have to have consumed alcohol, and many diseases (influenza, measles) require a certain aetiology (as well as pathology) . A large part of problem-solving involves subsuming things under concepts that make the solution easier to spot (Simon, 1 997 is a classic here) . It is easier for most of us to solve problems in analytic geometry if we represent them using concepts involving Cartesian coordinates rather than concepts involving polar coordinates. Experts often differ from novices at solving a problem in their field (e.g. physics , handicapping the horses) precisely because they specify i t i n terms of theoretical concepts (e.g. acceleration, force, energy) that make the problem easier to solve. There are formal models of various sorts of inference, for example, deduction, non-monotonic reasoning, B ayesian c onditionalization, inference to the best

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explanation. But things often become murky when w e apply such models t o real life. For example, once we get away from mathematics or computer programming, and logic classes, the 4istinction between deductive inference and inductive inference is often blurry. We can treat Ann 's argument as deductively valid (and hence deductive) if we supply a missing premiss that she might well endorse . Or we can treat it as inductive reasoning based solely on the considerations she mentioned. This fits naturally with the view that there is no useful analytic-synthetic di stinction. Still, some inference is clearly ampliative, leading to conclusions containing information that was not in the premisses or evidence. Here we g o beyond the information given (Bruner), or learn to go on in the same way (Wittgenstein) . This is often called inductive learning, and a great deal of learning, including language acquisition and concept formation, is learning of just this sort. Furthermore, inference is bound up with many other mental processes . For example, many of our explanations of things ( , what could motivate suicide b ombers? ' ) cite causes, and so causal inference plays a central role in explanation (Heit, 2000 surveys the empirical literature on some of these topics). C.I. Lewis remarked that knowing is for doing, and a great deal of thinking involves practical reasoning: deciding what actions are likely to satisfy our desires and how to carry them out most efficiently. Such reasoning ranges from forming intentions to computing traj ectories for the movement of our limbs. Different ways of framing a situation, characterizing it in terms of some concepts (e.g. gains) rather than others (e.g. losses) often influence practical reasoning and decision­ making, - leading, for example, to preference reversals , different content in the retrieval of memories, and so on (Swoyer, 2002 contains an overview) . 2. 1 1

Using Concepts

There are a number features of our use of concepts. I will note several of the more important ones here. ' . : . :...

:, . ;

+�' .

Projectibility We can only use some concepts in our inductive behaviour, for example, in prediction. Adapting Goodman's ( 1 946) predicate ' grue' to our ends, we stipulate that an object is grue just in case it is examined before 20 1 0 and found to be green and is otherwise blue. If all the many emeralds examined to date are green, it is reasonable (subject to the inevitable inductive risk) to conclude that all emeralds are. But now, in 2004, all the examined emeralds are equally grue, but it is not reasonable to conclude that all emeralds are grue. Some or our concepts are projectible, and some aren't. Green is; grue isn't. And the distinction makes a big difference to our inductive practices (try projecting grue and see what people think). Typicality effects In a series of classic experiments Eleanor Rosch and her co­ workers found that if experimental subj ects are asked whether a pictured animal is a bird, they respond more quickly to pictures of some birds (e.g. robins) than to pictures of others (e.g. chickens). In this sense robins are more typical birds than chickens, and such results are now called typicality effects . Typicality has a strong positive correlation with a number of other phenomena of psychological interest. Subj ects make fewer errors classifying typical specimens

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than when classifying atypical ones. When asked to recall the different kinds of birds in the pictures, they tend to Llllnk of the typical examples fIrst. When asked to list the typical features of birds they tend to list salient features of robins and crows, rather than of chickens and penguins. Finally, children tend to learn typical examples before atypical ones . Many of these effects occur with concepts like bird, fruit, furniture and colours . S omewhat surprisingly, many of them also turn up with concepts that seem to have precise defInitions (e.g. odd number) . Many philosophers hold that some sentences o r statements, for example, 'bachelors are unmarried adult males' , are analytic (true solely in virtue of the words they contain) . Moreover, many non-philosophers have fairly robust intuitions that some sentences are true by defInition or that some groups of sentences are inconsistent ( 'I don 't know where the witness lied, but he definitely contradicted himself ' ) . These intuitions need t o b e explained, but various facts suggest that i t is worth trying to explain them without appealing to notions like analyticity or synonymy. Among other things, people often believe that words and concepts have precise defInitions even when they can't begin to provide them. Moreover, many of our concepts - for example red, game, chair, sloppy drunk, person - simply seem to lack definitions .

Lexical intuitions

We can combine a fInite stock of concepts to form indefInitely many more complex concepts . For example, we can combine the concepts mediocrity, old, witch and negation to form the concepts mediocre w itch, old mediocre witch, o ld witch who is not mediocre, and so on. This phenomenon is known as productivity. Productivity is important because it allows us to think about indefInitely many things without having indefinitely many concepts . Furthermore, understanding is to some extent a package deal. I cannot really understand some concepts (e.g. old and mediocre) unless I can understand related ones (e.g. mediocre and old) . This phenomenon is known as systematicity. The most natural explanations of conceptual productivity and conceptual systematicity turn on the claim that concepts obey a principle of compositionality. On a compositional account the meaning or content of a complex concept is completely determined by the meanings of its constituents and the way they are combined. Productivity is then explained by the claim that we have a fInite stock of simple concepts and recursive rules for combining them, which allow us to generate an unlimited number of additional concepts. A related story explains systematicity. The notion of compositionality has fragmented into various subtypes , and one can certainly worry about the notion of simple concepts (as opposed to concepts that are treated as simple within a particular theory of content) . Still, it is often held that any theory of concepts must be compositional in some respectable sense, and theories that aren't - and there are a number of them - are often written off on this ground alone (Rips, 1 995 contains a good overview of the empirical literature) .

Productivity and systematicity

Conceptualism 3.

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What Concepts Are: Theories of Concepts

I t would b e premature t o w e d conceptualism to any particular theory of concepts , but I will quickly note the maj or theories with an eye to their implications for conceptualism and ability to explain the items on the above list of phenomena. 3. 1

Representations and Operations Are a Package Deal

Before getting down to details, we should note that theories of mental representations and theories of the mental operations that work on them are a package deal. We rarely have observational access to either (even in introspection), and so we postulate representations of a certain s ort (e.g. semantic networks) in tandem with mental operations of a certain sort (e.g. spreading activation) to explain phenomena of a given sort (e.g. retrieval from long-term memory) . It is the entire package that is tested and used to predict and explain. This can lead to real-life underdetermination of theory by data, since we can sometimes save a picture of concepts by tinkering with our account of the operations that process them, or vice versa (e.g. Anderson, 1 97 8 ) . Theories o f concepts are evaluated by the usual standards for empirical theories : simplicity, comprehensiveness and, above all, their ability t o explain the phenomena in their domain. An explanation requires at least two components : first, something to be explained, the explanation target; second, something to explain it. Theorists sometimes disagree about whether something constitutes a genuine target, but most of them view the phenomena noted in the previous section as genuine explanation targets . 3.2

The Classical View

The classical account of concepts dominated philosophy for centuries until, in the mid- 1 950s, it came under fIre from Wittgenstein, Quine, Sellars, Goodman and others. This account was als o popular in psychology until the work of Rosch and her co-workers in the early 1 970s. The leading idea of the classical view is that the content of a compound concept is given by a conjunction of other concepts, and that these provide necessary and sufficient conditions for something's being in the extension of the concept. Aristotle thought of defInitions of species (e.g. human) in this way, as the conjunction of a genus (e.g. animal) and a differentia (e.g. rational) . DefInitions in mathematics often fIt the pattern: a prime natural number is a natural number that is divisible only by itself without remainder. We could generalize the classical account to allow logical operations (like negation and existential quantifIcation) in addition to conjunction by adapting the operations in recent formal accounts of properties (e.g. B ealer, 1982; Menzel, 1 9 9 3 ; Swoyer, 1 997; 1 9 9 8 ; Zalta, 1 98 8 ) to concepts . The classical account is sometimes thought to provide precisely bounded necessary and sufficient conditions for something to fall under the concept, but if one or more of the defIning conditions is vague, the concept may be vague too . For example, our ordinary concept of being an adult is vague, so the concept being an adult unmarried male is vague, and hence the concept bachelor is vague too.

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Pros I will call concepts (if any) that conform to the classical model classical concepts and say that they have a classical structure , S ome concepts do seem to be classical, among them bachelor, prime number and deductively sound argument. The classical view can explain many roles of concepts in deduction, many cases of conceptual combination, and many lexical intuitions, for example, the intuition that bachelors are unmarried adult males. ' The account is compatible with typicality effects, since many classical concepts (even prime number) exhibit such effects , and with vagueness, providing the defining concepts are vague. Classical concepts can also be proj ectible, though of course many are not. Cons Despite its simplicity and intuitive appeal, the classical theory, construed imperialistically as a general theory of concepts, is dead. In many cases the anticipated definitions never turned up . There were warnings in Wittgenstein and other philosophers, and empirical work only reinforces the point. We cannot give necessary and sufficient conditions for something's being red, a game, a chair, or beautiful, and in many cases there is little reason to suppose that there are any definitions waiting to be found. Even when s omething resembling a definition is available, there are often problems . First there is the grounding problem: some of the concepts used to define others must at some point hook up with the world outside the mind, and it is not easy to find plausible examples of such concepts . It is als o p ossible to use a classical concept without knowing its full definition and, indeed, even when having false beliefs about it. I used to think that something is a first-degree murder just in case it is a premeditated killing, but I am told that in my home state this is incorrect. The classical theory is a pure case of the view that general terms have descriptive contents that determine their extensions . Hence it isn ' t surprising that the classical view makes too much analytic (since the defining conditions give the meaning of the defined concept) , too much necessarily true (on the c ommon assumption that the equivalence between the two parts of a definition is necessary), and too much a priori (on the common assumption that our knowledge of meanings or definitions is a priori) . 3.3

Similarity and Similarity-Based Accounts

Similarity has been a central notion in philosophy and psychology for a very long time. It is often natural to view the acquisition of a concept, especially one keyed fairly directly to experience (like red), as learning to go on to classify newly encountered items that are similar to the original red things as red too. Similarity is appealingly flexible: one thing may be similar to a second with respect to colour but not shape, and similar to a third with respect to shape but not colour. But flexibility is also similarity 's Achilles' heel. The relation is just too promiscuous ; any two things are similar in s ome ways and not in others (e.g. Goodman, 1 972). The point that any two things are similar in many ways and dissimilar in many others is compatible with the existence and importance of psychological similarities, those that influence how we categorize and think about things. But a good similarity­ based explanation of a cognitive process like classification must specify the relevant

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sorts of similarity. This is often where the real work is required, and the resulting account of what makes for the 'relevant' or the 'right' sort of similarity is what does . the real explanatory work. Study after study s h9WS that our assessments of similarity are highly sensitive to context (cf. Medin et al . , 1 99 3 ; Goldstone et al . , 1 997; Goldstone and Rogosky, 2002) . The features of things that we consider and the weight we give them in determining similarity are strongly influenced by our interests, the s ort of concept involved, and other features of the context. For example, beef is more similar to soybeans than to avocado if I am concerned with protein, but more similar to avocado than to s oybeans if I am concerned with fat. Judgements about relevant similarity in a domain also change as one becomes more skilled in thinking about things in the domain. Part of learning about French impressionism or classical mechanics is becoming attuned to the existence and role of resemblances that escape the novice. There are two theories of concepts that are based on similarity. Prototype theories As with the other theories we' ll examine, prototype theory is a family of accounts. We might motivate the general approach with a story. A child encounters creatures and is told which ones are birds . Eventually she gets the hang of things and can go on, with just the occasional error, to sort newly encountered things into birds and non-birds. How? She counts things as birds just in case they are sufficiently similar, ' in psychologically relevant ways ' , to the birds in her original sample. In the case of concepts like red, which lack obvious internal structure, we learn that certain things are red, and we have a cognitive mechanism that determines whether colours are similar enough to it to count as red too . With more complex concepts, for example, fruit, furniture or kinds of-animals, say birds, we form a mental representation that encodes salient information about typical birds ; this makes up a sort of prototype profile that might include features such as having a beak, feathers , and the ability to fly and build nests . We also have cognitive operations that determine the relevant sorts of similarity for this concept and .compute .how similar various things are; in these respects., to the infDrmation in our bird profile. A key innovation of prototype theories is that prototype profiles are not definitions. Prototype concepts have descriptive content (their profiles), but they do not have defInitions . Prototype theories can explain typicality effects (not surprisingly, since they were designed to) , though this would be more impressive if classical concepts didn' t exhibit the s ame effects . Prototypes theories can also account for vagueness and the fact that we often cannot fInd defInitions. Many prototype concepts are also projectible and natural. However, prototype theories have difficultly explaining many of our lexical intuitions, and they stumble over the fact that we may be able to use a concept like elm even when we know very little about it or its profIle, or even when we are mistaken about it. We can also master concepts that lack prototypes . These include concepts , like that of a Hobbit, which have no instances, though perhaps we could acquire profiles for these by reading Tolkien or seeing the movies . The features that loom large in our assessments of typicality sometimes depend on context (B arsalou, 1 987), though since assessments of similarity depend on context this isn ' t a problem in principle, though it does make things more complicated. And then there is the

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common problem about what features · are and how they latch onto the world outside the mind. One of the most persistent criticisms of prototypes is that they are not compositional (the discussion begins with Osherson and Smith, 1 9 8 1 ). To take the standard example, something is a pet fish just in case it is both a pet and a fish. But the prototype of pet fish is not a function (here some sort of conjunction operation) of the contents (here the prototypes) of pet and fish. In our culture most people's prototypes of pets include things like being a dog or a cat, but not fish. And our prototypes of a fish probably involve middle-sized fish like tunas and trout. But the prototype of a pet fish involves something more like goldfish and guppies, which is not in the intersection of the prototypes of pet and fish .

Exemplar theories The fundamental idea behind exemplar theories of concepts is that instead of storing profiles of features (modem analogues of Locke ' s abstract ideas) we store memories of specific instances we have encountered (rather like Berkeley's replacements for Locke's abstract ideas). For example, we store memories of the various birds we have encountered. We then compute similarities between newly encountered items and our exemplars in memory. From a philosophical perspective exemplar theories are akin to philosophical theories based on a general relation of similarity (basically what we find in Camap' s Aufbau) . A problem with such brute resemblance i s that i t is very complicated, context-dependent, and often isn ' t discriminating enough to divide things up into the concepts that we actually have . This can prompt a move toward resemblances of aspects, for example, colour-resemblance, shape-resemblance and the like. Such relations are easier to work with, but from a philosophical perspective they look uncomfortably like properties and from a psychological perspective uncomfortably like prototype profiles. In both cases they presuppose things, the relevant similarities or aspects, that many theorists think need to be explained. In some experiments exemplar models accommodate the data better than prototype theories do, but I won:t follow this up,�becaru;e .ex�mplar; .theories.have many of the same. pr.os ·and · o cons as prototype theories . 3.4

The Theory Theory

Similarity-based views have some plausibility for concepts keyed fairly directly to observation, but they fare worse with concepts like nation-building, global warming and (to cite a standard example) being drunk. There are no simple, easily observable similarities among people who are drunk: there are sloppy drunks, moody drunks , belligerent drunks . And we often need t o mobilize a good deal of knowledge to know when the concept drunk applies. Once we give up on definitions, it can be tempting to build a lot of this knowledge into the concept. On this view a concept is a sort of mini-theory, and we classify things under the concept that best explains them. Sam was drunk; that explains why he slurred his speech and insulted his wife. This approach is often called the theory theory of concepts. The theory theory reminds us that we often need to rely on more theoretical similarities than prototype and exemplar theories usually do. It also accounts for the role of inference and explanation in the application of many concepts . But

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combination of concepts now requires the combination of theories, and no one has a good account of this. There is also the now-familiar point that we can use many concepts despite being ignorant, or even wrong, about them and their extensions, and since the theory theory builds so much information into concepts it is especially vulnerable here. The approach is also too holistic to explain lexical intuitions . Indeed, all sorts of information may be relevant in applying a concept, but how much of it should be built into the concept? Once you start, is there any pi:incipled place to stop? The theory theory makes the important point that classificatory tasks can involve a wide variety of things. But to be a theory (not to mention a computational theory) of concepts it needs to involve more than a sprawling Quinean holism. It needs to tell us what information belongs in a concept, and why. 3.5

Atomism

In Section 2 we encountered arguments that some concepts , for example, e lm and red, lack descriptive content. On this view concepts are simple unstructured mental representations, cognitive atoms , and the only thing essential to a concept is that it denotes the property that it does (e.g. redness, being an elm, justice) .

Pros Conceptual atomism explains the lack o f definitions for many concepts and accounts for our ability to use a concept like elm without knowing much about elms . It nicely explains conceptual stability, since a concept may remain anchored steadfastly to a property throughout many changes in our beliefs about its instances . It also explains conceptual combination; something is a pet fish just in case it has the properties of being a pet and being a fish. Cons Conceptual atomism allows us to have the concept dog without having the concepts animal, eating, barking and having a head, which strikes many of us as counter-intuitive. It cannot explain lexical intuitions, typicality effects, or anything else that smells like des.criptiYe .c.ontenr, though it might be argued that such things need to be explained by something other than a theory of concepts. A maj or problem for conceptual atomists is to explain how a conceptual representation (e.g. red, elm, justice) hooks up with its relevant property. There are various proposals about this, most involving some sort of causal chain between the property and the concept, but none is without problems . The problem is especially acute for uninstantiated properties, particularly those not definable in terms of instantiated properties, because there are no causal chains running between the natural order (where we and our concepts exist) and abstract properties . 3.6

Conceptual Role Semantics

Conceptual role semantics (sometimes known as procedural semantics) was originally developed as a very general account of linguistic meaning (e.g. Sellars, 1 954; Harman, 1 987), but it is quite natural to reinterpret such an account as theories about the content of concepts . On such accounts the content of a concept is determined by its role in inference and other mental activities like perception and action, by its role in what Sellars calls the evidence-inference-action language

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game. As we noted in Section 2. 1 , the application of many concepts commits us to predictions (sugar: it will dissolve if I put it in water) and postdictions (forgery: it was produced by someone other than the person we would normally suppose). Indeed, this is the rule, not the exception. S ome concepts, for example, colour and taste, are geared fairly directly to the environment, and part of the mastery of such concepts includes acquiring the ability to recognize and classify things according to their colour or taste. ' B ut simply being able to respond differentially to red things is not enough to have the concept red. Having the concept involves having at least some of the following dispositions : knowing roughly the sorts of conditions under which red things won ' t look red, being able t o draw various inferences , for example, 'this i s red so it' s coloured' , 'this i s red so i t ' s extended' , 'this i s currently red all over so i t can ' t b e green all over too ' , 'this is scarlet so it's red' . More importantly, though more vaguely, it requires us to be able to think in a variety of ways about red things and about colours . Other concepts are more theoretical. Our concept of causation is b ound up with our ability to determine what causes what in many everyday circumstances, how dispositions of things lead them to cause certain things under certain conditions , for example, if the piece of metal is magnetized it will attract the iron filings, and knowing what sorts of evidence will support causal attributions, having a sense about how causation and counterfactual conditions are connected, and so on. Despite occasional claims to the contrary, there is nothing that requires conceptual roles to be entirely in the mind (as 'narrow content' ) , and they certainly weren' t thought o f i n that way by either S ellars o r Harman. M y concept red involves the ability to recognize red things out in the world. My concept water links up with water because of the way I apply the term 'water' to it. S ome philosophers supplement the view that the content of concepts is determined by their conceptual or psychological role with the view that concepts also have a directly referential component. Th is is always an..option, but it' s not how early theorists like S ellars or Harman­ thought about things ; indeed, Sellars urged that there is no single relation of reference, though there are many relations between concepts and things in the world that anchor our framework of concepts to the world outside the mind . There i s also nothing that commits the conceptual role theorists to either analyticity, on the one hand, or to an amorphous holism, on the other. S ome inferences and beliefs involving a concept are more central to the concept than others. Philosophers have offered various accounts of centrality, though I suspect it has a variety of sources . At all events , I ' ll simply note the intuitive point that it is more central to my concept dog that dogs are animals than it is that no dogs have over a trillion hairs. 3. 7

Fragmentation

It has become increasingly obvious that concepts have been asked to fill too many roles that are often incompatible, and that no existing accounts account for all of them. We can divide these roles, provisionally, into three general kinds.

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Role one: anchoring One role clusters around stability, conceptual combination, truth conditions , and lack of definitions . We might call this the ancho ring role. It also fits with many aspects, translated into the idiom of concepts, of direct theories of reference and externalism in semantics . The idea is that concepts directly refer to things in the world, and for a general term it is difficult to see what this could be other than a property (we might hope, though, that in re properties would be enough) . Role two: conceptual roles We just discussed cognitive or inferential role. It involves the cognitive functions of concepts discussed in S ection 2 . 1 . Role three: other psychological phenomena These include some o f the phenomena and effects discussed in S ection 2.2, including typicality effects and ease of classification. It' s an oversimplification, but the conceptual role of a concept is reminiscent of Marr's ( 1 9 82) picture of the function that a given bit of cognitive processing computes, while things like typicality effects may tell us something about how we go about computing it, what algorithm the mind uses. This might involve the ways we identify instances of a concept. Again, we might compute similarity in different ways, for example, by deploying rules that count and weigh features, or by more associationistic connectionist mechanisms . Again, it is part of the conceptual role of concepts like dog and all that if all dogs are animals and if Max is a dog, then Max is an animal. But we might work this inference out using some mental analogue of formal logic or we might use inheritance in a hierarchy of c oncepts . For example, it might be part of our network of concepts that dogs are a kind of animal and that Max inherits the feature of being an animal from the fact that he is a dog. What are our options when a single entity seems unable to meet all of the demands placed on it? First, we can introduce different kinds of entities, one to play each type of role. Bealer's ( 1 9 82) distinction between qualities an.d concepts is an imp()rtant example of this in philo sophy. In psychology we can posit various types of mental representations in addition to concepts, for example, semantic networks, B ayesian networks , or scripts. We can also introduce different kinds of concepts, for example, classical concepts , prototype concepts and so on (cf. Medin et aI. , 2000; Medin and Coley, 1 998). But these distinctions don't really solve the present problem, which is trying to find things that play the various roles in one and the same case; we want to explain the anchoring aspect of the concept water and its functional role in inference. Moreover, if we go down this route we will face difficult questions about how the various entities connect up with each other. Accounts that posit multiple aspects of a single sort of entity, just concepts, have been more popular. There are several theories of this sort going back for over twenty years (e.g. Osherson and Smith, 1 9 8 1 ; 1 9 82; Miller and Johnson-Laird, 1 976). The approach has become more sophisticated over the years . In his recent discussion Rips ( 1 995) argues that concepts have two aspects : the representation of a category of things, which is an atomistic directly referential aspect (to provide stability and related things); and, a representation about the category, in his case a

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version of the theory theory (to include the descriptive content that is often relevant in applying a concept and that helps explain some of the other phenomena mentioned above). There are several more degrees of freedom here. First, a number of recent theorists have proposed dual-process accounts of c ognition. Different theorists develop this idea in different ways, but the rough idea is that human beings have two quite different cognitive subsystems (or two types of subsystems) . There is an ' explicit' subsystem that is largely conscious, symbolic, verbal, rule-governed, serial, flexible and capable of reflection. B ut there is also an 'implicit' subsystem that is largely non-conscious , associative, impulsive, affective and that reacts automatically to stimuli (e.g. Sloman, 1 996; Chaiken and Trope, 1 999). We further increase the possibilities for multiplication if we hold that the brain houses various domain-specific modules that involve different sorts of processing. Various combinations are possible . The basic trick is to put enough in the head that concepts can play their causal, psychological roles, while having them anchored tightly enough to the world outside our heads that they can be stable over time and among people. My own preference is for an account of concepts with two aspects . The first aspect is conceptual role; the second psychological phenomena like those discussed above. But however this may be, there are enough degrees of freedom that we can play a number of things off against one another in a way that leaves empirical theories of concepts more than a little underdetermined by the evidence.

4.

Concepts and the Problems of Universals

Universals have been invoked to explain a wide range of phenomena. I will note some of these, say how properties have been used in attempts to explain them, then ask how well concepts might do instead. The list is by no means complete and not all of the targets are equally compelling, but many are of current interest. I have argued that argl.JT]1ents . in ontology are best construed as ampliative (l 98J.; .1999a),. but most of what follows is straightforwardly adapted to the view that philosophical arguments should aim to be deductively sound. I will divide the explanatory targets into four group s . 4. 1

Ontology

Traditional ontology S ome things are alike in certain respects : they are human beings, red, loud. And various groups of things can stand in similar relations , for example, loving one another. Possession of a shared property (humanity, redness, loudness) or standing in a shared relation (loving) have been said to explain such resemblances , while possession of different properties explains the differences. Furthermore, many things change over time. The table was brown before I painted it, but is white now. The table itself is present throughout the change in colour, so the mere ontological blob of a table can't explain the alteration. For that we must add that it exemplified b rownness yesterday and exemplifies whiteness today. Such accounts have struck some philosophers as pseudo explanations, and it is fortunate for realists that properties can be defended on the grounds that they explain

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other phenomena that more clearly need explaining. Still, the ability to explain qualitative recurrence and change is a perennial motivation for realism (e.g. Plato 's Republic, 507b ; 596a-b ; Armstrong, 1 9 84, p . 250). What about concepts ? Assuming some constraints imposed by the world outside the mind, the conceptualist can argue that the resemblances that seem natural to us only seem so because we are disposed, through our biological or cultural or linguistic heritage, to find s ome groupings more natural than others . Moreover, everything changes constantly in all sorts of ways. The ways that matter to us, the ones we tend to think of as 'real change ' , are likewise determined by the concepts and similitudes we find natural.

Recent ontology Recently some philosophers have argued that universal properties provide the best explanations of various features of measurement, causation, natural laws, supervenience, and the like (Swoyer, 1 999b contains an overview). In many of these cases properties play a central role in making things happen. The liquid in the glass caused the litmus paper to turn blue because the liquid is alkaline. But the fact that the liquid falls under the concept alkaline doesn' t explain why it turned blue. Concepts are not well suited to explain such things (though with luck in re properties might be enough for the j ob). 4. 2

Cognition and Epistemology

We have already noted the numerous roles concepts play in cognition, culture and the like.

Recognition and classification Most animals, including humans, are constantly classifying, sorting, categorizing. Many philosophers have argued that an organism's ability to recognize and classify newly encountered things such as cats , red obj ects and unwarranted insults is best explained by the view that the old instances and the new share a property . (e g . , redness), and,thatthe organism is S9:r:neJ1,Ow.attunes.l W recognize or respond to it. B ut if there is a plausible conceptualist metaphysical story about an objective basis in the world outside the mind that provides a foothold for classification, concepts may be able to explain the phenomena as well as properties. The idea here is to shift some of the burden from 'reality itself' to the realm of concepts . ..

Inductive learning and inductive bias Language learning, concept formation, mastering social norms and moral principles, calculating sums , projecting predicates, giving causal explanation and so on involve inductive learning. We are exposed to instances (e.g. grammatical sentences, typical members of the extension of a concept) and learn to classify new and novel things correctly (the p oint is a generalization of so-called poverty of stimulus arguments in linguistics; cf. Morgan and Demuth, 1 996; Chomsky, 1 975). The problem is that there are too many different, incompatible, ways one might go on. I see an object that is, among other things, green. Should I classify it as green, or grue, or being grue or else a prime number? The list is endless . If we are to succeed we cannot be completely open-minded. We need a strong predisposition

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( ,inductive bias ' ) to classify things one way (e.g. as green) rather than another (e.g. as grue) . A cognitive system without inductive biases cannot learn. S o although we need some basis in the world for our application of concepts, we also need a strong psychological disposition to classify in some ways rather than others. Since classification often involves thought without languages (as in learning our first language), this is very naturally explained by the view that we come into the world with certain concepts (e.g. the obj ect concept, various concepts needed to learn language) or at least with strong dispositions to form these concepts (given the dispositional nature of our use of concepts, thes e may not be as different as they at first seem) . In short, concepts and conceptual operations, ones involving concept acquisition and use, play a central role in inductive learning. A priori knowledge and de dicto necessity S ome philosophers , including several British empiricists , have argued that a priori knowledge is knowledge of the necessary connections among concepts (the concept bachelor includes or entails the concept male) . One might add that de dicto necessity, the necessity of sentence­ like creatures such as the thought that bachelors are unmarried, is also based on necessary relations among concepts . Perhaps, indeed, ' the only necessity is conceptual necessity ' (C.I. Lewis thought something like this) . It is not clear that there really is much a priori knowledge or necessary truth, but those who think there is might find concepts useful here. 4.3

Language and Semantics

Natural language and cognition involve some of the s ame things, for example, intensionality. The overlap is especially obvious if we think cognition takes place in a 'language of thought' .

Semantic values of abstract singular terms Abstract singular terms like ' avarice' , 'triangul
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plane figures ' . And 'Ponce d e Leon searched for the fountain o f youth' is, b y any normal standards, true. Properties have been proposed to explain such things ; for example, it can be argued that although 'three-sided plane figure ' and 'three-angled plane figure' are necessarily coextensive, they denote different properties and that this explains why we cannot always substitute one for the other in ways that preserve truth-value . But concepts can also have very fine-grained identity conditions, and i t i s plausible to hold that the concepts three-sided plane figure and three-angled plane figure (rather than any properties) are the semantic values of the associated predicates and that they express different properties . This would explain the failure of substitutivity just as well as properties do. Furthermore, although there isn ' t a fountain of youth, we can form the concept of one . This of course pushes things back to questions about the nature and provenance of the content of concepts, and a lot of work would be needed to account for this. But if the account succeeds , it will furnish much more detail than the realists ' bare claim that abstract singular terms and general terms have properties as their semantic values , end of story. 4. 4

Mathematics

Standard explanation targets in the philosophy of mathematics include the following. Sentences such as '7 + 5 = 1 2 ' have truth-values, they necessarily have the truth­ values they do, and there are infinitely many natural numbers . Furthermore, it is possible to have knowledge about the numbers, and much of it is a p riori. Abstract entities, either just the natural numbers themselves, set-theoretic surrogates for them, or properties have been posited to explain these phenomena in familiar ways. The general strategy is to argue that there are infinitely many numbers, that words like ' 7 ' denote them and function symbols like '+' express functions on the domain of numbers , and that these numbers necessarily stand in the relations that they do. But tbjs account stumhles with the epistemological claims that we have a priori knowledge of mathematical truths . B y contrast, concepts might help explain these epistemic phenomena, but taken alone we would need some sophisticated manoeuvres to use them to explain truth, necessity and cardinality. Various nominalistic accounts in the philosophy of mathematics suggest models for conceptualist accounts of such things, but none of them is free of problems . The field here for the conceptualist is open but hazy.

Conclusion

I have argued that concepts can do some, though not all, of the explanatory work that properties are often invoked to do. I also urged that conceptualism and in re realism are an attractive package. I have only begun to scratch the surface , but I hope to have said enough to show that while traditionally conceptualism and nominalism have tended to go hand in hand (having realism as their common enemy), the sort of conceptualism defended here can live more easily with a non­ Platonic, naturalistic realism about properties.

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Note For our purposes (monadic) properties (e.g., being red) and relations (e.g., the causal relation) are similar enough that I will lump them together under the label ' properties ' . I will take properties to be universals, but most of the discussion is straightforwardly adapted to the view that they are particulars (tropes). I am grateful to David Armstrong, Neera B adhwar, Hugh B enson, Monte Cook, Michael Dougherty, Ray Elugardo, Charles Gettys, Jim Hawthorne, Herbert Hochberg, Paul Meehl, Chris Menzel, Adam Morton, Ed Zalta and the editors of this volume for helpful discussions on the matters discussed here .

References Allen, C. and Bekoff, M. ( 1 997), Species ofMind: The Philosophy and Biology of Cognitive Ethology. Cambridge, MA: MIT Press. Anderson, John R. ( 1 97 8 ) , 'Arguments Concerning Representations for Mental Imagery ' , Psychological Review, 85, 249-77. Armstrong, D avid M. ( 1 984), 'Replies ' , in Radu B o gdan (ed. ) , Armstrong: Profiles, Dordrecht: D . Reidel. B argh, John A. and Ferguson, Melissa J. (2000) , 'Beyond B ehaviorism: On the Automaticity of Higher Mental Processes ' , Psychological Bulletin, 126, 925-45. B arsalou, Lawrence W. ( 1 9 87), 'The Instability of Graded S tructure: Implications for the Nature of Concepts ' , in U. Neisser (ed.) , Concepts and Conceptual Development: Ecological and Intellectual Factors, Cambridge: Cambridge University Press. Bealer, George ( 1 9 82 ) , Quality and Concept. Oxford: Clarendon Press. B enacerraf, Paul ( 1 973), 'Mathematical Truth' , Journal of Philosophy, 7 0 , 6 6 1 -7 9 . Brown, Donald E. ( 1 9 9 1 ) , Human Universals. New York: McGraw-Hill. Carey, Susan and Xu, Fei (200 1 ) , 'Infants ' Knowledge of Obj ects : B eyond Obj ect Files and Obj ect Tracking' , Cognition, 80, 1 79-2 1 3 . Carnap, Rudolf ( 1 950), 'Empiricism, Semantics, and Ontology ' , Revue internationale de philosophie, 4, 20-40, Ch aiken, She1l6Y and Trope , Yaacov (eds ) ( 1 9 9 9 ) , Dual-Process Th eories in Social Psychology. New York: Guilford. Chomsky, Noam ( 1 975), ' Knowledge of Language ' , in Keith Gunderson (ed . ) , Languf!ge, Mind, and Knowledge. Minnesota Studies in the Philosophy of Science, Vol. 7, Minneapolis, MN: University of Minnesota Press, pp. 299-320. Erickson, M . and Kruschke, 1. ( 1 99 8) , 'Rules and Exemplars in Category Learning' , Journal of Experimental Psychology: General, 127, 1 07-40. Goldstone, R.L., Medin, D.L. and Halberstadt, 1. ( 1 997) , ' Similarity in C ontext' , Cognition, 25, 237-5 5 . Goldstone, R . L . and Rogosky, B .J. (2002), 'Using Relations within Conceptual Systems to Translate Across Conceptual Systems ' , Cognition, 84, 295-320. Goodman, Nelson ( 1 946), Fact, Fiction and Forecast 4th edn 1 9 84. Cambridge, MA: Harvard University Press. Goodman, Nelson ( 1 972), ' S even Strictures on Similarity' , in Problems and Projects, New York: B obbs-Merrill, pp. 437-46. Originally published in 1 97 0 . Goodman, Nelson and Quine, W.V. O . ( 1 947) , ' S teps Toward a Constructive Nominalism' , Journal of Symbolic Logic, 12, 97-122. Harman, Gilbert ( 1 987), ' (Non-Solipsistic) Conceptual Role Semantics ' , in E. Lepore (ed.), New Directions in Semantics, London: Academic Press.

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Harman, Gilbert ( 1 999), Reasoning, Meaning, and Mind. Oxford: Oxford University Press . Harnad, Stevan ( 1 990), 'The S ymbol Grounding Problem' , Physica D, 42, 3 3 5-46. Heit, Evan (2000), 'Properties of Inductive Reasoning' , Psychonomic Bulletin & Review, 7, 569-92 . Kahneman, Daniel and Tversky, Amos (2000), Choices, Values, and Frames. Cambridge: Cambridge University Press . Kihlstrom, J.P. ( 1 996), ' Unconscious Processes in S ocial Interaction ' , in S . Hamewff (ed.) , Toward a Science of Consciousness, Cambridge, MA: MIT Press , p p . 93- 1 04. Kripke, S aul A ( 1 972), Naming and Necessity. Cambridge, MA: Harvard University Press. Marr, David ( 1 9 82), Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. S an Francisco, CA: W.H . Freeman. Medin, Douglas L and Coley, J.D. ( 1 99 8 ) , ' C oncepts and Categorization' , in J. Hochberg and J.E. Cutting (eds) , Handbook of Perception and Cognition: Perception and Cognition at Century 's End, S an Diego, CA: Academic Press, pp. 403-3 9 . Medin, Douglas, Lynch, Elizabeth B . and S olomon, Karen O . (2000) , 'Are There Kinds of Concepts ? ' , Annual Review of Psychology, 51, 1 2 1 -47. Medin, Douglas L , Goldstone, R.L and Genter, D . ( 1 993), 'Respects for Similarity ' , Psychological Review, 100, 254-7 8 . Menzel, Christopher ( 1 993), 'The Proper Treatment o f Predication i n Fine-Grained Intensional Logic ' , in James E. Tomberlin (ed.), Philosophical Perspectives, Volume 7: Language and Logic, Oxford: B lackwell, pp. 6 1-87. Miller, George A. and Johnson-Laird, Philip ( 1 976), Language and Perception. Cambridge, MA: Harvard University Press. Morgan, James L and Demuth, Katherine (eds) ( 1 996), Signal to Syntax: Bootstrapping from Speech to Grammar in Early Acquisition. Hillsdale, NJ: Lawrence Erlbaum. Nosofsky, Robert M . , Palmeri, Thomas J. and McKinley, S tephen C. ( 1 994), 'Ru1e-Plus­ Exception Model of Classification Learning' , Psychological Review, 1 0 1 , 53-7 9 . Osherson, Daniel N. ( 1 97 8 ) , 'Three Conditions on Conceptual Naturalnes s ' , Cognition, 6 , 263-89 . Osherson, Daniel N. and Smith, Edward E. ( 1 9 8 1 ) , ' On the Adequacy of Prototype Theory as a Theory of Concepts ' , Cognition, 9, 3 5-5 8 . O shers on, D aniel N . and S mith, Edward E . ( 1 9 8 2 ) , ' Gradedne s s a n d C onceptual CombiDation'� Cognition, . 12, . 1 99-2 1 8 . Routledge : Examination of the difficulties of conceptual combination for prototype theories. Patalano, Andrea L , Smith, Edward E . , Jonides, John and Koeppe, Robert (200 1 ) , 'PET Evidence for Multiple S trategies of Categorization' , Cognitive, Affective & Behavioral Neuroscience, 1(4) , 360-70. Porphyry, The Phoenician ( 1 994) , 'Isagoge ' , in Paul Vincent Spade (ed.), Five Texts on the Medieval Problem of Universals, Cambridge, MA: Hackett, pp. 1 - 1 6 . Rips , Lance ( 1 995), 'The Current Status of Research on Concept Combination ' , Mind and Language, 10, 72- 1 04. S ellars , Wilfrid ( 1 954) , ' S ome Reflections on Language Games' , Philosophy of Science, 21 , 204-28 . S ellars , Wilfrid ( 1 974) , Essays i n Philosophy and its History, Dordrecht: D . Reidel. S imon, Herbert A ( 1 997), The Sciences of the Artificial, 3rd edn. Cambridge, MA: MIT Press . S l oman, S teven A. ( 1 99 6 ) , 'The Empirical Case for Two S y s tems of Reasoning ' , Psychological Bulletin, 119, 3-22. S lovic, Paul ( 1 995), 'The Construction of Preference' , American Psychologist, 50, 364-7 L S mith, Edward E. and S loman, S . ( 1 994) , ' Similarity- vs. Rule-Based Categorization' , Memory and Cognition, 22, 377-86 .

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Sperber, Dan ( 1 996), Explaining Culture: A Naturalistic Approach. Oxford: Blackwell. S tich, S tephen P. ( 1 996), Deconstructing the Mind. Oxford: Oxford University Press. S trawson, P.P. ( 1 959), Individuals: An Essay in Descriptive Metaphysics. London: Methuen. S woyer, Chris ( 1 9 8 3 ) , 'Realism and Explanation' , Philosophical Inquiry, 5 , 1 4-2 8 . Swoyer, Chris ( 1 997), ' Complex Predicates and Conversion Principles ' , Philosophical Studies, 87, 1-32. Reprinted in Philosopher's Annual, 20, 1 9 9 8 . Swoyer, Chris ( 1 998), ' Complex Predicate s and Logics for Properties and Relations ' , Journal of Philosophical Logic, 27, 295-325. Swoyer, Chris ( 1 999a), 'How Metaphysics Might be Possible: Explanation and Inference in Ontology ' , Midwest Studies in Philosophy: New Directions in Philosophy, 23, 1 00-3 1 . Swoyer, Chris ( 1 999b), 'Properties ' , in Edward Zalta (ed. ) , Stanford Encyclopedia of Philosophy, http ://plato.stanford.edu/entries/properties/. S woyer, Chris (2002), 'Judgment and Decision Making: Extrapolations and Applications ' , in R . Gowda and J . Fox (eds), Judgments, Decisions, and Public Policy. Cambridge: Cambridge University Press, pp. 9-45 . Swoyer, Chris (forthcoming) , 'Abstract Entities ' , in John Hawthorne, Dean Zimmerman and Ted Sider (eds), Contemporary Debates in Metaphysic s . Oxford: Blackwell . Tenenbaum, Joshua B. (2000) , 'Rules and Similarity in Concept Learning' , in A. S olla, T. K. Leen and K.R. Muller (eds) , Advances in Neural Information Processing Systems . Cambridge, MA: MIT Press, vol. 1 2 , pp . 5 9-65. Waller, Niels G . and Meehl, Paul E . ( 1 9 9 7 ) , Multivariate Taxometric Procedures: Distinguishing Types from Continua. Thousand Oaks, CA: S age. Wisniewski, Edward J. and Medin, Douglas L. ( 1 994) , ' On the Interaction of Theory and Data in Concept Learning' , Cognitive Science, 18, 221-8 l . Zalta, Edward N . ( 1 9 8 8 ) , Intensional Logic and the Metaphysics of Intentionality. Cambridge, MA: Bradford B ookslMIT Press. .

Chapter 9

The Concept Horse .Harold W. Noonan

According to the traditional distinction, particulars are those things of which other things can be predicated, but which cannot be predicated of other things ; universals are those things which can be predicated of other things and can also be the subj ects of predication. Thus Socrates is a particular, because we can predicate various things of S ocrates but cannot predicate Socrates of anything else, whereas wisdom is a universal because we can both say things of wisdom (e.g. that it is a characteristic rarely possessed by the young) and ascribe wisdom to other things (e.g. by saying that wisdom is a property of S ocrates, or equivalently, just by saying that S ocrates is wise). The acknowledgement of universals in this sense can seem inevitable. For if it is insisted, for example, that wisdom can only occur as predicate, not as subject, then in the very act of insisting on this, it seems, one makes wisdom a subject of predication. Nevertheless, in Frege 's mature ontology there is no place for universals . His fundamental ontological divide is between obj ects , the referents of singular terms (in his terminology 'proper names ' ) and functions , the referents of function names. Within the category of obj ects he recognizes a distinction between those which are actual, that is, possess causal powers, and those which are non-actual. Planets, for example, are actual obj ects ; numbers , he argues, are non-actual obj ects . Within the category of functions he recognizes the special case of concepts, the referents of predicates ; which are fllli cticin's whose valu:e8 are truth-values . Ccincepts-"al:e essentially predicative: they cannot be referred to using singular terms . Thus, while there may be such a non-actual obj ect as wisdom, it is not what is predicated of S ocrates in the statement ' Socrates is wise' , and the concept which is the referent of the predicate cannot be made a subject of predication, not even by employing such a singular term as 'the concept wisdom' . Of course, this leads to paradox, since in saying that the concept which is the reference of the predicate 'is wise' cannot be made the subj ect of predication one apparently makes it the subject of predication. Frege is vividly aware of this apparent paradox and discusses it using the famous example of the concept horse, which he stoutly maintained is not a concept, but an obj ect. It is this paradox, and the background in Frege's thought which makes his opposition to the traditional distinction between universals and particulars intelligible, that is the subj ect of this paper. In the first part I give an exposition of Frege's functional theory of predication and a diagnosis of his troubles with the concept horse. In this part of the chapter I follow and elaborate on the writings of Michael Dummett ( 1 973) and, particularly,

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Peter Geach (Anscombe and Geach, 1 96 1 ; Geach, 1 976) . According to this account Frege is right when he says that the distinction between first-level and second-level functions (and so between obj ects, as arguments of first-level functions and concepts, as arguments of second-level functions) 'is founded deep in the nature of thing s ' ( 1 969, p . 4 1 ) , and the paradox o f the concept horse is unavoidable, for ' there are logical category distinctions which will clearly show themselves in a well-constructed formalized language, but cannot properly be expressed in language ' (Geach, 1 97 6 , p . 5 5 ) . Thus Wittgenstein' s saying/showing distinction is the proper development of Frege' s insight. Opposition to this view is expressed in an important recent paper by Crispin Wright (Wright, 1 9 9 8 ) , who suggests both that the paradox of the concept horse is a mere muddle and that the distinction between obj ects and concepts, far from being founded deep in the nature of things , does not exist at all: concepts are objects too . If Wright is correct, the traditional concept of a universal can be retained. In the second part of the chapter I explain and criticize Wright's reasoning. There is, I acknowledge, an important insight in Wright's paper, which does indeed necessitate some restatement of my favoured (Geachian) position, but it does not justify Wright's rej ection of the categorial divide between obj ects and concepts , and provides no alternative to the view that Frege and Wittgenstein are right to acknowledge that which cannot be said, but only shown. My conclusion, therefore, will be that Wright is wrong and that Frege is right to reject the traditional distinction between particulars and universals.

I

In a fragment of August 1 906 ( 1 979, p. 1 84) entitled 'What may I regard as the result of my work?' Frege wrote: It is . almost all tied up with the concept-script, a concept constmed 'IS a function, a relation as a function of two arguments. The extension of a concept or class is not the primary thing for me. Unsaturatedness both in the case of concepts and functions. The true nature of concepts and functions recognised.

These ideas form the backbone of Frege's 1 8 9 1 essay 'Function and Concept' (in 1 96 9 , pp. 2 1 -4 1 ) , which is complemented by his 1 904 essay 'What is a function? (in 1 969, pp. 1 07-1 6 ) . The problem of the concept horse, which they force him to confront, is discussed in his reply to B enno Kerry ' On Concept and Obj ect' ( 1 969, pp . 42-55). But already, in 'Conceptual Notation' , the notion of a function was central to Frege 's thought, his fundamental insight being the replacement of the distinction between subj ect and predicate with that between argument and function, and it is with this earlier discussion we should begin. Frege's starting point is the mathematical notion of a function, but we can approach his position most easily by considering his view of how arithmetical expressions are structured. In ' 2+3 ' we can recognize two types of expression: numerals ( ' 2 ' and ' 3 ' ) and a symbol for a mathematical operation ( ' + ' ) . The complex symbol '2+3 ' results from combining expressions of

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these two types in the appropriate way. Using other numerals and the same operator symbol we can construct other complex symbols, such as ' 3 +7 ' , and using the same numerals and other
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always a pattern they exhibit. The signs '+' , ' -<- ' , ' x ' and '-' are thus not themselves symbols for functions, but rather auxiliary means for constructing expressions which exhibit the patterns which do symbolize the functions in question. In some cases, in fact, no such auxiliary expressions are so much as present. Thus we can recognize '23' , 4 7 ' 5 1 6 ' and ' 5 5 ' as designations of the values of a certain two­ argument function (the function x raised to the power y) though there is no quotable bit of language in common to signify the function, and we can also recognize ' 5 5 ' , '77 ' , ' 1 6 J 6 > and s o on as designations of the values of a different (one-argument) function though there is no distinct quotable bit of language signifying it; and of course, we recognize that ' 5 5 ' is a designation which symbolizes a value of both of these functions, although there are not two quotable bits of language present which symbolize them. With this account of Frege's understanding of the notion of a function we can now go on to see how he extends it beyond its mathematical application. And the first point to notice is that just as we can regard what ' 2+3 ' symbolizes as the value of a function for a particular argument, so we can regard the expression '2+3 ' itself as the value of a function for certain arguments . Comparing '2+3 ' with ' 3 +4' , '7+4' , ' 3 3 +6 1 ' and ' 9 8 +2 ' , we can recognize it as the value of a function which takes a pair of numerals as arguments and yields complex arithmetical symbols as values . And, just as in '2+3 ' , ' 2 ' symbolizes 2 and ' 3 ' symbolizes 3, it seems right to say that it is this linguistic function that symbolizes in language the arithmetical function addition: we mention the arithmetical function by writing down some value or other of the linguistic function (compare Anscombe and Geach, 1 9 6 1 , pp. 1 43ff. ) . Earlier we mentioned the symbol for the arithmetical function being a linguistic pattern; the notion of a linguistic function seems an illuminating explication of this notion.2 The importance of the notion of a linguistic function is that it is linguistic functions Frege has predominantly in mind in the section of Conceptual Notation in which he introduces the notion of a function. '

' ,

His principal exampie-i,s ,the sentenc-e :

Hydrogen is lighter than carbon dioxide. If we replace the symbol for hydrogen with a symbol for oxygen or nitrogen we obtain two new sentences : Oxygen is lighter than carbon dioxide. Nitrogen is lighter than carbon dioxide. Comparing these three sentences, we can regard them as values for the arguments 'Hydrogen' , ' Oxygen' and 'Nitrogen' , respectively, of the linguistic function which maps a singUlar term onto the result of writing that singUlar term followed by 'is lighter than carbon dioxide ' , just as we can regard '2+3 ' as a value for the argument ' 2 ' of the function which maps a numeral onto the result of writing that numeral followed by ' + ' followed by ' 3 ' . Frege now introduces a second example, the sentence ' Cato killed Cato ' . He points out that this sentence can be analysed as : argument ' Cato ' , function 'killed

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Cato ' ; o r as : argument 'Cato ' , function 'Cato killed ' ; or, i f w e think o f ' Cato ' as replaceable at both occurrences, as : argument 'Cato ' , function 'killing oneself' . The example is analogous, of course, to the arithmetical example ' 3+3 ' introduced previously. That Frege. introduces the 'Cato ' example here makes it unmistakably clear, and despite his frequent references in the section to the function as the ' component' or 'part' of the expression which remains invariant, that he himself ' recognizes that the 'functions ' he is concerned with, though linguistic items, cannot be identified with quotable parts of sentences, but must be regarded. as patterns occurring in them. In 'Function and Concept' Frege extends the notion of a function beyond the linguistic level, insists on a sharp distinction between functional sign and function, and identifies the concepts spoken of in Foundations with a special kind of function - 'concept words ' thus being classified as a special type of functional sign. The incompleteness, unsaturatedness, or essentially predicative nature of concepts, which marks them off as fundamentally different from obj ects, now comes to be seen as a special case of the unsaturatedness of function s , which corresponds to an unsaturatedness in functional signs . As Frege puts it in 'What is a Function? ' : 'the sign for a function is "unsaturated" ; it needs to be completed with a numeral . . . The peculiarity of functional signs, which we here call "unsaturatedness" , naturally has something answering to it in the functions themselves ' ( 1 969, pp. 1 1 3- 1 5 ) . 'Function and Concept' begins with a n analysis o f the mathematician ' s notion of a function. Frege's first point is that a distinction must be drawn between a function and its name. A mathematitian of his time would probably have answered the question 'What is a function ? ' by saying: 'A function of x is a mathematical expression containing x, a formula containing the letter x' . According to this proposal the expression '2·x3+x' would be a function of x, and the expression ' 2 . 23+2' would be a function of 2 . But, Frege says, this confuses sign and thing signified, form and content. The distinction is clear if we consider the latter expression: '2 . 23+2 ' is a complex fu'ithmetical designation which stands for the same thing as ' 1 8 '. or: ' 3 · 6 ' : 'What is expressed in the equation "2.23+2= 1 8" is that the right hand complex of signs has the same reference as the left hand one ' ( 1 969, p. 72). But if ' 2 . 23+2 ' and ' 1 8 ' stand for the same thing , this thing cannot be identified with either expression. It is now tempting to say that the function is the reference of the mathematical expression. But this will not do either. If the function were really the reference of a mathematical expression, it would just be a number, and nothing new would have been gained for arithmetic by speaking of functions . It is natural to respond here by saying that the mathematical expressions which stand for functions are ones in which a number is indicated indefinitely by a letter, for example '2·x3+x ' . But this, Frege says, makes no difference. For whatever x is, 2·x3+x is just a number; the only difference between '2·x3+x ' and '2 . 33+3 ' is that the latter indicates a number definitely, the former indefinitely. Nevertheless , Frege thinks, it is only by attending to the notation in which 'x' is . used to indicate a number indefinitely that we can achieve a correct conception of the function. In

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people call x the argument of the function and recognize the same function: again in 2 · 1 3+ 1 2 -43+4 2 . 53+5 with different arguments, that is, 1 , 4 and 5 . Thus i t i s the common element o f these expressions that i s the sign for the function. This common element is what is left over if we remove the designation of the argument. We could write this as

But then we would have to indicate that the brackets must be filled with the same, numeral each time to designate a value of the function. We might think that we could designate the function by '2 ·x3+x ' or again, using Greek letters , as Frege later recommends, by '2· � 3+� ' . But a letter so used serves only to indicate where the argument sign is to be inserted and is in any case to be used only in the exceptional case in which we wish to symbolize the function in isolation (1 969, p. 1 14) ; the function is already designated in '2 . 33+3 ' along with its argument. In his 'Logic and Mathematics' of 1 9 1 4 Frege makes this absolutely clear: when we say 'the function 1 +�-�' , the letter '�' is not part of the function sign; for the proper name ' 1 +3-3 ' is composed of the function name and the proper name ' 3 ' , and the letter '�' does not occur in it at all. . . . the role of the '�' is to enable us to recognise where the supplementing proper name is to be put. ' " If I write '�-I; ' , I indicate, by using the letter '�' in both places, that the same proper name is to be put in both places, and s o what I have is the name of a function of only one argument. When I call this the ' name of a function' , this is to be taken cum grana salis. The proper name which we obtain by supplementing this function with a proper name, e:g. ' '3-':'3 ' , does no (c onfain the letter ' � ' , although it contains the function name in question. This '�' is therefore not a constituent of the function name but only enables us to recognise how the function sign is combined with the proper name supplementing it. This '�' gives us a pointer for how to use the function name. ( 1 979, pp. 239-40)

These considerations were already reviewed in the discussion of Frege 's notion of a function in Conceptual Notation. There we saw that we had to recognize that the sign for the function in such an expression as ' 2 . 3 3+3 ' had to be seen to be the common pattern it shares with '2 -43+4' , ' 2 . 53+5 ' and so on. In Conceptual Notation Frege shows himself to be aware of this by his use of the example 'Cato killed Cato ' . In 'Function and Concept' his example is carefully chosen to make the point unmistakably clear.3 The fact that signs for functions are patterns rather than quotable parts of ' expressions is what Frege means by calling them 'unsaturated' or 'incomplete ' . We s aw that such unsaturated signs, themselves called 'functions ' in Conceptual Notation, could indeed be regarded as a type of linguistic function (whether or not Frege himself recognized such patterns as functions). In 'Function and Concept' he

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does not call them 'functions ' , but h e does insist that the essence o f the function itself is unsaturatedness . In 'What is a function?' he makes it clear that this unsaturatedness of the function is to be explained in terms of the unsaturatedness of its sign. Functions are those entities which can be designated only by patterns exhibited in complex expressions . The function 2 ·x3+x is thus not designated by '2· 3+ " nor by ' 2 . 33+3 ' nor indeed by '2·x3+x' . For although these expressions exhibit the pattern which designates the function, none is that pattern. Thus any attempt to say of the function that it is a function, by attaching the predicate 'is a function' to a name, must fail. For any completion would have to employ a quotable expression. But no quotable expression can name a function. Thus, there is a paradox here. It is, of course, the general form of the paradox of the concept horse , so we must now tum to ' On Concept and Object' . Frege ends 'Function and Concept' insisting that the difference between fIrst­ level and second-level functions 'is not made arbitrarily, but founded deep in the nature of things ' ( 1 969, p. 4 1 ) . It is, of course , founded as deep as the difference between objects (the arguments of fIrst-level functions) and fIrst-level functions (the arguments of second-level functions) itself. And how deep that is it is the aim of ' On Concept and Obj ect' to explore. ' On Concept and Obj ect' was written by Frege in response to B enno Kerry's criticisms . Kerry had claimed, against Frege, that the distinction between concept and object was not absolute, that some entities were both concepts and obj ects . Frege emphatically denies this, arguing fIrst that we must recognize a distinction between what can occur only as an object, and everything else, and second that, in fact, nothing could be both a concept and an object. Frege argues for the fIrst, weaker, claim by appealing to an analogy Kerry uses. Kerry had said that there was no more difficulty in the idea of an entity being simultaneously an obj ect and a concept than there was in the idea of a man being both a father and a son. Frege retorts : Let us fasten on this simile. If there were, or had been, things that were fathers bu t could not be sons, such beings would obviously be quite different in kind from men who are sons. Now it is something like this that happens here. ( 1 969, p. 43)

The reason, Frege explains , is that the concept is predicative; in fact, it is the reference of a grammatical predicate. But a name of an obj ect is quite incapable of being used as a grammatical predicate. Apparent counter-examples are identity statements, in which the ' is ' is not the 'is' of predication, but has the sense of the relational expression 'is no other than' . Thus the proper name is not the whole predicate but merely part of it. In 'The Morning Star is Venus ' , for example, the predicate is not 'Venus' but ' is Venus ' , and what is predicated is not the object Venus but the concept is no other than Venus. Although this concept is one under which only one obj ect can possibly fall, it is nevertheless still distinct from the obj ect falling under it, that is, the planet Venus, and this obj ect can only ever occur as an object, never as a concept. The distinction Frege malces here between the 'is ' of identity and the 'is ' of predication is a familiar one and widely accepted, and so far, as Frege notes, what he has argued is not particularly radical. It is part of the traditional doctrine of

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universals, as we have noted, that as well as universals, which can occur' both as subj ects and as predicates, there are also entities, particulars, which can occur only as subj ect, never as predicate. However, Frege now goes further and denies that anything c an be both a concept and an obj ect. Immediately he runs headlong into the paradox of the concept horse: Kerry . . . gives the following example: 'the concept "horse" is a concept easily attained' , and thinks that the concept ' horse ' is an object, in fact one of the obj ects that fall under the concept ' concept easily attained' . Quite so; the three words ' the concept "horse'" do designate an object, but on that very account they do not designate a concept, as I am using the word. This is in full accord with the criterion I gave - that the singular definite article always indicates an object, whereas the indefinite article accompanies a concept­ word. ( 1 969, p. 45)

Despite the paradox, Frege defends the linguistic criterion of differentiation here indicated. As regards the indefinite article, he s ays, there are probably no exceptions to the rule except an obsolete formula for a councillor ( 'ein edler Rath ' ) . In the case of the definite article, he says, the only possible exceptions are cases in which the definite article precedes a singular noun standing in the place of a pluraL Thus Frege continues to insist on the absolute distinction between c oncept and object, recognizing only ' an awkwardness of language' if we say that the concept horse is not a concept. 'The concept horse ' , he here asserts, is a perfectly good proper name, but just for this reason: what it stands for is not a concept but an obj ect. What obj ect is suggested, rather coyly, in the following passage: If we keep it in mind that in my way of speaking expressions like ' the concept F' designate not concepts but obj ects, most of Kerry' s obj ections already collapse. If he thinks . . . that I have identified concept and extension of concept, he is mistaken, I merely expressed my view that in the expression 'the number that applies to the concept F is the extension of the concept like numbered to the concept F' the words ' extension of the concept' could be replaced by 'concept' . Notice carefully that hefe the WOLd ' concept' is combined with the definite article. ( 1 969, p. 48)

Extensions of concepts are objects, and thus not concepts, but if we form a phrase of the form 'the concept F ' , employing the definite article, the result is a proper name, a name of an object, and the obj ect thus named is the very one named by the phrase 'the extension of the concept F ' . And it is this object that is unintentionally spoken of when we aim to speak of the concept F. Thus as Frege puts it: I admit that there is a quite peculiar obstacle in the way of an understanding with my reader. By a kind of necessity of language, my expressions, taken literally, sometimes miss my thought: I mention an object, when what I intend is a concept. I fully realize that in such cases I was relying upon a reader who would be ready to meet me halfway ­ who does not begrudge a pinch of s alt. ( 1 969, p. 54)

Until this point in ' On Concept and Obj ect' , it must be said, Frege 's insistence on accepting whatever consequences of the absolute divide between c oncept and object may be deduced - the paradox of the concept horse, the unavoidable

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' awkwardness' o f language, the predicament i t is i n whereby ' our expressions taken literally ' must sometimes ' miss our thoughts ' - seems more like a stubborn dogmatism than anything else. But, at last, at the end of the article Frege reveals what lies behind his in�istence : not all the parts o f a thought can be complete; a t least one must be unsaturated; or predicative, otherwise they could not hold together. For example, the sense of the phrase 'the number 2' does not hold together with that of the phrase 'the concept p rime number' without a link. We apply such a link in the sentence 'the number 2 falls under the concept prime number' ; it is contained in the words 'falls under' , which need to be completed in two ways - by a subj ect and an accusative, and only because this sense is thus 'unsaturated' are they capable of serving as a lillie Only when they have been supplemented in this two-fold respect do we get a complete sense, a thought. I say that such words or phrases stand for a relation. We now get the same difficulty for the relation that we were trying to avoid for the concept. For the words 'the relation of an object to the concept it falls under' designate not a relation but an obj ect; and the three proper names ' the number 2 ' , 'the concept prime number' , 'the relation of an object to a concept it falls under' , hold aloof from one another just as much as the first two do by themselves ; however we put them together, we get no sentence. It is thus easy for us to see that the difficulty arising from the 'unsaturatedness ' of one part of a thought can indeed be shifted but not avoided. ' Complete ' and 'unsaturated' are, of course, only figures of speech, but all I wish or am able to do here is give hints . ( 1 969, p. 55)

The problem here identified is the traditional one of the unity of the proposition: what distinguishes a proposition, a sentence which expresses a thought, from a mere list of names? Frege's solution is that a sentence, unlike a list of names, exhibits patterns, which themselves have to be understood as having semantic values. Thus the sentence 'the number 2 is prime ' exhibits the pattern 'x is prime' , the pattern exhibited by any sentence consisting of a proper name followed by the words 'is prime ' . And it is this pattern which is the name of the concept prime, for it is only by recognizing a sentence . as exhibiting it that we recognize it as a predication of the concept p rime of an obj ect. But, n o w, we cannotreplace this pattern by the expression 'the concept p rime ' or any quotable part of a sentence. It simply makes no sense to speak of replacing a pattern exhibited by a sentence by a quotable part of a sentence. (We can replace the pattern by another, that is, rearrange the parts, or preserving the p attern, replace some or all of the parts by other parts, but that is all.) A fortiori we cannot make such a replacement salva veritate. But it has no significance to speak of two expressions as having the same reference unless one can be substituted for the other salva veritate. Thus we cannot think of 'the concept prime ' , or any other quotable expression, as another (saturated) name of what is also named by the predicate 'x is prime' . We might wish to insist that what is expressed in ordinary language by 'the number 2 is prime' is somehow more perspicuously expressed by 'the number 2 falls under the concept prime number' But again, to recognize that as s aying of the pair of objects, the number 2 and the concept prime number, that they are related by the relation falling under we have to recognize that sentence as exhibiting the pattern 'x falls under y ' , that is, the pattern exhibited by any sentence consisting of a proper name followed by the words 'falls under' followed by a second proper .

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Universals, Concepts and Qualities

name. And now we have to recognize that this pattern is not replaceable, d fortiori is not replaceable salva veritate, by ' the relation faIling under' or any quotable part of a sentence. The problem of the unity of the proposition is paralleled by (and for Frege is a special case of) the problem of the unity of the complex name. This explains the earlier explanatory footnote: What I call here the predicative nature of the concept is just a special case of the need of supplementation, the 'unsaturatednes s ' that I gave as the essential feature of a function in my work Funktion und Begriff. It was then scarcely possible to avoid the expression 'the function f(x) ' , although here too the difficulty arose that what this expression stands for is not a function. ( 1 969, p. 47)

And Frege returns to the point in the final paragraph in ' On Concept and Obj ect' : It may make it easier to come to an understanding . if the reader compares my work Funktion und Begriff. For over the question what it is that is called a function in Analysis, we come up against the same obstacle; and on thorough investigation it will be found that the obstacle is essential, and founded on the nature of our language ; that we cannot avoid a certain inappropriateness of linguistic expression; and there is nothing for it but to realize this and always take it into account. ( 1 969, p. 55)

To see how general the problem is that Frege is concerned with let us consider again the example from ' Function and Concept' : the function 2 ·x3+x. S ince we recognize 2 · P+ 1 2 -43+4 2 . 5 3+5 as three complex names designat.ing .the values . of this function for the argument-s, 1 , 4 and 5 respectively, we must recognize as the function name the common element of these expressions , that is , what is present in 2·x3+x over and above the letter ' x ' , and this, of course, is the common pattern they exhibit. Thus neither ' 2 ·x3+x ' , nor ' the function 2·x3+x ' , nor any quotable bit of language can be recognized as the name of the function, for no such quotable bit of language c an be substituted for the pattern which is the function name and a fortiori no such quotable bit of language can be substituted for the function name leaving the reference of the whole unchanged (as identity of reference requires) . But now we can go further. 'The reference of the function-name "2·x3+x'" is itself a quotable bit of language and thus cannot have the same reference as the unsaturated function name we recognize in these complex names . If it has any reference at all, its reference must be an object, not a function. The same is true, mutatis mutandis, of ' the reference of the predicate "x is a horse" ' . These consequences follow from taking seriously the idea that function-names generally and predicates, in particular, are unsaturated expressions . But if we now try to take account of the fact that it is such unsaturated expressions which refer to functions and concepts, again we must fail: the descriptions ' the reference of the function-

165

The Concept Horse

name which i s the pattern exhibited i n "2·x3+x'" and 'the reference of the predicate which is the pattern exhibited in "x is a horse'" are themselves quotable bits of language and thus can only refer to obj ects if to anything. Frege's 'paradox of t):1e concept horse' is thus not easily dismissed. After 'Function and Concept' Frege came to think that it was a mistake to say that such expressions as 'the concept horse' , and 'the function 2·x3+x' had as their references obj ects which intruded whenever we wished to speak of the functions in question; rather such expressions, and indeed the expressions 'concept' and 'function' themselves, are defective: 'the concept horse' would have to stand for a concept if it stood for anything; since it cannot, it stands for nothing. The predicates 'is a concept' and 'is a function' , which are constrained by grammar to be first-level predicates, can similarly only be understood as standing for self-contradictory concepts ( 1 979, pp. 1 77-8). Nevertheless, Frege insists, the distinction between saturated and unsaturatedness remains, and with it the unbridgeable gap between objects and functions . The conclusion we are driven to, Geach explains (Geach, 1 976) is that what Frege requires is the distinction made by Wittgenstein in the Tractatus Logico­ Philosophicus ( 1 9 6 1 ) between what can be said, and what c an only be shown. We can recognize as perfectly legitimate the first-level predicate 'x is an object' . Using this we can say of any object that it is an obj ect using a proposition of the form: x

is an obj ect

in which 'x' is replaced by a proper name. Similarly we can recognize as perfectly legitimate the second-level predicate expressible most conveniently in modem logical symbolism as : ' (\fx)(3y)f(x)=y' , which is true of all and only first-level one-argument functions (given Frege 's thesis that a function must be defined for all arguments) . Using this second-level predicate we can say, for example, of the function 2x3+x that it is a fIrst-level function: (\fx) (3y) (2x3+x=y)

, '. �

Again we can recognize as perfectly legitimate the second-level function expressible , as ' (\fx)(f(x)=the True or f(x)=the False) true of all and only first-level concepts . Thus we can say, of the concept horse, for example, that it is a c oncept: (\fx)(x is a horse=the True or x is a horse=the False) We can proceed similarly to construct ways of saying all that can be legitimately meant by saying that a particular second-level function is a second-level function, or that a particular first-level relation is a first-level relation and so on. But what we cannot do is to construct any legitimate way of saying that a particular object is not a first-level function, or that a particular first-level function is not an object - and so on. ' (\fx)(3y)(2x3+X=Y) ' says, in the only way that it can be legitimately said, that the function 2x3+x is a function. '-,(\fx)(3y)(2x3+x=y) ' says, falsely, that the function 2·x3+x is not a function. To say that Socrates, say, is not a function we

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166

must substitute a proper name of S ocrates for the first-level function name occuning in '-.('y1x)(:3y) (2X3+X=Y)' whereby we speak of the function 2X3+X• But since the function name is unsaturated and any name of S ocrates saturated, such a substitution is impossible - that is, there is nothing which could count as such a substitution. S o w e cannot say, truly, o f S ocrates that h e i s not a function. Mutatis mutandis w e cannot say, truly, o f the function 2x3+x that i t i s not an obj ect, for t o d o so w e would have t o substitute a name o f the function for the name o f S ocrates i n the false proposition 'S ocrates is not an obj ect' , but this would be the impossible substitution of an unsaturated expression for a saturated expression. Nevertheless , though we cannot say that Socrates is not a function and that the function 2x3+x is not an object, we can recognize that these things are so, and that they are so is something that, to quote Geach's use of Wittgenstein's language again, 'shows forth, and grasp of which will be manifested by proper use of a well­ constructed formalized language such as that of the Begriffsschrift' (Geach, 1 97 6 , p. 5 5 ) .

II

In the preceding, I hope, all I have been doing is expounding a view of the paradox of the concept horse due to Geach, albeit more explicitly and long-windedly than he does himself. But now I must confront the fundamental obj ection to this view made by Crispin Wright, who emerges as a latter-day B enno Kerry. Wright begins by asking : 'What form should be assumed by a semantics of predication? In particular, should a distinguished category of entity be associated with predication, as objects (or particulars) are associated with the use of singUlar terms ? ' He lists three possible responses : 1 . Yes , predicates stand for concepts , as singular terms stand for obj ects . Yes, but the .relation between a predicate and Jb.e. associated .entity is not · that which obtains between a singular term and its referent but is sui generis. 3 . No. 2.

.

.

He notes that Frege's response, as usually interpreted anyway (and therefore, I must add, the response so far outlined in this chapter) is a version of response 1 , but he himself endorses response 2 and goes on further to propose that the very entities to which predicates are related by the sui generis relation mentioned in 2 may also be the referents of singular terms , for example that that to which the predicate 'is a horse ' stands in the sui generis relation mentioned in 2 may also be, in fact, he thinks , is, the very entity which ' the concept horse' has as referent - so concepts are obj ects too. In the following I argue that Wright is correct to think that any form of response 1 is untenable, and so that some refashioning of the Geach-inspired account given so far is needed, but that Wright himself goes too far in positively denying the categorial divide between concepts and obj ects.4 Wright' s criticism of response 1, on wholly Fregean grounds, is entirely convin­ cing. The relation between a predicate and the concept associated with it, its

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semantic value (or in general, between a function name and its semantic value) , cannot, given standard Fregean doctrine, be the relation o f reference, that i s , that ' relation ,which holds between a singular term and the obj ect it stands for, since that is a relation between two objects, whereas the relation between function name and function is not. On the view I have been expounding it is a relation between two functions (since the pattern which is the function name is itself a function) . But even if one does not share that view (as Wright does not) either because cine thinks that the function-name is not a pattern at all or because one thinks that such patterns are objects, it is clearly not a relation between two obj ects but at best an unequal-level relation between an object (the function-name) and function (henceforth I shall go along with Wright's view that function-names are obj ects since it will make no difference to my criticisms) . Consequently it simply c annot be asked whether the predicate 'is a horse ' refers to the same thing as ' the concept horse' (or the singular term ' the reference of the predicate "is a horse" ' ) . Whether or not predicates are themselves objects, they cannot stand in the relation of reference (that first-level relation which relates singular terms and obj ects) to the concepts that are their semantic values . It follows that we cannot argue, for example, that ' the concept horse' and the predicate 'is a horse' have different referents because they are not substitutable salva veritate or even salva congruitate. The Reference Principle, as Wright calls it, that co-referential expres sions are substitutable salva veritate or at least congruitate, cannot yield this conclusion since it can only be applied to expressions which have reference. Nor, of course, can one argue by appeal to the Reference Principle that that to which 'is a horse' stands in the (in my view second-level and on Wright's view unequal-level) relation which any predicate stands to the concept with which it is associated is other than that to which 'the concept horse ' stands in the relation of reference. If we call that possibly second-level and at least unequal­ level relation ' ascription ' , then the point is that we cannot use the Reference Principle to argue that 'is a horse' and 'the concept horse ' have different referents , and neither. can· we use it to argue that what 'is a horse ' ascribes is different, from what ' the concept horse' refers to. All of this, I think, is undeniably correct, and it necessitates some adjustment to the Geach-inspired account of Frege given so far. But not much. For, of course, it could anyway n�ver have been a part of that account that the referent of 'is a horse' was distinct from the referent of ' the concept horse ' . That non-identity could have been no more something sayable (and therefore no more something inferrable by the Reference Principle from the failure of substitutivity of predicate and singular term) than the difference in category between concept and object. Just as 'X is distinct in category from Y ' can express a thought only if X is not distinct in category from Y, so 'X is distinct from Y ' can express a thought only if X and Y are both objects (for distinctness is j ust non-identity and identity holds only between obj ects). However, Wright now goes further. The Reference Principle, in the traditional formulation of the paradox of the concept horse, was used to infer that predicates and singUlar terms do not co-refer, but since predicates do not refer at all, it is powerless in this role. Furthermore, it cannot put any barrier in the way of the thought that the ascripta of predicates are the referents of certain singular terms, as

168

Universals, Concepts and Qualities

we have seen. And this, Wright goes on to suggest, is not merely something we are not debarred from saying, but is actually the correct thing to say. Concepts are obj ects too, because, for example, there is something which 'is a horse' ascribes which 'the concept horse ' (and 'the ascriptum of "is a horse'" and therefore 'the reference of "the ascriptum of 'is a horse"") refers to. We do not have to appeal to the unsayable in response to Frege 's paradox. There is not an unsayable categorial divide between concepts and objects. In fact, there is not a divide at all. It is at this point I demur. My reason is straightforward. As Wright himself says in his paper ( 1 99 8 , p . 243 ) , an existentially quantified claim can be true only if some instance is true. But the expression ' ascription' was coined to indicate just that unequal-level relation between predicate and concept which is analogous semantically to the first-level relation between singUlar term and referent. It is, in fact, that relation expressed by: ' ' ' . . . '' applies to something if and only if it . . . ' (e.g. 'is a horse' applies to something iff it is a horse) . 5 So if concepts are obj ects, in particular, if the concept horse is an obj ect because it is both the ascriptum of a predicate and the reference of a singular term, it should be possible to s ay so. How? We need: ' ''is a horse" applies to something if and only if it X and "the concept horse" refers to X' to be true for some reading of 'X' . But no such reading is possible, since what must replace the first occurrence of 'X' is a predicate (coextensive with 'is a horse' ) and what must replace the second occurrence of 'X' is a singular term (co-referential with 'the concept horse ' ) . Since no expression is both a singular term and a predicate, no instantiation of the existential claim that Wright needs to be true can be true. We could, of course, stipulate a use for ' ascribes ' parallel to that which Wright envisages for 'refers to ' (note 5), so that '''is a horse" ascribes is a horse' would be well formed. Then what would be required would be the truth of some instance of ' ' 'is a horse" ascribes X and "the concept horse" refers to X ' . B ut again, with this stipulation the instance would involve a dual use of an expression as a predicate and as a singular term. My conclusion , then, j.s that Wright's position is unsustainable. What he wishes to assert to be true in uttering the words ' Concepts are obj ects ' is precisely the thought that, on the Geachian view of Frege's position I endorse, cannot be expressed at all. And, indeed, it cannot be expressed, since if it could be, so could some instance of it (it is an existential claim) . But the expression of any instance would require an expression functioning simultaneously as singular term and predicate. It might be replied that the false step in this argument is the insistence that to say that the concept horse is both the ascriptum of the predicate 'is a horse' and the referent of the singUlar term 'the concept horse' I must employ an expression in a dual role and say something of the form: 'is a horse' applies to something iff it X and 'the concept horse ' refer to X . In fact, I can say that the concept horse i s the ascriptum o f the predicate ' i s a horse' and the referent of the singular term 'the concept horse ' by saying just that. I think that this is an unconvincing reply. If I can say that the concept horse is what 'is a horse' ascribes and what 'the concept horse' refers to in j ust those words , still that cannot be the only way I can say it. The technical vocabulary in this

The Concept Horse

1 69

sentence and, crucially, the syntactically inappropriate verb ' ascribes' we understand only by tracing back through the explanations in Wright's paper, and, in particular, by grasping the equiyalence of ' ''is a horse" ascribes the concept horse' and "'is a horse" is true of some.thing iff it is a horse ' . So it ought to be possible to express that same thought, if it is a genuine one, without employing the technical vocabulary. Otherwise there is a thought I can express (and think) only after reading Wright's paper and only by using a verb in a way that is syntactically inappropriate given the semantic role stipulated for it (for ' ascribes ' is grammatically on a par with 'refers " to' : "'is a horse" ascribes is a horse ' is not well formed, but ' ascribes nevertheless is supposed to indicate the unequal-level relation between a predicate and its semantic value) . But it is not possible to express the thought Wright wishes to assert in any other way. A defender of Wright's position must therefore bite the bullet and insist that the thought in question can indeed only be expressed using the technical vocabulary introduced in the paper (or an equivalent) and can only be expressed using an expression whose syntax does not fit its semantics. 6 This position is unattractive, but there is more to be said. For, of course, it is part and parcel of the Fregean position that there is an obj ect ' associated' (in a sense) with a predicate, namely the extension of the concept associated with the predicate. So there is a first-level relation which each predicate stands in to an obj ect which we could perfectly well express using the verb ' ascribes ' . Let us call this relation ' ascription-E' . Then it will be true that 'is a horse ' ascribes-E the extension of the concept horse (though it does not, of course, refer to it, given the Reference Principle) . It will then be true that: ' is a horse' ascribes-E the extension of the concept horse and 'the extension of the concept horse ' refers to the extension of the concept horse. If, following what Frege suggests in ' On Concept and Obj ect' and in the famous footnote in Grundlagen, we use ' the concept horse' as a singular term whose reference is the extension of the concept horse, we can say: 'is a horse' ascribes-E the concept horse and 'the concept horse ' refers to the concept horse. On· Fregean,prL.'1ciples this is ·a ·perfeetly coherent thought, and a true .one, ·a.lld its expression does not require any mismatch between syntax and semantics . But it is not the thought that Wright intends to express by saying: 'is a horse ' ascribes the concept horse and 'the concept horse ' refers to the concept horse, since that thought is supposed to be inconsistent with the existence of the Fregean divide. However, how are we to know (and how is Wright to know) that when he asserts : 'is a horse' ascribes the concept horse and ' the concept horse ' refers to the concept horse, he is asserting the anti-Fregean thought rather than the unproblematic Fregean thought that ' is a horse' ascribes-E the concept horse and ' the concept horse' refers to the concept horse? How are we to know that ' ascribes' does not mean ' ascribes­ E' ? We grasp Wright's notion of ascription if we grasp the equivalence of "'is a horse" ascribes the concept horse' and ' ' 'is a horse" applies to something iff it is a horse' (and, perhaps also , understand that something falls under the concept horse iff it is a horse and that 'the concept horse' refers to the concept horse) . But 'is a horse' ascribes-E the (extension of the) concept horse just in case 'is a horse' applies to something iff it is a horse (and something falls within the extension of the concept horse iff it is a horse and 'the (extension of the) concept horse' refers to

Universals, Concepts and Qualities

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the (extension of the) concept horse). So Wright's explanation of ascription does not distinguish it from ascription-E, without the crucial additional information that ascription is not a first-level relation between obj ects but an unequal-level relation between an obj ect and a concept, which is no more appropriately expressed by ' ascribes ' , therefore, than it is by 'refers to ' (unless the use of that is extended to render grammatical ' ' 'is a horse" refers to is a horse' , in which case ' refers to ' would no longer speak of a first-level relation). It is therefore essential to our grasp of the anti-Fregean thought Wright thinks that he can express by s aying: 'is a horse ' ascribes the concept horse and 'the concept horse ' refers t o the concept horse, that we can recognize that ' ascribes ' is here being used in a way which involves a mismatch between its syntax and its semantics. I see no reason to think that has provided us with the capacity to express such a thought by the explanations in his paper. ? Now I turn t o what seems t o m e another difficulty for Wright' s position - n o doubt related, but distinct. Remember where we are. Wright thinks that Frege' s position is a muddle. There is no (sayable or unsay able) divide between concepts and obj ects ; concepts are objects too since they are b oth the ascripta of predicates and the referents of (certain) singular terms. However, not all obj ects are concepts, there are also objects which are not concepts - individuals - which are available only for reference.8 It seems to me that if Wright's argument against the Fregean divide is good, an exactly parallel argument can be used against the existence of individuals. Recall the crucial steps in Wright's introduction of the notion of ascription. We are told or assumed to know :

1.

x falls under the concept horse iff x is a horse .

We ar e also told that: 2.

'is

a · horse.'

ascribes the concept horsG

is equivalent to : 3.

'is a horse' i s true o f something iff it is a horse ,

and that i t i s stipulatively true that: 4.

'the concept horse' refers to the concept horse.

All this puts us in a position to understand: "'is a horse" ascribes the concept horse and " the concept horse" refers to the concept horse' , whence we can infer: 'there is something that "is a horse" ascribes and "the concept horse" refers to that same thing (for some x, "is a horse" ascribes x and "the concept horse" refers to x) ' . And this is supposed to justify the conclusion that the semantic value of 'is a horse' is both a concept and an object. Consider now the following parallel explanation of what I will call manifestation. First:

The Concept Horse . 1*

.

X

171

is socratic iff x=Socrates

Second,. 2* .

' Socrates ' manifests that something is socratic

is equivalent to : 3*.

' Socrates ' refers to Socrates

Third, it is stipulatively true that: 4 * . 'is socratic ' i s true o f something iff i t i s socratic (abbreviated below as: 'is socratic ' expresses is socratic). These explanations put us in a position to understand: ' S ocrate s ' manifests that something is socratic and 'is socratic ' is true of something iff it is s ocratic, whence we can infer: there is something that ' S ocrates ' manifests that something is and 'is socratic ' is true of something iff it is that same thing (for some F, ' Socrates ' manifests that something is F and 'is s ocratic ' is true of something iff it is F). But now, by parallel reasoning to Wright's, we can conclude that the semantic value of 'Socrates ' is both an obj ect and a concept; it is both something a name manifests that something is and a predicate expresses . Generalizing, there are no individuals. r submit that this is unconvincing. Manifestation, as r have introduced it, is a perfectly good notion and 'is socratic ' is a perfectly good predicate, s o : "'Socrates" manifests that something is socratic and "is socratic" is true of something iff it is socratic' makes perfect sense, and says something true, namely : "'Socrates" refers to Socrates and "is socratic" is true of something iff it is socratic ' . B ut the truth of . this is -not inconsistent with the.Fmg€all and Wrightian view that the semantic value of ' Socrates ' is an obj ect that is not a concept. Generalizing, nothing that could emerge from the above explanation of manifestation could be inconsistent with the existence of objects that are not concepts . Mutatis mutandis, ' ' 'is a horse" ascribes the concept horse and "the concept horse" refers to the concept horse' makes perfect sense, and says something true, namely: "'is a horse" is true of something iff it is a horse and "the concept horse" refers to the concept horse ' . B ut the truth of this is not inconsistent with the Fregean view that the semantic value of the predicate is a concept that is not an obj ect. Generalizing, nothing that could emerge from Wright's explanation of ascription could be inconsistent with the Fregean divide. r conclude that Wright has given us no reason to deny that the division between concept and obj ect is founded deep in the nature of things . But, of course, we must understand that this is not to say that it is grounded on something other than the nature of language ; rather, it is precisely because the distinction between saturated and unsaturated expressions is the necessary origin of our grasp of the distinction between objects and functions that the Fregean paradox is unavoidable.

1 72

Universals, Concepts and Qualities

Notes

2

3

4

5

Objection: 'Aristotle' symbolizes the philosopher Aristotle in the true statement 'Aristotle was a philosopher' but not in the true statement 'Aristotle married a president' s widow ' , in which it also occurs , so this form of argument is invalid. Reply: this is so only when the quotable expression in question is ambiguous, but '+' is unambiguous: the explanation of '+' as the symbol for addition suffices to fix the meaning and reference both of '2+7 ' and ' 3 +3 ' . There is, however, a step from the premiss that symbols for functions are patterns to the conclusion that they are themselves functions and a further step to the conclusion that they are linguistic functions as just characterized (whose values are linguistic items), rather than, say, functions mapping complex mathematical expressions onto truth values - what Frege later calls concepts (both these possibilities are noted by Geach, 1 976). There seems to be no room in Frege' s ontology for any other location for patterns than within the category of functions, but despite his terminology in his earlier work (commented on in the next few paragraphs), after he distinguished function name and function Frege never explicitly stated that function names were functions, and in one place (in a letter to Russell) explicitly says that they are objects. This interpretative issue can, however, be put aside for the rest of this chapter. That function names and predicates in English are patterns rather than quotable bits of language is not obvious. B ut languages are possible, which are fully intertranslatable with English, in which it is obvious (see Appendix). That (a) function names in English can be regarded as patterns and (b) function names in fully intertranslatable languages must be regarded as patterns provides additional reason for the conclusion that function names in English are patterns. In fact, it is unclear what additional content, over and above (a) and (b), this conclusion has . Given (a) and (b), what would it be for English function names not to be patterns? Although Geach discusses and dismisses a view that sounds like Wright's ( 1 976), that is, that the difference between proper names and predicates is in their modes of significance, he is chiefly concerned to argue that this cannot be the only difference because proper names are quotable bits of language and predicates are not. This is essentially the position argued for below. And, of course, we could express it using 'refers to' , for we Gould (Wright, 1 998, p. 256) 'stipulate that "refers to" should have a use linking the name of a predicate to an expression, par excellence, the predicate itself, for its semantic value' . In that case, '''is a horse refers to is a horse" . . . would be well-formed, but - just for that reason - "refers to", so used, would not speak of the relation that holds between a singular term and the object for which it stands ' . Instead, it would spealc of the unequal-level relati on between a predicate and its semantic value, that is, the relation of ascription. Note though that the language used in this note, employed in the quotation from Wright, brings back the paradox. For if a predicate is an expression for its semantic value, for example if 'is a horse' is an expression for its semantic value, it is an expression for the semantic value of the predicate it is, for example 'is a horse' is an expression for the semantic value of 'is a horse' . But 'the semantic value of "is a horse'" is a singular term. So it has reference .. B ut the reference of a singular term is its semantic value. So the semantic value of 'is a horse' is an object, which is the semantic value of 'the semantic value of "is a horse"' . However, if two expressions have the same semantic value they must be intersubstitutable salva congruitate in all contexts (call this 'the Semantic Value Principle' ) . But the predicate 'is a horse' and the singular term 'the semantic value of "is a horse'" are not so intersubstitutable. The moral is that to take the full measure of the paradox we must recognize not merely that predicates do not have reference, but that no relation which a singUlar term stands in to an

The Concept Horse

6

7

8

173

obj ect is one in which a predicate can stand in to a concept. Since singular terms refer to, have as their semantic values and are associated with obj ects, none of the relations so expressed can relate predicates to concepts. This by itself is enough to show that Wright is wron g to think that he successfully introduced the term ' ascription' by telling us that it designates the relation which holds between a predicate and its associated concept, that is, the concept which is its semantic value. The defender must hold not qnly that the concept expressed by ' ''is a horse"· is true of something iff it is a horse' can be 'carved up in a new way ' and expressed as "'is a horse" ascribes the concept horse ' , but that in this reconceptualization the semantic value of ' ascribes ' is the unequal-level relation which is the semantic value of 'is true of something iff it' in the original. Of course, there is no reason to deny that '''is a horse" ascribes the concept horse' asserts that the relation of ascription (that unequal-level relation which obtains between a predicate and its associated concept) obtains between the predicate 'is a horse ' and the concept horse, nor to deny that that unequal-level relation is the semantic value of an expression occurring in that sentence. Presumably, ' the concept horse' abbreviates something like ' the concept something falls under iff it is a horse' and in "'is a horse" ascribes the concept something falls under iff it is a horse' we can regard (the pattern) 'ascribes the concept which something falls under iff it' as having ascription as its semantic value. We can therefore regard this as the semantic value of ' ascribes the concept' in the abbreviated version of that sentence. But what Wright needs is that it is legitimate to regard ascription as the semantic value of ' ascribes' . To every individual there will correspond a non-individual obj ect, for example corresponding to Socrates will be the ascriptum of the predicate 'is the same man as Socrates ' , but this will be distinct from the individual because it will be both an obj ect and a concept. It is a further question what relation, on Wright's view, will hold between these two objects and what Frege would recognize as the extension of the concept expressed by 'is the same man as Socrates ' , and, indeed, in general what relation will hold between the extensions of concepts and the ascripta of predicates .

References Anscombe, G.E.M. and Geach, P.T. ( 1 9 6 1 ) , Three Philosophers. Oxford: B asil Blackwell. Dummett, M.A.E. ( 1 973), Frege: Philosophy of Language. London: Duckworth; 2nd edn 1981. Frege, G. ( 1 879), Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: I. Nebert, tr. in ( 1 972), pp. 1 0 1 -203 . Frege, G. ( 1 8 84), Die Gntndlagen der Arithmetik, eine logisch mathematische Untersuchung uber den Begriff der Zahl. Breslau : W. Koebner, tr. as ( 1 968), The Foundations of A rithmetic, by J.L. Austin with German text. Oxford: Blackwell. Frege, G. ( 1 962), GrUlJ.dgesetze der Arithmetik. Hildesheim: Olms ; Preface, Introd. and sections 1-52 of Vol. I tr. as ( 1 964) , The Basic Laws of A rithmetic: Exposition of the System, ed. M. Furth. California: University of California Press. Frege, G. ( 1 969), Translations from the Philosophical Writings of Gottlob Frege , eds P. Geach and Max Black. Oxford: Blackwell. Frege, G. ( 1 972), Conceptual Notation and related articles, tr. and ed. with a biog. and introd. by T. Bynum. Oxford: Oxford University Press. Frege, G. ( 1 979), Posthumous Writings, tr. by P. Long and R. White. Oxford: B lackwell. Frege, G. ( 1 980), Philosophical-Mathematical Correspondence, tr. by H. Kaal. Oxford: Blackwell.

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Frege, G. ( 1 9 84), Collected Papers on Mathematics, Logic and Philosophy, ed. McGuinness, tr. M . Black et al . Oxford: Blackwell. Frege, G. ( 1 997), The Frege Reader, ed. M. Beaney. Oxford: Blackwell. Geach, P.T. ( 1 976), ' S aying and Showing in Frege and Wittgenstein' , in K.J.J. Hintikka (ed. ) , Essays on Wittgenstein in Honour of G.H. von Wright, Acta Philosophica Fennica 2 8 . Amsterdam: North-Holland, pp. 54�70. Wright, C. ( 1 998), 'Why Frege does not deserve his grain of salt: a note on the paradox of "the concept horse" and the ascription of B edeutungen to predicates ' , in J.L. B randl and P. S ullivan (eds ) , New Essays on the Philosop hy of Michael Dummett, Grazer Philosophische Studien 55. Vienna: Rodophi, 23 9-6 3 .

Appendix

Consider a fragment of English in which we speak about three people, Tom, Dick and Harry, and ascribe to them the properties of being rich, happy and bald and also the property of being a (Fregean) object. We also say of the properties that they are (Fregean) concepts. We also speak of the relations being taller than and being older than. We make in addition general claims about obj ects and also about properties and relations . We also speak of the names of the objects we speak about and the predicates we employ using quotation-mark names . The language contains the additional predicates 'is a proper name' and 'is a predicate' . It contains the relational expression 'names ' (using which we can say that the name 'Tom' names Tom) and the relational expression 'is true of' (using which we can say that 'is rich' is true of Tom) . The following displays a translation scheme based on S ellars 's ' Iumblese' (to be marketed as 'Iumblese XP' ) in which everything which can be said in this fragment can be written in a language in which predicates are obviously linguistic patterns. Tom = t; Dick = d; Harry = h x is rich = x ( ' x ' written in red) x is happy = x ( 'x ' written in 'green) x is bald = x ( 'x ' written in blue) x is an object = x ( 'x ' written in lavender) x is a proper name = x ( 'x ' written in tan) x is taller than y = Xy (superscript 'x' followed by 'y' ) x is older than y = yX ( ,y' followed b y superscript ' x ' ) (3x) = (3x) (the identity translation) (Vx) = (Vx) (the identity translation) x is a concept = (Cx) x is predicate = (Px) (3F) = (3 D (the left-hand square bracket written in fourteen point) (VF) = (VD (the left-hand square bracket written in fourteen point) (3G) = (3 D (the left-hand square bracket written in sixteen point) (\f G) = (\fD (the left-hand square bracket written in sixteen point) (Other second-level variables for properties can be represented by other point sizes) (3R) = (3 [ D (the left-hand square brackets written two spaces apart) (\fR) = (V[ D (the left-hand brackets written two spaces apart) (3S) = (3 [ D (the left-hand brackets four spaces apart)

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(\;IS) = (\;I [ D (the left-hand brackets written four spaces apart) (Other second-level variables for two place relations can be represented by extra spacing) 'Tom' = 't' 'Dick' = 'd' 'Harry' = 'h' x is inscribed in red = � ( ' x ' iriscribed in red with double strikethrough) x is inscribed in green = � ( 'x ' inscribed in green with double strikethrough) x is inscribed in blue = � e x ' inscribed in blue with double strikethrough) x is inscribed in lavender = � ( 'x ' inscribed in lavender with double strikethrough) x is inscribed in tan = � ( ' x ' inscribed in tan with double strikethrough) x is written as a superscript followed by y = xy ( 'x ' is written as a subscript followed by 'y' ) y is followed by superscript x = Yx ( 'y' written followed by subscript ' x ' ) x names y = x over y ( 'x ' written vertically over ' y ' ) F is true o f x = x. ( ' x ' inscribed i n a colour with double strikethrough and shadow outline) 'is rich' is true of x = x. ( 'x ' inscribed in red with double strikethrough and shadow outline) 'is happy' is true of x = X. ( 'x ' inscribed in green with double strikethrough and shadow outline) 'is bald' is true of x = x. ( ' x ' inscribed in blue with double strikethrough and shadow outline) 'is an object' is true of x = X. ( 'x ' inscribed in lavender with double strikethrough and shadow outline) 'is a proper name ' is true of x = x. ( 'x ' inscribed in tan with double strikethrough and shadow outline) Some translations : Tom is rich = t ( 't' written in red) Tom is older than Dick "" dt ('d' is follmved ·by superscript 't' ) Something is rich = (=lx) x (the second occurrence of 'x' occurs in red) Being rich is a concept = (ex) x (the second occurrence of 'x' occurs in red) 'is rich' is a predicate = (px) � (the second occurrence of 'x' occurs in red with double strikethrough) Tom has some property = (3 D t (the occurrence of the square bracket and the name 't' are written in fourteen p oint) Tom and Dick are related by some relation = (3 [ D t d (the two square brackets are written two spaces apart, as are the two names) The name 'Tom' is followed by the predicate 'is rich' = 'ot' (the letter 't' enclosed in quotes is inscribed in red with double strikethrough) 'Tom' names Tom = "'t'" over 't' (the letter 't' in quotes is written vertically above the letter 't' not in quotes) 'is rich' is true of Tom = to (the letter 't' is written is red with double strikethrough and shadow outline) 'is rich' is true of something iff it is rich = (\;Ix)(x. iff x) (the second occurrence of 'x' is written in red with double strikethrough and shadow outline, the third occurrence of 'x' is written in red) '

'

, ..

"

�

'.

.

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There is a property the predicate 'is rich' expresses = (3 [)(Vx)(x iff 'lit) (the oC'currence of the square bracket in fourteen point, the frrst occurrence of ' x ' in regular (twelve point) , the second in fourteen point, the third in regular in red with double strikethrough and shadow outline) . Every predicate expresses a concept = (V [) (if (Px) x then (3 [)((Cy) y & (Vz)(� iff z» ) (the frrst OCCUlTence of the square bracket in fourteen point, the first occurrence of 'x' in regular, the second in fourteen point; the second occurrence of the square bracket in sixteen point, the fIrst occurrence of 'y' in regular, the second in sixteen point; the first occurrence of 'z' in regular, the second in fourteen point with shadow outline, the third in sixteen point) .

Chapter 1 0

Universals and Particulars : Ramsey ' s Scepticism B ob Hale

Introduction

Frege held that expressions of all logical types have both sense and reference - that not only what he called proper names (singular terms, as they would more usually be called) , but equally predicates , relational expressions, sentential operators , and functional or incomplete expressions in general, are equipped not only with senses, but in virtue of that, stand for non-linguistic entities of appropriate kinds. In Frege's terminology, the non-linguistic correlates of proper names are objects, those of predicates and so on are concepts or, more generally, functions of one sort or another. Entities of these two broad kinds are, in his view, fundamentally and irreducibly different - just as objects are complete in a manner analogous to the complete expressions which refer to them, so concepts and functions in general have a kind of incompleteness matching that of predicates and incomplete expressions of other kinds. Taken together with its associated ontology, Frege's doctrine invites comparison with the more traditional doctrine of particulars and universals . Just as , in the traditional view, particulars exemplify or instantiate universals, but cannot themselves have instances, so, for Frege, objects· fall ilIider concepts , but cannot themselves · . have (other) objects falling under them. There are, of course, undeniable differences . In particular, the traditional view is standardly taken to incorporate the idea that whereas particulars may only ever figure as subj ects of propositions, universals may appear not only as predicates but equally as subj ects , it being supposed that reference to one and the same universal may be effected either by a predicate, such as ' (is) wise ' , or by a corresponding abstract noun, such as ' wisdom ' . By contrast, Frege's analysis of language and its accompanying ontology leaves no space for the idea that one and the same entity might be the referent of two expressions of different logical types, and for this reason he would have regarded this aspect of the traditional doctrine as mere confusion. l This difference is striking but its significance should not be exaggerated, for two reasons . First, while Frege would certainly have denied that 'wisdom' can be taken as standing for the (incomplete) entity that is the referent of the first-level predicate '� is wise' , he would hardly have held that it stands, instead, for a certain obj ect - on the contrary, he would have denied that 'wisdom' is a proper name at all. A sentence in which it appears as grammatical subject, such as 'Wisdom is a virtue' - precisely the kind of sentence which, in the

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traditional view, would express a · proposition having the universal as sUbj ect though perfectly intelligible, is merely a potentially misleading expression of what can as well be s aid by means of an equivalent sentence in which abstract nouns are replaced by first-level predicates, such as 'Anyone who is wise is to that extent virtuous' . S econd, while no concept or function can be the referent of a proper name, there remains, in Frege 's theory, something corresponding to the traditional doctrine that some universals may be predicated of, and so be exemplified by, others - for just as objects fall under first-level concepts, so concepts of lower level may bear a somewhat analogous relation to other concepts , of higher level. Frege' s doctrine may then, with some qualification as indicated, be viewed as underwriting a version of the traditional distinction between particulars and universals . Frege's doctrine may be questioned i n at least two ways, o n quite different grounds. Whilst his ascription of reference to singular terms is relatively uncontroversial, his belief that their reference is invariably mediated by a sense or mode of presentation has been forcefully challenged, at least in regard to what would ordinarily be counted proper names. In regard to predicates and other species of incomplete expression, scepticism has commonly taken the opposite form here, it is the ascription of reference that is most controversial. That such expressions possess senses which play their part in determining the truth-conditions of sentences containing them is undeniable, but Frege' s thesis that they do so by standing for correspondingly incomplete non-linguistic entitites - concepts, in Frege's sense, or more generally functions of various sorts - has been viewed as an at best unjustified and quite unnecessary ontological extravagance.2 When scepticism about Frege's doctrine takes this second form, it amounts, in effect, to a kind of scepticism about universals. My purpose in drawing attention to this form of scepticism here is not to assess its merits , but to c ontrast it with the very different - and in at least one important respect, far more radical - kind of scepticism about the traditional doctrine with which I shall be concerned: Ramsey' s . To the question ' whether there is a fundamental division of objects into two classes, particulars and universals ' ,3 Ramsey' s well-known answer is that there is no such division, and that the 'theory of universals ' is nothing but a ' great muddle ' generated by the erroneous belief that a logically important distinction can be made out between two types of terms or constituents of propositions - those terms which are or figure as subjects , and those which are or figure as predicates . The argument by which Ramsey supports this negative conclusion i s both long and complex, occupying virtually the whole of his paper. My first task here will be to provide an account of it in sufficient detail to enable me to pursue my main aim, which is to consider how, if at all, Ramsey's scepticism can be resisted, and in particular, whether it can be answered in the particular way some philosophers (notably Dummett4) have proposed. But before I set about this, I think it will be useful to make two preliminary remarks on the focus and character of Ramsey 's scepticism. The first point to be observed is that Ramsey insists that, if there is to be any significant distinction between particulars and universals at all, it must be drawn in ' logical' terms . He gives no general explanation of what is to count as a logical distinction, but at least part of what he intends can be gathered from the contrasts he makes with what he terms 'psychological' and 'physical ' distinctions . At the

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psychological level, Ramsey cites 'the difference between a percept and a concept, the objects of two different kinds of mental act' (p. 1 1 3 ) - he immediately dismisses this as 'unlikely to be a distinction of any fundamental importance' on the ground that 'a difference in two mental acts may not correspond to any difference whatever ' in their obj ects ' . With scarcely less abruptness, he rejects also the idea that any fundamental distinction can be made out in 'physical' terms , grounded in some difference 'between obj ects based on their relations to space and time' � such as that 'some objects can only be in one place at a time . . . [whereas] others , like the colour red, can be in many ' (ibid.) . This second step is especially worthy of notice, exerting as it does a maj or influence on the course and shape of his subsequent argument. Many philosophers - both before Ramsey's time and since - have supposed that it is precisely in some such terms (which might be thought more aptly described as metaphysical, rather than physical) that the particular/universal distinction is to be drawn: particulars are those entities that are/can be in one and only one place at any given time ; universals those which are!can be ' wholly present' in many places simultaneously. Ramsey argues that no such account can be accepted as going to 'the essence of the matter' , or as supplying the fundamental basis of the distinction, on the ground that two philosophers - he cites W.E. Johnson and A.N. Whitehead as examples - could agree that a certain table can be in one and only one place at any given time, but still dispute over whether it is a particular (a ' substantive' in Johnson' s terminology) or a universal (an ' adjective' , as Johnson would say) ; their disagreement must therefore be seen as concerning 'the logical nature' of the table. 5 In concluding, as he does, that if any important distinction can be made out at all, it must receive its most fundamental explanation in logical - rather than psychological or (meta)physical - terms, Ramsey is, in effect, in complete agreement with Frege's insistence on the priority of logical categorization of expressions over ontological categorization of entities corresponding to them.6 But of course, in another ultimately more important - respect, Ramsey is in fundamental disagreement with Frege, in a way which makes his scepticism much more radical than the second form of scepticism about Frege's doctrine identified above. S omeone who repudiates Frege' s ascription of reference to predicates as unj ustified may nevertheless agree with Frege that there is logically fundamental distinction between singular terms on the one hand and predicates on the other - on this view, Frege 's error lay simply in his investing a perfectly good distinction at the level of language and thought with unwarranted ontological significance. In sharp contrast, Ramsey has no qualms whatever about treating both proper names and predicates alike as having extra­ linguistic reference, and would agree that expressions of different grammatical categories - roughly, nouns and finite verbs - are required to compose a well­ formed sentence, but he denies that any logically important distinction can be made out, corresponding to the merely grammatical distinction between subj ect- and predicate-expressions, which could j ustify us in taking them to stand for entities of different types .

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Ramsey's Argument - Exposition

Ramsey 's A rgument in Outline As representative of the traditional doctrine, Ramsey considers the views of Russell and W.E. Johnson. B oth uphold a distinction between universals and particulars, but disagree about the nature of the difference between them. For Russell, entities are divided into individuals or particulars on the one hand and, on the other, qualities and relations - these together making up the class of universals. So far, Johnson agrees , save for an unimportant terminological difference - where Russell speaks of Particulars as opposed to universals, Johnson contrasts ' substantives ' with ' adjectives ' , and within the latter category, distinguishes 'transitive adj ectives' (corresponding to relations) from ' intransitive' (corresponding to qualities) . According to Johnson - whose view (as distinct from the terminology in which he expresses it) is probably in closer accord with tradition than Russell's - universals ( ' adj ectives ' ) may figure both as subjects and as predicates , whereas particulars ( ' substantives ' ) may figure only as subjects , never as predicates. According to Russell, however, universals can never be (genuine) subj ects , because they are essentially incomplete - as Ramsey puts it on Russell 's behalf, ' about an adj ective [i.e. universal] there is . . . some suggestion of the form of a proposition; so that the adj ective-symbol can never stand alone or be the subj ect of a proposition , but must be completed into a proposition in which it is the predicate' (p . 1 1 4) . Hence, in Russell' s view, the appropriate symbol for a universal, for example redness, is not an adj ective (in the normal sense) , such as the word 'red' , but a functional expression containing a variable 'x is red ' . Ramsey observes that various arguments might be mounted on either side, but claims that none of them is really decisive. The way forward, he proposes, is to reject an assumption common to both theories - the assumption, which Ramsey says 'has only to be questioned to be doubted' , that 'there is a fundamental antithesis between subj ect and predicate, that if a proposition consists of two terms copulated, these two terms must be functioning in different ways, one as subj ect, the other as predicate ' (p. 1 1 6) . On the contrary, says Ramsey, a pair of sentences such as ' Socrates is wise' and 'Wisdom is a characteristic of S ocrates ' both express the same proposition and assert the same fact. ' Socrates ' is the (grammatical) subj ect of the former, ' wisdom' of the latter. Which sentence we choose to express the proposition is a purely stylistic matter - if Socrates is the focus of our interest, we shall prefer the former, but if wisdom is, we shall favour the latter. But this 'has nothing to do with the logical nature of S ocrates or wisdom' and 'no fundamental classification of obj ects can be based upon such a distinction' (ibid.). Whilst Ramsey thinks this consideration 'throws doubt on the whole basis of the distinction between particular and universal as deduced from that between subj ect and predicate' (p . 1 1 7), he is careful to avoid claiming that it is decisive as it stands; rather, it lays down a challenge - to show that the particular-universal distinction is not merely an illusion engendered by superficial facts about language. The rest of his paper is designed to consolidate his initial scepticism over whether the challenge can be met. In essence, the structure of Ramsey' s central argument is quite simple. It has two main stages. He argues (stage 1) that the subject-predicate distinction

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can have no application t o compound propositions and, relate dIy, that there can be no complex universals. From this, he infers that if a logically significant distinction between subject and predicate is to be drawn at all, it can only be made out at the level of atomic propositions , so that, if there is to be any division of ' objects ' into particulars and universals, this division must be effected between the simple constituents of atomic facts . He then argues (stage 2) that, with this restriction in force, we can see that there is no basis for thinking that these simple constituents the 'objects ' composing atomic facts - must be of different types : on the contrary, for all we can tell, atomic facts are composed of ' objects ' of a single type, with none of them having any special sort of incompleteness - rather they may, just as in Wittgenstein's figure, 'hang into one another, like the links in a chain' . I want now to fill in the main details of this argument, leaving for later any critical discussion of it.

Ramsey 's Argument in More Detail - Stage 1 According to the view Ramsey opposes, a compound proposition such as that expressed by 'Socrates is wise or Plato is foolish' can be taken as having either Socrates as subject, or Plato, or both. In the first case, the proposition will involve a complex universal denoted by 'being wise unless Plato is foolish ' , and similarly for the other cases. Against this, Ramsey advances two arguments .

First argument (pp . 1 1 7-1 8 ) : Take any proposition of the form 'aRb ' . On the opposed view, there will be three closely related propositions - one asserting that the relation R holds between a and b, one asserting the possession by a of the complex property of having R to b and one asserting that b possesses the complex property of being R-ed by a. But on the one hand, these must be three different propositions, because they have different constituents, while on the other, they cannot be, since they all say the s ame thing, namely that a has R to b . Second argument (pp . 1 1 8-1 9):. Ramsey claims that his first argument .may be strengthened by considering the process of definition. Suppose we defme «>x = df aRx. Then there is, Ramsey argues, a dilemma: Either «>, thus defined, is a name for the complex property which x has iff a bears R to it, or it is not. If so, then «>x will be a subject-predicate proposition and so a distinct proposition from the relational proposition aRx. B ut this is absurd, since «>x is defined as simply an abbreviation of aRx, and so must be the same proposition. 'For if a definition is not interpreted as signifying that the definiendum and the definiens have the same meaning, the process of definition becomes unintelligible and we lose all justification for interchanging definiens and definiendum at will, on which depends its whole utility.' But if not, then it becomes a complete mystery how we can refer, in thought or speech, to the complex property - 'how can we ever speak of it, seeing that "<\>", its only possible name, is not a name for it at all but short for something else. And then what reason can there be to postulate the existence of this thing?' Although I shall defer critical assessment of these arguments until we have Ramsey 's whole argument before us, three more or less exegetical comments are in order at this point.

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1 . At first blush, it may seem odd - given that his ostensible target is the' idea that compound propositions have a subject or subj ects and a predicate - that Ramsey should switch attention, as he apparently does in his first argument, to atomic propositions of the form ' aRb' . But on reflection, the explanation is simple. Ramsey, as he himself declares, has no interest in niceties of English grammar. In standard traditional grammar, an expression is or functions as a subj ect when it stands in a certain relation to a finite verb. In this sense, a simple sentence of the form 'aRb ' , such as 'Ramsey admired Wittgenstein' has only one subj ect, namely 'Ramsey ' . 'Wittgenstein' is not the subj ect, but the (direct) obj ect. And to the question: 'What is the subj ect of the sentence "Either Socrates was wise or Plato was foolish" ? ' , the only possible answer is that, in that sense of ' subj ect' , the question is misdirected ­ ' Socrates ' is the subject of the first clause, and 'Plato ' of the second. But Ramsey, quite rightly, would not have taken this merely grammatical point as establishing his claim that the subject-predicate analysis has no application to compound propositions. Nor, equally, would he have regarded his claim as refuted by the fact that the latter sentence can be taken to express a proposition which is about both S ocrates and Plato (and so to have both as subjects, in that sense) , what is predicated of the former being that he was wise unless Plato was foolish, and what is predicated of the latter being that he was foolish unless S ocrates was wise. What Ramsey is really concerned to establish is that there cannot be complex universals . In view of this, his choice of example is perfectly apt - for if there could be complex universals , then even atomic propositions o f the form ' aRb' ought t o be analysable a s involving reference to them. For as well as the straightforward analysis , according to which such a proposition is composed of three things - the relation R and its terms a and b - there should be two other analyses, one with a single term a and complex universal Rb, the other with a single term b and complex universal aR. 2. Ramsey is evidently right to claim for his second argument only that it strengthens his first. It is clear that it cannot constitute an indep endent argument, since the first horn of the dilemma assumes that the first argument succeeds in its own right.. For the. frrst horn claims that the friend of complex universals is committed to holding both that ' <j>x' expresses a distinct proposition from 'aRx' and that it expresses the same proposition, and so is ensnared in a contradiction. This is precisely what the first argument tries to establish . Hence if that argument fails , so does the argument on the [rrst horn, so that Ramsey 's would-be dilemma collapses, regardless of whether the argument on the second horn is effective. 3 . In one way, it may not appear very important to take issue with this first stage of Ramsey's overall argument. Ramsey would surely agree that if different kinds of expression can be held to stand for particulars and universals, they will do so in complex propositions as well as in atomic ones - that if 'is wise' , say, stands for a universal in ' Socrates is wise' , then it equally does so in such compounds as 'Either S ocrates is wise or Plato is foolish' . But then the only position under threat from his first-stage argument is one according to which there are, as well as simple universals such as wisdom, complex universals such as being wise unless Plato is foolish, or again, complex universals such as bearing R to b, as well as plain R. And the view that there are such complex universals, while not obviously absurd or untenable, seems clearly to be an optional extra, from the point of view of friends of the particular/universal distinction. But this assessment of the situation is unduly

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sanguine. For although it might appear that a defender of the distinction could simply concede that there are no complex univers als , and agree with Ramsey that if the distinction can be drawn at all, it must be drawn with respect to atomic propositions, this conClusion is potentially much more damaging than it might at first appear, as becomes apparent when one examines the next stage of his argument.

Ramsey 's Argument in More Deti:1iI - Stage 2 Taking it as established that there can be no complex universals and that the distinction between subj ect and predicate must be drawn with respect to atomic propositions, Ramsey now asserts , j ust as we should expect, that:

The distinction between subj ect and predicate will then arise from the several names in an atomic proposition functioning in different ways ; and if this is not to be a purely grammatical distinction it must correspond to a difference in the functioning of the several objects in an atomic fact, so that what we have primarily to examine is the construction of the atomic fact out of its constituents . (pp . 1 20-2 1 ) There are, Ramsey claims, three views about this: Johnson's view that the c onstituents are connected together by a so-called ' characterizing tie ' ; Russell ' s view that the connection is made by one of the constituents - the universal - which is by its very nature 'incomplete or connective and, as it were, holds the other c onstituents together ' ; and Wittgenstein 's view, which holds that there is no connecting tie, nor any special incomplete constituent, but that 'the obj ects hang one in another like the links of a chain' . He quickly, and plausibly, dismis ses Johnson's 'real copula' view as hopelessly obscure, and clearly favours Wittgenstein' s doctrine, which he obviously regards as entirely consistent with rej ection of the particular/universal distinction (although he does admit that it does no better as an explanation than Johnson ' s ) . Hence the remainder of his argument is directed exclusively against Russell ' s view. Against Russell, Ramsey 's 1l1itia l o bje c lioli is thilt it is hard to see how or why one sort of obj ect rather than another should be held to be incomplete . There is a clear sense in which any object is incomplete - namely, ' it can only occur in a fact by connection with an obj ect or obj ects of suitable type' (p. 1 2 1 ) . This incompleteness at the level of obj ects is seen as matching the incompleteness of 'names ' .7 At the linguistic level, ' S ocrates ' is every bit as incomplete as 'is wise' - neither expression can stand on its own, but requires to be combined with s ome other expres sion(s) to form a sentence. And the claim is that the obj ects for which these names stand S ocrates and wisdom - are similarly and correspondingly incomplete. To have a(n atomic) fact, we must have at least two obj ects . Ramsey offers Russell two defences against this obj ection: (i)

(ii)

He might argue that the great convenience of his functional notation can only be explained by supposing that it 'corresponds to reality more closely than any other' . He might appeal to the intuitive evidence of a difference - conceded even by nominalists - between, for example, Socrates and wisdom, and argue that

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Universals, Concepts and Qualities only his account of the differcnce between them ' made them really- different kinds of obj ects , and not merely differently related to us or to our language ' (p . 1 22) . The idea, in other words , is that only Russell ' s account makes the difference an objective one (among obj ects themselves) as opposed to a merely subjective (mind- or language-dependent) difference.

Neither of these arguments , Ramsey argues , justifies us in claiming that there is a real difference between particulars and universals - that is, a difference in reality between two kinds of entity. 8 Against the second, Ramsey makes two claims : first, that ' S ocrates is wise' does not express an atomic proposition - so that, even if there were a genuine difference between S ocrates and wisdom, this difference could not (given the conclusion of S tage 1 ) consist in one of them being a particular and the other a universal;9 and second, that while there is an apparent difference between, say, ' S ocrates ' and ' wise ' , this appearance c an be explained away. The apparent difference is that there are two distinct ranges of propositions associated with ' wise ' , whereas there is only a single range associated with ' S ocrates ' . In the case of ' wise ' , there is a narrower range comprising ' S ocrates is wise ' , 'Plato is wise ' , ' S olon is wise ' , ' Jones is wise' and s o on, and then there is the wider range which includes all propositions in which ' wise' occurs, such as 'Either Socrates is wise or Jones is lying' , 'No one who is wise eats acorns ' and s o on, as well as those in the narr ower range. But with ' S ocrates ' , there is j ust a single range, comprising all the propositions in which ' S ocrates' occurs . Against this, Ramsey claims that there are two ranges of propositions associated with ' S ocrates ' , just as there are with ' wise ' . Maybe we don 't in fact think of collecting together two ranges of propositions with ' S ocrates ' , corresponding to the two ranges we c an collect with ' wise' - but we perfectly well could do s o . For we might think that among the things we can truly or falsely assert concerning S ocrates, s ome of them correspond to genuine qualities (qualities of S o crates, in case what we s ay is true), while others of them do. not. Thus one might think of ' S ocrates is . wise ' , ' S o crates is j ust' , ' So crates is a man' and so on as mentioning qualities of S o crates, but deny that this is so in case of propositions like ' S ocrates is neither wise nor just' , ' S o crates is neither tall nor handsome ' , ' S omeone is taller than S ocrates or fatter than Plato ' , and the like. And we might then distinguish a narrower and a wider class of propositions associated with S ocrates - the narrower class would comprise propositions ascribing genuine qualities to S ocrates , while the wider class would include also propositions ascribing what Ramsey calls ' compound characteristics or properties ' . Of course, this way of putting the p oint is not really acceptable to Ramsey, since he rej ects any such distinction between simple qualities and compound properties . He puts it in these terms only because he is arguing, ad hominem, that even a friend of the traditional doctrine ought to recognize that there are two ranges of proposition associated with S o crates, just as there are with wisdom. Expressed in terms congenial to Ramsey ' s own view, the p oint is that whenever S is an incomplete symbol, rather than a genuine name, there will be two kinds of propositions involving S - those in which S has widest possible scope (in Russell 's language, has primary occurrence) , and those in which S has narrower scope (secondary occurrence) . We can then defme a narrow range of

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propositions - those in which S has primary occurrence - and a wider range - those in which S has either primary or secondary occurrence. This is why there are two ranges associated with ' wise ' - but ' S ocrates' is also an incomplete s ymbol, so that for exactly the same reason, there are two ranges involving ' S o crates ' . As for the first line of defence he offers Russell, Ramsey concedes that something like Russell's functional symbolism is needed for certain purposes - for example, we cannot adequately represent the property of either bearing R to a or bearing S to b (to use his example) by writing Ra v Sb, because this fails to indicate whether the blanks (i.e. before R and before S) are to be filled by the same or differerit arguments . If the former, we have a property, which an object possesses iff it bears R to a or bears S to b; if the latter, we have rather a binary relation, in which (possibly distinct) obj ects x and y stand iff x bears R to a or y bears S to b. To distinguish between them, we must write either xRa v xSb or xRa v ySb . B ut this only shows that Russell 's functional symbolism is needed in cases where we are dealing with a complex propositional function. It gives no reason to suppose that when we are, rather, concerned with an atomic proposition, �a, one of the constituents must be thought of as accompanied by a variable. There is no need to regard ' � ' as incomplete in s ome way that 'a' is not, and we can take it, just as we can take ' a ' , to be a name (as opposed to an incomplete symbol) . In the interests of having a uniform notation for propositional functions , Russell ­ Ramsey argues -j ust ignores this difference, and represents all propositional functions alike by means of incomplete symbols. As Ramsey puts it, ' mathematical logic, being only interested in functions as a means to classes, sees no need to distinguish between these two sorts of functions, because the difference between them, though all-important in philosophy, will not correspond to any difference in the classes they define' (p . 1 3 1 ) . But while this procedure is entirely justified in mathematical logic, it does not justify ignoring the difference between propositional functions which can be simply named and those which must be represented by incomplete symbols . Hence it does not j ustify us in thinking that of the terms involved in an atomic proposition, one must be nmc.tioning in _som� speciaLway,. differ�ntly from the other(s);. qr that among the objects that ar e the constituents o f an atomic fact, there must b e one which i s o f a different type from the others. So the argument from the advantages (or even indispensability) of Russell 's symbolism lends no support to the claim that there is a fundamental distinction between particulars and universals . This completes my exposition of Ramsey 's central argument; but before I consider how we might best respond to his scepticism, I want to comment briefly on an initially puzzling passage near the end of Ramsey ' s paper in which he summarizes his conclusions . He writes (p . 1 32) : ..

So were it not for the mathematician' s biassed interest he would invent a symbolism which was completely symmetrical as regards individuals and qualities ; and it becomes clear that there is no sense in the words individual and quality . . . S o far, so good. B ut Ramsey continues :

all we are talking about is two different types of obj ect, such that two obj ects, one of each type, could be sole constituents of an atomic fact.

..

..

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This seems to concede that atomic facts must (at least) have constituents of diffe rent types. And this appears, at least at first sight, to be a puzzling c oncession: does n ' t it amount to allowing that there is, after all, something behind the particular/universal distinction? There are three things Ramsey goes on to s ay, which help to resolve puzzlement on this score, and which illuminate the real character of his rej e ction of the p articular/universal distinction. First, he immediately continues :

The two types being in every way symmetrically related, nothing can be meant by calling one type the type of individuals and the other that of qualities . S econd, dismissing a further argument of Russell 's which appeals to the idea that names can occur in propositions with any number of terms, whereas relations have fixed adicity, he replies :

But this assumes his [i.e. Russell's] theory a s t o the constitution o f atomic facts, that each must contain a term of a special kind, called a universal . . . The truth is that we know and c an know nothing whatever about the forms of atomic propositions ; we do not know whether some or all objects can occur in more than one form of atomic proposition; and there is obviously no way of deciding any such question. We cannot even tell that there are not atomic facts consisting of two terms of the same type. (p . 1 3 3 , my emphasis) Third, describing the procedure of the mathematical logician from the point of view for which he has argued, he writes :

H e takes any type o f obj ects whatever a s the subject o f his reasoning, and calls them individuals, meaning by that simply that he has chosen this type to reason about, though he might equally well have chosen any other type and called them individuals. (p. 1 34, my emphasis) The fIrst of these remarks substantially qualifIes , and the second effectively withdraws , the apparent concession that seemeq p)lzzling. In the light of the third, especially, Ramsey 's position appears to be as follows . If we are to engage in mathematical logic at all, we are obliged to treat some entities as individuals - that is, as constituting a lowest type , comprising the entitities which, at b ottom, we reason and think about (and as we might say, constituting the domain of the lowest level of quantification) . Once the type of individuals is fixed, other types - for example properties and relations of various levels - are determined. B ut which entities are taken to form the type of individuals is a matter for our choice or decision, and whatever choice we make, we could j ust as well have made a different one . There can therefore be no justfIcation for investing the particular choice we have made with philosophical signifIcance. We may draw no conclusions from it, or from the hierarchical structure of language to which it gives rise, concerning the nature of non-linguistic reality. In particular, there is no basis for thinking that there is, in reality and independently of our way of conceptualizing it, a division of entities into different types of anything like the sort claimed by proponents of the particular/universal distinction.

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Responding to Ramsey's Challenge

Some Prdiminaries Ramsey ' s argument is not a proof - either that no good distinction can be drawn, among non-linguistic entities, between particulars and universals, or that such a distinction cannot be grounded in a distinction at the level of language or thought but it does present a strong challenge . In considering how his challenge can be met, we should separate two questions : Can Ramsey ' s challenge be met on his own terms? and: Must we accept those terms? Accepting Ramsey ' s terms involves, fIrst, accepting that the distinction, if it is to be drawn at all (on the basis of a distinction between subj ects and predicates), must be made out for the constituents of atomic propositions/atomic facts, while agreeing with him - and with Wittgenstein, as Ramsey interprets him - that we can give no examples of atomic propositions (nor therefore of atomic facts) . Each claim, as we have seen, plays a leading role in Ramsey ' s argument. It may seem that if b oth are accepted, there is no hope of meeting his challenge. In particular, if the second claim is correct, does it not follow - just as Ramsey clearly believes - that we know, and can know, nothing of atomic facts and their constitution? That all we can know is that there are such facts? But that there must be atomic propositions - and so atomic facts c orresponding to those that are true, and so obj ects (constituents of atomic facts) and names for them - is something that is known or must be accepted on purely general theoretical grounds ; their existence is 'presupposed by other propositions ' , as Ramsey puts it, alluding to Wittgenstein ' s argument from determinacy of s ense . B ut this general argument gives us no knowledge of the nature of the constituents of atomic propositions or atomic facts, save that the former are names, not incomplete symbols, and that the latter are simple obj ects , not complex. So we can have no basis for supposing that obj ects must belong to different types. It . is not clear that this pessimi stic . conclusion is w3ITanted, even if both of Ramsey ' s claims are accepted. There is a defInite step from the premiss that we can give no examples of atomic propositions or facts to the conclusion that we can know nothing of the nature of their constituents . Neither Ramsey nor, so far as I have been able to see, Wittgenstein offers any argument to support it. There is no evident reason to suppose that any knowledge of the nature of the terms of atomic propositions or of the constituents of atomic facts must be acquired, if at all, by extrapolation from examples . So it remains at least possible that an equally general theoretical argument could be mounted to show that atomic propositions - whatever they are - must have a certain form or comp ositional character. Perhaps one c ould give a general argument from the nature of proposition s ; or perhaps it could be argued that Wittgenstein 's metaphor of obj ects hanging onto one another like links in a chain is at best misleading - that any detailed, literal account of facts or states of affairs requires a difference in type among their constituents. I shall not, however, pursue this issue here. For even if my fIrst question is to be answered negatively (i.e. it proves to be true that Ramsey ' s challenge can ' t be met on his own terms) , it is far from obvious that those terms must be accepted. On the contrary, w e may, as I shall now try to show, rej ect b oth of Ramsey ' s claims . .

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Of those two claims - that the subject-predicate distinction is inapplicable to comp ound propositions (together with Ramsey 's associated rej ection of complex universals) , and that we can identify no examples of atomic propositions - it is the second which is the more difficult to assess. Ramsey 's and Wittgenstein 's confidence in its correctness notwithstanding, it is, surely, a very puzzling claim. Ramsey clearly believed that we can know, in regard to at least some (and surely indefinitely many) propositions, that they are not atomic - he has , for example, no hesitation in classifying the proposition expressed by 'Either S ocrates is wise or Plato is foolish ' as compound. Whence this confidence in this verdict? The obvious (and indeed, the only obvious) answer is that he takes the grammatical structure of the sentence expressing the proposition - the fact that it is constructed out of two simple (or at least simpler) sentences by means of a sentential operator, and s o qualifies as a compound sentence - as a reliable criterion for the complexity of the proposition expressed. How could he do otherwise? How could talk of the complexity of propositions - if it is not to be merely idle speculation or, worse, a kind of logical mysticism - be other than grounded in facts about the structure of the logically simplest sentences by means of which they may be expressed? There is no faculty by means of which the structure of a proposition may be directly inspected. Indeed, it is quite unclear what talk of propositional structure c an mean, unless it is understood as derivative from, or cashed out in terms of, talk of the structure of sentences (or perhaps other means) by which propositions are expressed. Of course , the relation between sentential and propositional structure is often anything but simple and straightforward, so that the formulation of any general criterion is a difficult and delicate matter. Surface grammatical simplicity may mask propositional complexity : ' 1 7 is prime ' is a simple (in logician's j argon, atomic) sentence, but the proposition it expresses complex, since its grammatically simple predicate, ' . . . is prime ' , is to be understood as abbreviating the complex predicate ' there is no number distinct from 1 and . . . itself which divides . . . without remainder' . It is for this reason that any criterion for a proposition's being complex must be framed in terms ofthe complexity of the logicall y simplest. stSntence. expres sin.g. it Inregard to this example, along with many others that might be given, recognition that surface syntactical simplicity belies logical or semantic complexity relies on no philosophically controversial thesis or doctrine - it can be, and frequently is, just part of our ordinary understanding of a syntactically unstructured expression that any sentence containing it abbreviates s ome more complex sentence. 10 In other cases , the question whether the proposition expressed by a grammatically simple sentence is itself simple or complex may appear unanswerable without compromising philosophical neutrality. Ramsey ' s confident denial that ' Socrates is wis e ' expresses an atomic proposition is a case in point. As already noted, this might be supported by appeal to Russell ' s thesis that ordinary proper names are n o t genuine names, logically speaking, but are rather disguised definite descriptions . Of course , Russell' s view can be and has been disputed, and the opposed view - that ordinary proper names can and do function as devices of genuine singular reference - upheld. This is a large issue which need not be engaged here, save to note that there is no reason to suppose it beyond resolution (even if philosophical argument is required to resolve it) , and that the consequence - that whether the proposition expressed by a sentence is

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simple or complex may be to s ome extent a philosophical issue - need not be irreconcilable with taking propositional structure to be keyed to sentential structure. In any case, that issue is beside the point, as far as Ramsey 's position is concerned. For even if Russell ' s (ioctrine were accepted, it would not suffice for Ramsey ' s purpose, since its acceptance would do nothing t o undermine the claim of such sentences as 'This is wise' or 'That is red' to express atomic propo sitions . Ramsey 's denial that ' S o crates is wise ' does s o rests upon an appeal, not to Russell ' s doctrine, but to Wittgenstein's. Neither ' S ocrates ' nor 'wise ' are ' names of obj ects ' , according to Ramsey - both are rather 'incomplete symbols ' . Even if Ramsey had been disposed to support his denial that ' S ocrate s ' is a name by appeal to Russell 's doctrine, he clearly could not have justified his parallel denial that ' wise' is a name by claiming that it ' abbreviates ' s ome more complex predicate - or at least, it would have been pointless to do so, since he would then be required to argue that the simpler predicates composing any such complex predicate are not themselves names either, if he was to avoid conceding that we can, after all , identify s ome atomic propositions . This prompts the question what does underpin Ramsey 's c onfidence that we can never know, of any proposition, that it is atomic . Nothing he writes suggests a clear answer, but it is not easy to avoid the thought that for Ramsey, what makes a proposition atomic is that it is one which, if true, corresponds to an atomic fact. This view involves a complete rej ection of the idea that the structure of a proposition must be derivative from that of a sentence expressing it. Coupled with Ramsey 's claim that we can have no access to atomic facts, it has the c onsequence that there can be no effective criterion by which it c an be determined that a proposition is atomic, so that we can never be in a position to recognize an atomic proposition as such. B ut this conception of propositional structure rests upon a substantial metaphysical thesis, of questionable coherence, which - s o far as I can see - there is no compelling reason to accept. If that is right, we are free to rej ect Ramsey 's second claim. Ramsey 's first claim - that the subject-predicate distinction is inapplicable to compound propositions and that there can be no complex universals rests, as we have seen, upon two arguments . Of these, the second depends upon the first, which attempts to show that the opposed view is ensnared in a contradiction, because it involves acknowledging b oth that there are three distinct propositions expressed by the sentence 'aRb ' and yet that there is just one propo sition it expresses. But this argument, too, is eminently resistable. To engineer the contradiction, Ramsey makes two assumptions : �

(a) (b)

A proposition p is the same as a proposition q only if p and q have the s ame constituents ; A proposition p is the same as a proposition q if p and q assert the s ame thing .

He must further assume that there is (and that his opponent must accept that there is) s ome single notion of proposition such that (a) states a necessary and (b) a sufficient condition for propositional identity. For even if his opponent agrees that there are different constituents of the proposition asserted, depending upon whether what is asserted is that a bears the relation R to b, or that a has the complex property of bearing R to b, or that b has the complex property of a ' s bearing R to it,

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and so (applying (a» three different propositions asserted, he will only be caught in a contradiction if he further accepts that in the same sense o f ' proposition' , there is a single proposition asserted, because the same thing is asserted in each case. B ut this leaves Ramsey ' s opponent with an obvious reply. He can just deny that the same thing is asserted in all three cases: asserting that a bears the relation R to b is different from asserting that a has the complex property of bearing R to b, and both differ from asserting that b has the complex property of a ' s bearing R to it. Ramsey may insist that this reply misunderstands (b) , because ' assert the s ame thing ' is there to be understood as insensitive to these more refined distinctions among what is asserted, and requires only that p and q have the same truth-condition, and that this condition is indeed met. B ut Ramsey' s opponent can p oint out that what this comes to depends upon what is required for sameness of truth-condition. If all that is required is necessary coincidence in truth-value, then while one could perfectly well adopt (b) as a sufficient condition for identity of propositions, and while it is no doubt true that in this sense the same thing is asserted in all three c ases, there is little or no plausibility in the claim that (a) gives a necessary condition for identity of propositions in the same sense of ' proposition ' . If, instead, s ome finer-grained notion of truth-condition is invoked - say, one that pays attention to compositional structure - then Ramsey ' s opponent can again plausibly deny that he is committed to accepting that the same thing is asserted in each case. If what I have argued is correct, there is no clear reason to suppose that Ramsey 's challenge is unanswerable. Whilst neither of my arguments against his two claims suggests how an answer to it might run, the second of them - against his insistence that any attempt to meet his challenge must focus upon atomic propositions - does serve to remove a potentially troublesome obstacle. Any attempt to make out a logically robust contrast between singular terms and predicates , in which a distinction between particulars and universals might be grounded, would be effectively stymied by Ramsey ' s requirement that we restrict attention to sentences which can be independently recognized as expressing atomic propositions . For while , in advance of formulation of any general criterion by means of which expressions functioning as singular terms can be discriminated from others, we can distinguish, among the class of sentences as a whole, between those that are compound and those that are not, we evidently cannot identify the latter as those apt to express atomic propositions. Grammatically simple, that is, non-compound, sentences of c ourse include what, from a logical point of view, should be classified as atomic sentences . B ut in addition to (putatively) atomic sentences such as 'This is red ' and ' S ocrates is wise ' , they include also sentences which, though grammatically simple, are logically complex, such as 'A stranger called' and 'Smith bought a newspaper ' . In general, whether a sentence ' t ' should count as atomic depends , inter alia, upon whether ' t' should be counted a singular term. Thus with Ramsey ' s requirement in place, we should be caught in a vicious circle and could make no progress. B ut if my second argument is correct, we are under no obligation to accept Ramsey ' s requirement. This opens the way t o the response t o Ramsey which will occupy me for the remainder of this chapter. . . .

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Aristotle 's Contrast and the Aristotelian Criterion One respect in which, according to Aristotle, substances - or at least what he called primary substances - contrast with qualities is that whereas qualities have contraries or opposites, there is nothing corresponding to this with substances. A number of philosophers have been attracted by the thought that Aristotle's contrast c an be seen as providing the b asis for a logically important distinction between subj ect­ expressions (or singular terms) and predicates, and some have explicitly claimed to find in it an antidote to Ramsey ' s scepticism. Very roughly, l l the tliought i s that whereas for any given quality, such as being wise, there is another opposite quality (being unwise, or foolish) which any given object has just in c ase it lacks the quality in question, there is not, for any given obj ect, another ' opposite ' or ' contrary ' obj ect, which possesses a given quality j ust in case the given obj ect lacks it - an obj ect (Nonsocrates, as we might s ay) which is unwise if and only if S ocrates is wise, handsome if and only if S o crates is ugly, vicious if and only if Socrates is virtuous, and so on, for every quality. It is not hard to see why Aristotle ' s contrast, assuming it to be a good one, might be viewed as supplying the basis, at least, for an answer to Ramsey. What Ramsey questions is the idea that ' if a proposition consists of two terms c opulated, these two terms must be functioning in different way s ' - playing logically, as opposed to merely grammatically, different roles. It is natural to appeal to a contrast between referring to something, or mentioning or identifying it, on the one hand, and describing it, characterizing it or s aying something true or false about it, on the other. B ut so long as this contrast is left at an intuitive level, this is, as we have seen, quite inadequate as a response to Ramsey. Against the suggestion that in ' S o crates is wise ' , ' Socrates ' refers to something which the grammatical predicate 'is wise ' describes, Ramsey will simply reply that there is no solid reason to regard the referring role as discharged exclusively by the grammatical subj ect, and that we may just as well take the predicate as identifying what our proposition is about, and ' S ocrate s ' as indicati.ng what �ve are truly or·falsely asserting of it. If Ramsey is to be answered, what is needed is to point to s ome feature incontrovertibly possessed by one of the terms of our propo sition (or of the expressions c omposing the sentence expressing it) which cannot be claimed for the other - some feature which marks it out as functioning in a different way. Since we cannot, without begging the question against him, place any weight on the idea that the grammatical subj ect plays a referential role but the predicate not, this effectively requires that we p oint to s ome feature distinctive of the predicate. But that is precisely what Aristotle ' s contrast appears t o d o . The contrast is obviously closely related t o the fact that any given quality divides obj ects into two mutually exclusive 12 classes - those which possess it and those which lack it. B ut, since it could just as well be observed that any object similarly divides qualities into those which it possesses and those which it lacks , this latter fact cannot be regarded as fully c apturing the contrast. The essential claim involves a crucial existential c omponent. To a fIrst approximation, it is that there is, for any given quality, another quality - that is, another entity of the same kind - possessed by exactly those objects which lack the given quality ; 1 3 whereas n o parallel existential claim holds true for objects - i t i s false that for any given obj ect, there is another obj ect which possesses exactly those qualities which

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the given object lacks . It is this ' difference which may be seen as justifying the claim that obj ects and qualities are entities of fundamentally different types , and the further claim that, where the terms of a proposition refer to entities of these different types, they are - contra Ramsey - functioning in different ways. There is, then, at least a prima facie case for supposing that Ramsey's scepticism can be answered by appeal to Aristotle's contrast. But it is no more than that, and it is important to appreciate Why. The reason - or at least, what I take to be the most important reason - can be brought out by considering what ground we might have for supposing Aristotle's claim to be true. The contrast, as we have it thus far, is stated in the material mode, at the level of (types of) entities : for any given entity of one type (qualities), there is another entity of the same type, related to it in a certain way, whereas it is not the case that there is, for any given entity of the other type (obj ects), another entity of the same type so related to it. The difficulty here - the point on which any serious sceptic will bring pressure - lies in the crucial, but crucially unexplained, talk of entities of the same type. Use of the traditional terminology of ' objects ' and ' qualities' does no essential work in framing the contrast - we i:ould, if desired, dispense with it in favour of metaphysically unloaded, colourless labels, 'A: and 'B ' say, and formulate the contrast: for any given A, there is another A, such that any B bears a certain relation R to that A just in case it does not bear R to the given A ; whereas it is false that for any given B , there is another B, such that that B bears R to any A just in case the given B does not. Once we have got this far, nothing stands in the way of our simply stipulating that 'quality' is to refer to entities ' of type A, and ' object' to entities of type B . What is clearly presupposed, however, is that we understand what it is for entities to be of the same type or of different types. Only if we do so can we even begin to consider whether the constrastive claim is true. To put the point in more concrete terms : it may seem evident to us that ' is wise' and ' is not wise ' stand for suitably related entities of the same type, and that there is no other suitably related entity of the type of which 'Socrates ' denotes a particular instance ­ but the sceptic is entitled to ask: 'On what ground do you take the first pair of expressi ons to . denote . e.ntities of the same type?' , and he may also challenge ·us to ' explain why we refuse to allow that such an expression as 'It is not the case that . . . Socrates ' stands for an entity of the same type as that for which ' Socrates ' stands , related to the latter in just the mauner ruled out by the constrastive claim. Clearly it is of no use at this point to reply that the first two expressions stand for qualities, whereas of the second pair, only the latter, not the former, stands for an object - since that is precisely the contrast the sceptic is challenging us to explain. Can we do better? A plausible diagnosis of the difficulty just exposed is that it results from attempting to apply Aristotle 's contrast directly to obtain an ontological distinction, rather than treating it as, in the fIrst instance, supplying the basis for a logical distinction between expressions of different types. Certainly this diagnosis should commend itself to anyone, such as Dummett (and Frege, whose view Dummett is expounding14), who holds that logical distinctions among types of expression are necessarily prior to ontological distinctions among types of entity. Dummett himself expressly claims IS that Aristotle' s contrast provides us with the means to answer Ramsey's scepticism. It does so, he thinks, by supplying the basis for a test by which proper names (in Frege 's inclusive sense) may be distinguished from expressions of other logical types including, centrally, predicates.

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Recasting Aristotle's contrast as a criterion for an expression's functioning as a proper name or singular term is, as Dummett remarks, not entirely straightforward. Since its proper formulation involves , in any case, s ome difficulties I shall need to discuss , it will be useful to quote Dummett's explanation of it in full. He writes :

S uppose that we have a sentence ' S (t,u)' involving two expressions ' t' and ' u ' both of which pass the tests for proper names which we have already laid down. We now enquire, with respect to 't' , whether we may assert 'There is s omething such that S (it, that thing) if and only if it is not the case that S e t, that thing) ' : if we may, then ' t' is not a proper name. Likewise, with respect to ' u ' , we enquire whether we may assert 'There is something such that S ( anything, it) if and only if it is not the case that S (that thing, ul ' : if we may, then ' u ' is not a proper name. (In these schematic sentences, the 'it' relates to the ' something ' , and the ' that thing' to the ' anything' .) Thus, for example, if ' t' is ' S ocrates' and ' £I ' is 'wise ' , ' S (t,ul' being ' S ocrates is wise ' , then we may assert 'There is something such that anyone is it if and only if it is not the case that that person is wise' , and hence 'wise' is not a proper name; but we c annot assert 'There is someone such that he is anything if and only if it is not the case that S ocrates is that thing' , and so ' Socrates ' passes this tes t for being a proper name. 1 6 It is clear that this Aristotelian Criterion, as I shall call it, is not intended to function by itself as an adequate test for proper names. It is put forward as giving only a neces sary, not a sufficient, condition; as Dummett' s opening s entence indicates, it presupposes certain other tests . These require, for an expression ' a' to be functioning as a proper name in a sentential context 'A(a) ' , the validity of certain patterns of inference involving 'A(a) ' either as premiss or as (part of) the conclusion. The specific inferential tests Dummett proposes!? require that:

(1) (II)

From any sentence 'A(a) ' , we may validly infer ' There is something such that ACit) ' From two sentences 'A(a ) ' and ' B (ar , we may validly infer ' There is .something .such that A (it) and B (it) ' From ' It is true of a that A(it) or B (it) ' , we may validly infer 'A(a) or B (ar . . .

(ll)

' ' The restriction on the range of ' t' and u in the Aristotelian Criterion is, then, to expressions which pass these inferential tests . We shall return to this p oint. First, we should enquire how, precisely, Dummett thinks Aristotle' s c ontrast enables us to see where Ramsey goes wrong. Even someone firmly committed - as Frege, in sharp contrast to Ramsey, is - to a fundamental distinction between proper names and flIst-Ievel predicates must, Dummett observes, recognize the possibility of analysing simple sentences ostensibly composed of proper names and first-level predicates in another way, according to which the ostensible proper name functions as a second-level predicate. He must, as Dummett puts it, ' admit not only the analysis of "S ocrates is wise" as resulting from putting the proper name "Socrates" in the argument-place of the first-level predicate "s is wise", but also the analysis of it as resulting from putting the first­ level predicate "s is wise" in the argument-place of the second-level predicate , "cI>(Socrates) " . B ut there remains, or s o he will claim, a difference between, on the one hand, ascribing to the object, S ocrates , the first-level property of being wise

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and, on the other, ascribing a certain higher-level property - roughly, being instantiated by S ocrates - to that first-level property, and he will, accordingly, maintain a sharp distinction between the obj ect, S ocrates, and the second-level property of being instantiated by S ocrates. But that distinction is one that Ramsey ­ Dummett claims - rej ects , and by doing so, puts himself in conflict with Aristotle 's thesis:

On Ramsey's conception, there would be no genuine distinction between obj ects and second-level qualities . . . B ut, unless the distinction is maintained, it is impossible to recognize the correctness of the Aristotelian thesis that an obj ect has no contrary: we should be unable to understand generalization over obj ects , as opposed to generalization over all the things that might be true of a first-level quality. 1 8 That seems right. If there is no real difference between obj ects and second-level qualities , then - since second-level qUalities most certainly do have c ontraries obj ects cannot be contrasted, as having no contraries , with qualities, which do. But why should Ramsey not simply retort: ' S o what? S o much the worse for Aristotle . And as for your alleged distinction between generalizing over obj ects and generalizing over all the things that might be true of a first-level quality, I c an make nothing of that, precisely because I can see no real difference between obj ects and qualities, whether of first-level or other ' ? B ut Dummett is not finished ; he immediately continues :

A little reflection on such a state of affairs shows it to be impossible : we should be unable to explain, not merely generality, but the truth-conditions even of the most basic atomic statements. For these, the conception of a proper name as standing for an object ab out which we are asserting that the predicate is true of it is inesc ap able, whatever may be the case for the extension of this notion to other contexts . . . . [Thus the Aristotelian Criterion is] of value in showing the rationale of regarding the distinction between proper name and predicate in a singular statement as constituting a distinction between levels of expression - preyisely . t he view assailed by Ramsey. 19 Dummett's thought, then, is that if we follow Ramsey in denying a real distinction between obj ects and second-level qualities, we must reject Aristotle 's contrast - but that if we do so, we are powerless to explain the truth-conditions of the simplest statements of our language (and so, presumably, of all others, since any recursive explanation of the truth-conditions of more complex statements must be anchored, ultimately, in an explanation of the simplest ones). S o - assuming that such an explanation is possible - Ramsey must be wrong. There must be a basis for thinking of the distinction between proper names and predicates as one between expressions of different level, and this is provided by the Aristotelian Criterion. Although I am in general agreement with Dummett' s approach, it seems to me that there are at least two reasons for doubting that his specific way of exploiting Aristotle 's contrast constitutes an effective response to Ramsey ' s scepticism. It is, first, open to question whether Durnmett has correctly identified the exact focus of Ramsey ' s challenge, and consequently doubtful whether his response does full justice to it. He is, I think, strictly correct in claiming that Ramsey denies that there is any genuine distinction between obj ects and second-level qualities . B ut this

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1 95

does not, as it might at fIrst appear, commit him to denying either that we can draw distinctions of level with respect to the expressions of our language, or that we can discern within it a class of expressions of lowest level, whose members we shall naturally regard as names of obj ects , expressions of other kinds being assigned to higher levels and taken to stand for functions of various kinds. If this claim seems surprising, or even obviously false, we should recall Ramsey's closing paragraph, in which he describes what he takes to be the procedure of the mathematical logician who has taken the measure of his scepticism: He takes any type of objects whatever as the subject of his reasoning, and calls them individuals, meaning by that simply that he has chosen this type to reason about, though he might equally well have chosen any other type and called them individuals. The results of replacing names of these individuals in propositions by variables he then calls functions , irrespective of whether the constant part of the function is a name or an incomplete symbol, because this does not make any difference to the class which the function defines . (p. 1 34, my emphasis)

Thus Ramsey agrees that if we are to engage in mathematical logic at all (and perhaps more generally, if we are to attempt any systematic analysis of thought and language), we are obliged to treat some entities as individuals - that is, as constituting a lowest type, comprising the entitities which, at bottom, we reason and think about and which form the domain of the lowest level of quantifIcation) . Once the type of individuals is fIXed, other types - together forming a hierarchy - are determined. We may then explain that an atomic statement is true if and only if the ' obj ects ' to which its ingredient names refer stand in the relation designated by its predicate, and give the usual recursive explanation of the truth-conditions of more complex statements . Thus Dummett's charge - or so Ramsey will claim - is unfounded. But which entities are taken to form the type of individuals is a matter for our choice or decision, and whatever choice we make, we could just as well have made a different one. There can therefore be no justifIcation for investing the particular choice we have made wit'h philosophical signlfiduice : We may draw no conciusions fttn:ir it, or from the hierarchical structure of language to which it gives rise, concerning the nature of non-linguistic reality. This is the force of his denial that there is any genuine distinction - that is, distinction in reality, as opposed to the language we use to talk about it - between obj ects and (second-level) qualities. In particular, there is no basis for thinking that there is, in reality and independently of our way of conceptualizing it, a division of entities into different types of anything like the sort claimed by proponents of the particular/universal distinction. There is, second, a difficulty with the Aristotelian Criterion, at least as Dummett formulates it. As we have seen, Dummett restricts the application of the criterion to expressions which pass certain inferential tests . A little reflection discloses both that this is a very significant restriction and that it is problematic in the present context. To verify the fIrst part of this claim, it suffices to consider Dummett' s fIrst inferential test, which requires, for an expression 'a ' to function as a singular term in a context 'A(a) ' , that we be able validly to infer therefrom the conclusion ' There is something such that A(it) ' . Can we take 'a' to be any expression whatever, or is there some implicit restriction to expressions of a certain grammatical category?

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Suppose our candidate expression is . 'breathe s ' , and let 'A(a) ' be the 'sentence 'Anything that breathes has lungs ' . To apply the test, we have to decide whether from this we may infer 'There is something such that anything that it has lungs ' . The obvious problem is that this is not even a well-formed sentence, so that on the face of it, we cannot even begin to consider whether it can be validly inferred from this or any other preririss . It thus appears that the test simply cannot be applied. Of course, it might be said that precisely because our ungrammatical string fails to express a true or false proposition, it cannot be validly inferred from the given premiss - so that 'breathes ' fails the test. But it is obviously unsatisfactory to attempt to preserve the generality of application of the test by this means , since it would amount to simply assuming that genuine singular terms must belong to a particular surface grammatical category - why invest surface grammar with such significance ? Dummett' s inferential tests must therefore be understood a s applicable only t o a restricted range of candidates for singular termhood. This range will include an expression �a' only if for any well-formed sentence 'A(a) ' , the string 'There is something such that A(it) ' is also well formed. Any singUlar definite or indefinite noun or noun-phrase (including ordinary proper names) will lie within this range, but it will also include adj ectives occurring in complement position - as does ' wise ' i n ' Socrates i s wise ' , since 'There i s something such that S ocrates is it' i s well formed - but not when they occur otherwise. The test is not applicable, for example, to adjectives figuring as constituents in noun-phrases, as in 'the wise investor will neither buy nor sell until the market stabilizes ' (since 'There is something such that the it investor will neither buy . . . ' is gibberish) . And clearly the test cannot be applied to predicates in the strict sense - that is, expressions which can be completed into sentences by inserting a suitable number of names or other substantival expressions . Dummett's inferential tests will, then, at best discrimate genuine singular terms lying within the s omewhat broader, but still severely restricted, class of expre s s ions compris i n g , roughly, singu.lar -.substantives and adjective s in complement position . And since the class of expressions to which the Aristotelian Criterion applies comprises just those which pass the inferential tests , its range of application is similarly severely restricted - too severely, surely, if the criterion is to figure, without simply begging the question, in any sort of response to Ramsey. For to lay down, as giving a necessary condition for an expression to function as a singular term, a test which simply cannot be even so much as applied to predicates in the strict sense, is, in effect, to invest surface-grammatical differences with logical significance in precisely the way Ramsey deplores . We must, accordingly, lift the restriction. To avoid reliance upon surface-grammatical distinctions whose logical significance is in question, and challenged by Ramsey, we must reformulate the Aristotelian Criterion in more neutral terms . The most straightforward - and indeed the only obvious - way to do this is by recourse to substitutional quantification. Let ' a ' be an expression , of any grammatical form, and let ' qa) ' be any sentence containing it. Then we may employ ':Ea' and 'II�' as substitutional quantifiers , the substitution class for a comprising all and only those expressions which can replace ' a ' in ' qa)' preserving grammaticality, and that of � comprising, similarly, all and only those expressions which can similarly

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replace 'C( ) ' in ' C(a) ' . Thus a pair consisting of one expression from the ex class and one from the � class will always form a well-formed sentence , which we write schematically as (ex, � ). Our interest is in what logical role the expression 'a ' plays in the sentence 'C(a) ' . If, with Dummett, we wish to state a necessary condition for 'a' to be functioning as a singular term, then we may reformulate the Aristotelian Criterion in this way : ' a ' functions a s a singular term i n 'C(a) ' only if """L exrr� ((ex,�)

�

....., ( a, �))

thereby capturing the idea that lacking a contrary is characteristic of singular term. Notice that ex and � , and so ' a' and 'C( ) ' , can be expressions of any grammatical types whatever, subject only to the condition that they can be combined (without any auxiliary expressions) to make a well-formed sentence - so that the desired neutrality with respect to surface-grammatical differences is secured. Notice als o that, i f w e take having a contrary t o be characteristic of predicates, we might als o reformulate the criterion a s giving a necessary, and perhaps also sufficient, condition for functioning as a predicate: 'a' functions as a predicate in 'C(a) ' (if and) only if Lexrr� ((ex,�)

�

....., ( a,�))

So far, so good. But there is a difficulty to be reckoned with. To illustrate it, we may focus on the Aristotelian Criterion framed as a necessary condition for functioning as a singular term. Intuitively, it seems clear that, as we should wish, an expression such as 'Socrates' occurring, say, in 'Socrates is wise' , passes the test. We ask whether there is an expression ex, grammatically congruent with ' Socrates ' , such that no matter how � is chosen (consistently with the requirement of grammatical congruence with 'is wise' ) , the biconditional: (ex, �) � ....., ( Socrates, �) holds true. And it seems clear that there is not, that is, that there is no ex such that ' ex i s wise � ....., S ocrates i s wise' , ' ex smokes � ....., S ocrates smokes ' , and s o on, all hold true. The snag emerges when we consider whether 'is wise ' , as we should also wish, fails the test. It might appear that it straightforwardly does so. For surely we can, in this case, choose ex as the contradictory predicate 'is not wise' . D o we not then have the desired result, that no matter how � is chosen, the biconditional ' (is not wise, �) � ....., ( is wise, �) ' - that is, ' � is not wise � ....., � is wise' - holds true, so that 'is wise' fails the test for being a singular term? But a moment's reflection reveals that this is too quick. We are assuming, in effect, that � will always be chosen so as to be a singular term. B ut the � substitution class comprises all expressions which can replace ' Socrates ' without violence to grammar. Thus we can just as well take � to be, say, ' everyone' , or ' some philosopher' . And if we do, then the relevant biconditionals - 'Everyone is not wise � .....,Everyone is wise' and 'Some philosopher is not wise � ....., S ome philosopher is wise' - fail, the first from right to left, the second from left to right. It seems clear that no other choice of ex will fare any better. The upshot is that in its fIrst version, the Aristotelian Criterion fails to exclude 'is wise' (and fIrst-level predicates in general) from the category of singUlar terms . For essentially the same reason, the criterion in its second version will not merely fail to include 'is wise' , and so on, among the class of predicates , but will actually exclude them.

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Our difficulty results from the fact that in English - as in many other natural languages - generality is standardly expressed by means of singular substantival expressions : that is, by means of nouns or noun-phrases, such as ' everything' , ' something' , ' every man ' , 'some number' , and so on, which can, grammatically, occupy positions in sentences where proper names or other expressions which we should intuitively classify as singular terms can stand. When the Aristotelian Criterion is reformulated using substitutional quantifiers in the way we have proposed; such expressions have therefore to be recognized as belonging, together with proper names and other intuitive singular terms, to the substitution class of any variable having expressions of the latter sort among its substituends - with consequent disruption of the criterion's intended effect. It may then seem that we cannot avoid impalement on one or another horn of a dilemma. If we formulate the criterion in Dummett's style - without recourse to substitutional quantification, but restricting its application to expressions which pass his inferential tests - we lay ourselves open to the charge of simply assuming, without justification, that only (a certain subclass of) substantival expressions can function, logically, as singular terms, and that non-substantival expressions (and in particular, predicates strictly so called) must have some other function, simply because they are of a different surface­ grammatical form. If, on the other hand, we avoid this objection by restating the criterion in more neutral, substitutional terms, it then misfires in the way we have seen. The dilemma may seem lethal, but its second horn is not as sharp as it may at first appear. The difficulty canvassed does indeed show that we cannot regard ' a ' functions as a singular term in 'C(a) ' only if -'LaII� ((a,�)

H

-,(a,�))

as satisfactorily capturing a necessary condition for an expression to function as a singular term. The difficulty is not that some bona fide singular terms fail the test, but that first-level predicates will pass it - unless we can somehow exclude natural­ language q�lantifiers and quantifier-phrases from the .� substituti0n dass, when ' a ' is what we should intuitively classify as a first-level predicate - with the result that the test fails to make any useful contrast between singular terms and predicates . There i s , however, a straightforward way t o impose a suitable restriction on the � substitution class, using Dummett's inferential tests. For whilst those tests do not, by themselves, provide a satisfactory means of discriminating singular terms from expressions of all other kinds, they20 may plausibly be taken to accomplish the more limited but useful goal of separating the broader class of substantival expressions into those which function as singular terms and those which do not. That is, while the tests do not give acceptable necessary conditions for just any expression whatever, of arbitrary grammatical type, to function as a singular term, we can take them as giving necessary conditions for any substantival expression to do so. And that, in effect, is enough for present purposes . Since those substantival expressions which fail the inferential tests are precisely the ones which cause our present troubles, we may preserve the Aristotelian Criterion, as formulated above, as a quite generally21 necessary condition for singular terrnhood, by restricting the � substitution class to those expressions which are grammatically congruent with 'C( ) ' other than any which fail Dummett 's inferential tests.

Universals and Particulars: Ramsey 's Scepticism

1 99

Provided, then, that a version of Dummett's inferential tests can be relied upon to filter out natural-language quantifiers and quantifier-phrases, we can formulate a suitably .restricted version of the Aristotelian Criterion which enables us to distinguish between singular terms and first-level predicates as discharging different logical (as opposed to merely grammatical) functions , and to do so in a way which goes part of the way towards answering Ramsey' s scepticism. But if that scepticism is as I earlier represented it, this can only be part of an answer to it. Properly understood or so, contra D ummett, I suggested - Ramsey's challenge does not involve rej ecting altogether any distinction between singular terms and second-level predicates; what he denies, rather, is that we can be justified in attaching any ontological significance to such a distinction. In particular, whilst it may be inevitable that the expressions of our language be assignable to the various levels, with those standing for 'individuals' or objects forming the basis of a hierarchy, our choice of individuals is entirely arbitrary. The hierarchical structure of our language therefore gives us no justification for thinking of reality as comprising entities - particulars and universals, say - of different types . Viewed in this way, the threat Ramsey poses is the threat of relativism. Here I can do no more than indicate the lines along which, in my view, we should respond to it. We should begin by conceding to Ramsey that there are two respects in which what entities are recognized as obj ects - as opposed to properties and relations, and so on - is, while not entirely arbitrary, at least not inevitable. The recognition of entities as obj ects in our language or conceptual scheme shows itself in the presence of general terms standing for concepts of a certain kind - specifically, what are commonly called sortal, as opposed to merely adjectival, general terms and concepts. Roughly, the mark of a sortal concept is that it is associated - not only, as any general concept is, with conditions or criteria of app lication, which help to determine which entities fall under the concept, but - with criteria of identity, which regulate answers to questions of identity and distinctness of entities to which the concept applies . If we think of concepts as tied to - dependent for their existence upon linguisi:tie- or -other ·discrimiflatory · abilities, then -evidently the possibility of introducing a certain concept is one thing, and there actually being such a concept quite another. Possibilities for introducing concepts may or may not be realized in any given language or conceptual scheme. Since this applies to sortal concepts no less than to others, we should agree that our language or conceptual scheme might have developed in such a way as to involve recognition, as obj ects , of things which do not in fact receive recognition as such in our language or conceptual scheme as it is. And it is clear that the point holds in reverse, so to speak. That is, we should also concede that some - perhaps any - of the kinds of object which do receive recognition in our conceptual scheme might have gone unrecognized. Neither of these concessions to Ramsey is damaging, since neither goes any way towards undermining the idea that there is an absolute difference between objects (particulars) and properties and relations (universals). What would undermine that idea is the claim - implicit in Ramsey' s assertion that our 'choice' of which entities to treat as individuals is arbitrary - that entities which are recognized as objects in our language or conceptual scheme as it is might just as easily have turned up, so to speak, as properties or relations rather than objects , had we elected - as we might have done - to start with a different selection of entities as constituting the base

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level in our hierarchy. Evidently this claim goes far beyond the concessions we have already made to Ramsey and receives no support from either of them. In particular, from the fact that entities thought of as objects (referents of actual or possible singular terms) in our conceptual scheme as it is might not have been conceived as such at all, had our scheme developed differently, it clearly does not follow that they - those very entities - might instead have found their place in an alternative scheme in which they were thought of as properties (referents of actual or possible predicates). Indeed, not only does no such conclusion follow; the very intelligibility of the idea that these very things, which - as it happens - we pick out by means of singular terms and think of as obj ects, might just as easily have been designated by predicates and conceived as properties seems at best highly questionable.22 Obviously Ramsey did not think so. Over and over again he cites Whitehead's doctrine that 'material objects are adjectives of the events in which they are situated' in support of his view. He does not, of course, mean to endorse Whitehead's doctrine; indeed, he cannot endorse it, since - at least as he construes it - it involves an application of the very distinction he is challenging, between particulars and universals. But he has no need to do so. For his dialectical purpose, it would be enough that tables and chairs and their like - the orthodox metaphysician's paradigms of particulars - could, with the revisionary metaphysician (Whitehead as Ramsey glosses his view) be just as intelligibly conceived as ' adjectives ' (properties) of events, and so as universals. If the same entities can be just as well conceived either as particulars or as universals, there can be no fundamental cleavage in reality marked by these contrasted terms - or so Ramsey, as I understand him, means to argue; but the argument should not carry conviction. It is true enough that Whitehead occasionally suggests that 'objects can be looked on as qualities of events ' .23 But it is clear that he does not regard this as an accurate statement of his doctrine, precisely because it employs the 'metaphysical and difficult notion of inherent qualities ' . Stripped of the potentially misleading gloss Rarnsey puts on it, Whitehead's claim is that material objects dO llot constitutc a basic or fundamental type of entity - events, he argues, constitute a more b asic type. On a rough but uncontentious statement of his view, material objects are to be conceived as logical constructions out of events.24 There is nothing in this doctrine, taken on its own, that requires or even suggests rejection of the view that tables and chairs and so on are particulars. Denying that these things are basic particulars does not require denying that they are particulars at all - what is required is only that they be seen as derivative or dependent particulars.2s It would, of course, be a very different matter if, as Ramsey claims, any division of entities into particulars and universals must be made, if at all, at the level of atomic facts - that is, must be a division of the (simple) ' objects ' that compose atomic facts. For that claim not only rules out recognizing complex universals but equally precludes admitting ' complex particulars' , as we might call them - for example logical constructions out of more basic particulars. B ut, as we have already seen, Ramsey' s own argument for that crucial claim is fallacious, and there appears to be no other good reason to accept it.

Universals and Particulars: Ramsey 's Scepticism

201

Concluding Remark

' I have been concerned, as Ramsey was , with the question whether the particular/ universal distinction can be grounded in a logical distinction between subj ects (singular terms) and predicates . I have tried to argue that there is - as Dummett and others have suggested - a way in which the core idea in Aristotle 's contrast between primary substances and qualities can be made the basis of an answer to Ramsey's scepticism. Even if I am right in this conclusion, however, it should be emphasized that it falls substantially short of a vindication of the traditional doctrine that there is a fundamental division of non-linguistic entities into particulars and universals . What Ramsey questioned was, primarily, whether a logically significant distinction - as opposed to a merely grammatical one - could be made out among expressions (singular terms and predicates) in a way which might reasonably be taken to reflect a division in reality between two types of entities . He did not question the propriety of regarding both subject-expressions and predicates alike as standing for entities . What h e denied was, rather, that there i s any justification for thinking o f them as standing for entities of different types. But what Ramsey did not dispute - that predicates no less than singular terms serve to make reference to non-linguistic entities - may certainly be called into question. It is one thing to insistthat there is, pace Ramsey, a logically significant difference in function between singular terms on the one hand and predicates on the other, and another thing altogether to concede that a proper understanding of this difference in function requires us to think, as Frege did, of predicates as standing for non-linguistic entities of s ome sort. Why, on the contrary, should it not suffice to explain that difference in function, to observe that predicates are associated with general satisfaction conditions - that is, conditions for them to be true of objects - in contrast with singular terms , whose function is precisely to pick out such obj ects ? If it does so suffice , the prospects of grounding an ontological distinction between particulars and universals upon a logical one between singular terms and predicates remain as bleak as Ramsey believed them to be; albeit for sOlriewhat different reasons from' those ' which moved him.

Notes

2 3

See Michael Dummett, Frege: Philosophy of Language, London: Duckworth, 1 97 3 , pp. 56-7 and 257ff. Maybe worse, since paradox threatens in the shape of Frege' s notorious difficulties over the concept horse. F.P. Ramsey, 'Universals ' in The Foundations of Mathematics and other Logical Essays, ed. R . B . B raithwaite, London: Routledge & Kegan Paul, 1 93 1 , pp. 1 1 2-34 . All subsequent p age references to Ramsey are to this volume. The quoted words are from Ramsey 's opening sentence. Note Ramsey always uses 'object' in an inclusive sense, as we might use ' thing' or ' entity ' , and not as marking any distinction between types of non-linguistic entity, as when objects are contrasted with properties or relations. I shall occasionally use ' object' in this inclusive sense when reporting or discussing Ramsey ' s views, but will enclose i t i n single quotation marks to signal that I a m doing s o ; when I use the word without quotation marks , I intend a contrast with properties and relations .

202 4

Universals, Concepts and Qualities Others who have advocated a b roadly similar response include P.F. Strawson - see

Individuals, London: Methuen, 1 95 9 , Part Two and especially chapters 5 and 6.

Regrettably, I have space to discuss only Dummett' s version in any detail. Another argument to the same effect - though not one advanced by Ramsey, and perhaps one with which he would have h ad little sympathy - is that if there is a genuine distinction between particulars and universals, there is - at least prima facie - no clear or compelling reason to suppose that particulars must be concrete entities . On the face of it, individual numbers are particulars and their properties universals. If that is accepted, the distinction evidently cannot be adequately explained in terms of a capacity, or lack.of one, to be in many places at once. 6 S ee the first of the passages from Dummett cited in note 1 . 7 That is, expressions standing for ' objects ' . 8 This ·counter-argument runs right through to p . 1 32 . It begins with a long - but incomplete - discussion of argument (ii) (pp . 1 23-9) . Ramsey then combines the completion of his negative assessment of this argument with a similarly negative assessment of argument (i) (pp . 1 29-32). 9 More fully, Ramsey claims that ' S ocrates' and 'wise' are not n ames but incomplete symbols, from which he infers that 'the difference we feel is one between two s orts of incomplete symbols , or logical constructions, and we c annot infer without further investigation that there is any corresponding difference between two s orts of names or obj ects ' (p. 1 2 3 ) . It might be supposed that in claiming that ' S ocrates is wise ' is not an atomic proposition, and that ' S ocrates ' is not a genuine name but an incomplete symbol, Ramsey is simply reiterating Russell' s view that ordinary proper names are not names from a logical point of view, but disguised or abbreviated definite descriptions, and so incomplete symbols . But if that were all Ramsey intended, one could just switch to a better example using what Russell would count as a logical proper name, such as 'This is red' , which would be reckoned, by Russell at least, to be a genuine atomic proposition. Ramsey is going further - he is endorsing (what he takes to be) Wittgenstein ' s doctrine, that we just can't give any examples at all of genuine atomic propositions , or of genuine names . So all we c an do is stick with examples like this one, recognizing that the symbols involved (not just ' S ocrates ' , but 'wise' as well) aren' t names, standing for ' objects ' , but incomplete symbols which stand, if for anything, , for logical constructiotrs:' This is why, evert if there.'prove"d to' be a genUine difference" between the way, ' S ocrate s ' functions and the way 'wise' functions , we could not infer that there is any genuine difference among names, or the ' obj ects ' for which they stand. 10 Similarly, it may be part of our ordinary understanding of a syntactically complex expression that its syntactical complexity is semantically and logically insignificant. 1 1 This statement is probably stronger than anything which could be justified as an interpretation of Aristotle's texts . In particular, it not clear that he holds every quality to have a contrary. But it is a fair statement of the thought which has been seen as potentially supplying a basis for the distinction between names or singular terms and predicates . 12 But not, necessarily or in general, exhaustive. In particular, where a predicate F is vague, there will be - on at least s ome accounts of vagueness - obj ects which neither definitely possess nor definitely lack the quality for which it stands . 1 3 Since this other quality will be, in Ramsey' s terms, a complex universal, any appeal to Aristotle's contrast presupposes that his arguments for the conclusion that there c an be no such things are unsound - as we have seen they are. 14 Cf. Dummett, Frege: Philosophy of Language, pp. 5 6-7 . Whilst it is Frege's view that Dummett is primarily concerned to set forth, it seems clear that he is in agreement with it. So am I. 5

Universals and Particulars: Ramsey 's Scepticism 15

16 17

18 19 20

21 22

23 24 25

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Cf. ibid. , p. 63. Immediately before making this claim, Dummett considers the suggestion that Ramsey 's scepticism might be answered by appealing to Frege's distinction between complete and incomplete expressions and - interestingly, in the present context rej ects it for essentially the same reason as Ramsey brings against any attempt to argue for the particular/universal distinction from the advantages or even necessity of employing Russell's functional symbolism. Ibid. , p . 64. Cf. ibid., pp. 5 8-60 . Dummett does not claim that these tests , either by themselves or in conjunction with the Aristotelian Criterion, give a sufficient c ondition for an expression's functioning as a proper name. For one thing, the possibility of reading ' something' in the conclusions of the inferences involved in tests (I) and (II) as expressing second- rather than first-level generality threatens to subvert their intended application. Dummett seeks to dispose of this difficulty by providing a separate, supplementary test for level of generality. This - as I have argued elsewhere - gives rise to further difficulties, though not - as I have tried to show - insuperable ones. See B ob Hale, ' S trawson, Geach and Dummett on Singular Terms and Predicates ' , Synthese, Vol . 42, No. 2, 1 979. Dummett, Frege, p . 66 Ibid., pp. 66-7 . More accurately, a revised version of those tests - since some revisions are needed to deal with other, quite independent problems confronting the tests as originally formulated. For some discussion, see B ob Hale and Crispin Wright, The Reason 's Proper Study, Oxford: Oxford University Press , 200 1 , chs 1 , 2. More recently, further difficulties have been raised by Ian Rumfitt in his contribution to a symposium on 'The Reason 's Proper Study' published in Philosophical Books, Vol . 44, No . 3 , 2003 . These are briefly addressed in our reply, published in the same issue. Note that there i s n o restriction upon the range of application o f the criterion - 'a' can be of any grammatical form. There is, of c ourse, nothing incoherent in the idea that, in addition to conceiving of Socrates, say, as an object - the referent of the proper name ' S ocrates' and of many other singular terms - we might also introduce a second-level predicate - perhaps written ' Socrates ' - standing for the second-level property of being a property possessed bY' Socrates. B lil (he secon:d� level 'property cleady-presupposeS (the e'xis tence of) the object - there is no sense in the suggestion that they are merely one and the same entity conceived in different ways . Cf. The Principles of Natural Knowledge, Cambridge: Cambridge University Press, 1 9 1 9 , p . 60. There is an obvious and tempting analogy between Whitehead's doctrine of material objects as composed of events and Hume ' s 'bundle theory' of the s elf as a collection of psychological episodes . Perhaps in S trawson's sense - see Individuals, Part One, especially ch. 1 .

Chapter 1 1

How Not to Trivialize the Identity of Indiscernibles Gonzalo Rodriguez-Pereyra

I

The Principle of Identity of Indiscernibles (PIT, hereafter) says that no two things differ solo numero. That means that when two things differ numerically there is also a further difference between them. This further difference I shall call qualitative difference. This qualitative difference can be an internal difference between things or a difference as to how things are related to things . These differences can also be explained in terms of properties : in the former case qualitative difference consists in a difference with respect to intrinsic properties, in the latter case it consists in a difference with respect to relational properties. Relational properties may depend on the identity of the relatum (or on the identity of relata of the relatum), or they may be purely qualitative. Properties that depend on the identity of a relatum, like being twO miles from the Eiffel Tower, are often called impure properties . ! Thos e that do not depend on the identity of a relatum, like being two miles from a tall tower, are called pure properties. Since intrinsic properties do not dep�nd on the identity of any relatum, they are also dassified as pure.-Bufgiveii inY un derstanding of ' qualitative ciifrf� ence' , b b th· .. pure and impure properties can make a qualitative difference. 2 Given that the difference can be captured in terms of properties, PIT is normally taken to assert either that there are no two things that share all their properties or, in its necessitated version, that there can be no two such things. Here is a formal statement of the non-necessitated version: PIT (x) (y) [(F)(Fx == FY ) ::::l (x = y)] 3 B oth in the necessitated and the non-necessitated version the domain of properties over which one quantifies is crucial for the truth of PIT. Indeed the more one restricts the domain of properties quantified over, the more likely for PIT to come out false. And if one puts no restriction at all on the domain of properties quantified, then PIT comes out true but, as it is often pointed out, trivially true. The triviality of this version of PIT depends on certain properties being included in the domain of property quantification. I shall call those properties that render PIT trivial trivializing properties. Since PIT, far from being a trivial principle, is one of

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the most substantive and . controversial ideas in metaphysics, it is important to determine which properties must be excluded from the domain of quantification to get a metaphysically serious version of PIT. If one excludes from the domain of quantification all and only trivializing properties, then one ensures a non-trivial and to that extent a metaphysically serious version of PIT. That version will be the weakest non-trivial version of PII. For every other non-trivial version of PIT will entail the truth of the version that excludes all and only trivializing properties. But that it is the weakest does not make it unworthy of metaphysical discussion. That weakest version will make a non-trivial claim and establishing it may be as difficult as establishing other versions of PIT. I shall not discuss whether the weakest non-trivial version of PIT is true. But it is significant that, as it will have become clear in Section 7 , the weakest non-trivial version of PIT will quantify over some impure properties, like being the father of a or being one metre apart from a. Thus I disagree with Peter Strawson, who said that the only version of PIT which is worth discussing is one according to which there exists, for every thing, some description in purely universal or general terms such that only that thing answers to that description (Strawson, 1 959, p. 1 20).4 Indeed, normally the following three versions of the principle are distinguished (here I present only the non-necessitated variant of each version) : PIl l : PII2 : PIT3 :

No two things share all their intrinsic properties No two things share all their pure properties No two things share all their properties

PIl l is the strongest version, PIT3 the weakest. Philosophers typically claim or suggest that these are the only three versions of PIT and that PII3 is a trivial version of PIT (to cite only a few: Adams, 1 979, p. 1 1 ; Forrest, 2002, § 1 ; van Cleve, 2002, pp. 3 8 9-90) . While I agree that PII3 is trivial, I disagree that the other two are the only non-trivial versions of the principle. Indeed, part of the significance of the discussion to follow is that it shows the existence and importance of the foUowin-g ' version of PIT, weaker than PIT2 but stronger than PII3 : PII2. 5 :

N o two things share all their non-trivializing properties

I take Pll2.5 to be the weakest non-trivial version of PIT. And since not all impure properties are trivializing properties, Pll2.5 quantifies over some impure properties. The main aim of the chapter is then to specify the class of trivializing properties. But I want to produce a philosophically illuminating specification of such a class. That is, I want to be able to say what makes a certain property trivializing. This is why I shall specify the class of trivializing properties intensionally rather than merely extensionally. In the next section I shall introduce the paradigmatic kind of trivializing properties. In Section 3 I shall discuss other trivializing properties and I shall argue against giving a characterization of trivializing properties in terms of the notion of entailment between properties . In Section 4 I shall discuss, and eventually find unsatisfactory, another way of characterizing trivializing properties, in terms of the notion of property containment. In S ections 5-6 I shall present and discuss my own characterization of trivializing properties . Section 7 is a brief conclusion.

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II

When one quantifies over all properties of things, what PII asserts is that no two things share all their Properties . This version of PII is true but trivially true, as it has been widely recognized. To see why this version of PII is true, consider property ( 1 ) below, which is an instance of what I call properties of identity: s

(I)

being identical to a.

If one quantifies over all properties , PII is true because if any things a and b share all their properties, including ( 1 ) , then they are identical and so they are not two things . We can deploy the structure of the argument in the following way: (i) (ii) (iii) (iv)

a and b share all their properties . a has the property of being identical to a. b has the property of being identical to a. Therefore, a = b.

Since (i) asserts the indiscernibility of a and b, the argument (i)-(iv) derives identity from indiscernibility by using a property of identity. (i) is the assumption of indiscernibility between a and b needed to get the argument started. (ii) follows, assuming properties of identity, from the general law that everything is self-identical, that is, (x)(x = x) . (i) and (ii) entail (iii), which states that b has the property of being identical to a, but if b has the property of being identical to a, it follows that b is identical to a, that is, (iv) .6 S o , if a and b are indiscernible, they are identical; that is, PII is true.? This argument for PII is simple and clear and it turns the denial of PI! into a contradiction, since denying it would amount to saying that there are two non­ identical particulars that share all their properties, including their properties of identity, and therefore t.l:ley are identical. B ut note that this argument supports PH only because it is a case of a general argument that can be applied to every two particular things that are supposed to be indiscernible. Taken in itself the argument only proves that there is nothing indiscernible from a, not that there is no pair of indiscernibles. B ut, since everything is self-identical, this argument can b e generalized. Other instances of the argument will u s e other properties of identity, such as being identical to b, being identical to c, or any others . So properties of identity make PII true. But they make it trivially true. No doubt the proof of this version of PII has an undeniable air of triviality, but what matters here is not the triviality of the proof but the triviality of what is proved. 8 For it is trivial to claim that no numerically distinct things share all their properties, including their properties of identity. Properties of identity are trivializing properties, since they do not make a qualitative difference. They must be excluded from the domain of quantification to get a metaphysically serious version of PII.

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If properties of identity were the only trivializing properties, our problem would be trivial. But although they are paradigmatic trivializing properties , there are other trivializing properties . For if properties of identity trivialize PlI, then so do conjunctive properties like (2) :

(2)

being identical to a and being green.

Suppose a certain thing a is green; one can then show that there indiscernible from it in the following way : (v) (vi) (vii) (viii)

IS

nothing

a and b share all their properties . a has the property of being identical to a and being green. b has the property of being identical to a and being green. Therefore, a = b .

This argument is generalizable i n the relevant way, for even i f n o t everything i s identical to a and green, everything has some conjunctive property o n e of whose conjuncts is a property of identity and the other is some other property. S o conjunctive properties like (2) establish PlI. But what they establish is trivial, since all the work in the proof is done by ( 1 ) . The reason why in the argument above the real work is done by the property of being identical to a is that everything having the property of being identical to a and being green must have the property of being identical to a. S o a and b cannot share (2) without being identical. In other words, property (2) entails property ( 1 ) in the sense that nothing having the former can lack the latter.9 Since every property entails itself, if all and only trivializing properties entail properties of identity, then we have a solution to our problem: D1

F is

a

trivializing property

""def.

F entails

a

property of identity.

But D 1 is wrong, if only because there are trivializing properties that do not entail any properties of identity. lo Consider property (3) : (3)

being numerically distinct from a.

Property (3) is the complement of property ( 1 ) , the property of being identical to a. I shall call any complement of a property of identity a property of difference. Property (3) does not entail property (1) and, in general, properties of difference do not entail properties of identity. Yet property (3) can be used to show there is nothing indiscernible from a. For since indiscernibles are those that share exactly the same properties, indiscernibles are those that lack exactly the same properties, and so we can run the following argument: (ix) (x) (xi)

a and b lack exactly the same properties . a lacks the property of being numerically distinct from a . b lacks the property of being numerically distinct from a.

How Not to Trivialize the Identity of lndiscernibles

(xii)

Therefore, a

=

209

b. l l

Again, although this argument refers to a and b only, it is generalizable to apply to any two things supposed indiscernible, and thus properties of difference establish PlI. But the thesis established is trivial, for the work in such arguments is again done by properties of identity, since lacking a property of difference is equivalent to having a property of identity. So properties of difference must als o be excluded from the domain of quantification of any metaphysically serious version of PlI. Properties of difference are not the only trivializing properties that do not entail properties of identity. Consider property (4) :

(4)

being numerically distinct from a or not being green.

Property (4) is the complement of property (2) . Since no two things can lack property (4), it can be used to deploy an argument similar to (ix)-(xii). Since that argument is generalizable in the relevant way, properties like (4) prove PII. B ut it should be clear that the thesis thereby established is trivial since all the work in such arguments is done by the property of being identical to a. For lacking the property of being numerically distinct from a or not being green is equivalent to having the property of being identical to a and being green, and no two things can share this one because they would share the non-shareable property of being identical to a. This suggests that trivializing properties are those having or lacking which entails having a property of identity. Since lacking a property is having its complement, we may attempt to define trivializing properties as follows: D2

F is a trivializing property =def. (1) F entails a property of identity or (2) the complement of F entails a property of identity.

But D2 is wrong, for not all trivializing properties satisfy it. Consider properties (5) and

(5) (6)

(6) ;

being identical to a or being green. being identical to a or not being green.

Neither (5) nor its complement entail a property of identity. The same is true of (6) and its complement. Many things could and do have them and many things could and do lack them. Nevertheless they make PII true. For nothing can have both of them. But they make it trivially true, because having both of them entails having property ( 1 ) . It is only thanks to this entailment that together they make PII true . The same is true of the complements of properties (5) and (6), properties (7) and (8) respectively: (7) (8)

being numerically distinct from a and not being green. being numerically distinct from a and being green.

For although neither having nor lacking either (7) or (8) entails having a property of identity, lacking both of them does entail having ( 1 ) , the property of being

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identical to a. In general, properties like (7) and (8) are such that lacking b oth of them entails having a property of identity. So such properties make PIT trivially true. One might decide to exclude from the property domain of PII only one property from such pairs like (5) and (6) . But this would be arbitrary. There is no reason to count either of them as trivializing that does not apply to the other. Thus we should count both of them as trivializing properties . The same is true for (7) and (8). This suggests we replace D2 by D3 below: D3

F is a trivializing property =def. (a) F or its complement entails a property of identity, or (b) F or its complement is the conjunct of a conjunctive property which entails a property of identity and the other conjunct(s) neither individually nor jointly entail a property of identity.

D3 rightly makes (5) and (6) trivializing properties, since they are the conjuncts of (5)&(6), and so they satisfy condition (b) in D3. The same is true for (7) and (8). B ut D3 has a crucial defect: it counts as trivializing some properties that are not. Consider properties (9) and ( 1 0) below: (9) ( 1 0)

being green. being (identical to a or not green) and being green. 1 2

The defect of D3 is that it makes (9) a trivializing property, for (9) satisfies the second disjunct in its definiens. In effect, (9) is a conjunct of ( 1 0) , which entails a property of identity, but the other conjunct of ( 1 0) , namely (6), entails no property of identity. But (9) is the property of being green. And the property of being green is a paradigmatic non-trivializing property. I do not see how to solve this difficulty in terms of the notion of entailment. But even if there is such a satisfactory solution, trying to define trivializing properties . as those that.-somehow or other entail properties of id�ntity is marred frem the . beginning. For any definition that counts properties that entail properties of identity as trivializing properties assumes that no pure properties entail properties of identity. But suppose things had pure individual essences . Imagine, for the sake of example, that being the greatest philosopher was the individual essence of Plato. In that case the property of being the greatest philosopher would entail a property of identity, namely the property of being identical to Plato. If all things have pure individual essences , then PII is true, and it is true thanks to these pure individual essences . But a property like being the greatest philosopher does not trivialize PII. If what one proves is that numerically different things must have different pure individual essences, then one has established that every numerical difference goes accompanied by a qualitative difference - and this is no triviality. !3 The point can perhaps be better appreciated by considering Leibniz 's position. For Leibniz all things (individual substances) have qualitative essences , expressed by their c omplete concepts (and therefore more complex than anything like the property of being the greatest philosopher) . These essences entail properties of identity and so they guarantee PlI, But no doubt Leibniz' s was not a trivial version of PII.

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Whether or not things have pure individual essences is not the question here. The point is simply that, whether or not things have such essences, D3 is inadequate as a characterization of trivializing properties . First, if things have such essences, D3 is extensionally wrong. Second, even if things do not have such essences, a fonnulation of a non-trivial version of PII should not presuppose that things do not have such essences . Third, even if things do not have such essences, and all trivializing properties satisfy D 3 , the mere conceptual possibility of things having pure individual essences shows that D3 does not tell us why trivializing properties trivialize PlI. IV

We need a different kind of definition of trivializing properties. Since it seems clear that trivializing properties are those related in some special way to properties of identity, the question is: how are trivializing properties related to properties of identity, if not by entailment? The intuitive answer is that they contain properties of identity. And this marks the difference between a trivializing property like (6), which contains the property of identity ( 1 ) , and a non-trivializing property like (9), which does not contain any property of identity. This approach looks promising. Indeed Katz proposes a solution in terms of a notion of containment. But what Katz does is to specify the class of trivializing predicates, which is not the same as specifying the class of trivializing properties if only because presumably, as Katz acknowledges, there are properties which no predicate expresses. What is Katz's definition of trivializing predicates ? He first introduces what he calls basic identity properties (BIPs) as follows : F is a BIP if and only if ( 1 ) it is possible that (::Jx)(Fx) and (2) it is necessary that (x)(y)(Fx & Fy :::> x = y) . Let us call predicates expressing BIPs EIP-predicates. Katz s ays that a BIP-predicate is a trivializing predicate and that a predicate 'P' contains a BIP-predicat[':cessentially provided 'P' contains a BIP-predicate but is not logically equivalent to a predicate that does not: 'x is numerically distinct from a' contains a BIP-predicate essentially, but 'x is green and (identical to a or numerically distinct from a)' does not. Then Katz says that a predicate 'P' expresses a trivializing property if and only if 'P' contains a BIP-predicate essentially or 'P' may be defined in terms of some predicate that does. This , of course, makes such properties like ( 1 )-(8) above, and also ( 1 0) and others, trivializing properties. Needless to say, this does not make a property . like (9) a trivializing property. 14 What are we to say about Katz's definition of trivializing predicates? First, I would say that it wrongly makes trivializing properties those expressed by superlative predicates, that is, predicates like 'being the tallest man' , 'being the widest river' and so on. Such superlative properties ' are BIPs. But superlative properties in general do not trivialize PlI. Superlative properties, being BIPs, cannot be shared, for example no two things could be the tallest man. But they do not serve to prove PII, since not everything must have one of them. The most one can do with them is to assert that if something has a superlative property then that thing has no indiscemibles, but this, of course, is far from asserting that nothing has indiscemibles,

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which is what PII requires. If they do not make PII true, superlative properties c annot make it trivially true. But does perhaps everything have a superlative property relative to a certain reference class? I am not sure. In a world like that imagined by Max Black ( 1 952, p . 1 56), consisting o f only two indiscernible iron spheres, there seems t o be no superlative property that either sphere has relative to any reference class. In any case, even if everything has a superlative property relative to some reference class, the problem with Katz's proposal is that it makes those properties that are superlative relative to no class (or relative to the most inclusive class) trivializing, which they are not. In any case the difficulty with superlative properties can be met by just letting BIPs be properties of identity - in that case superlative properties will not count as trivializing properties for they will not be expressed by trivializing predicates. Second, Katz does not explain what it is for a predicate to contain another. S o it is not clear which predicates contain BIP-predicates and which do not, and therefore it is not clear which predicates express trivializing properties and which do not. For although it may be intuitively clear that the predicate 'is green' does not contain any BIP-predicate, intuition suggests that the predicate 'thinks about a' and 'is one metre apart from a' contain the BIP-predicate 'is identical to a ' . But these predicates do not express trivializing properties , since properties like thinking about a and being one metre apart from a can be shared and they do not make PII true unless conj oined with properties like being identical to a o r not thinking about a or being identical to a or not being one metre apart from a. But it is these latter properties that trivialize PII. Third, it is possible to define trivializing properties, rather than predicates , since all we need is a precise notion of property containment. For instance, one may introduce a notion of property containment via some stipUlations like the following: Every property contains itself. Every property that is a Junction of other properties c.ontains those properties..(i.e:c a conjunctive property contains its conj uncts ; a disjunctive property contains its disjuncts ; a negative property contains its negated property) . The relation of property containment is transitive. Then, following Katz, we say that a property F contains a property of identity essentially provided F contains a property of identity but is not logically equivalent to a property that does not. Then, to avoid the problem of superlative properties , we define trivializing properties in terms of their containment of p roperties of identity, rather than B IPs : D4

F is a trivializing property

= def.

F contains a property of identity essentially.

D4 rightly counts properties ( 1 )-(8) and ( 1 0) as trivializing properties . Furthermore, thanks to the precise specification of the containment relation, it rightly excludes properties like thinking about a and being one metre apart from a from the class of trivializing properties .

How Not to Trivialize the Identity of Indiscemibles

213

But D 4 has several problems. First, i t does not seem to count a s trivializing the property of being a member of raj. For being a member of {aj does not seem to be a property of identity, nor the complement of a property of identity, nor a conjunctive or disjunctive property having a property of identity as one of its conjuncts or disjuncts. But being a member of {aj is a trivializing property. For one could argue for PIT thus: if a and b have all their properties in common, then since a has the property of being a member of {aj , b has this property as well; but since whatever is a member of { a } is identical to a, a = b. But clearly what is doing the work here is the property of being identical to a, which must be had by whatever is a member of { a } . Being a member of {aj seems to contain the property of being identical to a in the sense that it is a relational property whose relatum ( { a } ) is specified in terms that depend on the identity of a and so, in that sense, on the property of being identical to a. But if we redefine containment so as to make the property of being a member of {aj contain the property of being identical to a, then we should make sure we avoid making thinking about a or, even more to the point, being the only lover of a, contain a property of identity. But even if this can be done, a definition of trivializing properties in terms of a notion of property containment will still be lacking, even if extensionally correct. The problem with such a definition is that it does not explain why trivializing properties are trivializing properties. Why should properties containing properties of identity trivialize PIT? It is not evident why this should be the case. Furthermore, it is clear that merely containing a property of identity is not what makes a property trivializing, since there are properties, like being green and (being identical to a o r being numerically distinct from a), which contain properties of identity but do not trivialize PIT. This is why D4 does not define trivializing properties purely in terms of containment, since the explanation of what it is for a property to contain a property of identity essentially makes reference not only to the properties it contains but also to the properties it is logically equivalent to. B ut the relation of equivalence is not a containment relation. IS It may be claimed .that this . 1ack oLpurity .is not a. symptom DL �xplanatQry deficiency. Why should it matter that the definition defines trivializing properties purely in terms of property containment? Even if it does not define them purely in terms of property containment, that does not show that D4 fails to provide an explanation of why trivializing properties are trivializing. Perhaps what explains why they are trivializing properties is that they contain a property of identity and are equivalent only to properties that do. B ut why should such properties be trivializing properties ? It is not clear why this should be the case. Furthermore, there are reasons to doubt that this is what explains why tlivializing properties are trivializing. Consider property (5). It contains a property of identity and is not logically equivalent to a property that does not. But this does not show it is a trivializing property - after all, property (5) can be shared and so it does not suffice to establish PIT. The same applies to (6). S omeone may say that even if (5) and (6) can be individually shared, they are such that in virtue of what they contain the pair of them cannot be shared (i.e. no two things can have both of them) . But this does not explain why they are trivializing properties , since (6) and (9) are also such that in virtue of what they contain the pair of them cannot be shared. But (9) is not a trivializing property.

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Universals, Concepts and Qualities

It may be claimed that the relevant difference between (5) and (9) is that (5) contains a property of identity while (9) does not. But we saw earlier that there are properties that contain properties of identity but do not trivialize PIT. Furthermore, saying that it is in virtue of containing a property of identity that (5) is prevented from being shared with (6) does not work. For it is no less by virtue of containing the property of being green than containing a property of identity that (5) is prevented from being shared with (6) . But it is by virtue of containing the property of being green that (9) is prevented from being shared together with (6).

v

This second obj ection to D4 applies only if we are interested in more than mere extensional correctness . But extensional correctness cannot be the goal of our enql!iry. For extensional correctness per se does not provide an explanation of why trivializing properties trivialize PIT. So even if we hit an extensionally correct definition of trivializing properties, we may still have serious difficulties in recognizing it as a correct definition, for there may be properties such that it is not intuitively clear whether they trivialize PIT. Furthermore, even if we knew that a certain definition is extensionally correct, it may not be philosophically illuminating. For we might know that without having answered the question of why trivializing properties trivialize PII. But knowing what features make trivializing properties trivialize PII puts us in a position to define trivializing properties: trivializing properties are those that have the features in question. So the question I shall answer in this section is What makes trivializing p roperties trivialize PI!? Trivializing properties are those that can be used to establish a trivial version of PIT. So in order to find out what makes trivializing properties trivialize PII, we first need to understand why the trivial version of PIT is trivial. Once we know this it 'should be. easy. to. see what makes. triviali zing.pmperties trivialize .PII, namely that they have those features that enable them to be used to establish a trivial version of PIT. The trivial version of PII is the version established by arguments like those considered in Sections 2-3 . I shall focus on argument (i)-(iv), which by using properties of identity is a paradigmatic trivializing argument. So why do arguments like (i)-(iv) establish a triviitl thesis? PII is meant to be a thesis about the connection be.tween qualitative identity and numerical identity, namely that qualitative identity entails numerical identity: there cannot be qualitative identity without numerical identity. Equivalently, there cannot be solo numero difference : things that differ numerically must also differ qUalitatively. B ut (i)-(iv) establishes that if a and b share all their properties, and therefore are qualitatively identical, they are numerically identical because they share a property of identity. B ut sharing a property of identity is being numerically identical. S o what the argument shows is that qualitatively identical things that are numerically identical are numerically identical . This is trivial. In other words, the argument establishes only that any numerically different things differ in their properties of identity, without requiring that they differ in any . .

·

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215

other property. But difference with respect t o a property o f identity i s numerical difference, not qualitative difference. So all the argument establishes is that numeriqilly distinct things are numerically distinct This is trivial. So (i)-(iv) establish.es a trivial version of PIT because it only establishes the numerical difference of numerically distinct things. What the argument establishes is only the letter of the principle when formulated using umestricted property quantifiers - that no two things can share all their properties - but it does not establish the spirit of the principle - that there cannot be qualitative identity .

without numerical identity.

What features of properties of identity account for this? That differing with respect to them is differing numerically. For since differing qualitatively is more than differing numerically, simply establishing a difference with respect to properties of identity establishes only a numerical difference, not a qualitative difference. I am not saying that properties of identity are trivializing' because differing with respect to them entails no more than a numerical difference. I am saying that they are trivializing because differing with respect to them is differing numerically. This is so even if differing with respect to properties of identity entails a qualitative difference. In that case one still cannot establish a qualitative difference by simply establishing a difference with respect to properties of identity : one needs to invoke the fact that a difference with respect to properties of identity entails a qualitative difference. This also applies to properties of difference. They are the complements of properties of identity. S o having a property of difference is lacking a property of identity and lacking a property of difference is having a property of identity. So differing with respect to properties of difference is differing with respect to a property of identity and so differing with respect to them is differing numerically. Thus establishing a difference with respect tQ a property of difference only establishes a numerical difference, not a qualitative difference. So properties of . difference are trivializing properties. There are two things to distinguish. , One.,is. what the trivializing character Of . properties of identity and difference consists in; the other is what makes them have that character. The trivializing character of properties of identity and difference consists in that merely establishing a difference with respect to them only establishes a numerical difference between the things in question. What makes properties of identity and difference have that character is that being numerically different is differing with respect to those properties. The trivializing character is common to all and only trivializing properties. Every property such that merely establishing a difference with respect to it only establishes that the things in question are numerically different is a trivializing property. Such a property can be used to establish a trivial version of PIT and so it is a trivializing property. And every property such that merely establishing a difference with respect to it establishes more than a numerical difference is such that establishing a difference with respect to it establishes a qualitative difference. S o , since establishing a difference with respect to it cannot be used to establish a trivial version of PIT, such a property is not trivializing. But although the trivializing character is common to all and only trivializing properties, only in the case of properties of identity and difference what accounts

··

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for their trivializing character is ' that · differing with respect to them is ' differing numerically. 1 6 So how can a property F be trivializing without b eing a property of identity or difference? Even if differing with respect to F is not differing numerically, differing with respect to F may consist in differing numerically. If differing with respect to P may consist in differing numerically; merely establishing a difference with respect to F only establishes a numerical difference. So if differing with respect to 'p may consist in differing numerically, F is a trivializing property. Differing with respect to F may consist in differing numerically if and only if differing with respect to F may consist in differing with respect to a property of identity or property of difference. So properties such that differing with respect to them may c onsist in differing with respect to a property of identity or difference are trivializing properties . How can a property be such that differing with respect to it may consist in differing with respect to a property of identity or difference? Consider conjunctive properties . A conjunctive property is such that having or lacking it is having or lacking other properties. So differing with respect to F &G is simply differing with respect to F or G or both. So differing with respect to F &G may consist in differing with respect to F. So some conjunctive properties containing properties of identity are such that a difference with respect to them may simply consist in a difference with respect to a property of identity. Consider the property of being identical to a and being green. Differing with respect to it consists in differing with respect to either of its conj uncts . So differing with respect to it may consist in differing with respect to the property of being identical to a. And so differing with respect to the property of being identical to a and being green may simply be differing numerically. The same applies to conjunctive properties containing properties of difference, like the property of being numerically distinct from a and being green. The same is true of disjunctive properties like being numerically distinct from a or not being green and being identical to a.or:heing.g.reen; ·TIllscis why· such-eonjunctive.and disjunctive pl'0perties· are trivializing properties . It should be clear now why properties like being green, being square and being hot are not trivializing properties . Differing with respect to them must consist in more than simply differing numerically: it must consist in differing with respect to colour, shape and temperature. Por similar reasons impure properties like being the father of a, loving b , being close to c and being in the same place as d are not trivializing properties. Differing with respect to these properties must be more than differing with respect to a property of identity or difference: it must be differing with respect to fathering a, loving b, being close to c and being in the same place as d. Let e be the father of a. Even if origin is essential, and so e cannot fail to be the father of a provided a exists , there is more to being the father of a than being such that a exists and being identical to e. The extra is all that is involved in fathering a . Similarly i n the other cases . l 7 This also explains why superlative properties are not trivializing properties. Differing with respect to being the tallest man is more than differing with respect to a property of identity or difference : it is also differing with respect to height from other men. It als o makes clear why there are some complex properties containing

."

'�

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217

properties o f identity that are not trivializing properties, namely those properties that contain properties of identity but are logically equivalent to properties that are not trivializing, like the conjunctive property of being green and (being identical to a or being numerical {y distinct from a). Properties like these are such that differing with respect to them must consist in differing with respect to a non-trivializing property, in this case the property of being green. Thus establishing a difference with respect to those complex properties will be establishing more than a numerical difference. Therefore such complex properties are not trivializing properties, in spite of containing properties of identity. 1 8 VI

So far, so good. B ut how about the property of being a member of raj ? This is a trivializing property but it does not appear to satisfy our characterization of trivializing properties. For even if differing with respect to it will require differing with respect to being identical to a, it seems to require differing with respect to being a member of { a } , and so it seems that a difference with respect to it cannot simply consist in a difference with respect to the property of being identical to · a . Of course a is a member of { a } in virtue of being identical to a - that is, it has the property of being a member of {aj in virtue of having the property of being identical to a. But this cannot be what makes the property of being a member of {aj trivializing. For that one property is had in virtue of another only means that there is a particular relation between the two - the in virtue ofrelation. l9 1t does not mean that differing with respect to one of those properties consists in differing with respect to the other. But what if it were the case that all of the properties of a thing were had in virtue of being that thing? In that case a would have all of its properties simply in virtue of being a. Perhaps the world is like that. Perhaps things cannot share all their properties. because, they .have their properties in virtue. ofbeing_the things .. they.care., . Or perhaps things cannot share all their properties because every thing has a qualitative property that is necessarily peculiar to it in virtue of being the thing it is. In either case PIT would be true but it would be non-trivially true. For even if things were qualitatively different in virtue of being numerically different, differing qualitatively would still be more than differing numerically.20 But that any thing numerically different from a must also differ from a with respect to being a member of { a } is a trivial fact. However mysterious the singleton membership relation is, it appears that differing with respect to being a member of a singleton is no more than differing numerically. How can this be? This is because, if sets exist, the identity of the members fixes what sets they belong to. And this is, in tum, because given a set S with certain things as members, there is no more to being a member of S than being one of those things. So, given { a } , there is no more to being a member of { a } than being a, that is, being identical to a. Thus the property of being a member of {aj is the property of being such that {aj exists and being identical to a. It is frequently asserted that a belongs to { a } in virtue of being a rather than being a in virtue of belonging to { a } . My proposed account of the property of being

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a member of {aj nicely explains why this is so: being a member of { a } consists in satisfying two conditions, one of which is being identical to a, but being identical to a does not consist in being a member of { a } . This also goes s ome way to dispel the mystery associated with the singleton membership relation. According to D avid Lewis, the relation of singleton to member holds in virtue of qualities or external relations of which we have no conception whatsoever. That is, we do not clearly understand what it is for a singleton to have a member (Lewis, 1 99 1 , p. 3 5 ) : If my account of the property of being a member of {aj is right, then we have a conception of the relations in virtue of which a thing is a member of a singleton: these are existence and identity. But there is a sense in which Lewis is right that the singleton membership relation is mysterious . Singletons are atoms and the connection with their members is primitive and thereby in some sense mysterious and opaque. So we do not know in virtue of what a certain singleton has a certain thing as its member. That is, we do not know in virtue of what the property of being a member of {aj is the property of being such that {aj exists and being identical to a rather than the property of being such tha t {aj exists and being identical to b. After all, if { a } exists, b has the property of being such that {aj exists and being ide.n tical to b, but this does not make it a member of { a } . But this is a mystery that we should expect. For there is nothing in virtue of what { a } is the singleton of a as opposed to the singleton of b: it j ust is. So there is nothing in virtue of what the property of being a member of {aj is the property of being such that {aj exists and identical to a rather than the property of being such that {aj e.x:ists and identical to b:. it just is one rather than the other. Nothing in my account of the property of being a member of {aj helps with this. All my account says is what the property of being a member of {aj consists in, and makes the property of being identical to a part of that property. So, given that being a member of { a } consists partly in being identical to a, my account makes clear why a is a member of { a } in virtue of being a rather than being a in virtue of being a member of {a } . But nothing in my: account explains . w hy being. a member of . { a.} , ," consists partly i n being identical t o a rather than being identical t o b. To understand this we should, I think, know in virtue of what a singleton has its members . B ut there is nothing in virtue of which a singleton has its members, so that my account does not explain this should not be seen as a problem for it.2 1 I t may be thought that a problem for m y account is that it does n o t make clear why the singleton membership relation has the formal features it has , for example irreflexivity, asymmetry, intransitivity. But there is no reason why an account of what the property of being a member of {aj consists in should make clear why singleton membership has those formal features . This is not an account of singleton membership in general: it is an account of what it is for a thing to be a member of its singleton. What matters is simply that my account be compatible with those formal features of the singleton membership relation, and it is. The property of being such that {aj exists and being identical to a is a conjunctive property one of whose conjuncts is the property of being identical to a, and so differing with respect to being a member of {aj may consist in differing with respect to the property of being identical to a. Thus differing with respect to being a member of {aj may be differing numerically. Even more, since whenever two . .

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things differ with respect t o being a member o f { a } both o f them are such that { a } exists, differing with respect to being a member of {a} must, and therefore does, consist in differing numerically. So there are properties such that differing with respect to them consists in differing numerically and there are properties such that differing with respect to them may consist in differing numerically. In both cases such properties can be used to establish a trivial version of PH, since establishing a difference with respect to them establishes no more than numerical difference. These are the trivializing properties. But it will be impossible to establish a trivial version of PH by establishing a difference with respect to a property such that differing with respect to it must consist in more than differing with respect to a property of identity, and so it must consist in more than differing numerically. These are the non-trivializing properties.

VII

We can now define trivializing properties as follows : D5

F is a trivializing property differing numerically.

=def.

Differing with respect to F is or may be

D5 is an intensional definition of trivializing properties : it purports to tell us what being a trivializing property consists in rather than merely specifying the class of trivializing properties. Since it tells us what it is to be a trivializing property, D5 is philosophically illuminating in a way in which a mere specification of the class of trivializing properties is not. By saying what trivializing properties are, D5 specifies a certain class of properties as the class of trivializing properties. D5 is right in this respect to the extent that the class it specifies includes the properties . of identity and all the .other trivializing properties we have considered. But is D5 extensionally c orrect? Do all and only trivializing properties satisfy D5 ? Yes . For, as I have argued, D5 is intensionally correct. So it is extensionally correct. . We now know what trivializing properties are. So we know what properties should not be quantified over in order not to trivialize PII. Since not all impure properties are trivializing properties, it should now be clear that one can quantify over some impure properties without trivializing it and so that there are at least three non-trivial versions of PH: PH I , PH2 and PH2. S . 22

Notes

2

Often, but not always. In Individuals Strawson calls them universals-cum-particulars ( 1 959, p. 1 37). No doubt my understanding of the phrase ' qualitative difference ' is idiosyncratic, since normally only pure properties would be taken to make a qualitative difference . But I have found no better phrase to express what I want to express, namely that difference

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Universals, Concepts and Qualities which is not merely numerical difference, that is, which is not a solo numero difference. As I said, what I mean by qualitative difference is any difference that is not merely a numerical difference. But differing with respect to some impure properties , for instance differing with respect to the impure property of being two miles from the Eiffel Tower, is more than differing merely numerically. In what follows, the reader should bear in mind that in this chapter qualitative difference is neither synonymous nor coextensive with difference with respect to pure properties . . If one takes second-order variables to range over sets , then the principle in the text is merely a set-theoretical analogue of PIT, rather than PIT itself. One can also express PIT as a first-order principle, for example (x)(y)(z) [(x has z == y has z) :;) (x y)] , where 'x has z' is true if and only if z is a property of x. In this chapter I shall stick to the canonical second-order formulation in the text. But whether the principle must be formulated as a first- or second-order principle is not relevant for the purposes of the present chapter. There is another dimension in which I would disagree with Strawson, since in that passage he also makes the necessitated version of PIT the only one worth discussing (Strawson, 1 95 9 , p. 1 20). But I cannot discuss this issue here. It is important to be clear what properties of identity are. Having recourse to the property abstraction A-operator makes that clear. The A-operator binds a variable from a first-order open sentence to designate the property expressed by that open s entence. Thus properties of identity are those that in their A-expression the open sentence from which the A-operator binds a variable consists only of an identity sign flanked by an individual variable and an individual constant. So properties like being identical to a and being identical to b are properties of identity because their A-expressions are, respectively, ' (:A..x) (x a) ' and ' (:A..x) (x b) ' . But the properties of being identical to something or being self-identical are not properties of identity. Their A-expressions, ' (:A..x) (x y) ' and ' (:A..x) (x x) ' , do not satisfy our characterization. That b is identical to a follows only on the assumption that if a thing has property F then it is F. This is unexceptionable, and should not be confused with the more controversial principle that if a thing is F then it has property F. Informal versions of (i)-(iv) appear in Brody ( 1 980), p. 9, Katz ( 1 9 83 ) , p. 3 7 , Legenhausen ( 1 9 89), p . 6 2 6 , and Whitehead and Russell ( 1 925), p . 57. The trlvializingnatur@ 0f properties 0f identity is .reCQgnized in, amongo.others,Adams ( 1 979), p. 1 1 , Ayer ( 1 954) , p. 29, Black ( 1 952), p. 1 5 5 , Katz ( 1 9 8 3 ) , pp. 37-8, Legenhausen ( 1 9 89), p. 626 and O ' Connor ( 1 954), pp. 1 03-4 . This is the sense i n which I shall conceive o f property entailment i n this chapter and this is the usual way of conceiving property entailment. S ee, for instance, Carnap ( 1 9 8 8 ) , p . 1 7 , Katz ( 1 9 8 3 ) , p. 44 and Lewis ( 1 9 8 3 ) , p. 1 99 . I t may be thought that the problem with D l is that, given that i t is necessary that everything is self-identical and that if any thing is self-identical then that thing has a property of identity, all properties entail properties of identity and so, according to D 1 , all properties trivialize PIT. This would show D l to b e wrong, since some properties, like being green , do not trivialize PIT. But this is not a problem for D l . For even if it is necessary that everything is self-identical and that if any thing is self-identical then that thing has a property of identity, it does not follow that all properties entail properties of identity. For all that follows from this is that every property F is such that it is necessary that if any thing has F, then that thing has some property of identity. But it does not follow from it that for every property F there is a property of identity F* such that it is necessary that if any thing has F, then that thing has F*. And only in this latter case does every property F entail a property of identity. I have found no version of (ix)-(xii) in the literature, but something similar to it is in =

4 5

=

=

6

7 8

9 10

11

=

=

How Not to Trivialize the Identity of Indiscernibles

22 1

Katz ( 1 98 3 ) , p. 40. There are also arguments that derive discemibility from numerical difference, like the following two, which I shall deploy using the A-operator: (i2) (ii2) (iii2) (iv2)

a#b

(Ax)(X a)(a)' -,(Ax)(X a)(b) =

=

(:IF) (Fa & -,Fb)

(ix2) (x2) (xi2) (xii2)

a#b

-,(Ax)(X # a)(a) (Ax) (X # a)(b) ( :IF) (-,Fa & Fb )

These arguments are contrapositive versions of (i)-(iv) and (ix)-(xii) . Informal versions of (i2)-(iv2) and (ix2)-(xii2), or of mixtures of them, appear in Adams ( 1 979), p. 1 1 , Ayer ( 1 954) , p. 29, B ergmann ( 1 95 3 ) , p. 77, Black ( 1 952), p. 1 5 3 , B road ( 1 9 3 3 ) , pp. 1 72-3 , Greenlee ( 1 968), p . 760, McTaggart ( 1 9 2 1 ) , p . 96, O ' C onnor ( 1 954), pp. 1 034, Odegard ( 1 964), p . 204 and Russell ( 1 959), p . 1 1 5 . The arguments (i)-(iv), (i2)­ (iv2) , (ix)-(xii) and (ix2)-(xii2) are clearly related to each other, but they have never been clearly differentiated and, sometimes, they are thought of as a single argument (e.g. Adams , 1 979, p. 1 1 , footnote 1 1 , seems to confound several of them) . 1 2 Let us resort to A-formulations to make clear what property ( 1 0) is. Where ' Gx' stands for ' x is green' , ( 1 0) is the following property: (Ax)((X a v Gx) & Gx) . 1 3 To make the point of this paragraph I do not need to invoke pure individual essences . Invoking the possibility of impure individual essences that are not trivializing would have been good enough. But the point is more forcefully made by invoking the possibility of pure individual essences . 14 I have altered Katz 's terminology. He calls BIP-predicates identity-predicates and he calls trivializing properties identity-properties. So what he actually says is that ' a predicate, P, expresses an identity-property if and only if P contains an identity predicate essentially or may be defined in terms of some predicate that does ' (Katz, 1 9 8 3 , p. 4 1 ) , I changed Katz' s terminology because o f its potential for confusion. 'Identity-predicate' suggests a predicate that expresses a property of identity, but as we shall see below not all BIPs are properties of identity. 'Identity-property' suggests a property of identity, but as we have seen not all trivializing properties are properties of identity. Katz was of course aware that not all trivializing properties are properties of identity, and although he did not realize that not all BIPs are properties of identity, nothing here should be 'taken to imply that Katz llsed ·his terminology wufu$!ugly or confusedly. He ·used his terminology clearly and consistently, but nevertheless his terminology has potential for confusion. 15 Katz's definition of trivializing predicates has the same feature of not being purely in terms of containment. 16 Note that the trivializing character of properties of identity and difference consists in that merely establishing a difference with respect to them only establishes that the things in question are numerically different - not that the things in question differ only with respect to properties of identity and difference. The latter is not true. For instance, if a and b differ with respect to properties of identity and difference, then they differ with respect to conjunctive properties having their properties of identity and difference as conjuncts . 1 7 An interesting case is the property of having all parts in common with a. This is trivializing because muong the parts of a is its improper part, namely a itself. So this property leaves open the possibility that a and b differ only with respect to their improper parts , in which case they differ only numerically. S ome people think that no two things can share all their proper parts . If it is true that no two things can share all their proper parts , then there is a non-trivial version of PI! that is true. But this does not make the property of having all proper parts in common with a trivializing. Differing =

-,

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18

19

20

21 22

Universals, Concepts and Qualities with respect to such a property is differing more than merely numerically. Furthermore, the insight that no two things can share all their proper parts , if indeed it is true, is not a trivial but a substantive metaphysical insight. There are other properties containing properties of identity that are not trivializing, and in this case the explanation of why they are not trivializing must be different. C onsider the property of being identical to a ,o r being numerically distinct from a. This property is not trivializing because it must be shared by everything and so, since no two things can differ with respect to it, not even a trivial version of PI! can be proved by its means. The propeliy of being identical to a and being numerically distinct from a is als o such that it c annot be shared, though this time because nothing can have it. This relation between the properties in question is different from their being necessarily coextensive. For, assuming that necessarily a exists if and only if so does { a } , the necess ary coextension of the properties is symmetrical: nothing can have one of the properties of being identical to a and being a member of faj without having the other ­ but although a has the property of being a member of faj in virtue of having the property of being identical to a, it does not have the latter in virtue of having the former. It is important to emphasize that the non-triviality of PI! in these situations would not be due to our ignorance that things have all their properties, or some properties necessarily peculiar to them, in virtue of their identity. Even if we dis covered this, through metaphysical argument or any other means, it would be a discovery of a non­ trivial fact. Here I g o beyond Lewis, who seems to think that there may b e something in virtue of which singletons have their members . I am grateful for comments to the following: Bill Brewer, D avid Charles , John Divers, B ernard Katz, Robin Le Poidevin, Hugh Mellor, Alex Oliver, Oliver Pooley, Ralph Wedgwood, Tim Williamson and, especially, Arnie Koslow.

References Adams , R.M. ( 1 979), 'Primitive 'rhisness and Primitive Identity ' , The Journal of Philosophy, 6: 5-2 6 . · · · ... . . . . . . . Ayer, A.J. ( 1 954), 'The Identity of Indiscernibles ' , in his Philosophical Essays. London: Macmillan. Bergmann, G. ( 1 953), 'The Identity of Indiscernibles and the Formalist Definition of Identity ' , Mind, 62: 75-9 . Black, M. ( 1 952) , 'The identity of indiscernibles ' , Mind, 6 1 : 1 5 3-64. Bro ad, C . D . ( 1 93 3 ) , Examination of McTaggart 's Philosophy. Cambridge: Cambridge University Press. Brody, B. ( 1 980), Identity and Essence. Princeton: Princeton University Press. Carnap , R. ( 1 9 8 8 ) , Meaning and Necessity. Chicago : University of Chicago Press . Forrest, P. (2002), 'The Identity o f Indiscernibles ' , The Stanford Encyclopedia of Philosophy (Summer 2002 Edition), Edward N. Zalta (ed.), URL . Greenlee, D. ( 1 96 8 ) , 'The Similarity of Discernibles ' , The Journal of Philosophy, 65: 75363. Katz, B . ( 1 9 83 ) , ' The Identity of Indiscernibles Revisited ' , Philosophical Studies, 4 4 : 3744. Legenhausen, G. ( 1 989), ' Moderate Anti-Haecceitism ' , Philosophy and Phenomenological Research, 49: 625-42. .

. ...

..

.

=

'

.

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Lewis, D . ( 1 98 3 ) , 'Extrinsic Properties ' , Philosophical Studies, 44: 1 97-200. Lewis , D. ( 1 9 9 1 ) , Parts of Classes. Oxford: B asil Blackwell. McTaggart, J.M.E. ( 1 92 1 ) , The Nature of Existence, vol. l , Cambridge: Cambridge University Press . O ' Connor, D . J . ( 1 954), 'The Identity o f Indiscemibles ' , Analysis, 1 4 : 1 03-10. Odegard, D . ( 1 964), 'Indiscemibles ' , The Philosophical Quarterly, 14: 204- 1 3 . Russell, B . ( 1 959), My Philosophical Development. London: George Allen & Unwin. Strawson, P.P. ( 1 959), Individuals. An Essay in Descriptive Metaphysics. London: Methuen & Co. Van Cleve, J. (2002) , 'Time, Idealism and the Identity of Indiscemibles ' , in Philosophical Perspectives, 16: 379-9 3 . Whitehead, A . N . and Russell, B . ( 1 925) , Principia Mathematica, v o l . 1 . Cambridge: Cambridge University Press.

Chapter 1 2

Universals and the Defence of Ante Rem Realism George Bealer

1.

Terminological Preliminaries

In traditional philosophical discussions , the following sorts of entities have at one time or another been deemed universals : qualities, quantities, kinds, types, forms, properties, relations, categories , general ideas, concepts . If we are permitted to simplify matters, we may distinguish two main traditional uses of the expression 'universal' - one quite restricted, the other more liberal. According to the restricted use, universals form a privileged subset of entities of the indicated types, namely, those that play a fundamental (maximally 'basic ' or perfectly ' natural ' ) role in the ultimate constitution of reality. In this connection, they are thought to be the entities suitable for ultimate general explanations . They are also thought to underlie genuine resemblances and, as such, are supposed to be 'repeatable ' entities and so in that sense 'universal' . (It should be noted that these criteria are not equivalent: for example, there evidently are perfectly 'natural' properties that are not repeatable, e.g. being an absolutely perfect being, being an even prime.) According to the more liberal use, universals are the sorts of entities expressed by meaningful linguistic predicates and, relatedly, which are the predicate entities of propositions. There is no gemini! constraint that they need to be fun damental ( 'basic ' or 'natura!' ) : for example, such properties as the property of being a parricide - what Locke would call mixed modes - qualify as universals on this use. Accordingly, such properties need not play a privileged role in explanation. Nor must universals always underlie resemblances (and so be 'repeatable' ) . Since both uses o f 'universal' are well established i n the history o f philosophy, it is not helpful to proceed as if there is only one correct use, for doing so renders various significant historical discussions unintelligible. The best strategy is simply to make clear the use that one is employing. In this chapter, I will be employing the more liberal use - although, in Section 5, I will take up the important question of whether there is a special subclass of universals meeting the requirements of the more restricted use. Properties are the most common examples of universals (in both uses of 'universal' ) discussed in the philosophical literature. Now it is a truism that the property of being F is a property. This canonical gerundive form identifies the primary sense of the term 'property ' in ordinary English and is therefore suited to anchor usage in philosophical discussions of properties. S ome philosophers, however,

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hold that 'basic ' or 'natural' properties are the only properties there are', B ut this flies in the face of ordinary usage; for example, if one truly takes there to be no non-basic properties, one is evidently forced to deny the truism that the property of being a parricide is a property ! Other philosophers take this trend even further, holding that the only 'natural' properties are physical magnitudes (Putnam, 1 972) or those having causal powers (Shoemaker, 1980), But pace Putnam and Shoemaker, there are 'natural' properties that neither are physical magnitudes nor have c ausal powers, for example, various ' natural' logical and mathematical properties (being a valid argument, being prime, etc,), The same point holds mutatis mutandis for relations (logical consequence, identity, greater-than, etc , ) , Of course one could always explicitly introduce a non-standard use of 'property ' , but such proliferation of terminology is unhelpfuL 1

2.

Epistemological Considerations

Many realist defences of universals are unconvincing to sophisticated nominalists ; such realists are talking past their nominalist opponents , For example, many recent advocates of universals defend their view by noting that, when taken at face value, our common opinions seem committed to the existence of universals ,2 This style of defence should not convince nominalists with s ophisticated doubts , for such nominalists may question whether common opinion is justified, After all, common opinion can be egregiously mistaken, To meet these doubts one has no choice but to put one ' s belief in universals on a more secure evidential basis, One might try to do this purely a posteriori for example, by showing that universals are indispensable to the simplest theory based on the empirical evidence (phenomenal experiences and/or observations), But the writings of W,V O , Quine should prevent us from slipping into dogmatic slumber on this point A purely empirical justification of universals is doomed: when one brings to bear all the ingenious Quinean techniques of regimentatioil, the simplest theory based solely on empirical evidence will 'be a fully extensional theory having ontological commitment to nothing beyond actual particulars and perhaps sets formed ultimately from actual particulars , Bearing in mind that this sort of purely empirical theory is not constrained by common opinion or intuition, I feel compelled to agree,3 Fortunately, intuition is a source of evidence as welL The use of intuitions is ubiquitous in logic, mathematics and philosophy (e,g, the use of Gettier intuitions to show that justified true belief is not knowledge), Given this, radical empiricists who hold that all evidence is empirical end up in an epistemically self-defeating situation, Here in broad outline is one such self-defeat argument.4 Simply to proscribe intuitions as evidence would be an arbitrary departure from our epistemic norms, Doing so would therefore generate a reasonable doubt that one would be justified in accepting the theories formulated on the basis of the proposed circumscribed body of evidence, Appealing to those very theories to overcome this reasonable doubt would be question­ begging. Alternatively, appealing to theories which admit other sources of evidence (e,g, intuition) would not count as justified according to the empiricist principle that only observation and/or phenomenal experience is evidence, Either way, then, radical empiricists would have no way of overcoming the reasonable doubt -

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Once intuitions are acknowledged as having evidential weight, there is hope of showing that universals exist and settling their modal status. Some philosophers take a direct approacl;l. For example, from the intuition that honesty is a virtue, or that some things have a property in common, these philosophers would infer directly that universals (properties) exist. But s ophisticated nominalists are unimpressed, for this direct approach disregards the prospect of deflationary interpretations of the language used to report these intuitions, interpretations that allegedly preserve the truth of these reports while avoiding commitment to universals (properties). The inspiration for these interpretations derives from techniques developed in the vast anti-realist literature in philosophy of mathematics, which is often neglected in debates about universals . For example, sentences with apparent commitment to abstract entities have been interpreted as disguised intensional­ operator or adverbial sentences having no such commitment. (So-called modal interpretations of mathematics fall into this family.) Fictionalism inspires another kind of deflationary approach. For example, on some versions of fictionalism, we have the indicated intuition only against the background of a tacit acceptance of a realist theory of properties ; consequently, the intuition supports only the very weak conclusion that, given the fiction of properties, the property honesty exists . Another kind of deflationary approach is based on substitutional quantifi c atio n . Substitutionalists would accept the iriference from the intuitive premiss that honesty is a virtue to the conclusion that there exists a property (i.e. honesty), and they would accept the indicated premiss. But they would also hold that this argument does not show what the realist hopes because the quantifier 'there exists ' in the conclusion is a mere substitutional quantifier, not an obj ectual quantifier; consequently, no ontological conclusions may be drawn. If these or any other deflationary interpretations of the relevant intuitions are acceptable, then these intuitions would no longer win the ontological conclusions that realists had claimed. The prospect of such deflationary interpretations has rendered the direct intuitive arguments for abstract objects (whether they be numbers or universals) unpersuasive. This, I takdt,. is where the most heated contemporary dehates about universals are occurring. With this in mind, I will offer an argument designed to handle these deflationary approaches. 5 The argument focuses on the behaviour of atomic intensional sentences (sentences of the form 'It is F that A' ) in modal contexts .6 The argument, if successful, shows not only that universals exist, but also that they necessarily exist. For example, according to this conclusion, the property of being red necessarily exists and so would exist even if there were no red things, thus establishing the thesis of traditional ante rem realism.7 3.

The Existence and Modal Status of Universals

Logical Form

The argument begins with four premisses about logical form. I put the argument in terms of sentences (versus thoughts or propositions) in order not to beg the question in favour of realism . It may also be understood in terms of linguistic tokens (sentence tokens, etc.).

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( 1 ) The intuitive validity of arguments such as the following support the premiss that 'is true' , 'is possible ' , 'is necessary ' , 'is explainable ' , 'is justified' , 'is known by a ' , and so forth function there as one-place predicates : 8 Whatever i s necessary is true. Whatever is true is possible. :. Whatever is necessary is possible.

(Vx)(Nx -7 Tx) (Vx)(Tx -7 Px) :. (Vx)(Nx

-7

Px) .

At this stage, it is not supposed that the quantifiers here are objectual.9

(2) Given premiss (1), 'that' -clauses function as singular terms when they are combined with predicative uses of the expressions isolated in ( 1 ) ; 10 otherwise, intuitively valid arguments such as the following would be fallacies of equivoc ation: Whatever is true is possible. It is true that A. :. It is possible that A.

(Vx)(Tx T[A]

-7

Px)

:. P[A] . 1 1

(3) Analogous considerations lead to the premiss that ' that' -clauses may contain externally quantifiable variables . (4) Extrapolating from the foregoing, w e arrive a t the further premiss that gerundive phrases 'being such that p.: may function as singular terms (with or without externally quantifiable variables). Now consider an arbitrary English sentence ' It is F that A' in which 'F' functions as a predicate and 'that A' functions as a singular term. We may symbolize such sentences thus : ' F[A] ' . I will call sentences of this general form atomic intensional sentences.

Truth- Conditions for Atomic Intensional Sentences When is an arbitrary atomic intensional sentence in an arbitrary language true (or not) ? That is, what are the truth-conditions for an arbitrary intensional sentence in an arbitrary language? We are able to answer comparable questions for a wide variety of other forms of sentence (conjunctions, negations, etc . ) . So why not in the case of atomic intensional sentences? The question of the truth-conditions for atomic intensional sentences makes good sense and it would be a mystery if it did not have an answer. , S o , under what conditions are atomic intensional sentences 'F[A] true in an arbitrary language L? Our answer is that such sentences have referential truth­ conditions . This will be our next premiss. In the case of English: ' It is F that A' is true in English iff there is something12 that in English ' that A' designates and to which 'F' applies. More generally, for any atomic intensional sentence 'F[AJ ' in any language L :

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'F[AJ ' is true in L iff there is something which, in L, ' [AJ ' designates and to which 'F' applies. These truth-conditions. take no stand on the sort of entities designated by ' [AJ ' . 13 So these tmth-conditions are compatible with nominalism, conceptualism and realism. The argument for this premiss is that the non-referential alternatives fail. These alternatives fall into three general types - operator approaches, fictionalist approaches and substitutionalist approaches. Operator approaches. Consider, for example, approaches which attempt to give truth-conditions for operator sentences of the form 'F-ly, A' and then use them as the tmth conditions for sentences of the form 'It is F that A' . First, these approaches cannot be made systematic: non-referentialists have no clue about how to state in general the conditions under which sentences of the form 'F-ly, A' would be true for an arbitrary 'F' in an arbitrary language L. 14 Moreover, this approach breaks the logical connections that 'F[AJ ' has to other kinds of sentences involving the predicate 'F' . For example, it is silent about sentences of the form 'Ft' , where 't' is a name, definite description, or variable rather than a 'that' -clause. IS On this approach, therefore, there would be no way to explain why arguments like the following are logically valid:

Leibniz's Law is necessary. Leibniz's Law is that identical things have the same properties. :. It is necessary that identical items have the same properties.

Ft t = [A] :. F[A] .

The logical connection between the premisses and the conclusion is a complete on the sentential-operator 9.pproach

mystery

..

The second non-referential approach is fictionalism mentioned earlier. According to a representative version of this approach, sentences of the form 'F[AJ ' are likened to ordinary vacuous-name sentences such as 'Apollo is a Greek god' : in both cases the singular terms are deemed not to refer to anything at all. The sentence 'Apollo is a Greek god' is true because it is suitably 'backed' by relevant beliefs or discourses on the part of the ancient Greeks. On analogy, perhaps 'F[AJ ' is true because it is 'backed' by some relevant body of beliefs (or discourses) . There are several problems with this proposal. First, what prevents the fictionalist strategy from being used against entities which even nominalists would refuse to abandon (e.g. amoebas)? S econd, we standardly use 'that' -clause constructions to talk about beliefs, so these constmctions would, on pain of a vicious regress, require a referential account. Third, there are not 'enough' beliefs to 'back' every tme sentence of the form 'F[AJ ' . Consider, for example, the epistemically crucial family of contingent sentences : 'It is causally necessary that A: , 'It is probable that A' , 'That A is explained by the fact that B ' , 'It is observed that A' , and so forth. Here it seems plain that the world, above and beyond our mere beliefs (or discourses), is needed Fictionalism.

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in order to separate these sentences into true and false. 16 Of course, it wonld do no good to ' modalize' the fictionalist proposal, for the result would Qe expressed with sentences of the form 'Possible [Ar .

Substitionalism. 17 Suppose that someone proposes to meet the demand for truth­ conditions for atomic intensional sentences by asserting the same sentence as we do CIt is F that A' is true iff there is an x such that 'that A' designates x and ' F ' applies to x ) but goes o n t o say that his assertion is free of ontological commitment because the quantifier on the right-hand side of the truth conditions is intended only substitutionally (versus objectually) . I want to show that this is an untenable p osition. Let us set aside atomic intensional sentences for a moment. Suppose that in a discussion in philosophy of mathematics you assert the sentence 'There is an x such that x is F' and then go on to say that you were merely using (or intending) the quantifier 'there is an x' substitutionally and that you thereby avoided (genuine) commitment to the (genuine) existence of a (genuine) obj ect x meeting the indicated condition, that is, of being F. (For simplicity I will sometimes suppress use of ' genuine ' .) Suppose such moves are new to me. Not seeing how this really avoids the indicated ontological commitment, I ask you: how could 'There is an x such that x is F' be true and not require the existence of an obj ect x? That is, under what conditions is the sentence you asserted true? What are the truth-conditions ? Presumably, your answer will be something like this: 'There is an x such that x is F ' is true iff, for some closed term n, 'n i s F ' i s true. But still not seeing that your original assertion really avoids the indicated ontological commitment (i. e . to a genuine obj ect x that is F) , I ask you how it is that an atomic sentence 'n is F' could be true without there really being an object to which 'F' applies. You will successfully answer this question if you can give the truth-conditions for the sentence 'n is F' in such a way that its truth does not require the existence of an obj ect x meeting the indicated condition (i.e. of being F) . What, then, are the truth-conditions of this sentence (understood your way)? There are three general strategies for answering . ( 1 ) You could assert the sentence " ' n i s F " is true i ff there exists a n x such that "n" designates x and "F" applies to x ' , and then go on to say that you were using the quantifier 'there exists an x' objectually that is, you were using it with the intention of genuinely committing yourself to the existence of some obj ect x meeting the indicated condition (i.e . that on' designates x and 'F' applies to x) . B ut, of course, this answer fails for your purposes, for it implies that your original assertion with its allegedly new kind of quantification had the very same ontological import as it would have had if it had originally been intended objectually. And this is exactly what at the outset you said you were avoiding. (2) You could, just as in ( 1 ) , assert the sentence ' ''n is F" is true iff there exists an x such that "n" designates x and "F" applies to x' , but this time go on to s ay that you were using the quantifier 'there exists an x' substitutionally and that you thereby avoid the commitment incurred in ( 1 ) because 'There exists an x such that "n" designates x and "F" applies to x' is true iff, for some closed term 'm' , "n" designates m and "F" applies to m' is true. But this takes us round in a circle because you are right back to holding that an atomic sentence containing a closed term (this time, the closed term Om') can be true without ontological commitment -

Universals and the Defence of Ante Rem Realism

23 1

to an associated obj ect x designated by that term. As a result, your overall effort to explain how your original assertion (of 'There is . an x such that x is F ' ) avoids genuine ontological commitment fails . (3) You could try to explain how 'n is F' avoids genuine ontological commitment by giving one of the other styles of non-referential truth-conditions we have been considering that do not depend on substitutional quantification. For example, you could give non-referential truth conditions for 'n is F' in the way sugg ested for sentences like 'Apollo is a Greek god' . Assuming this is otherwise successful, your explanation of how your original quantificational assertion (of 'There is an x such that x is F ' ) avoids genuine ontological commitment would succeed. (Or so I am willing to grant for the sake of argument. ) The moral is this. S ome people think that a t no stage of discussion can we ever 'read ontology off semantics ' . They think that, no matter what c onclusions are reached by the objectualist semanticist, a substitutionalist can always come in and assert the very same sentences but hold that doing so creates no ontological commitment because he is taking them substitutionally. Our discussion shows that this is not so generally: the substitutionalist may do this only if he is able to give the semantics of the underlying atomic sentences, not objectually or substitutionally, but some third way that is non-referential. Return, now, to our proposed referential truth-conditions for atomic intensional sentences: 'F[A) ' is true iff there is an x such that ' [A) ' designates x and 'F' applies to x. At the outset, we supposed that our substitutionalist opponents happily assert this biconditional but hold that a true atomic intensional sentence 'F[Al ' is nevertheless free of ontological commitment because the quantifier on the right-hand side of the truth-conditions is to be understood substitutionally. When we apply the above remarks to this position, two conclusions follow. First, our substitutionalists must have a non-referential way to give the truth-conditions for ' ' ' [A] '' designates n and "F" applies to n' . If this can be done, the technique could be used to give non-referential truth c onditions for 'F[A) ' directly without the detour into substitutional quantifi c ation, and therefore substitutional quantification would be a gratuitous complication and . so should play . no role. And if there is no such technique, taking the proposed truth-conditions substitutionally is illegitimate. S econd, and more to the p oint, if our survey of non­ referentialist methods for attempting to give truth-conditions for atomic intensional sentences is representative, then in view of the failure of those methods substitutionalists will be unable to meet this requirement and, therefore, their proposal to take our referential truth-conditions substitutionally is illegitimate. l s

The Transmodal Argument S o what type of entities are designated by 'that' -clauses ? 1 9 For terminological convenience, let us call entities of this general type propositions. This is not question-begging, for it does not prejudge the question of what these entities really are. Are they sui generis and irreducible; or are they linguistic entities, psychological entities, extensional complexes (e.g. ordered sets or sequences), possible-worlds constructs , or some other such entities ? Nor does it prejudge the question of the modal status of propositions . Are they in re or ante rem ? (I will come to post rem views in a moment.)

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Advocates of the in re view hold the following two tenets : fIrst, for all x, necessarily, the proposition that . . . x . . , exists only if x itself exists ; second, necessarily, for all y, the proposition that . . . y . . . is actual only if y is itself actual. Advocates of the ante rem theory of propositions deny this. In contemporary philosophy, the most familiar example of an in re theory identifIes propositions with extensional complexes - ordered sets or sequences . (For an example see note 2 3 . ) I will now defend the ante rem view. , I begin with a preliminary logical point. Given that 'F[A] has referential truth­ conditions, wholly general semantical considerations entail that the following is always true: F[A]

-+

(:3z)(z = [A] & FZ) .20

According to the standard conception of logical truth, a sentence is logically true if .its truth is guaranteed by wholly general semantical considerations concerning canonical truth-conditions . So given this standard conception, it follows that 'F[A] -+(:3z)(z = [A] & Fz) ' is a truth of logic. Suppose now that we modalize b oth sides of this conditional. For the left-hand side we have: o F [Al

For the right-hand side there are two candidates : (a) (b)

0 ( 3 z) (z = [A] & Fz). (:3z) (z = [A] & 0 Fz).

These two candidates correspond to two ways of taking the scope of the singular term ' [A] ' : (a) narrow scope and (b) wide scope.2 1 Given that 'F[A] -7 (:3z)(z = [A] , & Fz) ' is logically true, we may be assured that, if '0 F[A] is true, then (a) or (b) or both must be true . This generalizes to more complex cases ; when a �that' 7clause occurs in a modal context, it has either a narrow-scope reading or a wide-scope reading (or both) ; accordingly, it may be existentially generalized with, respectively, either a narrow-scope quantifIer or a wide-scope quantifIer. With this preliminary in place, the defence of the ante rem view now proceeds by exclusion, eliminating fIrst the in re view with a two-pronged reductio. The focus is on a family of intuitively true sentences which I call transmodal sentences. Here is an illustration: Every x is such that, necessarily, for every y, the proposition that x is either possible or impossible.22

=

y

We may symbolize this sentence thus: (i)

(Vx) 0 (Vy) (Possible [x

=

y]

v

Impossible [x

=

y] ) .

We know that the embedded 'that' -clause has either narrow scope o r wide scope (or both) . S uppose it has narrow scope. Then (i) would imply :

Universals and the Defence of Ante Rem Realism

(ii)

('dx)

0

233

('dy) (3z) z = [x = y] .23

That is,. every x is s1,lch that, necessarily, for every y, the proposition that x exists. Therefore, given the first tenet of the in re view, this implies : ('dx)

0

=

y

(3v) v = x.

That is, everything is such that, necessarily, it exists . A false conclusion, for surely there exist contingent objects . On the other hand, consider the wide-scope reading of (i). On this, (i) entails that every x is such that, necessarily, for all y, there exists an actual proposition that x = y.24 In symbols, (iii)

('dx)

0

('dy) (3 actual z) Z = [x = y] .25

But, given the second tenet of the in re view, this implies : o

('d y) y is actuaL

That is, necessarily, everything (including everything that might have existed) is among the things that actually exist. Again, a false conclusion: clearly it is possible that there could have existed something which is not among the things that actually exist.26 So, on both of its readings, the intuitively true sentence (i) entails falsehoods if the in re view is correct. So the in re view is incorrect. (In the following section we will rebut a possible-worlds response to this argument.) Clearly, much the same sort of transmodal argument carries over mutatis mutandis to post rem theories of propositions, according to which propositions are some sort of mind-dependent psychological entity. This leaves the ante rem theory. But what are propositions? There-nre··two-positions ,- reductionism and the view that they are sui generis irreducible entities. Most reductionist theories of propositions are either in re or post rem theories. For example, according to nominalist reductions, the entities designated by 'that' -clauses are identified with linguistic entities (e.g. sentences in a natural language or a 'language-of-thought' ) or with ordered sets formed from contingent particulars - either concrete particulars (e.g. you and me) and/or abstract particulars (e.g. tropes). And according to conceptualist reductions, the entities designated by 'that' -clauses are identified with mental entities (mind­ dependent conceptual entities). Since each of these reductions is in re or post rem, the transmodal argument shows that they fail. 27 The difficulties evident in all the failed alternatives fall into a distinct pattern having to do with the fact that they treat propositions extensionally, as entities that are somehow ' composed of' or parts . of other entities. The underlying error is to think that things are literally in propositions. As Frege says (in 'The Thought' ) : ' [W]e really talk figuratively when w e transfer the relation o f whole and part to thoughts.' The way to avoid this problem is to treat propositions as irreducibly intensional. The deeper philosophical point is that entities which are irreducibly intensional in this way are uniquely equipped to be the vehicles of 'transmodal'

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Universals, Concepts and Qualities

content which can exist independently of whether any relevant contingent particulars exist. If we are forced to admit that 'that' -clauses designate irreducibly intensional entities, uniformity supports the thesis that our other category of intensional singular terms - namely, gerundive phrases 'being F' - likewise designate irreducibly intensional entities. 28 These intensional entities are universals - the property of being an x such that Fx, the relation of being an x and y such that Rxy. We are thus led to the view that universals are irreducible ante rem intensional entities.29 4.

Possible-Worlds Reductions of Propositions and Properties

So far, we have been assuming an actualist framework. Suppose one were to adopt a possibilist framework. Do propositions have a nominalistic or conceptualistic reduction in that setting? No. To illustrate, consider the familiar possible-worlds reduction of propositions to sets of possible worlds (or to functions from possible worlds to truth-values) . This reduction is beset with a number of other problems. The best known is the problem of logical omniscience: as it stands, the possible­ worlds reduction implies that all necessarily equivalent propositions are identical ­ a plainly unacceptable consequence.3 0 (E.g. Leibniz's Law is that identical things have the same properties ; Leibniz's Law is not that water = H2 0.) S ome possible­ worlds reductionists have responded to this problem by holding that propositions are really ordered sets (sequences, abstract trees) whose elements are possible­ worlds constructs built up ultimately from possible particulars. For example, on this theory, the proposition that you dream is the ordered set (dreaming, you), where the property of dreaming is treated as the set of possible dreamers. Although this revisionary view avoids the problem of logical omniscience, it is faced with yet another problem.3! Intuitively, it is necessary that some proposition is necessary. 32 Let us apply a possible-worlds reduction of properties to the property of being a necessa,�j proposition. For example, on a representative approach this property · would be reduced to the set of possible entities that are necessary propositions. This set has as a member the proposition that some proposition is necessary (because, as just indicated, this proposition is itself necessary). Thus, this proposition belongs to the property of being necessary. But, according to the revisionary theory, this proposition is itself an ordered set, one of whose elements is the property of being necessary. Hence the property of being necessary belongs to an ordered set which belongs to the property of being necessary. That is, being necessary E . . . E being necessary. Hence the property of being necessary cannot be a set-theoretical construct built up entirely from possible particulars. But the goal of nominalistic possible­ worlds reductions is to reduce everything either to a particular or to a set ultimately built up entirely from particulars. Therefore, such reductions fail for the property of being necessary. An analogous difficulty besets conceptualist possible-worlds reductions. And, in general, all such reductions fail for every iterable property (not just the property of being a necessary proposition, but pretty much every philosophically interesting property). There is no choice but to acknowledge that these properties are irreducible sui generis entities. But if these are irreducible sui generis entities, uniformity supports the thesis that all other properties are as well.

Universals and the Defence of Ante Rem Realism 5.

235

Qualities and Natural Universals

Traditionally, not all properties were counted as qualities. Is there really an objective distinction between those universals that are qualitative and those that are not? Qualities may be contrasted with ' Cambridge-like' universals such as the property of being grue. The reason for accepting the ontology of qualities, bysides its immediate intuitive appeal, is that it has wide-ranging applications and, given that we already have justified the ontology of universals , the alternatives are less economical. The applications included: the general characterization of the structure of phenomenal experience, the statement of supervenience principles and principles of induction, the solution of Nelson Goodman's new riddle of induction, the statement of truth-conditions for counterfactuals, and the analysis of a host of philosophically central notions - the notions of theoretical explanation (and perhaps c ausation itself) , change, non-arbitrary classification, similarity, orderliness and randomness.33 Other 'natural' universals (e.g. distinguished sortal universals such as the property of being a person) can be shown to play similar roles . S ince qualities and these other 'natural' universals are examples of universals in the narrow sense (isolated in S ection 1 ) , this use of 'universal ' is vindicated. Furthermore, from our earlier c onclusion - that all properties are irreducible ante rem entities - it follows that universals in the narrow sense are as well.

Notes

2 3 4 5 6

7 8

For example, Lewis ( 1 9 8 3 ) does this when he proposes to use the term 'property' for classes of possible particulars ; so if (as I will argue in Section 5) properties in the standard sense (e.g. the property of being a necessary proposition) are not reducible to classes of pos sibilia, they would not be called 'properties ' on Lewis 's proposed usage. See Lewis ( 1 97 3 , §4. 1 , especially p. 88) and Armstrong ( 1 9 8 9 , § l .iv) . Putnam ( 1 972) endorses a similar methodology but in connection with ,our common scientific beliefs . Michael Devitt ( 1 9 8 0) makes some related criticisms ofihe ' common opinion' approach' to philosophy. In 'The Incoherence of Empiricism' ( 1 992) I develop this argument in detail. See my 'Universals ' ( 1 993) for full details . I f thi s argument succeeds i n showing that universals exist, I take i t that i t will b e pointless t o try t o resist realism, a t least i n some form, i n philosophy of mathematics. Note that here and below I will use single quotation marks where c omer quotation marks are, strictly speaking, called for. Throughout the argument here I will assume that possibilism and Meinongianism are mistaken. But I believe that with suitable supplementary argument, this assumption may be lifted. Many treatments in the literature which are superficially different are really just special cases of this. For example, on the higher-order sentential-operator approach 'Whatever is necessary is possible' is represented as ' (\fp) ( O p � p) ' . The sentential operators ' 0 ' and " function as predicates inasmuch as they take singular terms (e.g. 'p ' ) as arguments and these singular terms are open to quantification. S imilarly, on an adverbial treatment the sentence would be represented along the following lines : ' (\fp) (p­ ly(Necessary) � p-Iy(True»' , where ' -ly(Necessary) ' and ' -ly(True) ' function as predicates inasmuch as they take singular terms (e.g. the variable ' p ' ) as arguments. In

236

9

10

11

Universals, Concepts and Qualities neither case need we take a stand at this stage on the semantical significance '(if any) of these variables . Dorothy Grover's prosentential approach i s a t odds with our premiss, however. Perhaps the main problem with this approach is that, syntactically, it is rigidly typed whereas the parts of discourse that the theory is designed to capture are manifestly type-free . See, for example, note 1 5 , O f course, there are also expressions occurring i n analogous sentences that function as two-place predicates : 'asserts ' , 'knows ' , 'justifies ' , and so on. For simplicity, I will suppress this point in what follows. I choose this example because of its naturalness. It has been pointed out that the validity of this argument can be explained by the fact that its conclusion is already a truth of logic. To avoid this concern, just change this and the ensuing examples so that none of the lines is a truth of logic, Davidson's paratactic theory conforms to this premiss as a special case. Note that this thesis allows for occurrences of ' that' -clauses in other s orts of contexts, at least prima facie, not to function as singular terms (as Marc Moffett and D elia Graff have each shown) . Advocates of free logic might claim that the original argument is not strictly speaking valid unless it is supplemented with the premiss 'That A is something' or 'There is something identical to that A' , To accommodate the free logician, we would simply supplement our symbolized version with the premiss ' (:Ix) x [A] " where ' [A] ' is a singular term. Incidentally, the standard higher-order sentential-operator approach is a variant on our position in the sense that entire sentences 'A' are substituends for quantifiable variables and, hence, count as singular terms. Later in the discussion I will consider the question whether the quantifier 'there is something' is objectual or substitutional. Instead of the relation of designation, there are other, perhaps less direct, s eman tical relations that might hold between a ' that' -clause and the associated item of which the predicate ' F ' is true. For example, someone might propo s e to treat ' that' -clauses in a manner reminiscent of Rus sell's 'no-class ' treatment of class abstracts . Nevertheless, , it would still be the case that 'F[A] would be true only if there is an appropriate entity semantically- associatEd with ' [Ar , and 'F' has ' an appropriate semantical relation to that entity. This is the point that will matter later on in our disproof of nominalism. A disquotational approach will not work, for we are seeking an answer which works for arbitrary languages, including those with sentences not translatable into English. To put the point another way, the following is not even a s entence of English: 'F[A] ' is true in L iff F-ly, A. (Nor is the following: For all F and A, 'F[A] ' is true in L iff F-ly, A.) Incidentally, if the referential approach were adopted, it would be trivial to give general truth-conditions for sentences of the form 'F-ly, A' for arbitrary 'F' : 'F-ly, A' is true iff 'F[A] ' is true. There is no assurance that there will always be a sentence 'A' that makes 't [A] ' true. For example, a sentence 'A: that makes ' Romanticism [A] ' true. The problem is compounded by the fact that there are not type restrictions on 't' . For example, when 't' is ' that which is most valuable' , we need not know the category of the thing 't' designates . ' I t is F that A: is thus fundamentally different from the category of atomic proper-name sentences 'Fa' . For it is at least plausible that there are general non-referential techniques for giving the truth-conditions for vacuous proper-name s entences 'Fa ' , for example, when ' a ' is 'Apollo ' . =

12 13

14

15

=

=

16

Universals and the Defence of Ante Rem Realism 17 18 19 20 21

22 23

237

For a recent discus sion of substitutional quantification see Azzouni (2004) . Such considerations are what led me to focus on atomic intensional sentences rather than quantified s entences. We allow for the possibility that some entities of this general ontological type are not designated by any ' th at' -clauses, due to the expressive deficiencies of natural languages . Since 'F[A] ' has referential truth-conditions, our discussion o f substitutionalism ensures that the existential quantifier '::Iz' is objectual, not substitutional. I include the wide-scope reading i n order t o accommodate i n re theorists who might think of ' [A] ' on analogy with a definite description. One could replace 'x y' with 'if x and y exist, x y ' . On an extensional-complex theory, (ii) might be represented thu s : =

=

( V'x) 0 ( V' y) (::Iz) z

=

(x, 'identity ' , y).

Yet, necessarily, a set exists only if its elements exist. So (ii) would imply: ( V'x) 0 (::Iz) z

24

25

=

x.

That is, everything necess arily exists . This is the implausible consequence we are in the midst of deriving in the text in a more general setting. ' ( V'x)(::Iz) z [x y] & 0 ( V' y) Possible z v Impossible z' is not an acceptable wide­ scope reading of (i) , for this expression is not even a sentence since ' y ' occurs free. In re theorists seeking a wide-scope reading of (i) need to invoke an ' actuality-quantifier' which may occur within modal contexts and which nevertheless has the force of indicating the existence of things that are now actual, as wide-scope quantifiers standardly do. The expression ' (::I,ctua! z) ' is designed to serve this function. On an extensional-complex theory, (iii) might be represented thus: =

=

( V'x) 0 ( V' y) (::I ,ctua! z) z

=

(x, 'identity' , y) .

But, necess arily, a set is actual only if its elements are actual. So G l (V' y) y is actual:

26

27 28

(iii) would imply: . ;.,'-

That is, necessarily, everything (includi;lg everything that might have existed) is among the things that actually exist - the same implausible consequence we are deriving in the text in a more general setting. This argument is entirely consistent with actualism: I am not supposing that there are things which are not actual; I am only supposing that it is possible that there should have existed things which are not among the things that actually exist. Nowhere in the argument am I committed to the existence of non-actual possibilia, for the relevant quantifiers always occur within intensional contexts : 'it is possible that ' , ' necessarily ' , and s o on. For this reason, thes e quantifiers have n o range o f values. For example, that it is possible that there should have been more planets than there actually are does not entail that there are possible planets . To hold that there is such an entailment is an intensional fallacy. If you knew that, necessarily, God exists and has all the requisite concepts, you might be able to avoid this conclusion. An exception is the propositional function theory, according to which gerundive phrases 'being F ' designate extensional functions from obj ects to propositions . S e e my 'Propositions' ( 1 998) for criticism of this theory.

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29 . The above transmodal considerations allow us to reach an even stronger conclusion: necessarily, if a property, relation, or proposition could exist, it actually exists . See my 'Universals' for the argument. 30 The problem is not limited to psychological contexts. For example, it is a truth of logic that all triangles are triangles but not that all triangles are trilaterals. 3 1 This difficulty i s not a Cantor-style worry about cardinality. I am willing to assume that the latter can be avoided with some new kind of set theory. Incidentally, there are variants of the present problem that beset the original possible-worlds reduction. 32 Possible-worlds theorists might deny this by appealing to a Russell-style theory of types, but there are persuasive arguments that a type-theoretic treatment of modal language is unacceptable. They might also respond by holding that there is no property of being a necessary proposition, but in the context this would be absurd. 3 3 For such arguments, see my Quality and Concept ( 1 9 82) and Lewis ' s 'New Work for a Theory of Universals' ( 1 9 8 3 ) .

References Armstrong, David M. ( 1 989), Universals: an Opinionated Introduction. B oulder: Westview. Azzouni, Jody (2004) , Deflating Existential Consequence: a Case for Nominalism. Oxford: Oxford University Press . Bealer, George ( 1 979), 'Theories o f Properties , Relations, and Propositions ' , The Joul71al of Philosophy, 76: 634-48. Bealer, George ( 1 982), Quality and Concept. Oxford: Clarendon Press. B ealer, George ( 1 992), ' The Incoherence of Empiricism' , The Aristotelian Society, Supplementary Volume, 66: 99- 1 3 8 . Bealer, George ( 1 993), 'Universals ' , The Journal of Philosophy, 9 0 : 5-32. Bealer, George ( 1 99 8 ) , ' Propositions ' , Mind, 1 07 : 1-3 2 . Devitt, Michael ( 1 980), ' ''Ostrich Nominalism" o r "Mirage Realism" ? ' , Pacific Philosophical Quarterly, 61: 433-9 . Lewis , D avid K. ( 1 9 8 3 ) , ' New Work for a Theory of Universals ' , Australasian Journal of Philosophy, 6 1 : 343-77. Putnam, Hilary ( 1 972), ' On Properties ' , Mathematics, Matter and Method: Philosophical Papers, Volume 1. New York: Cambridge University Press, pp. 305-22. Shoemaker, Sydney ( 1 980), ' Causality and Properties ' , in Peter van Inwagen (ed.) , Time and Cause. Dordrecht: Reidel, pp. 1 09-3 5 .

Chapter 1 3

Particulars Have Their Properties of Necessity David Armstrong

I assume here that particulars have properties, properties in the sparse sense, such things as mass, shape, size, velocity, as opposed to ' mere-Cambridge' properties , properties that are mere shadows of predicates. Suppose i t is true that a particular a has property F. Is this truth contingent or is it necessary? It is common in the empiricist tradition to think that, with the possible exception of certain essential properties, this truth is a contingent one. Certainly, this is the way I have thought about the matter in the past. (Furthermore, I rej ected essential properties except for the Lockean notion of properties that are essential relative to s ome concept in our minds . ) Now, however, I wish to argue that for theories such as mine, and for some other theories as well, these truths are necessary. Among those philosophers who accept properties in re, there are a number of different theories about the nature of properties, and a number of different theories about the way properties stand to the particulars that are said to have them. Of particular interest . to us here are, first, the dispute 'between those who take properties to be particulars (tropes) and those who take properties to be universals ; and second, the dispute between those who take particulars to be bundles of properties and those who take properties to be attributes of particulars . Since these disputes are largely independent of each other, thls blds to four types of position: " bundles of tropes, bundles of universals, tropes as attributes of particulars, universals as attributes of partiCUlars. What I shall argue is that for each type of theory it is plausible, at least, to think that such predications are necessary. Famously, David Lewis always remained neutral between the positions just sketched. But I argue that he too should have embraced the view that these predications are necessary.

Bundle Theories

We may begin with bundle theories, and it will not really be necessary to bother about the question whether the bundle is a bundle of universals or of tropes . For is it not clear that if a particular is just a bundle of properties , then it is a necessary truth that any particular property is a member of the bundle ? We may not know just what properties a certain particular has, but for each such property it is necessary that the particular has that property because the property helps to constitute what that particular is. The situation seems to be just a particular case of class membership:

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a ' s being F, on this view, is a matter of F being a member of the class { F, G, H, . . } where the members bear to each other a certain bundling relation. And the relation of a member of a class to its class is a necessary one. A natural reaction to this little argument, one that I would have had myself in the past, is that it is nevertheless possible that the bundle as a whole might have existed except that it lacked F. And if this 'is tme, does it not show that in some less superficial sense, F's membership of the bundle is contingent? In reply, I concede, rather gmdgingly, that this shows that a sense can be given to ' it is contingent that a is F ' . But the point to be insisted on is that it is not a sense that stands in any contradiction to ' it is necessary that a is F' . (I am indebted to John Heil for this way of putting the matter.) For, after all, a without F is something less than a, and therefore is not a. All that is true is that there is something genuinely contingent involved. I grant that the particular a is a contingent being. The proposition ' a exists ' i s contingent, hence a might not have existed. Furthermore, I grant there might have existed, at the same place and time, a counterpart of a, something that closely resembles a, although it is not a. If anyone chooses to call that contingency a, so be it. But this is, as j ust argued, a ' contingency' compatible with necessity of the truth that a is F. It is a fundamental principle of modal theory, I suppose, that if a tmth is necessary, then it cannot also be contingent (and vice versa) . I think the principle should be upheld. So I argue that this story about counterparts, a story that, I accept, does no more than explain why, given a bundle theory, we might wrongly think that 'a is F' is contingent. .

David Lewis

Lewis 's theory of possibility is no more than a variation on this theme. He analyses the possibility that a particular in our world, such as the late Hubert Humphrey, might not have had some property that he actually does have in the following way : i t i s a matter o f a counterpart o f H.B; i n another world than this one lacking that property, but otherwise closely resembling the original particular. Against Kripke ' s initially strong-seeming objection that we want the possibility t o be a possibility for our Humphrey, Lewis contends, and with great force, that it is impossible that we can do any better than a counterpart, a counterpart that cannot, strictly, be identified with the actual Hubert Humphrey. But if so, then it is surely necessary that Humphrey has just the properties he has and no other. If it is impossible for him to be different, then that is a way of saying that he has his properties necessarily. This means that Humphrey does not have his properties contingently. Again, Lewis 's counterpart story can explain why we might be led to think or say that Humphrey has his properties contingently, but it c annot be an analysis of that contingency because there is no such contingency to give an account of! For it is, or it should be, of the essence of contingency that it is incompatible with necessity. And Lewis himself has given us the reason why it is necessary that Humphrey has the properties he actually has . It is because his counterparts cannot be him.

Particulars Have Their Properties ofNecessity

24 1

Subject/Attribute ,vith Tropes

It is not quite so obvious that subj ect/attribute anaiyses of particulars must yield the necessity of predications . This is because a subj ect/attribute analysis creates a certain 'distance' between a particular and its properties, a distance not present in bundle theories . On the subj ect/attribute view the particularity of a particular is not exhausted by the bundling together of its properties . But if so, cannot we introduce the notion of the 'bare' or 'thin' particular which has its properties contingently? Mere bundling is essentially a bundling of certain items. Bundling is therefore like the class operator; just what is bundled is of the essence of the resulting entity. But given a subject/attribute analysis, the subject, the particular, seems to stand in s ome way or degree outside its properties . So may not the connection between subj ect and its attributes be contingent? If these attributes are tropes, then we have the sort of subj ect/attribute theory of particulars that is favoured by C . B . Martin and John Heil. They substitute tropes for universals. They hold, further, in Martin's phrase, that tropes are non-transferable. By this is meant that it is part of the being, part of the identity-condition, of a trope that it is a property of the particular that it is an attribute of. A minor dispute in trope theory may illustrate the view. Consider two exactly resembling tropes that are attributes of different particulars . Is there a possible world in which the two tropes are swapped around between the two particulars? I used to argue that trope theory is forced to accept this as a possibility, but then, I said further, it is doubtful that it really is a genuine possibility. This 'swapping problem' was, of course, at best a minor difficulty for a trope theory. And if tropes are non-transferable, as Martin and Heil claim they are, then the difficulty vanishes . There is no such possibility. But with non-transfe rability comes necessity. Given this particular and this trope, then the trope must of necessity attach to this particular. The particular and the trope are presumably contingent existences, but once they exist their place in the world is fixed. On this view the true predication of a trope is, or should be, a necessary truth. However, it is not very clear how the essential premiss that tropes are non­ transferable is established. How is the alternative hypothesis that tropes attach contingently to their particulars refuted? S uppose that one distinguishes between the identity-condition and the identification-condition of a trope . And suppose that then one grants that the identification-condition of a trope is tied to a specification of the particular particular that the trope is an attribute of. How is it to be further shown that being an attribute of this particular is of the essence of this trope? It might be replied to this that the trope must have some identity-condition and what condition is available except its being the trope of this particular? But could there not be an intelligible conception of a trope that is, as it were, its own identity­ condition without reference to the particular it happens to qualify? (On pain of regress , apparently a vicious one, there must either be such tautological identity­ conditions, Gertrude Stein identity-conditions as one might call them after her remark that a rose is a rose is a rose - or else a virtuous circle of identity­ conditions.) I am not clear just how Martin and Heil can rule out tautological identity-conditions for tropes .

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It seems, nevertheless, that the MartinlHeil view might be supported by a more classical argument. The argument is a reductio. Suppose the link between a particular and its tropes is not necessary. Then it is contingent. But if it is contingent, then it seems that we have a clear case of a relation between the particular and its trope, and an external relation at that. But then a Bradleian regress ensues: a's being F, G, . . . becomes a's having R to F, G, . and the same question applies to contingent R. How does dyadic R stand to a and a ' s attributes? This, perhaps, reduces the contingency view to absurdity. So, Martin and Heil may argue, although the 'distance' between subj ects and their attributes remains , a distance that distinguishes their view from a bundle view, there is nevertheless a necessary connection between subj ect and attribute. (Of course F.H. Bradley would have said that what is reduced to absurdity is the subj ect/attribute analysis.) I do have to say, though, that the deeper rationale of such a necessary connection is not at all clear. I hope, below, to provide such a rationale in the case where the attributes are universals . And perhaps the 'partial identity' solution suggested there can be adapted for tropes. Non-transferability as it were glues tropes to their particulars. Notice that this means that states of affairs (a particular'S having a property) are obtained at no further ontological cost. States of affairs are important to have, particularly, I think, as the relata for singular causal connections . (You need particulars for causation, yet at the same time it is some and only some of the properties of a particular that are involved in the causal transaction. It is the mass and velocity of the billiard ball that are relevant to its making the second ball move, not its colour or smelL So it is the ball 's having certain properties - a state of affairs - that is the first term in the singular causal relation.) As we shall see, all subj ect/attribute theories deliver us states of affairs, whether the attributes be tropes or universals . . .

Subj ect/Attribute with Universals

Is this account of the predicative tie compatible with making it contingent? I now think that this conception of particulars makes the tie a necessary one. l S ome background is necessary. Under the influence of Donald B axter of the University of Connecticut I have come to a new view of the 'relation' between a particular and a universal that instantiates it. B axter starts from a variant of the problem of the 'fundamental tie ' that we have j ust seen in the case of the MartinlHeil view. In their view the tie holds between particulars and their properties, with the properties conceived as tropes . But B axter starts by asking how we are to understand the link between particulars and properties conceived of as universals . We need first t o be clear that i f you accept universals and have particulars instantiating them, then you will have to recognize facts or states of affairs , such as a 's being F. a and F form a unity of some sort with a and F as parts . a and F are linked in some special way; they form a fact or state of affairs . B ut what is this link? B axter's suggestion that I have embraced is this: what we have here is a partial identity2 of the particular and the universal (B axter, 200 1 ) , Consider, first, that a particular i n some way embraces its properties : the latter are in some sense parts of the particular, at least if we confine ourselves to non-

Particulars Have Their Properties a/Necessity

243

relational properties. (A term that I find convenient for these special sorts of parts is ' constituents ' although I don' t think of this bit of terminology as solving any ontological problems .) I think then of the particular as a one running through the many properties, a ' one in the many ' , a uniting factor in virtue of which they are all properties of the s ame p articular. This is not a bundle theory, however. The factor of particularity is not analysed away as it is in bundle theories . (It is worth noticing that this account of particulars seems to be as much available to those trope theorists who accept a substance/attribute view as it is available to upholders of universals. Ordinary particulars can be thought of as ones that run through many tropes in virtue of which the tropes are all properties of the one particular.) But partial identity is symmetrical, of course. The universals are partially identical with their particulars . But equally the particulars a universal instantiates will have to be partially identical with the universal. And here I break with B axter. He thinks that it is a contingent matter what particulars instantiate what universal.3 B ut it seems to me that if a universal is partially identical with its particulars, then it will be necessary that the universal instantiates the particulars it actually instantiates . A universal that instantiated a different set of particulars could not be identical with ' the original universal. So I now think that where F is a universal it is a necessary truth that a has property F. As with Lewis , a simulacrum of contingency can still be offered. Particulars are contingent beings . So a particular might not have existed and instead, in its vacated place, there could have been a particular very like the really existing particular. And if one further holds, as I hold, that universals are also contingent beings, then any universal might not have existed, but instead a universal very like the really existing universal might have existed. But this does not make predications contingent. What we have instead, I suggest, is a necessary connection between c ontingent entities, the particular and the universal. Just as in the case of non-transferability of tropes, given particulars and given universals, states of affairs are then nothing over and above the particulars and universals that 'participate' in each other. The particulars are contingent beings, ,and, as .! have just said, I'd argue that the pr.Qp.e.rties ar.� a.lso. contingent beings, and so, therefore, the states of affairs involved are also contingent beings. But the link between particular and property is necessary. Perhaps the young Socrates in Plato 's Parmenides got it right first go when Parmenides asked him how particulars stand to Forms. Socrate s ' first suggestion was participation. Perhaps he should have stopped there ! On the other hand, in the dialogue the Forms appear to be transcendent entities, which seems to rule out genuine participation. Participation goes better with a down-to-earth account of universals , an Aristotelian or perhaps 'Aristotelian' view, the sort of view that I favour. The universal is a one that runs through its particulars just as the particular is a one that runs through its properties .

Relations

So far I have confined the discussion to the intrinsic or non-relational properties of particulars. But what of the relational properties of things ? Are they to be given the same treatment as non-relational properties ? I think not the same treatment, but it

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will be better at this point to switch the discussion to relations rather than relational properties . A fairly traditional way of classifying relations in metaphysics , going back to Hume at least, is into internal and external relations , where internal relations are those necessitated by their terms . For instance, given two obj ects of different sizes, with a bigger than b, then this relation bigger than holding between a and b is internal. (I' m making the assumption here, a plausible one I think, that size is a non-relational property of obj ects . ) This bigger than relation seems to supervene on the two objects having the size they have, and I'd argue that ontologically there is nothing there except the objects with their sizes . Contrast this with the two objects being a mile apart, an external relation. The moral that I would draw from this is that, although true predications of internal relations are necessary, we need not pay them a great deal of attention. In particular, we do not need to recognize states of affairs over and above any states of affairs that may be involved in the terms . External relations , however, do, I think, yield states of affairs . Concentrating o n external relations, then, how d o they stand t o their terms ? I f we have given a partial identity account of the instantiation of property-universals monadic universals - it will be natural, if we can, to give a partial identity account of the instantiation of (external) relations - polyadic universals . And, pace B axter again, this partial identity will, I maintain, have as a consequence that each instantiation of a polyadic universal is a necessity. There will, of course, be the possibility of simulacra of these universals that do not instantiate just these particulars, but they can be no better than counterparts. In the past I would have said that internal relations are necessary but external relations are contingent. Now I say that both are necessary but that internal relations do not,4 and external relations do, involve states of affairs . The external relations will be universals that are constituents of these polyadic states of affairs . But how are w e t o understand this partial identity between polyadic universals and the particulars that instantiate them? It may seem a rather opaque idea (even by the standards of this chapter, some may consider) . My present idea is to provide more clarity by exploiting the link between external . relations and whaLl . call structural properties. The latter are monadic, but they attach to a particular in virtue of the way that the proper parts of that particular are related to each other. For a simple example think of a blade and a handle fitted together to make a knife. Having a blade and a handle standing to each other in this way is a structural property of an object, the object that is the mereological sum of this blade and this handle. Now consider any dyadic external relation, for an example being two miles apart. In every concrete situation where this relation holds there will be two particulars , a and b, that are two miles apart. B ut now consider the particular a + b , the mereological sum o f the two particulars . This particular will have a structural property, a monadic property: having at least two parts separated by two miles . The suggestion then is that it is this monadic structural property that is partially identical with the particular that has this structural property. Provided that the mereological sum of the terms can always be regarded as a particular, even if a particular of otherwise little practical interest or importance, then it seems that this solution can be extended to cover all external relations . So the partial identity of universals that are external relations with their particulars is construed as the partial identity of the

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corresponding monadic structural universal with the particular that is identical with the mereological sum of the terms of the relation.5 One il1teresting thing about this suggestion is that it reduces all instantiations of universals by particul m:s to the monadic case. Taken ontologically, the form of all instantiations is x is P. We are now accustomed to write R(a, b). But, for the case of external relations, the true form according to this new theory is x is S, where x is the mereological sum of the terms of the relation (a + b), and S is a structural property of this particular. External relations become, as it were, the cross-bracings of certain non-simple obj ects . By contrast, the true ontological form of R(a, b) where R is internal is no more than Fa + Gb, a mere mereological sum. You have no doubt observed, as Don B axter observed to me, that the words ' internal' and 'external' have become pretty unsatisfactory. It might be better to reverse them ! But for the present, at least, I pour the new wine into the old bottles . Let me note once again that states of affairs are contingent existences, and so are their constituent universals and particulars. B ut once given those universals and those' particulars, then the states of affairs are necessary, they are fIxed. (And equally, given the states of affairs, the constituent universals and particulars are fIxed.) These contingent existences might not have existed, and other closely resembling states of affairs existed instead. It is interesting to notice that this situation does not contravene the Humean interdiction of necessary connection between distinct existences, at any rate if ' distinct' here is read as ' wholly distinct' . The particulars and universals involved in states of affairs are not wholly distinct because they are partially identical.

Relational Properties

We should now clear up the status of the relational properties of particulars . For the purposes of ontology they do not seem to be a very important category. For suppose that we are given all particulars and. their non-relational properties , and are also given all the external relations between particulars . Then, it would seem, not only do all internal relations supervene, but so do all relational properties . This holds both for what have been called pure relational properties being a mother and impure properties being the mother ofAlexander.

..

-

-

-

Higher-Order Relations

If the theory advanced about the instantiation of universals by particulars is correct, then it will presumably apply to higher-order instantiations . In particular, it ought to apply to those links between universals that I identify as laws of nature. These, as I now think, are best represented as causal or quasi-causal links between what I call states-of-affairs types.6 Thus, very schematically, I now see the simplest sort of law (perhaps too simple for any actual instances) as having the form something being F causes that same something to be G, with F and G universals . Causing, or determining something to be the case, is in my view a relation that we are actually given in experience in favourable cases such as pressure on our bodies and the

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operation of our own will. That, of course, is just causality in the particular case. But I suggest that it is a plausible hypothesis that the relation that we experience at the level of particulars may also hold for states-of-affairs types. Ordinary language suggests this: we say, for instance, that arsenic causes death, which on the surface is a linking of types (universals). It is perhaps only our long unhappy love affair with Humeanism that insists on putting this into the form of a universally quantified proposition. It will be seen that if the same sort of relation that is experienced to hold in the singular case can also hold in the case of states-of-affairs types, then the inference to the regularity. of the causal sequence becomes rather perspicuous (though informal) . My new account of external relations sees them all as the instantiation of a structural property by one obj ect only, the obj ect formed by the mereological sum of their terms . This account seems to be available for higher-order connections. The nomic relation or relations will become a monadic but structural property of a certain obj ect. This obj ect will be the mereological sum of the states-of-affairs types that are nomic ally connected. There is a lot of complication to be added here. We need to deal with laws that are merely defeasible, laws that are probabilistic only, and to expand the account to include the all-important case of functional laws . B ut I am here interested only in the modal status of laws. I used to argue, as did Michael Tooley and Fred Dretske, that these connections between universals were contingent only. It sounded like a decent empiricist theory. But if the instantiation of a monadic universal holds of necessity and if this extends to polyadic universals , then it should extend to relations between universals . There should be a partial identity holding between the causal relation and the states-of-affairs types that it, the causal relation, links together in higher-order states of affairs . The higher-order states of affairs will be contingent existences, as will the particulars and the universals that are the constituents of the higher-order states of affairs . But giveD�just these Gonstituents, the way they stand to each other will . be necess ary. That has the consequence that the very same universals must stand in these higher-order states of affairs . All that could stand in different higher-order states of affairs - different laws on the suggested account of laws - are counterpart universals. So laws are necessary, not contingent.

Notes 1 2

3 4 S

See my 'How do Particulars stand to Universals ? ' (2004) . In earlier drafts of this chapter I said this would be a non-mereological partial identity. This seemed necessary when the link between particular and property was conceived as contingent. B ut it may be that the theory advanced in this chapter can operate with mereological parti al identity. If this is true it would be a welcome simplification. See B axter (200 1 ) , pp. 449 and 462. More strictly, 1'd say that there seems to be no pressing call to postulate states of affairs in the case of internal relations , so I do not postulate them. I hope this suggestion is an improvement on the quite different suggestion to be found in my ' How do Particulars stand to Universals?' (2004) .

Particulars Have Their Properties ofNecessity 6

247

For states-of-affairs types see my ( 1 997), 3 . 5 and p. 229.

References Armstrong, D.M. ( 1 997), A World of States of Affairs. Cambridge : Cambridge University Press. Armstrong, D.M. (2004) , 'How do Particulars stand to Universals ? ' Oxford Studies in Metaphysics, voU , ed. Dean Zimmerman, Oxford: Oxford University Press, pp. 1 3 9-54. B axter, Donald L.M. (200 1 ) , 'Instantiation as Partial Identity ' , Australasian Journal of

Philosophy, 79, 449-64.

Chapter 1 4

Properties in Abundance

*

Wolfgang Kiinne

A Homage to the Copula

I.

Dear Russell, I believe that our problems can be traced down to the atomic propositions . This you will see if you try to explain precisely in what way the Copula in such a proposition has meaning I therefore now think about 'Socrates is human' (Good old S ocrates ! ) . . . Yours most, etc . , etc. Ludwig Wittgenstein. 1 . . .

Doing what Wittgenstein did in summer 1 9 1 2 will not do us any harm. S o let us brood upon the structure and content of elementary predications . The declarative sentence (E)

Socrates is courageous

consists, as philosophers have known for a long time, of a singular term, the name of good old Socrates, and a predicate, full stop. Well, it is not for such a long time that philosophers have known this. B efore Frege they kept on s aying for many centuries that sentences like (E) consisted of three components : a subj ect, a copula and a predicate. Obviously 'pr�dicate ' is used differently in these descriptions of sentential structure. According to the Fregean conception of a predicate, which I endorse, you extract a predicate from a sentence that contains at least one name (singular term) by deleting at least one name-occurrence. Thus understood, predicates are sentence-forming operators on singular terms, and the copula 'is ' is part of s ome of these operators . Notice that this is a far cry from the claim, upheld by at least one important post-Fregean philosopher, that the word 'is ' occurs in a predicate in the same way as its echo occurs in the word 'Islam' , as a fragment of a semantically seamless whole. An important distinction that was emphasized by Michael Dummett should be mentioned at least in passing even though it does not affect the contrast I want to stress. It is most easily explained for the case of dyadic predicates. In o n e sense of the word 'predicate' the following three sentences, (a) (b) (c)

Romeo is in love with Juliet Narcissus is in love with Narcissus Dorian Gray is in love with Dorian Gray

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contain one and the same predicate, 'is in love with ' . 2 In another sense (b) and (c) have a predicate in common that distinguishes them from (a) , since (b) and (c) are, unlike (a) , substitution-instances of the open sentence 'x is in love with x' . This open sentence can be used to draw our attention to something which is not a component of (b) and (c), but rather a feature they share. Predicates in the first sense are detachable: they can indeed be extracted from sentences. Predicates in the second sense are distinguishable but not detachable : 3 they can only be abstracted from sentences . Leaving the realm of elementary predications for a moment, consider the following conjunctions : (d) (e) (f)

Ann is bright, and B en is tall Ann is bright, and Ann is tall S am is bright, and S am is tall.

From each of these sentences we can extract the predicates 'is bright' and 'is tall' . But from (e) and (f) we can abstract a complex predicate that distinguishes them from (d), for only (e) and (f) share the feature of being a substitution-instance of the open sentence 'x is bright, and x is tall' .4 But no matter whether the predicate is conceived of as a detachable part or as a distinguishable feature of a sentence, the copula belongs to the predicate. s In what follows it will do no harm if we think of predicates as separable. In order to avoid terminological confusion I shall shun the old use of the word 'predicate ' . How then are we to classify the adj ective in (E) ? Appropriating another entry in the dictionary of traditional logic, I shall call it a general term. 6 The copula, we can now say, is an operator which takes general terms as input and delivers predicates as output. Even within the realm of elementary predications, a general term may very well be more complex: in ' Socrates is a man ' it is a phrase consisting of an indefinite article and a noun. Furthermore, as we all know, not every elementary predication contaills the copula in the shape of a word like 'is' . · After all, when Plato reflected for the first time on the structure of elementary predications, his paradigm was ' Theaetetus sits ' . B ut very soon afterwards his greatest pupil tried to uncover a copula even in sentences like 'Theaetetus sits ' or

( £)

Socrates walks .

I am alluding to Aristotle' s notorious constructio periphrastica: It makes no difference whether we say of a man that he walks s ay that he is walking (�Cl.8ti;; cov wnv)·7

(�Cl.8ti;;£l ), or whether we

(We ' d better forget about the English progressive aspect in this context.) Not only the S choolmen have followed Aristotle's footsteps in this respect: C 'est la me,ne chose de dire 'Pierre vit ', que dire 'Pierre est vivant'.8 [ ' To b e ' ] is the only verb recognised by Logic; inasmuch a s all others are compound; being resolvable, by means of the verb ' to be' , and a participle or adj ective: e.g. 'the

25 1

Properties in Abundance

Romans conquered' : the word ' conquered' is both copula and predicate, being equivalent , to 'were (Cop.) victorious (Pred. ) .9 Each inflected verb .that is different from the word 'is ' can be replaced, without any essential change of meaning, by the combination of 'is ' with the (present tense) participle derived from that verb. 'A [verb l s ' is tantamount to 'A is verb [ing) ' (ledes bestimmte Zeitwort, das von dem Worte 1st verschieden ist, kann ohne aile wesentliche Veriinderung des Sinnes, dll1'ch das Wort 1st verbundell mit einem von dem gegebenen Zeitworte abgeleiteten Particip, vertauschet werden. A thut, ist durchaus gleichgeltend mit: A ist thuend. lO) .

But one may very well wonder whether the construction 'is' + participle is really tantamount to the finite form of the full verb, I I and in any case it would be fine if we could avoid such linguistic contortions . What plays in (E) the role that is played in (E) by the word 'is ' ? What transforms the ' S ocrates ' -free fragment of (E) into a predicate? It is the verb-ending. In an expanded sense of 'copula' we might as well say that in (£) the verb-ending is the copula. 1 2 Frege, not exactly famous for being a friend of the copula, s aw this quite clearly: Often the word 'is' serves as copula, as a mere form-word of the Aussage. As such it can sometimes be replaced by a verb-ending. Compare, for example, ' this leaf is green' and 'this leaf greeneth' . ([Oft dient das Wort 'ist') als Kopula, als bloj3es Fonnwort der

Aussage. Als solches kann es zuweilen durch die bloj3e Personalendung vertreten werden. Man vergleiche z.B. 'dieses Blatt ist griin ', 'dieses Blatt grUnt '. 13) In the word ' greeneth' the verb-ending replaces the copula, while the verb-stem indicates the proper content. ([In dem Wort 'griint' vertritt) die Personalendung die Stelle der

Kopula . . . , wiihrend der Stamm einen eigentlichen Inhalt anzeigt. l4)

When apostrophizing the Christmas fir-tree, Germans didn' t sing ' Thou art green , in winter' but rather 'Thou greenest in winter [Du griinst im Winter] . (These days Germans no longer sing.) The component of the predicate 'is green' which 'indicates the proper content ' is the general term. In an . expanded sense of 'general term' we might as well say that in the one-word predicate ' greeneth' the verb-stem is the general term. Let me mention in passing that at one point Aristotle reports on paraphrastic strategies that go against the grain of his constructio periphrastica: Some, like Lycophron, did away with the word 'is ' : others wanted to alter the language in such a way that ' [The fir-tree is green) ' is replaced by ' [The fir-tree gree n eth) ' . 15

Of course, I have smuggled in the allusion to the German Christmas carol, but in the Greek text, too, the proposal concerns the ' verbification' of a colour word (A,£UKOS). On behalf of Lycophron, the eliminativist, one could point out that several languages manage rather well without a word that functions as copula: what is indispensable is some means or other for marking the difference between strings of words which are j ust that, and sentences. 1 6 Doing away with the copula in English can lead to more or less serious communicative failures : '1 was told of a telegram sent by a j ournalist to check on the age of Cary Grant: HOW OLD CARY ' GRANT. Came the reply: OLD CARY GRANT QUITE WELL STOP HOW YOU . 1 7

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252

In calling the copula 'is' a mere form-word Frege does not declare it to be semantically irrelevant What does he mean by 'Aussage' ? This term is often used in the sense of 'Behauptung (statement, assertion) ' , but the presence of the copula in a well-formed sentence does not ensure that the sentence is a proper vehicle for making a statement (ein Behauptungssatz, a declarative sentence), as you can see from 'Is S ocrates courageous ? ' Actually, 'Aussage ' in Frege is not an alternative title for the kind of speech-act he calls Behauptung. 18 In traditional German grammar­ books the predicate is often called the Aussageteil of a sentence, and this usage stands behind Frege's phrase ' bloj3es Formwort der Aussage ' : it is meant to pick out that element of a certain part of a sentence S in virtue of which that part is the predicate of S . 19 So Frege, too, seems to think of the copula as a predicate-forming operator on general terms . Invoking the broad readings of 'copula' and ' general term' for which I have pleaded, we can now specify the truth-conditions of elementary predications in such a way that light is thrown on the linguistic meaning of the copula. In his 'Plea for the Copula' David Wiggins has shown how the format of a Davidsonian truth­ conditional meaning-theory can be adjusted to accommodate the copula. 2 o Ignoring tenses, we have a general schematic principle like this : T

An elementary predication of the form singular term a + (copula + general term F) expresses a truth iff F applies to the obj ect which is denoted by a.

Grammar tells us which copula goes with which kind of general terms. Axioms fix the meanings of the atomic terms in elementary predications :

a ( 1) F (1) F (2) F (3)

The object denoted (designated) by 'Socrates ' = S ocrates For all x , 'courageous ' applies to x iff x i s courageous For all x, 'a man' applies to x iff x is a man For all x, 'walk' applies to x iff x walks. 2 1

Principle T and the axioms a(1 ) and F( 1 ) imply the theorem

( 19-)

' Socrate s ' + (copula + 'courageous ' ) expresses a truth iff S ocrates is courageous .

Such a theorem also answers the question which proposition i s expressed by the sentence it is about, for we can replace the fragment ' expresses a truth iff' in ( 19-) salva veritate by ' expresses the proposition that' . Principle T together with the axioms for the simple general terms and for the names in our elementary predications fixes the linguistic meaning of the copula. Along these lines, we can give a satisfactory answer to Wittgenstein's question: In what way has the copula in elementary sentences meaning?22

Postscrip t Like Frege and Wiggins, I have neglected tenses and modal expressions, and I shall continue to do so in the remainder of this chapter. Nowadays they are standardly

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treated as sentence-forming operators on sentences .23 B ut at least p rima facie there are two further options : perhaps they are (A) general term modifiers, or (B ) copula modifiers , ad-copulae., as it were. Under both readings, 'Ann was a model' is not to be parsed as 'It-was-the-case-that (Ann is a model) ' , nor 'Ann is necessarily human' as 'Necessarily (Ann is a human) ' . Let us use 'PAST- ' and 'NEC- ' as ambiguous representations of the non-sentential modifiers. Under (A), our examples would be regimented as 'Ann is PAST-(a model) ' and 'Ann is NEC-human' respectively. (We can read the modified general terms ' a former model' and ' essentially human ' . ) By contrast, under reading (B) the tensed example would be parsed as 'Ann PAST-is a model' .24 The regimentation of the modal example would be 'Ann NEC-is human' De dicta necessity would be treated as that special case of de re necessity in which the res is a dictum and the general term is 'true' : thus, for example, 'The proposition that every human is human NEC-is true' .25 In the temporal case strategy (B) is closest to the syntactical surface: after all, 'PAST-is ' is just a fancy rewriting of 'was ' . What i s the copula i n ' B en turns (grows , becomes) pale' , ' B en remains pale ' , or ' B en looks pale ' ? (These examples are metaphysically resonant: recall the oppositions B ecoming and B eing, Appearance and Reality.) Our account of the copula as a predicate-forming operator on general terms allows for two answers . Answer (A) : the copula is the ending of the verb, and the general term is c omplex, 'turnlremainllook pale ' . (Sometimes our language provides us with an atomic verb that plays the role of 'turns ' + adjective: according to my dictionary 'pales ' means the same as 'turns pale ' , and in German the same holds for ' erbleicht' and ' wird bleich ' , and - outside the Christmas carol - for 'grunt' and 'wird grun ' .) Answer (B) : the copula is the verb that precedes the adj ective, the latter functioning as general term. Again, (B) is closer to the syntactical surface. If we regard both parsings as equally legitimate, then we must concede that what the copula in a given sentence is may be relative to a way of decomposing that sentence. I take this concession to be Fregean in spirit.26 In eaeh of the cases·ceonsidered in this postscript, the cupula ,under 'f'eading (B ) does more than just mark a predicate as predicate. Unsurprisingly, Frege's view does not hold for modified copulae. .

ll.

General Terms and Properties

The general term in our elementary predication (E)

Socrates is courageous

applies to the philosopher whom the singular term in (E) denotes and to some other persons . Should our semantics associate with a general term, over and above the obj ects to which it applies (if any), an additional entity? My answer is 'Yes ' . Let me first spell out this answer, before giving my reason for it. Our semantics should assign to a general term G (as used in context c) the property or attribute which the combination copula + G (as used in c) Can be employed to ascribe or to attribute to an object. So in the case of the general term in (E) the extra entity is the property of

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being courageous.27 (S ome general terms are equivocal, and some are' context­ sensitive. The bracketed supplements are meant to take this into account. Which property is ascribed by 'is a bank' depends on the intended reading of the general term. Which attribute is attributed by 'is taller than that man' or by 'is a foreigner' depends on which man is demonstrated by the speaker or on where the utterance is produced, and what is ascribed by 'is good' depends on the substantive the context provides for the substantive-hungry general term: B en may be a good violinist but a bad conductor.28) In associating general terms with properties I may seem to be following Frege, but I am not. What Frege calls properties (Eigenschaften) or, most of the time, concepts (BegrifJe), 2 9 are referents (Bedeutungen) of sharply defined monadic predicates , coextensive predicates have the same referent, and the referents of predicates are 'in need of completion' or ' unsaturated' . All this , Frege adds, is to be taken 'with a grain of salt' . Concepts are a special kind of function, and because of their incompleteness functions are not obj ects (Gegenstande). Now the referent of a singular term, if it has one, is always an object. So Frege feels obliged to declare singular terms like ' the concept F' or 'the referent of "F'" (as well as predicates like 'is a concept' that require completion by such a singular term) to be systematically misleading.3o Frege' s eyebrows would lift at the very sentence I used to explain the motivation for his verdict ( 'Concepts are . . . ' ) . One may wonder whether the blame for this aporia, which Frege puts on ordinary language, is not rather to be put on some move in his theory. Be that as it may, the entities I call properties differ vastly from what Frege calls properties or concepts . First, they are more finely individuated (as we shall see in the next section) . S econd, a term need not have a sharply bounded extension in order to have a property associated with it. Third, properties (in my usage of this word) are objects, hence they are not 'in need of completion' . Fourth, they are semantical values of general terms (rather than of predicates). Finally, the semantical relation between a general term and a property is not the same as that between the name ' Socrates ' and the man Socrates ; that is to say, genera.l terms do not denote ( ,refer to ' , ' stand for' ) properties . The general term ' courageous ' , I shall say (borrowing a word, but not much more than this word, from John Stuart Mill) , connotes the property of being courageous,3! and all and only those obj ects to which this term applies exemplify this property. A general term G in language L connotes a property X iff in L the combination copula + G serves to ascribe X to an obj ect. Only general terms stand in this relation to properties . So the picture I recommend is shown in Figure 1 . Thus , as regards (E), semantical values are assigned both t o ' Socrates ' and to 'courageous ' (but not to 'is courageous ' ) , and (E) can be said to express a truth just in case the semantical value of the former term (i.e. the obj ect it denotes) exemplifies the semantical value of the latter term (i.e. the property it connotes). The property that is connoted by the general term in (E) is denoted by the singular term in the following sentence:32 (P*)

Courage is a virtue.

The singular term in (P*) denotes a property which Socrates shares with all and only those who are courageous . Unlike Socrates, his first cold and his last stroll,

Properties in Abundance

,----- ----

general term

255

----..

connotes

property

--

exemplify

Figure 1

courage is neither locatable nor datable: it is not a particular, but a universal, ' a thing that i s b y its nature capable o f being predicated o f several things ' . 3 3 It has become customary to call obj ects that are particulars 'concrete' and to call objects that are not particulars (including not only universals in the narrower sense, that is, properties and relations, but also classes, types, numbers and propositions) ' abstract' . In a derivative sense, a term is classified as abstract [concrete] if it purports to denote an abstract [concrete] object or if it purports to apply only to abstract [concrete] objects . 3 4 So all terms in (P*) are abstract. The general term 'a virtue' as used in (P*) applies only to properties, and it connotes, according to the semantic account depicted in my figure, a property of properties . So (P* ) seems to deserve its asterisk: after all, in Raphael's fresco The Schoo l of Athens Plato i s pointing upwards . Other philosophers , both inside and outside the School of Athens, are bound to suspect that we have been led by linguistic will-o ' -the-wisps into metaphysical swamp s . Ever since Diogenes the cynic,35 advocates of particula rism have complained that, though well acquainted with tables, they have never come across any such thing as tablehood, ' all Things, that exist, being Particulars ' , as John Locke put it.36 Nowadays particularists are commonly referred to as nominalists .37 I do not adopt this usage (Harvard, vintage 1 947) because I think that the historically resonant title 'nominalism' is more appropriate for a special brand of partiCUlarism which we will briefly encounter in Section IV. I shall call the denial of particularism, again departing from contemporary usage, anti-particularism. No doubt, Plato was an anti-particularist, but anti-particularists need not accept Plato ' s conception of non-particulars. A fortiori they are not obliged to maintain, as Plato seems to do in some of his moods , that only non-particulars (really) exist. Therefore I shall not stick the label 'Platonism' on the denial of particularism.38 There are several kinds of particularism. The main division is that between ( I ) reductive and (2) non-reductive particularism. Advocates o f the former promote either ( L a) plain particularism or ( 1 .b) refined or metalinguistic particularism, that is,

256

Universals, Concepts and Qualities

nowinalism. All reductive particularists claim that statements seemingly about non­ particulars, if true, are truths about particulars. For the time being, let us only consider what I have dubbed the plain variety of reductivism. Adherents of this view maintain that truths ostensibly about a (first-level) non-particular called F-ness are really truths about particulars which are F. (In this chapter I use 'F-ness ' as a schema for abstract singular terms that are derived from a general term 'F' , no matter what the suffix is or whether there is any, thus covering ' steadfastness ' , ' wisdom' , 'generosity' , 'bravery' , 'courage' , etc.) Plain particularists regard our (P*) as a potentially misleading formulation of a claim about people who are courageous. Now what does the earth-bound paraphrase of (P*) look like? Not, it is hoped, like this: 'Whoever is courageous is virtuous' ,39 for there are ever so many scoundrels who are courageous . The truth of (P*) is even compatible with no courageous person being virtuous : all courageous people may be so full of glaring faults that none of them is virtuous . (Unlike Plato 's Socrates, and like most other philosophers, I take for granted that you can possess one virtue without possessing all of them.) The following paraphrase looks more acceptable: 'Whoever is courageous is virtuous in at least one respect.' But does this help our plain particularist? A respect in which several particulars resemble each other is hardly itself a particular. It looks as if the plain particularist avoids the appearance of referring to a single abstract object by quantifying over abstract objects, and this impression cannot possibly please him. Moreover, 'Whoever is a reader of this chapter is virtuous in at least one respect' is as true as can be, I'd like to think , but this statement does certainly not entail that being a reader of this chapter is a virtue. So why should the truth that whoever is courageous is virtuous in at least one respect ensure that courage is a virtue? 40 Even if the plain particularist were to succeed in this simple case, is there any reason for believing that she would always succeed whenever abstract terms are used in the course of making a statement? A look at almost any page of theoretical writing confirms the suspicion that the particularist reductive proj ect is a Sisyphean task. But let us assume that the particularist is happier than Sisyphus: take any 'F' you like, there is- no sentence in which F-ness seems to be denoted for which she cannot provide a paraphrase that preserves its linguistic meaning and contains no abstract terms. What would this success prove? The relation connoted by 'a meaning­ preserving paraphrase of' is symmetrical. So anti-particularists can tum the tables and claim: what paraphrase salvo sensu shows is not the dismissibility of reference to abstract entities, but rather its admissibility.41 Particularists do not have to go in for reduction. Non-reductive particularists uphold either (2. a) the Figure-of-Speech View or (2.b) the Error Theory or (2.c) the No-Statement View. Adherents of (2.a) contend that what is literally said in utterances of sentences seemingly about non-particulars is always false, but what is figuratively said is sometimes true. Proponents of (2.b) claim that utterances of such sentences always express falsehoods (full stop). Advocates of (2.c) maintain that what such utterances express is not in the market for truth at all. At least in the case of properties the No-Statement View does not seem to be a serious contender, or would anybody want to argue that utterances of 'Courage is a virtue ' or ' S quareness is a geometrical property' are not truth-evaluable?42 Non-reductive particularists are not intent on paraphrases that preserve the linguistic meaning of the sentences which offend their sensibilities. Let us first

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consider the theory I have nicknamed the 'Figure-of-Speech View ' .43 The relation connoted by the phrase 'a literal paraphrase of' is. not symmetrical. A sentence may be a literal paraphrase of another sentence although the latter is not a literal paraphrase of the former, as in the case of the following unfavourable verdicts on one of our acquaintances :

(ex) (A)

S am is an ass S am is a stupid person.

What is literally said by (A) , let us assume, is true, and it is the same as what is metaphorically said by (ex) . S ince S am isn' t a long-eared equine quadruped, what is literally said by (ex) is false. Particularists might regard the relation between a ' dead' metaphor and its literal paraphrase as an attractive model.44 Take

(�) (B)

There is a difference in age between Ann and B en Ann is older than B en, or B en is older than Ann.

A particularist might try to treat this pair along similar lines as the ftrst pair. Assuming that in (/3) we have an 'unobtrusive existential metaphor' ,45 he might argue : ' (B ) is a literal paraphrase of (�), whereas (�) is not a literal paraphrase of (B). What is literally said by (B) , let us assume, is true, and it is the same as what is metaphorically said by (/3). But there are no such things as age-differences, so what is literally said by (/3) is false.' Of course, you may find the alleged analogy less than convincing. You may be ready to grant without further ado that S am isn' t a quadruped but protest when being told that there are no age-differences: 'Do you seriously expect me to believe that all creatures are of the same age ? ' But let us suppress this worry and move on. Particularists can go a step further from here. Metaphors that are ' alive ' tend to defy literal paraphrase, for sometimes we can only make our point by using a - 'metaphor:46 . Perhaps one should treat certain' statements ostensiblY ' about abstract obj ects along similar lines.47 Compare

(y) (8)

The number of children in Siena divided by the number of mothers in S iena equals 3 . 3 . The number of orbiting planets divided by the number of stars equals 3 . 3 .

A particularist might propose t o replace (y) b y the answer to the question how many bambini and mamme there are in Siena (at the relevant time) . This answer would not contain any abstract singular term that purports to denote a number (it could be formulated by using only quantifters, the identity operator and two predicates) , but no information about the Sienese population would get lost - on the contrary. To be sure, this sentence would not even remotely look like a synonym of (y), but that is no objection to non-reductivists . By contrast, we are unable to replace statement (8), for which cosmologists might have strong evidence , by answering the question how many stars and planets there are. So (8) seems to be the kind of statement of which advocates of the Figure-of-Speech View would say that the ' existential metaphor' is not eliminable.48

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Universals, Concepts and Qualities

But how, you may very well ask, could the metaphorical character of each discourse that is seemingly about abstract entities have remained unnoticed for millennia? Standardly, when we are not aware of the fact that we are using a metaphor in an assertion we recognize the metaphor for what it is as soon as we realize that what we are saying, if taken literally, is too obviously false (' S am is an ass ' ) or too obviously true ( , S am isn' t an ass ' , 'No man is an island' ) .49 Surely, cases such as 'There are numbers ' or 'There are properties ' are vastly different. Such statements do not strike us as trivially false if taken literally, nor do their negations strike us as trivially true if understood literally. When a philosopher declares such existential statements to be false he makes a controversial metaphysical claim. Asked for a reason, he will presumably tell us that there are no entities of kind X unless Xs are particulars, and if he does not content himself with delivering a declaration of metaphysical faith he might argue for particularism from premisses that are germane to epistemology or to the philosophy of language. This philosopher seems to be an Error Theorist. In the following passages Quine portrays philosophers who do not acknowledge the existence of properties or numbers as 'Error Theorists ' . (As regards numbers, he is not one of them. ) One may admit that there are red houses, roses, and sunsets, but deny, except a s a popular and misleading manner of speaking, that they have anything in common.50 When we [say, 'There are prime numbers between 10 and 20' , the nominalist] will know better than to demur on account of his theory . . . In practice, he will even stoop to our idiom himself, both to facilitate communication and because of speech habits lingering from his benighted youth. This he will do when the theoretical question is not at issue, just as when we speak of the sun as rising . . . [H] e will agree that there are primes between 10 and 20, when we are talking arithmetic and not philosophy. When we turn to philosophy he will condone that usage as a mere manner of speaking, and offer the paraphrase. 5 1

According t o Error Theorists, the arithmetical sentence is related t o its 'nominalist' paraphrase as 'The sun rose at 7 a.m.' is related to ' The sun became visible at the horizon at 7 a.m.' One may lrnow that Ptolemaic astronomy is wrong and yet acquiesce in reports on sun-risings, but strictly speaking what is said in such reports is false, for it implies the falsehood that the sun moves. Of course, one cannot reasonably claim synonymy for a paraphrase that differs in truth-value from what it is a paraphrase of: such a paraphrase is only expected to 'serve any purposes of [the original] that seem worth serving' 52 and not to share its most serious drawback, falsity. Thus Error Theorists are prone to declare large stretches of discourse to teem with falsehoods although even ardent particularists don ' t rej ect them as false before they 'turn to philosophy ' . Strictly speaking, they maintain, we are bound to be wrong when we assertively utter, 'Ann and her mother have some very unpleasant features in common' , or 'Napoleon had many of the qualities of a great general' , no matter how things stand with the two ladies or with the emperor. This is very hard to swallow, and I for one refuse to swallow it.53 If in the course of a conversation we agree to an assertoric utterance of ' a and b have nothing in common' , then our reason is not that we subscribe to particularism and 'renounce '

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shared properties . Rather, we agree because we regard the domain of quantification as tacitly restricted to a contextually relevant sub-kind of characteristics (e.g. to features one tends to dislike in a person) and we take the message to be that a and b have none of those features in common. If you strongly dislike Ann's mother you will be pleased to be told before your first meeting with Ann, ' She has nothing in common with her mother' .54 Let me break off at this point and simply give voice to a conviction or two. At least as far as properties are concerned, the paraphrastic endeavours of reductive particularists are doomed to failure ; this holds also for the refined variety of reductive particularism that we shall encounter at a later stage, and even if these endeavours were successful, the success would not show what it was meant to show. 55 As for non-reductive particularists, it is fair to say that they have not yet made out their case.56 If I am right about reductive particularism, then the (literal) truth of statements like (P*) ensures that there is at least one abstract obj ect. The argument for this is very simple: 1 2 1, 2 4 1 , 2, 4 1 , 2, 4

(1) (2) (3) (4) (5) (6)

C ourage i s a virtue. All virtues are properties . Courage is a property. All properties are abstract objects . Courage is an abstract obj ect. There is at least one abstract object.

Assumption ( = P*) Assumption 1 , 2 (Modus Barbara) Assumption 3 , 4 (Modus Barbara) 5 Existential Generalization

I take it that all assumptions in this argument are conceptual truths,S7 hence this bit of reasoning is a priori through and through. (Since the argument purports to prove the existence of entities of a certain kind, it has an air of pulling a rabbit out of a hat. This impression has moved advocates of the Figure-of-Speech View to construe higher-level predications like (pol') as metaphorical truths,58 whil:,: Error.Theorists would regard the argument as valid but not sound. ) Anti-particularists should not let themselves be bullied by the epistemological question of how an abstract entity like the property F-ness could ever become cognitively accessible. 'By understanding the abstract singular term "F-ness'' ' , is the proper answer, or at least the beginning of a proper answer.59 (This answer may serve to dispel the air of hocus-pocus I mentioned a moment ago : if the question is whether certain intelligibilia, obj ects of thought alone, exist, why shouldn' t the intellect have the power to answer it affirmatively in some cases ?)60 If you acccept ( 1 ) , alias (P* ) , as well as the categorial classifications (2) and (4) at face value, you are ' ontologically committed' , as they s ay, to [acknowledging that] abstract entities [exist] . The kind of commitment that matters here is, as it were , ontological commitment light, or non-philosophical ontic commitment. Suppose a philosopher of mathematics who is opposed to 'Platonism' is asked by his little daughter whether there are any prime numbers between 10 and 20, and unguardedly he answers, 'Yes, dear, there are several prime numbers between 1 0 and 20.' But then suddenly h e remembers his philosophy, he coughs and adds , in a dispiriting tone of voice, 'But of course, that was only a loose and popular manner

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of speaking: there aren' t really any nuinbers.' 6 1 He should not be surpris'ed if his daughter will never again ask him for help, How are we to understand the double-talk of our embarrassed particularist? What is the 'really' doing in his solemn final statement, 'Such things don 't really exist' ? A model which I find more appropriate than the appeal to meta-fictional talk and games of make-believe that is popular nowadays is one of our obj ectual uses of 'true' (which parallels one use of 'real ' ) , Here is an example, Is Ann' s beloved showpiece, the antique cupboard in her sitting-room, made of mahogany wood? Only the hard reddish wood that is yielded by certain large tropical American trees (genus Swietenia) is true, or real, mahogany. But various trees in Africa (of the genus Khays) yield a similar wood that is also called mahogany, So, if you are an expert in these matters and want to boast with your expertise, you may point at Ann's cupboard and annoy her by saying, quite consistently, 'That is mahogany, but it isn ' t true mahogany' . Generally, something which neither is nor has a propositional content is a true (real) F, under this acceptation of the phrase, iff it satisfies the strictest standards for being an F,62 What commonly passes for an F may not measure up to the most demanding standards for being an F, If something is a true (real) F, then it is an F, but the converse does not hold, Now let me try to apply these observations to our particularist's talk of existing, but not really existing. Of course, ' exist' does not play the same logical role as the expressions for which 'F' did duty in my reflections on a certain use of the phrase 'a true F' , It may help to exhibit the analogy I have in mind if I replace 'Properties don ' t really exist' by a stylistic variant in philosophers ' English, 'Properties are not real existents ' , If so-and-sos are real existents, then they are existents , but the converse does not hold: what commonly passes for an existent, our particularist maintains, may not measure up to the strictest standards for being an existent. Actually, we c an make the same point by using the existential quantifier. We can hear our embarrassed particularist as first conceding, 'Loosely spealcing, there are properties, numbers, etc.' and then insisting; 'But strictly speaking, there are no such things .' To what standards does he- appeal when he upholds this view? He claims that sensu stricto so-and-sos exist only if they stand in spatio-temporal relations to us , At the centre of the apparently interminable ' debate between particularists and anti-particularists lies, it seems to me, the question whether particularists have any good reason for insisting on this restrictive standard, (I think the answer is 'No ' . ) Does my explanation of the particularist's double-talk oblige me to declare ' exist' in his mouth to be ambiguous ? I don't think SO.63 Again a comparison might help . Suppose, somebody says, 'Ann and B en are the same age ' , Is it true what she says? 'Yes ' and 'No ' may be equally legitimate answers, depending on the degree of fineness of discrimination that is deemed relevant when the question is considered ( ,Yes , they were both born in 1 9 8 0 ' ; 'No, he was born in July, while she was born in S eptember ' ) . But that is no good reason to declare that sentence, or any of its components , to be ambiguous. Things stand similarly, I believe, with 'Properties exist' if the particularist is right in invoking a restrictive standard. If he is wrong (as I think he is), then 'Loosely speaking, so-and-sos exist, but strictly speaking, they don ' t' makes as little sense as 'Loosely spealcing, Rome is the capital of Italy, but strictly speaking, Rome isn't the capital of Italy.'

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A philosopher 'who i s suspicious o f abstract entities ' like properties and numbers, Rudolf Carnap once observed, will ' probably . . . speak about all these things like anybody else but with an uneasy conscience, like a man who in his everyday life does with qualm many.things which are not in accord with the high moral principles he professes on Sundays' .64 Non-philosophical ontic commitments are incurred on work-days, so to speak, and only these commitments matter for the semantics of " our everyday talk. So let me return, at last, to my proposal to enlist abstract objects for the semantics of general terms . The particularists ' global worry should not be confused with the objection against any such proposal that was raised by Victor Dudman, among others : [T]he invoking of an extra entity, a property or class, over and above the objects of which the predicate is to be true, and the associating of it with the predicate, is a quite gratuitous step. After all, what is the semantic role of a one-place predicate? This, I should have thought: to be true of each severally of a number (perhaps nought) of objects and false of (perhaps) some others . . . Why, then, . . . should we go beyond this conception, to the extent of positing additional entities? 65

Neglecting for a moment the difference between general terms and predicates , Dudman's semantical predicate 'is true of' (just like its Tarskian converse, 'satisfies ' ) corresponds to the semantical predicate ' applies to ' in my Figure 1 . Dudman's question obtrudes itself even if anti-particularists are in the right against particularists . Obviously, the denial of particularism does not by itself entail that any abstract entity stands in the relation I dubbed 'being connoted by' to any concrete general term. Certainly there is no need to assign abstract obj ects to general terms for the sake of specifying the truth-conditions of elementary predications like (E), ' S ocrates IS courageous ' . This sentence expresses a truth, we can say (and we did say it at the end of Section I) if and only if 'courageous ' applies to the obj ect denoted by 'Socrates ' : " so far there is no 'need to characterize general terms as c6Iinoting" a property. If all terms in a given language are concrete, semanticists don ' t have to call abstract entities into service. Incidentally, properties are not needed either when it comes to explaining why (E) expresses a truth. ' B ecause (E) means that Socrates is courageous, and S ocrates is courageous ' is a sufficient answer to that question.66 S o what is the point of assigning properties to concrete general terms? It enables us to explain certain data in less primitive languages which would otherwise remain mysterious. In a rich language like ours we can ascribe a property to an object, using a copula and a general term, and we can make an identifying reference to it, using a singular term. The ascriptive mode of ' introducing something into discourse' 67 is exclusively used for properties (and relations ) : only properties (and relations) are ascribables, and it has priority over the referential mode: we are not able to refer to properties unless we have learnt to ascribe them. Now it is a remarkable fact that sometimes we use both modes almost in one and the same breath. For example, when we argue as follows :

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[A]

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(P I ) (P2) (C)

Socrates is courageous . That is a virtue. Therefore, Socrates has at least one virtue.

Intuitively, this argument is valid, and if we assign properties to general terms as their connotata we can easily explain why. The general term in (P I ) connotes the property that is denoted by the singular term in (P2) .68 If the premisses are true, then that property is both exemplified by Socrates and a virtue, and it is conceptually impossible for that to be true while conclusion (C) is not true. As it stands, argument [A] is not formally valid (in first-order logic) . Never mind, it is valid,69 and it can be turned into a formally valid argument by a transformation of (P I ) which every speaker who understands [A] i s ready to carry out: (P I * )

Socrates has (possesses, exemplifies) courage.7o

(Due to the anaphoric pronoun in premiss (P2), the argument ' (P I *), (P2), (C) ' is formally valid only in the slightly relaxed sense in which 'Socrates is courageous, and he is wise, so somebody is courageous and wise' goes through as formally valid.) In accepting [A] as sound we are committed to properties. After all, if Socrates has at least one virtue, a property it is good to have, then there is at least one property. Thanks to the 'invocation of an extra entity' (to repeat Dudman ' s phrase) we can make sense of the interaction between concrete general terms and abstract singular terms as witnessed in argument [A] , and I for one cannot see any other (and equally intuitive) explanation of this phenomenon. But could the invocation of classes not do the same job, and give us the additional advantage of not insulting Quinean sensibilities ? Let us say that a class is a set if it is a member of a class and that it is an ultimate class if it is a member of none.71 Then properties can at best be sets, since properties themselves have properties . B ut we cannot identify courage with the set of all and only those who are courageous . This set is identical with the set of those who -are courageous and die before their 200th birthday, but there might ha¥e been a courageous Methuselah who managed to reach this biblical age. And even if courage had been no more exemplified than omniscience, courage would still be different from omniscience, even though the set of the courageous would then have been identical with the set of the omniscients. These objections would no longer arise if we were to follow D avid Lewis ' s footsteps and identify courage with the set o f those who are courageous i n some possible world or other.12 But if we were to accept this recommendation, we would lose the strategic advantage of being on good terms with Quine, since possible heroes are no more to Quine's liking than is heroism (as a property ) . More importantly, the identification of properties with sets has unpleasant consequences which are independent of any reservations against an ontology of possibilia. Each set has the property of being a set. If Lewis were right, this property would have to be identical with the set of all sets . But Cantor's theorem shows that there cannot be any such set.73 So perhaps we'd better acknowledge properties as abstract objects sui generis (if we are ready to acknowledge them at all). In this section I have confessed to having a strong leaning towards anti­ particularism, and I have argued that assigning properties to general terms pays

c

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explanatory dividends when it comes to understanding our understanding of our own language. In the next section I shall pile on the particularists ' agony.

III.

Interlude : General Terms and Concepts

The general term in our elementary predication (E)

Socrates is courageous

connotes, I said, the property of being courageous , and now I add that it expresses the concept courageous.74 All and only those obj ects to which the general term 'courageous ' applies fall under this concept.75 I shall soon explain what I take this addition to be good for, but let me first spell it out a bit. The completed picture is shown in Figure 2 .

�---- � app

,?: T �

. exemplify

general term

t

expresses

concept

�

---- ----,

......-- ------'

connotes

determines

property

Figure 2

Each general term (as used in context c) expresses exactly one concept, and it connotes at most one property. (The question why in the case of properties I say ' at most one' rather than ' exactly one' will be answered in Section VI below.) On my understanding of the term, concepts are situated on the level of Fregean Sinn. This separates them from properties, as we shall see.76 When is the property of being F identical with the property of being G? My answer declares a Modal Condition (MC) to be both necess ary and sufficient (provided that there is such a thing as the property of being F [G] ) : (MC)

The property of being F is identical with the property of being G if and only if necessarily all and only Fs are G.

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(As I just said, the need for the proviso will be considered later on. ) According to (MC) a property that is connoted by a general term differs from the extension of that term. Even if the terms 'a vertebrate with a heart' and 'a vertebrate with a liver' apply to the same objects , the property of being a vertebrate with a heart is different from the property of being a vertebrate with a liver. Like all other general terms that don' t apply to anything, the terms 'a witch' and 'a golden mountain' have the same extension, but the property of being a witch is not identical with the property of being a golden mountain. On the other hand, according to (MC) the property of being a (Euclidean) triangle is the same as the property of being a closed plane rectilinear figure whose internal angles add up to 1 80°, for the corresponding universal quantification is a necessary truth. In this case, the property identity can be recognized a priori for what it is, but Hilary Putnam has taught us that this isn ' t always the case.?7 According t o (MC) the property of being a lump of common salt is identical with the property of being a lump of sodium chloride, but the corresponding universal quantification is a necessary truth that we can only know a posteriori. Criterion (MC) is partly legislative: it tries to tidy up our diffuse employment of the word 'property ' . If somebody were to protest against (MC) by saying, ' B ut triangularity is not the same property as trilaterality ! ' , one could not accuse her of misusing the word 'property ' . At this point I am wholly with Lewis who writes about this very example: Necessarily, all and only triangles are trilaterals. Yet don't we want to say that [triangularity and trilateralityJ are two different properties? Sometimes we do, sometimes we don' t . I don't see it as a matter of dispute . . . It's not as if we have fixed once and for all, in some perfectly definite and unequivocal way, on the things we call ' the properties' . . . Rather, we have the word 'property' , introduced by way of a varied repertory of ordinary and philosophical uses. The word has thereby become associated with a role in our commonsensical thought and in a variety of philosophical theories . . . It is wrong to speak of the role associated with the word ' property ' , as if it were fully and uncontroversially settled.78

Furthermore, I believe that the intuitions which underlie that protest can be budgeted for by distinguishing properties, as conceived in accordance with (MC), from concepts . Let us begin with some reflections on possessing a concept (in the exacting sense of 'commanding it' , 'having mastered it' ) . If one is able to think of an object as F, then one possesses the concept F, and if one fully understands the (univocal) general term 'F' (or any of its synonyms) , in other words, if one completely grasps its conventional linguistic meaning, then one possesses the concept F A speaker' s understanding o f a general term does not ensure that she possesses the concept expressed by that term unless she fully understands it. Partial understanding of a term by a speaker may suffice, though, for correctly ascribing to her a propositional attitude with a content clause containing the term. Take any general term 'F' and any propositional attitude verb 'V ' ; it may not be true that a person commands the concept F although it is true that she V s that . . . F . . . 79 Putnam once confessed that he is unable to distinguish an elm from a beech. 8 o So his grasp of the meaning of the terms 'elm' and 'beech' is less than perfect, and it does not make him a speaker

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who has mastered the concepts elm and beech. B ut we c an be sure that he knows that ' elm' and 'beech' both apply only to deciduous trees and that he would not predicate either term of typical birches, say, or of weeping willows when he sees them clearly, so he has some knowledge about the extensions of ' elm' and 'beech' . Furthermore, he defers to other members of his linguistic community whose understanding of those terms leaves nothing to be desired; that is, he submits his applications of 'elm' and 'beech' to the judgement of those speakers of the language who are entitled to claim authority in this matter. So he can correctly be said to believe that no elm is a beech.8 1 S omebody who has not (yet) acquired an ability may have partially acquired it. If the content clause of a true ascription of a propositional attitude to a person contains 'F' , then she has at least partially acquired the concept F, but she may not yet command it. The concept F differs from the concept G if it is possible that somebody is thinking of an obj ect x as F without being able to think of x as G. S omebody who is able to think of a figure on the blackboard as a triangle need not be able to think of it as a closed plane rectilinear figure whose internal angles add up to 1 800• After all, not everybody who is able to recognize figures as triangles has had lessons in geometry. Somebody who is able to think of the content of a tureen as a liquid that contains too little salt need not be able to think of that content as a liquid that contains too little sodium chloride. After all, not everybody who is able to recognize that the soup needs more salt has had lessons in chemistry. B oth examples show that the concept F may differ from the concept G even if the property of being F is identical with the property of being G. So my answer to the question, 'When is the concept F the same as the concept G?' declares a Cognitive Condition (CC) to be both necessary and sufficient: (CC)

The concept F is identical with the concept G iff thinking of something as F is thinking of it as G.

individuates concepts veri finely. One cannot think of a bottle a s ·half full · without being able to think of it as half empty, and vice versa. Nevertheless, half full is not the same concept as half empty, for optimists tend to think of the bottle as half full rather than as half empty, while pessimists have the opposite tendency. S o even i f i t i s self-evident that all and only F s are G, F and G may be different concepts . On the other hand, thinking of an object as an equiangular figure, or of a person as an ophthalmologist, surely is thinking of that obj ect as a figure with equal angles , or of that person as an eye-doctor, so these are cases of concept-identity. One entry in Figure 2 still awaits comment. A concept x that is expressed by a general term determines (in a given context c) the property y just in case every general term that expresses x connotes y (in c). We saw that several concepts can determine one and the same property, and in Section VI we shall see that not every concept determines a property. B ut in a given context no concept determines more than one property. (The relativization to contexts is meant to budget for cases like this : When B en says, '1 am a foreigner' , the general term expresses the same concept no matter whether he is speaking in the country whose citizen he is or somewhere else. But only in the latter case does the concept expressed by the general term in his utterance determine a property that he exemplifies . 8 2) This

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In order to grasp what somebody said who predicated the general term 'F' of an object it does not suffice to know which property is connoted by 'F' . B oris, a monoglot Russian, may lmow, because a scientifically well-informed bilingual compatriot told him so, that the English term 'a bottle of water' connotes the property of being a bottle filled with H2 0, whereas he does not yet know what is said about a bottle when this term is predicated of it. In order to understand such a predication fully, he must come to know which concept is expressed by ' a bottIe of water' . Similarly, B oris may know, because a polyglot Russian Plato scholar told him so, that the English term 'courageous ' connotes the property which was the topic of a debate between Plato 's Socrates and two Athenian generals, but B oris does not yet know what is s aid about a man when this term is predicated of him. 83 One cannot understand such a predication completely unless one knows which concept is expressed by ' courageous ' . B y now the point of assigning not only properties, but also concepts , to general terms will have come into sight, or so I hope. In the remainder of this chapter the focus will be on properties . That's why I called this section an interlude.

IV.

Elementary Predications and their Quasi-Platonic Counterparts

In this section I shall compare the elementary predication (E)

S ocrates is courageous

with its quasi-Platonic counterpart, as one might call it, which has also found its way into Figures I and 2 : 84 (QP)

S ocrates exemplifies (possesses, has) courage.

Plato 's own variant of (QP) was 'Socrates participates in courage (0 LCD1CPO::'"CllC; 1l£'"C£X ct '"C1lC; o::v 8pcto::C;) ' ; in B olzano this became simply ' S okrates hat Mut' ,85 and we shall soon come across converse formulations such as 'F-ness belongs to a' and 'F-ness is a characte ristic of [characterizes] a' .86 Most of the time I shall use ' exemplifies ' as the canonical representative of all these verbs and verbal phrases.87 Obviously quasi"Platonic sentences like (QP) differ syntactically from elementary predications like (E) : we find a verb and a noun in (QP) that do not occur in (E) . My question is whether they differ only syntactically. No doubt, (E) and (QP) are close relatives . S ocrates cannot be courageous without having courage , and he cannot have courage without being courageous: so (E) and (QP) are intensionally equivalent; that is, the biconditional 'E iff QP ' expresses a necessary truth. But, of course, from the fact that two sentences are intensionally equivalent it does not follow that they differ only syntactically. First of all , any two sentences which express necessary truths are intensionally equivalent, but obviously the difference between 'No day is longer than a week' and 'All red roses are red' is not merely grammatical. Second, even two sentences which resemble (E) and (QP) in expressing contingent truths can be intensionally equivalent yet differ not only syntactically, as witness 'In almost every kitchen you ' ll find a lump

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of salt' and ' In almost every kitchen you'll find a lump of sodium chloride' . S o the observation that (E) and (QP) are intensionally equivalent does not foreclose the possibility that they differ semantically. Now the truth expressed by the biconditional 'E iff QP ' is not merely necessary; it is a conceptual truth (and hence a priori knowable). But from the fact that two sentences stand in this more demanding intensional relation it does not follow that they differ only syntactically. Consider the sentences ' Caesar is dead' and 'Anyone who were to believe that Caesar is dead would be right in so believing ' . Their biconditional expresses a conceptual truth. Nevertheless, they differ semantically, for understanding the latter is conceptually more demanding than understanding the former. 88 So the observation that (E) and (QP) are more than just intensionally equivalent does not foreclose the possibility that they differ semantically. B ernard B olzano, Frank Ramsey and Peter Strawson deny that there is any semantical difference between the members of such pairs : , It is evident that the meaning of a sentence of the form 'A is B never differs from that of 'A has b' if b is the abstractum that belongs to the concretum B. [Einleuchtend istJ, daj3 Siitze von der Form: A ist B , nie einen anderen Sinn haben, als den a uch der Ausdruck: A hat b, andeutet, sofem b das zu dem Concreto B gehorige Abstractum vorstellt.89

[Ilt seems to me as clear as anything can be in philosophy that the two sentences

(E) (QP)

Socrates is wise Wisdom is a characteristic of Socrates

express the same proposition. They are not, of course, the same sentence, but they have the same meaning, just as two sentences in two different languages c an have the s ame meaning. Which sentence we use is a matter either of literary style, or of the point of view from which we approach the fact. If the centre of our interest is Socrates we say ' (E) ' , if we are discussing wisdom we s ay '(QP) , ; but whichever we say we mean the , s ame thing . . . ' (QP) means no more and no less than '(E) ' , it is merely a lengthened veTbal fOInl.90 The syntactical variation between 'Socrates has courage' . . . and ' S ocrates is courageous ' . . . is not more than that - a syntactical variation.9 1

Note that Ramsey's pragmatical explanation of the fact that we sometimes prefer one formulation to the other - notwithstanding their (alleged) synonymy - would work equally well as answer to the question why we sometimes stress the singular term in (E) and sometimes the general term.92 By contrast, B ertrand Russell maintains that elementary predications and their quasi-Platonic counterparts differ semantically : The proposition [QPl

Humanity belongs to Socrates

is equivalent to [El

Socrates is human

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but it is a distinct proposition. In [El the notion expressed by 'human' occurs in a different way from that in which it occurs when it is called 'humanity' [as in [QPll , the difference being that in the latter case, but not in the former, the proposition is about this notion. 93

Russell' s positive statement that [QP] and [E] are ' equivalent' is correct, of course , but i t is a n understatement, for h e is thinking o f extensional equivalence, that i s , sameness of truth-value.94 Perhaps Russell's negative statement that members o f such pairs express distinct propositions i s also correct. How is his argument for this verdict to be understood? The proposition expressed by [QP] , he says, 'is about' something which the proposition expressed by [E] is not about. What is this something? If Russell's 'notion' is to mean CONCEPT (which is not a far-fetched conjecture) , then his [QP] does not really express the relevant proposition. That would rather be done by the sentence ' Socrates falls under the concept human' . In this sentence a concept is indeed referred to ( 'called' ) which is ' expressed' rather than referred to in Russell's [El But under this reading Russell ' s argument would not speak to the issue we are concerned with; for the question to be answered in this section is not about pairs of sentences of the form 'a is F' / ' a falls under the concept F' . However, if Russell's 'notion' is to mean PROPERTY, his argument is to the point, and what he says about [QP] and [E] comes fairly close to the following claim: in [QP] a property is denoted, and in [E] this property is connoted rather than denoted. Isn ' t that plausible, and doesn' t it mark a semantical difference between those sentences? Wilfrid S ellars concurs with Russell, but he has a very different reason for insisting on semantical distinctness . His reasoning shows that a fundamental metaphysical disagreement lies beneath the surface of their agreement: Russell is an adherent of anti-particularism, whereas Sellars is an advocate of refined or metaiinguistic particularism. It is this variety of particularism that deserves the title 'nominalism' , for S ellars really follows Roscelin's and Abelard' s footsteps.95 His twelfth-century pr�cursor,s were agreed that a universal, that is, a predicable, i s ,not a (non-linguistic) res but rather a nomen, 'there being nothing in the world Universall but [Common] Names,' as Hobbes was to reinstate their view five centuries later.96 A name, Roscelin maintained, is a vox (a vocal utterance) , and his pupil Abelard added that it is not j ust a vocal noise (flatus vocis) but rather a vox significativa, or sermo, a meaningful audible sign-token. 97 Sellars 's amendment of early medieval nominalism is this : statements seemingly about an abstract entity F-ness are statements not only about (audible or visible) tokens of the general term 'F' but about all tokens that play the same role as 'F' -tokens : 'Courage' merely looks (to the eye bewitched by a certain picture) . . . as though it referred to something non-linguistic. Applying to expressions in any language which do a certain j ob, its inter-linguistic reference is confused with a non-linguistic reference. 9 8

This is the background of Sellars 's thesis that quasi-Platonic sentences are crypto­ semantical sentences. (QP) , he contends, has the same content as the explicitly semantical sentence

Properties in Abundance

(Sem)

269

Every sign-token that is functionally equivalent with tokens of 'courageous ' in the language of this very utterance applies to Socrates.99

If that is correct, then (E) does certainly not have the same content as (QP) ; for the statement that Socrates is courageous does not have any linguistic subj ect matter. Is metalinguistic particularism plausible? I don't think so. Remember B oris, our monoglot Russian. He has no 'information whatsoever about the English word ' courageous ' ; he has not even partially mastered the concept of functionally equivalent tokens, but he does know quite a lot about Socrates . B oris certainly does not believe the proposition that is expressed by (S em) , but this does not prevent him from believing that Socrates possesses courage. Hence what is said by (QP) has a property which it does not share with what is said by (Sem) , namely the property of being a content of B oris 's thoughts. So quasi-Platonic sentences and their Sellarsian counterparts do not express the same proposition. Now the question to be settled was this: Is our quasi-Platonic sentence just a stylistic variant of the corresponding elementary predication? S ellars 's negative answer may be correct even if his argument for this verdict fails . And so it is, I believe. On the other hand, there is something to be said for the affirmative answer, too . Russell and S ellars are actually right, but B olzano, Ramsey and Strawson would have been right if the language to which (QP) and (E) belong had been expressively poorer than it actually is. Let me explain. It will tum out to be helpful to step back for a moment and to compare the following two sentences : (S l ) (S2)

kicked the ball B en kicked the bucket.

Ann

Sentence (S l ) contains two singular terms and a two-place predicate. It entails, among other things, that there is something Ann kicked (namely a ball), and it makes sense. to ask whether the ball she kicked is the same as the one Ben had kicked the day before. Things stand very differently with (S2). If we understand and believe this slangy death notice, we are not inclined to conclude that there is something that B en kicked (namely a bucket) . It would not make sense to ask whether the bucket he kicked is the same as the one that had been kicked the day before by a policeman in B aghdad. (S2) seems to consist of one singular term and a one-place predicate. The general term 'kick the bucket' , as used in our rude statement, is an idiom: it has no semantic structure. We do not owe our understanding of this expression to our comprehension of its components 'kick' and 'the bucket' . In a semantics of the Davidson-Wiggins type sketched at the end of Section I the term 'kick the bucket' would be treated in the same way as 'walk' , that is, as semantically atomic. Now back to (QP) . If this sentence is in the same boat with (S l ) in that it also contains two singular terms and a two-place predicate, then there is a semantical difference between (QP) und (E) . But we cannot find out whether the word 'courage' occurs in (QP) as a singular term, rather than in the way in which 'the bucket' occurs in (S2), as long as we keep on staring only at this sentence . Quine saw the decisive point when he wrote in Word and Object:

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The move that ushers in abstract singitlar terms has to be one that simultaneously' ushers in abstract general ones . . . [T]he emergence of abstract singular terms is not to be separated from that of abstract general terms 100

If the word 'courage' in (QP) really is a singular term, then one does not understand it as such unless one has learned to use it also in higher-level predications like (P*)

Courage is a virtue,

where it enj oys the company of a (pure) abstract general term. Strictly speaking, this argument is only concerned with abstract general terms that are pure. What is the point of this restriction? A higher-level predication, in my usage of this phrase , is never intensionally equivalent with an elementary predication about a particular. So we cannot define 'higher-level predication' simply as 'sentence which consists of n abstract singular terms and a predicate that results from applying a copula to an n-adic abstract general term' . The latter condition is satisfied by ' Courage is exemplified by Socrates' , for what follows the copula is a (monadic) abstract general term. 101 But this sentence is intensionally equivalent with ' S ocrates is courageous ' . If we call an abstract general term pure just in case it does not contain a concrete singular term, then we can give the following definition: A higher-level predication is a sentence which consists of n abstract singular terms and a predicate that results from applying a copula to a pure n-adic abstract general term. 102 Furthermore, j ust as it is an essential feature of concrete singular terms that they can flank the identity operator in statements which are contingently or necessarily true ( ' S ocrates is Plato 's most important teacher' , ' George Orwell is Eric Blair ' ) , so the word ' c ourage ' only functions as a singular term if it c an also occur in contingently or necessarily true identity statements, such as ' Courage is the virtue about which S ocrates had a debate with two Athenian generals' and 'Courage is the virtue that is opposed to the vice cowardice ' . Finally, just as it is an. essential feature of concrete singular terms that we can quantify into their position (' Somebody is courageou s ' ) , so the word ' courage ' only functions as a singular term if we can quantify into its position - for example, by concluding from (P*) that there is at least one virtue. As part of a language in which higher-level predications can be formulated, (QP) is not merely a stylistic variant of (E) . But since no (pure) abstract general term j oins 'courage' in (QP) , one can call this sentence, again following Quine, a ' degenerate specimen of that higher part of language' . 1 03 But let us look now at the other side of the coin. 104 Imagine a variant of English, call it B asic English, that is expressively poorer than the language I am currently trying to speak: it does not provide its speakers with the resources for higher-level predications like (P*) . (Particularists would presumably delight in this language. ) I n B asic English n o abstract general terms are available. However, sentences o f the type ' a exemplifies F-ness ' do belong to B asic English, too, but 'F-ness ' never occurs in any other position than at the right-hand side of ' exemplifies (has, possesses) ' . In B asic English sentences of the form 'a exemplifies F-ness ' contain only one singular term and a non-relational predicate which results from applying

Properties in Abundance

27 1

the polysyllabic c opula, ' exemplifies ness ' , to the general term 'F' . Such sentences of Basic English are in the same boat with ' B en kicked the bucket' in English. 1:n that death notice the predicate is also obtained from a semantically atomic general term ( , J.9.ck the bucket' ) by applying a copula (more precisely: the tensed copula ' -ed ' ) to the verb-stem 'kick' . In B asic English ' exemplifi- courage' is treated as an idiom (that is, it is treated as though it had no semantic structure) , hence in that language the difference between (QP) and (E) i s indeed simply a matter of stylistic variation. Consequently, in a semantical account of B asic English (set up in the Davidson-Wiggins format) the general term ' exemplifi- courage ' would be dignified by a special axiom, just like ' courageous ' , whereas in such a semantical account of English the specification of the truth-conditions of predications of the former term is derivable as a theorem from the axioms for its components . l 05 It is instructive to consider Stephen Schiffer's 'pleonastic ' conception of properties in this light (if light it really is): --

A striking feature of properties is how swiftly and easily we appear to get committed to their existence. They exhibit . . . a something-from-nothing feature: A trivial transformation takes one from a sentence in which no reference is made to a property to a sentence that evidently contains a singular term whose referent is a property. Thus , from

(E)

Socrates is courageous,

whose only singular term is ' Socrates ' , we can infer its pleonastic equivalent [qp]

S ocrates has the property of being courageous

wherein the ostensible singular term ' the property of being courageous ' evidently refers to the property of being courageous . . . [S]ubject to a certain qualification, each predicate 'F' determines a property, the property of being F, thanks to determining a nominalization, 'the property of b eing F ' , which can ' t fail of reference. 1 06

' The reason for the caveat k the finiiJ. state�ellt wiil be considered in Sectiori Vi. (ii' was for the same reason that I refrained from saying that every general term connotes a property or that each concept determines a property.) S chiffer' s [qp] does not have the s ame structure as our (QP) , since it invokes the categorial concept of a property. l07 B ut this does not very much alter the situation. For again I claim that the more verbose sentence would be just a stylistic variant of the shorter one if expressions of the type 'the property of being F' were only to be found at the right­ hand side of 'has ' . As a sentence of Basic English, [qp] contains only one singular term, and the phrase 'has the property of being ' is a polysyllabic copula. To be sure, the predicate in [qp] very much looks as if it contains a singular term, but that also holds for the English idiom 'kicked the bucket' . How could you incur an ' ontological commitment' that you had not shouldered before just by moving from a sentence to its pleonastic equivalent? How can the latter have additional existential implications? Even Strawson and Quine are agreed on this question (though not on much else) : The idea is that (QP) [ ' Socrates possesses bravery' ] commit[s] us, as . , . regards bravery, in a way in which we are not at all committed . . . by (E) ' S ocrates is brave' . But this is

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absurd. The theory of ' commitment' by noun, but not by adjective is as absolutely implausible as any philosophical view could be. !Os He was right about the implausibility and absurdity of the idea, but wrong in supposing, if he did, that the idea was mine. The difference between [(E) and (QP)] is too frail a reed to bear the weight of an ontology l 09 . . .

. . .

If it is true that in maintaining (E) we do not commit ourselves to belief in the existence of properties, we see only a 'nothing-from-nothing transformation' when staring at the move from (E) to [qp] . In English, as opposed to B asic English, that part of [qp] which Schiffer sometimes calls, with justified caution, an ' ostensible singular term' really is a singUlar term, for it also occurs in higher-level predications. About such predications S chiffer himself says : 'I doubt that the statement that [courage] is a virtue is pleonastically equivalent to any statement not containing a singular term referring to [courage] . ' 1 10 If the particularists ' reductive aspirations are doomed to failure and in any case deeply misguided and if the proposition expressed by (P*) is literally true, then in stating that courage is a virtue we commit ourselves to acknowledge the existence of properties . As is clear from Section II above, I am ready to affirm the antecedent. The weight of an ontology is borne by irreducible (and literally true) higher-level predications rather than by the difference between adj ective and noun. One cannot participate in the language-game of higher-level predications unless one has learnt to understand elementary predications like (E) , but one need not be able to take part in any of those higher-level games in order to understand elementary predications . 1 1 I This one-sided dependency claim as regards comprehension is to be sharply distinguished from the dubious reducibility claims upheld by many particularists . Furthermore, the one-sided dependency I emphasized does not entail that we cannot understand any abstract singular term which purports to denote a property of a particular, unless we understand a concrete general term from which the former is derived by nominalization. Not only does this not follow; it isn't even true. No wore! of present-day English stands in the same morphological relation to ' animosity' in which ' curious ' stands to ' curiosity' .

V.

Nominal and Non-Nominal Quantification

Our elementary predication (E)

Socrates is courageous

implies the existential quantification (EI)

Somebody is courageous There is somebody who is courageous 3x (x is courageous). 1 1 2

moving to (E I ) we quantify into the position of a singUlar term, and that's something we also do in our language when we move from the premiss

In

Properties in Abundance

(QP)

273

Socrates exemplifies courage,

to the existentially quantified conclusion (QP])

Socrates exemplifies something There is something that Socrates exemplifies :lx (Socrates exemplifies x) .

As far as logical grammar is concerned, each of these existential quantifications would receive Quine 's (and anybody else's) blessing. Conclusions (E ]) and (QP ] ) both comply with a principle which Quine upheld of early and o f late : Variables are pronouns, and make sense only in positions which are available "to names. l l 3 [S]ingular terms are accessible to positions appropriate to quantifiable variables, while general terms are not. 1 1 4 To put the predicate letter 'F' in a quantifier . . . is to treat predicate positions suddenly as name positions , and hence to treat predicates as names . . . Variables "eligible for quantification therefore do not belong in predicate positions . 1 l 5

By Quinean lights, (non-substitutional) quantification is always nominal, or first­ order, quantification. When he says , 'variables are pronouns ' , he means that they are pro-names, that is, place-holders for singular terms. It is universally agreed that variables are pro-forms, but that they can only be pro-names is very implausible. In the sentence 'Not only Socrates is courageous, Nicias is so as well' the pro-form 'so' is an anaphoric place-holder for ' courageous ' , and 'There is something Socrates and Nicias both are ' seems to be as sigrrificant as 'There is something Socrates and Nicias both exemplify' . Therefore many have objected to Quine that the argument Socrates is courageous, so Socrates is something " There is something Socrates is :l (Socrates is <1» is just as valid as that from (E) to (E]) . 1 l 6 Here we quantify into the position of ' courageous ' , but in making this move we do not ' suddenly treat that position as name position' (as Quine suspects) . This becomes clear as soon as we expand our conclusion by a ' namely' rider: 'Socrates is something, namely courageous ' . The (second) 'is ' in (E2) is the copula from (E) ; a copula isn ' t a sentence-forming . operator on singular terms, so the 'namely' rider for �) cannot present a name. As regards information value, there is a vast difference between (E] ) , ':lx(x is , courageous) ' , and (E2 ) , ':l (Socrates is <1>) : 1 17 it is not a matter of course that anybody is courageous, but it goes without saying that good old Socrates is something or other. If we do not want to force open doors in using quantifications in the style of (E2) , we have to take a deeper breath and say, for example, (E2+)

Socrates is something praiseworthy :l (Socrates is & it is praiseworthy to be <1» .

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But as regards information value, (QP1) does not seem to be better off than (E2) : that Socrates has some property or other is hardly electrifying. l l 8 So the fact that (E2) does not convey any news does not give any reason for declaring it to be linguistically meaningless, and for all I know it has never been offered as a reason for such a verdict. Since the copula of the premiss (E) survives in the conclusion (E2 ) , the position quantified into is not that of a predicate, but that of a general term. But the term 'courageous ' isn't a name either, so the obj ection stands : the variable in our quantification is not a pro-name . 1 19 The move from (E) to (Ez) also shows that the predicate 'is courageous' is by no means a semantically seamless whole that contains the general term, as Quine put it, 'merely as a constituent syllable comparable to the "rat" in " S ocrates'" . 1 20 Surely we cannot quantify (non-substitutionally) into the position of a syllable. Looking back at the quotations from Quine on p. 273 , we see that the verdicts in the second and third passages do not coincide. The '
Socrates walks

we can not only conclude that there is at least one walker but also that (EZ )

S ocrates does something. There is something Socrates does . 3

Strawson is completely right when he says: ' Socrates does something' (or ' S oCrates is something') is just as good, and just as dli'eet, a generalization from ' Socrates swims ' (or ' Socrates is brave' ) as ' Someone swims' (or ' Someone is brave' ) is. The phrase ' does something' ( 'is something' ) replaces specificity with non-specificity just as the phrase 'someone' does 122

When moving to (E2) we quantify into the position of the verb-stem, but this is not to 'treat this position suddenly as name position' , as can be seen from the expansion of our c onclusion, 'He does something, namely walk' . 1 23 Now just as in the case of (Ez) it needs to be emphasized that the position quantified into when moving to (Ez) is not that of a predicate. In natural languages like English or German there simply is no such thing as quantification into predicate position. This difference between our language and the Conceptual Notation of the venerable Quantifex Maximus tends to be overlooked by both friends and foes of non-nominal quantification. 1 24 But the point to be made against the Quinean obsession with name variables remains entirely unaffected by this observation, for neither in (Ez) nor in (E2 ) do we quantify into the position of a singular term. We c an now characterize the special semantical status of the copula as follows : the only word position in (E) which one cannot quantify into is that of the copula. 1 Z5

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275

The copula in any of its guises does not denote anything, nor does it connote anythin g . C o n s equently, it d o e s not denote , and it d o e s n o t connote, exemplification. 1 26 Notice that the copula in (QP)is not the word ' exemplifies ' , for that is a two-place predicate . The copula in (QP) is the verb-ending, and the stem of that verb is the generaI'term that conIlotes exemplification. Quine has always maintained that the existential quantifier is the formal counterpart to everyday locutions like ' there is an obj ect (entity) such that' . 1 27 This reading is of a piece with his conception of variables as pro-names, and it distorts his view of non-nominal quantifications. If the 'is' in (E2) is the copula of (E) , then (E2) is not tantamount to 'There is an obj ect such that Socrates is it' , and (e2) can certainly not be understood in the sense of 'There is an obj ect such that Socrates does it' , for the latter doesn't make any sense at all. Unlike 'there is an obj ect' the quantificational expression ' (there is) something ' is trans-catego rial: we can use it for quantifying into singular- and general-term positions . Let m e pause here and say a few words i n defence o f ' something ' . I feel that an apology is called for, because two philosophers , both equally free from Quinean prejudices against non-nominal quantification, have found fault with this word when it is used in the move from (E) to (E2) and also , presumably, when it is used in the transition from (e) to (e2) ' S ellars fears that 'the "thing" in "something" suggests reference to an obj ect' - a fear to which 'quelque chose ' and 'qualque cosa ' could also give rise - and he suggests that we would do better to use ' somehow ' when quantifying into general-term position. I 2 8 Recently Timothy Williamson gave voice to the same kind of uneasiness : Quantification into anything but name position is always liable to be misunderstood in a natural language such as English, which cannot express it unequivocally. We can move from 'She is charitable and her mother was not charitable' to ' She is something her mother was not ' , but even with the latter sentence we say some thing ' [ 2 9 '

.

What the English (French, Italian, . . . ) indefinite pronoun may ' suggest' because of its composition is not suggested by its German and Polish countetparts, 'etwas' arid 'ces ' , but I don't think that Poles and Germans are thereby privileged in understanding second-order quantifications in their native languages . And then, would the situation for speakers of English really improve if Sellars ' s well-intentioned proposal were implemented? First, the general-term position into which we quantify may be occupied by a noun-phrase, and I wonder whether ' S ocrates is somehow, namely a philosopher' is acceptable to native speakers . Second, ' somehow ' is standardly used for quantification into the position of certain adverbials ( ' Socrates refuted Laches' contention somehow ' ) , so now a philosopher like Sellars might fear that the 'how' in 'somehow ' suggests reference to a manner. In any case, I cannot see that the move from (E) to (E2) or the analogous transition in Williamson's example, ' is 'liable to be misunderstood' . No speaker of English will have the slightest inclination to hear ' She is something her mother was not' as tantamount to the scarcely comprehensible sentence ' There is an obj ect such that she is it but her mother was not it' . Admittedly, without any clue from the context we cannot say whether 'There is something Socrates is ' should be translated into Loglish as '3<\> (S ocrates is <\>) ' or rather as '3x (Socrates = x) ' . B ut this ambiguity also arises with

Universals, Concepts and Qualities

276

the German ' etwas' , so one should not blame the 'thing' in ' something' . The ambiguity is due to the word 'is' (or ' ist' ) . Does it function as copula or as a two­ place predicate ? In the second case it has the same meaning as the more verbose predicate 'is identical with' in which the fIrst word is again the copula. I 30 All in all, the indefinite pronoun ' s omething ' does no harm to our understanding of quantifications into general-term position. Its transcategorial role does not c ause any confusion in our linguistic practice. It is noteworthy that even the noun 'thing' can cross the border between grammatical categories . Consider the sentence ' In many respects , Alcibiades wants to be like S ocrates, but there is one thing Socrates is which Alcibiades does not want to be at all (namely a philosopher) ' . Here 'thing' subserves non-nominal quantification. If we replace ' thing' by ' object' the result makes no sense. So not even 'thing' by itself always ' suggests reference to an obj ect' . What is the relation between the quantification (E2)

Socrates is something 3<\1 (Socrates is <\1)

that is sneered at by Quine (for no good reason) and its quasi-Platonic counterpart (QP 1 )

Socrates exemplifIes something 3x (Socrates exemplifies x)

that is kosher also by Quinean lights? In Basic English ' exemplifIes courage' is an idiom like the predicate in the slangy death notice, and from ' B en kicked the bucket' you wouldn ' t want to infer 'Ben kicked something' . So in B asic English (QP 1 ) is just gibberish. But of course, in English it is not. In our language abstract general terms are available, and (QP 1 ) can become part of sentences in which the bound variable steps out of the shadow of ' exemplifIes ' , as in 'There is something which S ocrates exemplifies and whi(:h is. a virtur;.' , or in Loglish, '3x (Socr(lte s exemplifies x & x is a virtue) ' . Since one can understand (E2) without being able to cope with higher-level predications, (QP 1 ) is conceptually more demanding than (E2) , but it is a conceptual truth (and hence a priori knowable) that S ocrates cannot be something or other without having some property or other, and vice versa. But it is high time now to face the question: What is the proper semantical account of quantifications into the position of general terms? In his 'Running Repair to Frege's Doctrine' (which was my main source of inspiration in section I above) D avid Wiggins writes: [S]econd-level quantification is over what i t seems t o be over, viz. entities like man, [L]et us call them concepts . . . [S]econd-level quantification is not quantification over things that are incomplete. 1 3 l

horse, wise, sit

. . .

Wiggins ' s catalogue of entities is hard to understand. What kind of entities are sit or wise? Italicization may perhaps serve here as a shield against ungrammaticality, but it does not really further comprehension. 13 2 Wiggins does not mean by ' concepts ' Fregean concepts : so much is clear from the last sentence I quoted. !33 It is equally

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277

clear from his paper that he does not mean to use 'concept' in the way I recommended in Section III above. He wants his 'concepts ' to be distinguished from 'properties ' , but not, he says, from 'forms or characters or traits or universals ' . 134 But aren ' t characters and traits properties , and aren 't properties a sub-kind of universals ? However, I agree with Wiggins that i n quantifications into general-term position we do indeed quantify over certain entities . S entences like (E2)

3$ (S ocrates is $)

are, I take it, second-order quantifi cations over properties. 1 35 The bound variable ' $ ' is associated with a range of obj ects, that is, properties, which are its values. So it is (not substitutional but) objectual, or ontic, quantification. B ut it is quantification into general-term position. 136 Hence it is not nominal, or firltt -order, quantification like (E l ) or like (QP l )

3x (Socrates exemplifies x).

Permissible substituends for '$' do not denote the values of this variable. That is done by singular terms such as 'courage' which can replace the variable 'x' in (QP l ) . Permissible substituends for ' $ ' connote the values of this variable. So this variable res.embles those in first-order quantifications in having values, but having a value is not the same for both. (�) expresses a truth if and only if there is at least one object within the range of its variable, that is, a property, which meets the following condition: the obj ect denoted by ' S ocrates' is such that it exemplifies that property. l 37 The truth-conditions of (EO, thus understood, and those of (QP l ) coincide, which is not to say that ·these sentences have the same meaning. (The sentences 'The bottle is half full' and 'The bottle is half empty ' are not synonymous , and yet they have the same truth-condition. The same holds for ' Snow is white ' and ' S now is white, or snow is white ' .) Proceeding along these lines we conceive of quantiflcations into the position of geueriU terms. as (non-nominal) qllantifications. · over the very same entities which we s aw reason to assign to general terms quite independently of quantification into their position. So this gives us a pleasingly unified picture. The assumption that the same objects can be values of first-order and of second­ order variables may seem strange. But why? As we saw, there are two modes of introducing properties singly into discourse: one can ascribe a property to an obj ect, using a copula and a general term that connotes that property; and one can identifyingly refer to it, using an abstract singular term that denotes it. So it should not come as a big surprise that we c an also quantify over properties in two different styles. And here, too , we can use both modes almost within one breath, as in the next sentence : Socrates has several qualities Alcibiades would also like t o have (p rudence, for example), but there is one thing S ocrates is which Alcibiades does not want to be (namely a philosopher) , without thereby becoming incomprehensible.

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Universals, Concepts and Qualities

Admittedly, if you assert that there is something Socrates is, you do not presuppose the existence of any obj ect which you were not yet committed to when claiming that S ocrates is courageous , 138 If a theorist in his attempt to give a semantic account of a language L explicitly invokes the assumption that there are properties, he does not thereby ascribe this commitment to the speakers of L He may reasonably refrain from doing the latter. A semanticist may take certain binary connectives in L to be associated with truth-functions, maps from pairs of truth-values to truth­ values , but steadfastly refuse to ascribe to the speakers of L an ontology of functions and truth-values. !39 One can scarcely be committed to accepting the statement that there are Fs if one has not even partially mastered the concept F. Speakers of L do not incur a commitment to properties before they employ abstract general terms in higher-level predications and endorse claims to the effect that Socrates has some virtue, for example, or that he has many of the qualities of a great teacher. At this point the commitments of L-speakers begin to line up with those 'of the semanticist who assigns properties to the general terms in L (as their connotata) and to variables in the position of those terms (as their values). If L-speakers have reached that stage, they understand both (E2) , ' Socrates is something' , and (QP 1 ) , 'Socrates exemplifies something' , and they move as smoothly from one formulation to the other as they move back and forth between (E) , ' S ocrates is courageous ' , and (QP), 'Socrates has courage' . A negative answer to the question, D o we incur a commitment to any obj ect other than Socrates when we assertively utter (E) ?, does not imply that we commit ourselves only to the existence of Socrates when we make that assertion. Participants in the debates about ontological commitments tend to take a Quinean presupposition for granted even if they reject Quine's views on quantification into general-term position. S uppose somebody as sertively utters the following second-order quantification: (L2)

There is something which nobody is (namely omniscient) .

Does she betoken an ontological commitment? The answer is 'No' if ontological commitments are always commitments to objects. Now Frege and Heidegger, to mention a rather unlikely couple, emphatically deny the Quinean antecedent. Functions in general and concepts in particular are not obj ects , the former says (and soon comes to regret this particular way of putting it), and the latter accuses traditional metaphysics of confusing being (Sein) with entities (Seiendes). 140 Maybe Quine was far more right than he thought when he said, 'Though no champion of traditional metaphysics, I suspect that the sense in which I use this crusty old word (sc. ' ontology ' ) has been nuclear to its usage all along.' 141 Of course, if one incurs an ontological commitment by stating that (L2) , then this commitment must already be present when one makes the more specific statement that (L)

Nobody is omniscient.

'And so it is,' critics of the Quinean presupposition will reply. ' In making the statement that (L) one commits oneself to there being something nobody is. Similarly, in asserting that Socrates is courageous one commits oneself to there being somebody

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Properties in Abundance

who is courageous and to there being something S ocrates is .' I cannot see any fault in this reply. Whether it is objectual or not, whether it is 'light' or not, ontological commitment is primarily somethin � that asserters and believers incur. 1 42 By contrast, validity is a property of arguments . An argument is valid if and only if it is conceptually impossible for (all) the prerniss(es) to be true without the conclusion being also true. Not every valid argument is also logically, or formally, valid. The argument (E) (E2 )

Socrates is courageous, so 3<1> ( Socrates is <1»

is formally valid (in second-order logic), and the argument (QP) (QP 1 )

Socrates exemplifies courage, so 3x (Socrates exemplifies x)

is formally valid (in first-order logic). Now under my construal the conclusion of the former argument has the same truth-condition as that of the latter. The argument from (E) to (QP 1 ) is not forn'l'ally valid (neither in first-order nor in second-order logic), but it is valid all the same. Its validity is already ensured by the conceptual impossibility of there being an obj ect without any property. (If there were such an obj ect it would have the property of being propertiless, which is absurd. 1 43) So let's modify the example: (E+) (E 2+)

Socrates is courageous , and it is praiseworthy to be courageous, so 3<1> (Socrates is <1> & it is praiseworthy to be <1» .

Under my construal (E2 +) has the same truth-condition as (QP.1 +) - 3x ( Spcrates exemplifies

x

& it is praiseworthy to exemplify x) .

.

In some possible world that is even worse than the actual world nobody, not even Socrates, has a property it is praiseworthy to have, so (QP 1 +) , unlike its shorter predecessor, does not express a truth with respect to every possible world in which Socrates exists . But there is no possible world with respect to which (E+) expresses a truth without (QP 1 +) doing so as welL For it is conceptually impossible that (E+) although Socrates has no property it is praiseworthy to have. So my semantical proposal does not endanger the validity of the argument from (E+) to (�+) . But it is not yet plain sailing, as we shall see towards the end of the next section.

VI.

Limits of Abundance

A general term that does not apply to any object in the actual world ( ' a witch ' ) , or not even to any object in any possible world ( ' a knife without a blade' ) , may nevertheless connote a property, and its nominalization may denote it. According to this generaLIs conception of properties, a property may be unexemplified or even

280

Universals, Concepts and Qualities

unexemplifiable. (If we stick to the Modal Condition of Section ill above, the property of being a knife without a blade is the same as the property of being a female drake : there is only one unexemplifiable property [that is determined, in the sense of S ection ill , by countless concepts] . ) Not all friends of properties subscribe to the generous view, It is, or should be, uncontroversial that a property is something that can be ascribed, truly or falsely, to an obj ect: what could be more obvious than that an attribute can be attributed? But HusserI and Strawson, among others ; deny that there is any unexemplifiable property, though they concede that there are unexemplified properties, 144 and some philosophers find even that too liberal: 'If ' everyone were well,' Aristotle said, 'health would exist but not sickness . ' 145 Nowadays D avid Armstrong is the best-known advocate of a parsimonious conception of properties . He embraces the Scientia Mensura principle: the natural sciences are ' the measure of all things, of those that are, that they are, and of those that are not, that they are not' . According to Armstrong, there is no such thing as the property of being F unless 'F' (or some synonym thereof) belongs to the b asic vocabulary of science when it is at its best. 1 46 B ad prospects for my paradigm of a property: the term ' courageous ' is not likely to become accredited by science as an indispensable part of its vocabulary. Armstrong is ready to acknowledge that the title 'property' is normally understood less restrictively: [W]hat ordinary discourse refers to as properties and relations are often not properties and relations in the sense in which the terms are used in this book . , . The properties and relations of ordinary discourse , " are mere creatures of ordinary discourse , . . [T]hey are mere shadows cast on the world by our predicates 1 47

Does the generous conception of properties, does ' ordinary discourse ' really imply that there is no property for which we have no predicate? Does it even imply the stronger thesis that properties owe their existence to ' our predicates ' ? 1 48 I c annot see that either implication obtains. If the first person plural in ' our predicates ' is to embrace all and only contemporary speakers, one ri1ay very well wonder why an advocate of the generous conception should believe that the languages currently spoken contain the resources for ascribing a property which physicists may discover 2000 years hence. In a possible language, perhaps an expansion of English, such a predicate is available, but that simply follows from the fact that properties are ascribables. Are properties , generously conceived, ' creatures of ordinary discourse' ? Whatever has been created exists contingently. B ut does a property like courage exist contingently? (Whether it is exemplified is a contingent matter, of course, but according to the generous conception the existence of a property is not dependent on its being exemplified.) Invoking the intensional equivalence of 'a is courageous ' and 'a exemplifies courage' , Schiffer argues convincingly that the answer is 'No' : 149 necessarily either there are beings who are courageous or there aren' t. So necessarily either there are beings who exemplify courage or there aren' t. Hence necessarily courage is exemplified or it isn't. So necessarily there is such a thing as courage. Hence it is not a product of ' ordinary discourse' (or of anything else) . 15 o So Armstrong's picture of the generous conception is somewhat distorted. B ut a philosopher who finds properties in abundance indispensable for semantics , say, or

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for the debate o f the question whether truth i s a property, 15 1 should concede that only a small selection of his abundant properties is needed for the explanatory and prognostic purposes of the natural sciences in general and of physics in particular. In doing this he would .follow Lewis 's prudent advice: I would not recommend that we enter into debate over whether the properties really are abundant or whether they really are sparse. We needn ' t choose up sides . . . If w'e have the abundant properties . . . then we have one of them for each of the sparse properties. So we may as well s ay that the sparse properties are just s ome - a very small minority - of the abundant properties. We need no other entities, just an inegalitarian distinction among the ones we've already gOt. 1 5 2

Generosity may be praiseworthy even in metaphysics, but prodigality is not. 153 First of all, it should be clear that not every abstract singular term that purports to denote a property really does so. Here is a sombre example which should suffice to drive this point home : 'the virtue for which all survivors of the holocaust love Hitler' . Second, not every (significant) general term connotes a property, and consequently not every abstract singular term that is derived by nominalization from a general term denotes a property. Let us first consider the less dramatic reason for this. (It CVas pointed out by Dummett. l54) The sentence ' Vulcan is a planet in the orbit of Mercury ' contains a non-denoting name which gained currency because of an astronomical error, and it contains this name in such a way that the proposition expressed by that sentence is not true. 155 If a believer in Le Verrier's Vulcan hypothesis looks through a telescope and exclaims : (M)

That is a satellite of Vulcan,

then what he says is not true. Arguably, the italicized general term in (M) does not connote a property : there is no such thing ' as the property of being a satellite of Vulcan. l 56 (By c ontrast, according to our generous conception there is such a thing as the property of being a natural satellite of lhe moon, even though the' moon has no natural satellite.) If we overdo generosity as regards properties we even get entangled in a contradiction. This is shown by the property version of Russell's paradox. l 57 It runs as follows. Some properties exemplify themselves . Like every other property, the property of being incorporeal is itself incorporeal, and the property of being self­ identical, like everything else , is self-identical. But normally properties do not exemplify themselves. The property of being a philosopher isn' t a philosopher, and, whatever Plato may have thought, courage is certainly not courageous . Let us call a property p-normal iff it does not exemplify itself. Then we can truly say: (N)

Courage is p-normal.

Now does the general term in (N) connote a property? Is there such a thing as the property of being p-normal? If so, the question arises whether it is itself p-normal. And the logically embarrassing answer is : if it is p-normal then it is not p-normal, and if it is not p-normal then it is p-normal. So if there were such a thing as the

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property of being p-normal it would have contradictory properties . Hence there cannot be such a thing as the property of being p-normaL 158 Consequently, the general term in (N) does not connote, and the term which results from its norninalization does not denote, any property. In uttering (N) we rightly s ay about a certain property that it does not exemplify itself, but we do not thereby ascribe a property to it. The paradoxicality of the paradox is due to the fact that we find the assumption so very natural that one ascribes a property to an obj ect whenever one is right in saying of that obj ect that it is such-and-such. This assumption was not yet challenged by (M) and its ilk, for we cannot correctly s ay of any obj ect that it is a satellite of Vulcan. 159 The paradox is also relevant for the question that we confronted in the last section: how are quantifications into general-term position to be understood? How relevant it is has been shown by several authors . 1 60 Again using 'p-normal ' as abbreviation for 'non-self-exemplifying' , we can say : (R)

There is something courage and cowardice both are (namely p-normal) , but [as Russell taught us] there is no such thing as the property of being p­ normaL

This statement seems to be consistent. If appearances are not deceptive, then the truth-conditions of the first conjunct of (R) cannot be those of a second-order quantification over properties. So my account of quantification into general-term position threatens to collapse. Prima facie at least, three reactions to this problem seem to be possible : (i) (ii) (iii)

Appearances are deceptive. (R) is inconsistent, for the first conjunct can only be understood as a second-order quantification over properties . (R) is consistent, but we must understand the quantification in the first conjunct along other lines than in standard c ases . (R) is consistent;. so quantifications into general-term position should never be understood as quantifications over properties (or over anything else).

Let us put reaction (i) aside here. B oolos, Van Cleve, and Rayo and Yablo use (R) in their pleas for (iii), and other philosophers have als o denied that variables in (non­ substitutional) quantifications into the position of general terms have values . Higher­ order quantification, they claim, isn't a special kind of objectual quantification but rather sui generis. 161 The delicate question is then, of course, what the semantics for such quantifications is to look like. We can specify in the meta-language a sufficient condition for the truth of a sentence like (E2) , ':3<1> (Socrates is <1>) ' , if we quantify over sentences : (Ez) expresses a truth, we can say, if there is a substitution­ instance of the open sentence ' Socrates is <1>' that expresses a truth. But this isn't good enough because we need a biconditionaL Now suppose that our meta-language is English and our object-language is a fragment of English enriched with the ':3<1>'­ quantifier. Then we can u s e the second-order quantifier i n our meta-language when it comes to specifying the truth-conditions of second-order quantifications in Loglish and say, for example: the sentence ':3<1> (Socrates is <1» ' expresses a truth if and only if there is something the entity denoted by ' Socrates ' is. That' s the key idea. 16 2 I do

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not know o f any argument that shows that a n account of non-nominal quantification along these lines cannot work. On the other hand, I don ' t think that (R) shows that the sui generis account, as one might call it, is the only game in town. Reaction (ii) is at least as plausible, I think. If one reads the first conjunct of (R) as a higher-order quantification over properties, the conjunction is inconsistent. B ut there is a different reading under which (R) is consistent and which doe� not boil down to alternative (iii) . Here is a somewhat similar problem-case in the area of first-order quantification:

(Z)

There is an Olympian goddess who is depicted on several paintings in this gallery (namely Venus ) , but as we all know, there are no goddesses, Olympian or not.

This statement is inconsistent if the quantifier is given the same reading in both conjuncts. But the impression of inconsistency disappears if we understand the first conjunct along the following lines: 'There is a true positive answer to the question which Olympian goddess is depicted on several paintings in this gallery (namely the answer that Venus is depicted on several of those paintings) .' Now (R) can be treated, and I think it should be treated, in a similar fashion. Enlightened by the property version of Russell 's paradox, we see that the expression 'There is ' in the first conjunct of (R) cannot be understood as second-order quantification over properties . The first conjunct should rather be understood along the following lines : 'There is a true positive answer to the question what courage and cowardice both are (namely the answer that they are both p-normal) .' Thus we read the recalcitrant conjuncts in (Z) and in (R) as first-order quantifications over propositions . 1 63 The Russellian trouble has taught us that the conclusion of an argument of the form ' a is F, so a has F-ness' may not be true although the premiss is true: in ' Courage is p-normal, so courage has p-normality' we move from a truth to an untruth. (In Section IV we s aw that instances of ' a is F ' l ' a has F-ness ' never have .the same -meaning; and now we see that sometimes they even differ as to. . truth· value.) Consequently, we have to restrict the assumption that there is such a thing as the property of being such-and-such whenever an obj ect is truly said to be such­ and-such. So it should come as no surprise that we also have to restrict the assumption that there is such a thing as the property of being such-and-such whenever it can be truly said of an object that there is something it is (namely such-and-such) . 164 But if the general term 'F' is not paradox-inducing, we can continue to say that the property of being F is ascribed to an object whenever that obj ect is correctly asserted to be F. Similarly, if we have banned general terms that engender paradox, we can continue to read quantifications into the position of general terms as quantifying over those entities that we saw reason to assign to them quite independently of the use of second-order quantification.

Notes *

Precursors of this chapter have been presented to audiences in Dresden, Hamburg, Paris and Venice. It has profited from objections, questions and suggestions by Paul

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Universals, Concepts and Qualities B oghossian, Ingar B rinck, Manuel G arcia-Carp intero, Justin B roacke s , Nick Haverkamp, Paul Horwich, Pierre Jacob, Kevin Mulligan, Fran90is Recanati, Tobias Rosefeldt, Sven Rosenkranz, Philippe de Rouilhan, Peter Simons , Jan Szaif and Mark Textor. I thank you all. My greatest debt is to B enjamin S chnieder: more than anything else his dissertation made me reconsider several claims I upheld in my book on Abstract Objects some twenty years ago . Wittgenstein ( 1 980), p. 234. If we never delete more than one name-occurrence at once, we obtain six monadic predicates from (a-c). They are, as Frege puts it at one place ( 1 903 , p. 372, n. 5 ) , something that can be unterschieden but not abgeschieden. Cf. Ryle ( 1 960) , p . 5 8 . Cf. Dummett ( 1 973 ) , pp. 27-33 (and the modifications in his 1 9 8 1 , pp. 3 1 7-1 8 that were triggered by the criticism in Geach, 1 975). The second example reveals the motivation behind Dumrnett' s terminology ' simple vs. complex predicates ' . In view of the first example I find it misleading. The modern conception of predicates as sentence-forming operators on names is certainly due to Frege: 'If the concept-sign is supplemented by a proper name, the result is a sentence (Das Begriffszeichen, durch einen Eigennamen ergdnzt, ergibt einen Satz) ' (Frege, 1 9 14, p . 25 3 ) . About the ' predicative part' of the sentence ' 2 is a prime number' he s ays : 'We regard the copula "is" as belonging to that part of the , sentence (Die Kopula 'ist' rechnen wir mit zu diesem Satzteile) (Frege, 1 906a, p. 1 92 ; cf. 1 9 1 9 , p . 1 54 ) . B ut very often Frege applies the expressions 'Prddikat' , 'Begriffszeichen' and 'Begriffswort' not to sentence-forming operators on names but to general terms, mainly to nouns (without article or with an indefinite article) which he calls 'nomina appellativa' His own term of art ' concept-word' is rather unsuitable for his theoretical purposes. In Dumrnett ( 1 973), p. 2 1 5 they are called 'predicative expressions ' (as opposed to ' predicates ' ) . Aristotle, De Interpretatione 1 2 : 2 1b9- l 0 ; cf. Metaphysics Y, 7: 1 0 1 7 a27-30 ; Anal. Pr. 1, 46: 5 1b l 3- 1 5 . Antoine Arnauld and Pierre Nicole ( 1 685), III2. Richard Whately, 'Elements of Logic ' ( 1 826), quoted by Prior ( 1 976), p. 50, who calls the book ' our Engli"h Swnmulae' "p. 1 6) : Bolzano ( 1 837), n, 1 0 . Actually, Whately' s copula + adj ective example does seem to capture the meaning of the verb (in its intransitive use), and for predicates like ' smokes' which also have a dispositional reading, the combination copula + (indefinite article + nomen agentis) delivers a synonym - for this very reading: 'is a smoker' . D avid Wiggins ( 1 9 84), p. 3 1 8 and Peter Strawson ( 1 9 87), p. 8 5 ; ( 1 990), p. 3 1 8 ; ( 1 994), p . 2 4 do s ay it, and I shall follow suit. Frege ( 1 892), p . 1 94. Frege ( 1 89 1 ) , p . 1 0 1 . Cf. Frege ( 1 9 1 9 ) , p . 1 54. Aristotle, Physics I , 2 : 1 85b27-9 . Cf. Plato, Sophist 262 B-D . Quine ( 1 9 8?), p . 3 7 . Frege uses the noun 'Aussage ' and the verb 'aussagen ' primarily in contexts such as ' Sentence S contains an Aussage about X' and 'In S something is ausgesagt about X ' . This i s remarkably close t o Russell's use o f ' assertion' i n the Principles: 'We may s ay, broadly, that every proposition may be divided, s ome in only one way, some in several ways, into a term (the subject) and something which is s aid about the subj ect, which is something I shall call the assertion. Thus "Socrates is a man" may be divided into Socrates and is a man . . [I]t might be s aid: "Socrates was a philosopher, .

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and the same is true of Plato ." Such statements require the analysis of a proposition into an assertion and a subj ect' (Russell, 1 90 3 , §43). (In §48 Rus sell offers 'A is greater than B ' as an example of a ' proposition' that is multiply decomposable. ) I n a letter Frege wrote that the copula 'has n o sense o f its own and only serves to mark the predicate 'as such (keinen eigenen Sinn hat und nur das Priidikat als solches kenntlich macht) ' (Frege, 1 9 1 9, p. 1 5 6 ) . The second part of this remark confirms my interpretation, and it is plausible in itself. The claim that only the general term in the predicate 'is courageous ' bas a ' sense of its own' would be false if it were meant to deny that the copula makes its own distinct contribution to what one grasps when one understands the expression 'is courageous ' as a predicate : the copula does certainly not lack conventional linguistic meaning. But then, there are ever so many conclusive reasons for not identifying Fregean Sinn with conventional linguistic meaning. Wiggins ( 1 9 84), pp. 3 1 8- 1 9 (and Strawson, 1 9 87 , pp. 85-6 ) . (Wiggins embellishes his formulations of T and F( I-3) with bracketed additions which I have not adopted: '''[ . . . J'' is true of x (or, in the Fregean terminology, x falls under the concept that "[ .]" stands for) ' . I don' t think that the bracketed phrase simply renders in a different terminology what precedes it. I don't accept Wiggins ' s assumption that both general terms [for which he uses various other titles] and names ' stand for' something (see Section II below), and I find his reading of ' c oncept' , which is actually not Frege' s , rather difficult to fathom (S ection V) . Not ' a walk' , o f course, for that i s a general term which applies t o walks , not to walkers . Of course, I do n o t venture to s ay that i t solves the problem, whatever i t was, that worried Russell and Wittgenstein in 1 9 1 2 . For a well-taken criticism of the orthodoxy as regards the modalities s e e George B ealer ( 1 99 8 ) , pp. 1 3 3-4. Cf. Aristotle, De Interpretatione 3 : 1 6b6 and 1 0 : 1 9b 1 3- 1 4 on the tensed copula. This is the central move in Colin McGinn (2000), pp. 75-82 . (Although McGinn celebrates the copula in his treatment of the modalities, he neglects it in his general theory of predication. Or so I shall complain in a note to S ection II.) Cf. Frege ( 1 892), pp . 1 9 9-200; ( 1 906b), pp. 203 , 209 ; and Andreas Kemmerling ( 1 990). If my account of general terms that ar e contained in monadic predicates and. properties is correct, then the same account holds mutatis mutandis for general terms that are contained in polyadic predicates and relations. In order t o save ink I stipulate that conjunctive general terms like ' wise and courageous' (as used in c) are employed to ascribe one property. If you state that S ocrates is wise and courageous, you should be prepared to ascribe wisdom to him, but according to my stipulation you do not do it in making that statement. Cf. Frege ( 1 8 92), p. 20 1 . Frege ( 1 892) , pp. 1 96-7 ; ( l 906a), p . 1 92 ; ( 1 906b), p . 2 1 0 . I n Kiinne (2003) , p . 4 ( e t passim) the verb ' signify ' plays more o r less the s ame role as ' connote' in this chapter. For reasons that will surface in S ection V, I now prefer to s ay of general terms (rather than predicates) that they connote properties . My earlier use of ' signify' coincides largely with Crispin Wright' s use of ' as cribe' in his ( 1 99 8 ) , p p . 25 8ff. (The latter term is potentially misleading, since we s tandardly use i t for a speaker's activity rather than for a semantical relation, and at one p oint (p. 258) Wright uses it almost in one and the same breath for both. In S ection III it will become clear why I think that Wright' s talk of ' concepts or properties ' blurs an important distinction.) I agree with Wright on an essential point: an expression that is used to ascribe a property does not stand in the s ame relation to that property in which a name stands to its bearer. Frege's semantical theory does not provide for . .

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Universals, Concepts and Qualities what I distinguish as connotation from denotation, and I think that my framework spares us (in a similar way as Wright' s) the notorious crux about the concept horse that isn't a concept (Frege, 1 8 92, pp. 1 9 6-7) . I also agree with the criticisms of earlier attempts at solving the puzzle in Wright ( 1 99 8 ) , pp . 249-5 1 , 253 . This is the point where m y u s e o f ' denote' and ' c onnote' converges with that in Mill ( 1 843 ) , Bk. I, Ch. II, § §4-S. At least prima facie McGinn flatly contradicts what I have s aid about ' courageou s ' and ' courage' when he contends : ' [PJredicates are as much singular terms as their nominalizations are . . . [TJhe entities they purport uniquely to denote are properties ' (McGinn, 2000, p. 65). It is less than clear what he means by 'predicate ' , for he assumes that the capital letter in the schema 'Fa' is a place-holder for 'predicates' (p. 53), but his examples are always expressions that are components of substitutes for 'F' : 'bald' , ' man' . . . (pp. 57ff. ) . At any rate, it remains a mystery how one could explain on McGinn' s ' singular term view of predicate s ' (p . 65) that ' S ocrates courage' is just a list and that ' S o crates is c ourage' with copulative 'is' is ungrammatical. Certainly (E) is a context in which co-denotative terms are exchangeable salva veri tate . Hence (E) cannot degenerate as a result of such an exchange into a list of objects or into ungrammatical garbage. So either McGinn commits a glaring mistake, or his use of ' denote ' is idiosyncratic. Aristotle, De Interpretatione 7 : 1 7 a39-40 . I f this is meant t o be a definition o n e may wonder whether being an even prime number is to be classified as a universal. As it stands , the definition does not forbid an affIrmative answer, for Aristotle does not s ay ' c ap able of being truly predicated of several things ' . So far, even being a round square can lay claim to the title (but see below, S ection VI) . Quine ( 1 974), pp. 2 1 7- 1 8 ; cf. Kiinne ( 1 9 8 3 ) , pp. 3 5-40. What is an abstract obj ect (in the modem [QuineanJ acceptation of this term) ? Whatever the answer to this delicate question may be, it must not exclude properties and sets from the realm of abstract objects. Cf. Diogenes Laertius , Vitae Philosophorum, VI, § 5 3 , and esp. Plato ' s description of 'pansomatism' in the Sophist (246 AB). For a reconstruction of the debate between foes and friends of abstract objects in that dialogue see Kiinne (2004) . Locke, An Essay Concerning Human Understanding, III.iii . l . I borrow the term 'particularism' from Nelson Goodman ( 1 9 5 1 ) , pp. 1 04-6 . 'We do.,not hdieve in ahs.tract·'entities . No orre Sllp poses that abs�ract entities ' � classes, relations, properties , etc . - exist in space-time; b u t we mean more than this. We renounce them altogether.' With this blare of trumpets Goodman and Quine begin their j oint paper ' S teps Toward a Constructive Nominalism' ( 1 947, p. 1 7 3 ) . As for classes, Quine soon came to confess that he was unable to stick to their global 'Renunciation of Abstract Entities ' . As to the term ' nominalism ' , the authors actually put different readings on it. For Goodman nominalism is the claim that different entities are never composed out of the same elements , which removes the term almost entirely from its original habitat. For Quine nominalism is what Goodman calls particularism (Quine, 1 986, p. 1 62), and the Quinean usage of ' nominalism' came to prevail. Goodman 's 'principle of nominalism' is not meant to ban non-particulars. I think there are particulars as well as non-particulars that falsify that principle. A house of cards is made up of the same elements as a certain collection of cards , but the latter easily survives the former, so they are two . The meaning of 'a beautiful daughter of an ugly mother' is not the s ame as the meaning of ' an ugly daughter of a beautiful mother' , yet both meanings are composed out of the same elements (B olzano, 1 837, I, pp. 244, 434, 446) , and I have just mentioned two English noun-phrases even though they consist of the same seven typed words . The contemporary use o f 'Platonism' does not have a long history either. I t is a generalization of Paul B emays ' use of this label as a nickname for an anti-formalist

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and anti-constructivist conception of the ontological status of mathematical obj ects (B ernays, 1 935). Thus Ryle ( 1 932), p . 48, and Quine ( 1 960), p . i 22, though with a c aveat: ' such a program [to sweep abstract objects aside] cannot without diffic ulty be carried far' . On the topic of this 'paragraph see Arthur Pap ( 1 959); Frank Jackson ( 1 977); D avid Armstrong ( 1 97 8 ) , I, pp. 5 8-63 ; KUnne ( 1 9 8 3 ) , pp. 1 2 8-32 ; D avid Lewis ( 1 9 8 3 ) , pp. 1 94-6. The standard reference here i s William Alston ( 1 95 8 ) . His point was anticipated in Straws on ( 1 952), p. 228 and taken up in Wright ( 1 9 8 3 ) , pp. 3 1 ft. ; KUnne ( 1 9 8 3 ) , pp. 45-6. The author of the Tractatus comes at least close to being a proponent of the No­ S tatement View concerning equations . ' 3 x 2 6 ' , for example, is taken as codifying a rule which licenses the step from ' B en wrote three papers , but Ann wrote twice as many' to 'Ann wrote six papers ' where premiss and conclusion can be used to make genuine statements. For discussion see B ob Hale ( 1 987), pp. 1 1 5-22 (where the view is ascribed to S imon Blackburn). It is a late-comer on the philos ophical scene. For all I know, in the late 1 990s S tephen Yablo was the first analytical philosopher who applied it across the board to all abstract entities. I eschew the label 'fictionalism' , for in the literature that tends to be applied to (2.a) as well as to (2.b). (Field annonnces his view as fictionalism.) Cf. Yablo (2000a) , pp. 305-6. The phrase is Yablo ' s : (2000a) , p. 299 and (2000b), p . 2 1 9 . He concedes that statements seemingly about non-particulars 'strike us as hardly figurative at all' (a: 2 1 4/b : 293) and works hard to explain Why. In such cases, the metaphor is used ' inopiae causa' (Cicero, De oratore, III , 3 8 , 1 55), or 'quia necesse est' (Quintilianus, Institutio oratoria, VIII, 6 , 9 ) . Cf. Yablo (2000a), pp . 290-304 == (2000b), p p . 2 1 1-26. See Joseph Melia ( 1 995) (who does not advocate the Figure-of-Speech View) and Yablo (2000a) , pp. 295-6 or (2000b), pp. 2 1 6- 1 7 . Yablo makes the somewhat surprising . claim that whether or n o t we are speaking figuratively is 'very often unconscious, and resistant to being brought to consciousness' (2000a, p . 298 or 2000b, p . 2 1 8) , This sounds a bit as if we needed help from psychoanalysts , For a · sitnilar· objection against Yablo's (rriulti·faceted } J3osition see Jason Stanley (200 1 ) , pp . 46-7 . Quine ( 1 948), p . 1 0 . Quine ( 1 968), pp . 99-100. Quine ( 1 960), pp. 2 1 4 , cf. pp. 1 5 9-60, 1 82 , 257-62. A s regards mathematics, I admit that Hartry Field, the most prominent advocate of an Error Theory, comes at least close to giving a plausible answer to the question how mathematical theories can be so extremely useful in physics if they are invariably false (see Field, 1 9 80). For discussion cf. Hale ( 1 987), pp. 1 03- 1 5 . This restrictive interpretation o f (first-order) quantifiers is routine. We don' t hear ' Nobody is tired (so let's continue) ' as a report on the state of all persons in the world at the time of utterance. As we shall see in Section V below, the s ame holds mutatis mutandis for second-order quantifiers. Here is Wright'S epitaph on this kind o f reductionism: "'Ontological reduction" b y analysis is . . . a radically misconceived endeavour' (Wright, 1 9 8 3 , p . 69) . Note the restriction 'by analysis ' : the contention is not meant to cover all varieties of reductionism. A few years ago, Yablo would have agreed, and perhaps he would still do s o today. In an appendix to the original version of his 2000b (which has no counterpart therein) he s ays about mathematical sentences which are in the same boat with (P*) and its ilk =

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Universals, Concepts and Qualities that he wants 'to make an extremely tentative and undeveloped proposal about how to understand these contexts within the spirit of the make-believe approach' , and he adds in a footnote: 'I suspect that story will be easier to tell with . . . numbers than . . . [with] properties ' (Yablo, 2000a, p . 309). As far as I know, he has not yet tried to tell the story with properties. (Why 'make-believe approach' ? Drawing on work by Kenneth Walton, Yablo endorses a pretence account of metaphor. It is worth mentioning that Walton himself does not pretend to offer a general theory of metaphor.) Our everyday use of 'property' is such, I take it, that it is correct to call courage a property. But some philosophers and linguists withhold this title from courage: they distinguish courage from (the property of) being courageous - along similar lines as the kind Grizzly, ursus horribilis, is usually distinguished from the property of b eing a grizzly. They can replace ( 1 ) by 'B eing courageous is a property it is good to h ave ' . M aking the corresponding adjustments i n (2), ( 3 ) and (5) , they will also arrive at (6) . Yablo contends : 'Nobody supposes that there are easy proofs , from a priori or empirically obvious premisses, of the existence of abstracta' (2000a, p . 275 or 2000b, p . 1 97 ) . Rudolf Camap ( 1 950), Arthur Prior ( 1 954) (mentioned as a 'possible exception ' , whatever that may mean) and Alan Ross Anderson ( 1 96 1 ) are counter­ examples. 'As regards the calm sense of existence, . . . the Platonists win hands down. In fact, the issue is one of the few I know of for which ordinary Aristotelian syllogistic reasoning almost suffices to establish a point of interest' (Anderson, 1 96 1 , p . 1 47) . As to the ' almost' , see the step from (5) to (6) in my little deduction. Cf. Kunne ( 1 9 8 3 ) , pp. 1 3 8-85. If we may assume that Kant would call all conceptual truths analytic, then he was wrong in claiming that 'every reasonable man must admit that every existential statement is synthetic' (Kritik der reinen Vernunft, B 626). Existential sentences such as ' There is a month between June and August' and 'There are more than two sharp keys in the circle of fifths ' also express conceptual truths. Of course, Kant' s verdict follows from his 'official' (and far too narrow) containment account of analyticity and his thesis that ' exist' is not a predicate. Anderson also told u s the parallel story for a radical version o f anti-particularism according to which only properties, places and times (really) exist: 'We ask Plato if there are any 3hips in the harbar, and he answers' yes - but then suddenly he remembers · his philosophy, and goes on to say, "Well, in a way you might s ay that there are ships in the harbor, but really it is not like that; the only thing that exists in the full sense, or has real existence, is ship- hoo d'' ' (Anderson, 1 95 9 , p. 45 1 ) . Compare the distinction in Anderson ( 1 962) between the ' calm ' , ' casual ' , or ' easy going' use of ' exist' and its ' honorific ' , 'profound' , or 'frenetic' use. Employing the same kinds of example (as we just s aw) Quine also distinguishes the ' c ommonsense' use of this verb from its ' philos ophical' use. He wants the latter to be ' respected as literal and b asic' (Quine, 1 96 8 , pp. 98-1 00) . Cf. B olzano ( 1 837), I, pp. 109- 1 0 ; Frege ( 1 9 1 8) , p . 59; Alan White ( 1 970) , pp. 3-6; Kunne (2003), pp. 1 04-6. 'F' may also be an adj ective ( ' truly courageous ' ) or, as we just saw, a mass noun ( , true mahogany ' ) . In order to avoid prolixity, I use only the count-noun s chema. C ontrast Dummett ( 1 973), p . 497 ; ( 1 9 8 1 ) , p . 3 8 6 . Carnap ( 1 950), p . 205 . Dudman ( 1 976), p. 7 3 . Similarly Quine ( 1 948), p. 1 0 ; Goodman ( 1 977), p. 49 ; Michael Devitt ( 1 980), pp. 94-9. More on this in Kunne (2003), pp. 1 5 0-57 , 229. The locution is b orrowed from Strawson ( 1 959), pp. 1 46ff. and Pt II, passim. In his

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( 1 974b), chpts 1 and 5 , § 2 , h e u s e s ' specifying ' rather than ' introducing' , b u t the point is the s ame. Cf. als o Straws on ( 1 987), p. 8 8 . Following Swoyer ( 1 999), pp. 1 6- 1 7 , I assume that (P2) bears this interpretation. If you feel uncomfoitable about this, replace (P2) by ' Courage is a virtu e ' . 'Xanthippe is a wi d ow, so Xanthippe was married' and 'Xanthippe is a widow, so it's not the case that Xanthippe isn' t a widow ' are equally valid, since in both cases it is conceptually impossible for the premiss to be true without the conclusion also being true, but only the second argument is logically, or formally , valid. This 'transformation' will be the topic of S ection IV below. Following Quine ' s terminological recommendation: cf. Quine ( 1 987), p . 2 6 . Lewis ( 1 9 8 3 ) , pp. 1 89-90 ; ( 1 986), pp. 1 73-4 ; ( 1 9 87 ) , p . 5 0 n. Cf. Andy Egan (2004), p . 49 n. (with a bow to Vann McGee), and Benj amin Schnieder (2004) , pp. 1 9-20. Egan goes on to show that Lewis's identification comes to grief over accidental (and temporary) properties of properties such as b eing a topic of philosophical discussion. He argues convincingly that they no longer make for problems if we identify properties with functions from <world, time> p airs to extensions . This may very well be the best strategy for those who follow Lewis in aiming at reducing properties to some kind of set-theoretical entities built out of possibilia. (I have no idea why Egan calls such a reduction a ' nominalist strategy ' (p. 4 8 ) ; after all , it remains within the field of abstract entities. ) Cf. Kunne (2003) , p. 4 ( e t passim). It takes s ome effort to recognize that this is metaphorical talk, and as such it is actually not without competition. B olzano used to s ay that objects stand under concepts; nowadays, presumably because of Frege 's influence, we let them fall under concepts . B oth metaphors place concepts in the upper position. Christopher Peacocke ( 1 992, p. 2) and George B ealer ( 1 99 8 , p. 1 4 1 ) also emphasize this differenc e . But many philo sophers do not seem to see here any need for differentiation. Three examples may suffice. 'If one really did accept the existence of properties ,' s ays Michael Jubien, 'there would be little motivation for thinking (for example) that the concept of mass was anything other than the property of having mass' ( 1 997, p. 1 6) . This is not implausible if one describes the anti-particularist position (that is favoured by Jubien) the way he does : ' (Just about) every declarative sentence that has -subjcct-preai:.:ate fonn 'uttributes a property - the one expressed by the predicate - to an entity - the one denoted by the subj ect. In this way properties come to serve as the meanings of words and phrases of our language' ( 1 997, p. 37 [first italics mineD . When we s ay about Socrates that he is courageous, do we ascribe to him the meaning of ' c ourageous ' ? According to Paul Horwich, F-ness and G-ness are identical iff 'F' and 'G' have the same meaning, s o it comes as no surprise when he says: 'I see no good reason not to identify properties with concepts ' (Horwich, 1 99 8 , p. 2 1 ) . B ut why should we accept his biconditional? Chris S woyer writes ' [AJbstract singular terms like "honesty" denote the property that the associated predicate ("honest") denotes or expresses ' ( 1 999, p. 17). I maintain that the general term 'honest' does not denote anything (for that' s the job of singular terms) and that it does not express a property but a concept. Putnam ( 1 970). Lewis ( 1 9 86), p . 1 7 6 . O n e c a n conduct the s ame kind o f pointless debate about the property of being an even prime number greater than 2 and the property of being a round square (or, arguably, about the property of being a unicorn and the property of being a centaur) : according to (MC) there is just one necessarily unexemplified property, yet don ' t we want to s ay that they are different properties? Again, the latter intuition can be accommodated if we distinguish properties and concepts .

290 79 80 81

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Universals, Concepts and Qualities This distinction as well as the ' argument that follows in this paragraph are due to Peacocke ( 1 992), pp. 27-3 3 . Putnam ( 1 975), p. 226. We can s ay that he has a conception of elms , that is, he has a view about elms in general, and the s ame goes for beeche s . (These conceptions are not ' exactly the s ame ' , as Putnam suggests [lac. cit. ] , for it is part of his conception of elms that no elm is a beech.) B ut the fact that he has a conception of elms does not warrant the claim that he has the concept of an elm. The ' of' in the former phrase connotes aboutness which is arguably a relation. The ' of' in the latter phrase no more connotes a relation than does the ' of' in ' the City of Rome ' . (That singular term translates into Latin and German as ' Urbs Roma' and 'die Stadt Rom ' , and these terms which are in toto in the nominative lack even the faintest intimation of relationality.) The last three words in ' the concept of an elm' serve the same purpose as the italicized word in ' the concept elm' : they single out what is expressed by the general term ' an elm ' . Things may stand somewhat similarly with the general term ' a bottle of water' as used in non-scientific discourse . The colourles s and odourless liquid that fills the seas on Earth, falls from the sky above us Earthlings and quenches our thirst is (give or take s ome impurities) H2 0 . B y contrast, so Putnam asks us to imagine, the colourless and odourless liquid that fills the seas on Twin Earth, falls from the sky above Twin­ Earthlings and quenches their thirst has a very different chemical comp osition: it is (give or take some impurities) XYZ. Now the ways non-scientists on Earth recognize something as what they call 'water' are the s ame as the ways their Doppelganger on Twin Earth recognize something as what they call 'water' . S o in non-scientific discourse this word expresses the same concept no matter whether it is used by Earthlings or by their doubles on Twin Earth. B ut when Earthlings use the general term ' a bottle of water' the concept expressed determines the property of being a bottle filled with H20, but when Twin-Earthlings employ this term the concept expressed determines the property ' of being a bottle filled with XYZ. (1 supplant the word 'water' by the phrase 'a bottle of water' because the status of mass nouns vis-a-vis the distinction general/singular terms is less than clear.) S o 'a bottle of water' is implicitly indexical, more or less in the s ame way in which the term, 'a bottle filled with what we know as water' is explicitly indexical. (Compare Putnam, 1 97 5 , pp. 234, 245 . ) (MC).dees not'-imply that all true identity statements·in which ' i s (identic-al with) ' is " flanked by two property designators are necess arily true. Of course, that courage is the virtue which was the topic of a debate between Socrates , Laches and Nicias isn ' t a necessary truth: after all, the three Athenians might never have debated this topic. (MC) is only applicable if on the left-hand side we have two abstract singular terms that are the Ilominalizations of the general terms used on the right-hand side. Incidentally, (MC) does not say that all truths of the form ' F-ness G-ness ' are necess ary, since the necessity operator stands on the right-hand side. I have borrowed the nickname for (QP) from Ryle ( 1 932), pp. 47-9 . B olzano ( 1 837), n, p p . 9-24. A quasi-Platonic counterpart to (E), 'Socrates walks ' , is 'Socrates exemplifies walking' (cf. S trawson, 1 974a, pp. 65, 8 1 ) . The variants of ' exemplifies ' mentioned above require in such cases the insertion of a categorial apposition: 'Socrates has the property of walking ' , and so on. I shall not use 'instantiates ' because that verb is needed for a different purpose. Suppose we conceive of S ocrate s ' courage as something that can only exist as long as he exists and that is different from everybody else's courage just because it is his courage. Thus conceived, S ocrates' courage may reasonably be s aid to instantiate the universal courage. (Of course, it doesn' t exemplify that property, since it isn' t courageous . ) Such a conception of property-instances i s promoted i n Aristotle, =

84 85 86

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Categories, ch. 2, on the traditional reading; Husseri ( 1 9 1 3 ) , pp. 1 09 , 1 5 5 ; and

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Straws on, this volume, Chapter 1 5 . Cf. Kiinne (2003) , pp. 47-8 o n conceptual balance. Bolzano ( 1 837), II, p . 10. In Bolzano 's terminology, the concept that is expressed by ' courageous ' in (By is a concretum, and the concept that is expressed by ' courage ' in (QP) is the abstractum that belongs to that concretum (Bolzano, 1 837, I, pp. 259-60) . Ramsey ( 1 925), pp. 60, 7 1 (sentence-abbn,viations added). ' Strawson ( 1 990) , p. 3 1 8 . Cf. John Cook Wilson ( 1 926), I, pp. 1 1 4ff. ; and the comments in Strawson ( 1 957), p . ' 476, and ( 1 959), p . 144. Russell ( 1 903), §48 (sentence-abbreviations added) . This passage refutes Prior's conjecture that Russell was inclined to s ay that ' a is F' and ' a has F-ness ' are 'just different ways of saying the s ame thing' (Prior, 1 954, p . 30). Cf. Russell ( 1 903), § § 1 4- 1 9 . M y distinction between plain and reflned particularism corresponds t o Michael Loux' s distinction between ' austere' and ' metalinguistic nominalism' (Loux, 1 9 9 8 , p p . 5 879). Thomas Hobbes, Leviathan I, 4. Geyer ( 1 9 1 9-27), pp. 8-3 2 . Sellars ( 1 97 3 ) , p . 1 8 3 . I have replaced S ellars ' s example ( ' Triangularity' ) by mine . S ellars ( 1 962), p . 244; ( 1 963b), p . 2 6 7 . This is not the place for going into the tricky details of Sellars 's machinery of ' dot-quotes ' . But a brief comment on the following passage may be apt: ' [Nominalizing devices such as] ' -ity ' , ' -hood ' , ' -nes s ' , and ' that' (as used to form propositional clauses) are to be regarded as quoting devices which (a) form sortal predicates which apply to expression tokens in any language . . . which are doing in that language . . . that which is done in our language by the design with which they are conj oined; [and] (b) turn these sortal predicates into distributive singular terms' ( 1 969, p. 220) . (Incidentally, nominalizing is not always a kind of ' conjoining' ; in cases like ' courage o us' and 'mutig' it is rather a ' disjoining' .) Sellars ' s canonical rephrasing o f (QP) is, i n fIrst approximation, (Sem*)

1 00 101

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The ·courageous · applies to Socrates .

(In the n�xt s tep the semanticai. concept o f ap plication, o r truth-of, is replaced by that of truth: The ·Socrates is courageous· is true. We can neglect this move here.) In (Sem*) the grammatical subject is a generic description (a ' distributive singular term ' ) like the subj ect in 'The whale is a mammal' . We are asked to understand the sortal general term 'a ·courageous· ' in such a way that it applies to all and only those sign-tokens that play, in whatever language, the same role that is played by tokens of 'courageous ' in our language. (Sem*) is a sentence that is only available in an expansion of English, (Sem) conveys its point in dot-quote-free English. The indexical s elf-reference is to ensure that (Sem) can be translated in toto, that is, including the quoted expression. If the quoted expression were left untranslated when (S em) is translated into German, say, truth would not be preserved (under the self-referential reading of the indexical). (For misgivings on the Sellarsian rendering of (P*) by ' The ·courageous· is a virtue-word' see Kiinne, 1 9 8 3 , pp. 1 32-5 . ) Quine ( 1 960) , pp. 1 1 9-20 (my italics) . Cf. also Schnieder (2004) , pp. 59-60. S o , there i s a n (impure) abstract general term i n (QP) , too : i t i s the complex general term from which the copula builds the predicate ' Socrates exemplifles ' (whose more familiar passive variant, 'is exemplifled by Socrates ' , I used above) . But isn' t the simple general term ' exemplifi-' that is followed in (QP) by ' courage' a pure abstract general term? No, it isn't. The field of the relation ascribed to pairs of

'

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Universals, ConcepTs and Qualities obj ects by means of the copula and that general term is categorially inhomogeneous . The right field only comprises abstract objects; the left field also contains concrete obj ects. So we should refrain from calling the general term ' exemplifi-' either abstract or concrete. The same abstinence is to be recommended for transcendental terms like ' an obj ect' or ' self-identical ' , and for intentional terms such as 'referred to in this chapter' , whose range of application is also categorially heterogeneous (cf. Kunne, 1 9 8 3 , pp. 32-3 , 43) . Quine ( 1 953), p. 1 14. It is one of the great merits of Schnieder's (2004) that he does look at both sides. S chnieder appeals here to a very illuminating analogia proportionalitatis: our understanding of 'a exemplifies F-ness ' in a language without those more complex moves with 'F-ness' is related to our understanding of that sentence in our language in the same way as our understanding of 'a is an element of the class of all Fs' in what Quine calls the theory of virtual classes is related to our understanding of that sentence in genuine set theory. In the language of simulated set theory 'a E ( x : x is F ) ' is just a stylistic variant of ' a is F' (Quine 1 96 3 , pp. 1 5-2 1 ; 1 970, pp. 68-72) ; Schnieder (2004), pp. 6 1-7) . Schiffer ( 1 996), pp. 149, 1 64; cf. Schiffer (2003) , pp. 2-3 , 6 1 ff. I took the liberty of replacing Schiffer's example by mine and of adding, here as well as in the quotations from S trawson and Quine below, the sentence-abbreviations. On this difference cf. B olzano ( 1 837), II, p. 5 1 . Strawson ( 1 974b), p. 33; cf. ( 1 974a) , p . 82. Quine ( 1 980), p. 1 64 (commenting on the extract from Strawson ( 1 974b), p. 3 3 ) . Schiffer (2003), p. 70; cf. ( 1 996), p. 1 5 1 . Cf. John S earle ( 1 969), ch. 5 , § 1 ; Anthony Quinton ( 1 973), p . 252; Kunne ( 1 98 3 ) , pp. 1 83-5 ; James van Cleve ( 1 994), p . 585. (Quinton seems to think that one can accept the dependency claim only if one endorses the reducibility claim (pp. 252, 28 1 ) . ) Strictly speaking, the Loglish formulation is equivalent with the others only if we take the range of the variable ' x ' to be restricted to persons. (Cf. Dummett, 1 97 3 , pp. 36-7 on the difference between restricted and unrestricted quantification.) Quine ( 1 939), p . 1 9 8 . Quine ( 1 950), p. 220. Quine ( 1 970}, pp. 66,-7. E.g. Geach ( 1 9 5 1 ), pp. 1 3 2-3 ; S ellars ( 1 960); Strawson ( 1 96 1 ) , p. 65, ( 1 974a), ( 1 974b), pp. 32-4; Prior ( 1 97 1 ) , pp. 35-7 ; Dummett ( 1 973), pp. 6 1 , 2 14ff. ; George B oolos ( 1 975); Martin Davies ( 1 9 8 1 ) , pp. 1 3 6-42; Kunne ( 1 9 8 3 ) , pp. 1 05-8, 1 1 8- 1 9 . I f we may take Peter Simons a t his word, a whole nation once opposed this aspect of Quine's conception of quantification: 'All Poles rej ected it' (Simons, 1 997, p. 263) . S trawson ( 1 9 6 1 ) , pp. 72-3 ; ( 1 974a), p. 84. In a conversation about the differences between some ancient philosophers we don't understand the remark 'Plato is something Socrates isn't' as conveying a message that is logically equivalent with the proposition that Plato *' S ocrates. When asked ' namely what?' we will hardly reply 'identical with Plato ' , but rather, say, 'rich' or 'a writer' . It seems that we take the domain of quantification to be tacitly restricted, whatever talk of domain may come to here. (I shall soon confront this issue.) S trawson ( 1 959) , p . 237. The observation of the last note has its counterpart here. In a conversation about the differences between some ancient philosophers we don' t understand 'Plato has a property S ocrates doesn't have' a s conveying a message that is logically equivalent with the proposition that Plato *' Socrates . When asked 'namely what?' we will hardly reply ' the property of being identical with Plato' , but rather, s ay, ' the property of being rich' or ' the property of being a writer' . We take the

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domain of quantification to be tacitly restricted to a sub-set of properties. (This repeats a point already made in Section II above.) In any case, there are more quantifiers in natural languages than are dreamt of in QUine's philosophy of logic. From 'A and B met in the garden [at midnight] ' we can infer, 'A and B met somewhere [somewhenJ ' . This is quantification into adverbial positions, as the appropriate 'namely' rider shows: 'namely in the garden [at midnight] ' . Surely this does not force u s to view adverbials as singular terms . Cf. Strawson ( 1 9 6 1 ) , p. 72, n. 2; ( 1 974a) , pp. 73-5 ; ( 1 997), p. 6 ; Prior ( 1 9 7 1 ) , p. 37 ; and the excerpts from the O:iford English Dictionary in Agustin Rayo and Stephen Yablo (200 1 ) , p. 9 1 , n. 1 . Quine ( 1 974), p . 220. I n Section I above, I took the indefinite article, a s it occurs i n ' Socrates is a man ' , to be part of the general term. This is a (minor) deviation from standard usage: Usually, naked nouns are classified as general terms (cf. , e.g., Quine, 1 974, pp. 2 1 7 et passim), and Strawson concurs when he talks of 'a copula such as "is" or "is a" or the inflections which yield a finite form of the verb' ( 1 9 87 , p. 85, my italics ; 1 990, p . 3 1 8 ; 1 994, p . 24). I can now motivate my deviant usage. Just a s 'S ocrates i s courageous ' implies 'There is something Socrates is (namely courageous) ' , so ' S o crates is a man' implies 'There is something Socrates is (namely a man) ' . In both cases, I take it, the 'namely' rider specifies the general term. So the letter 'F' in ' S ocrates is F' permits replacement by 'a man ' just as well as by ·'courageous' . (In German the indefinite article is sometimes optional [ 'Ich bin Philosoph' ] , but not always [ 'Bukephalos ist

ein Pferd' ] . )

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Strawson ( 1 974b), p. 3 3 . From 'The owl complains t o the moon' we can infer 'There is something s h e does (that is, complain to the moon) ' . The line in Thomas Gray' s 'Elegy' which is echoed in the premiss, 'The moping owl does to the moon complain ' , makes it easier to recognize that in the conclusion we quantify into the position of a verb-stem. The corresponding proform of laziness is 'so ' , as witness, 'The owl complains to the moon, and so does the wolf' . Exceptions are Dudman ( 1 976), pp. 80, 8 3 ; B ede Rundle ( 1 979), pp. 1 1 0-1 1 ; Wiggins ( 1 984), pp. 3 1 7, 326 ; and S trawson ( 1 990), p. 3 1 8 ; ( 1 997), p. 5 . When L .s ay. �quantification' La.lway's ,mean non"subgtitutiqI).al ,qp!lnti:fiGa(i(lll . .. Substitutionally we can quantify into any position if it is bccupied' by ari element of a class of permissible substitutes that was fixed in advance (e. g . the class of all binary connectives) . Similarly Wiggins ( 1 9 84), pp. 3 1 8 , 327 and Strawson ( 1 987), p . 84; ( 1 994), p. 25 . Unfortunately their use of ' stand for' blurs the. difference between denotation and connotation. Thus Quine ( 1 939), p. 1 9 8 ; ( 1 953), p . 102; ( 1 960) , p. 242; ( 1 96 8 ) , pp. 97, 106; ( 1 970), p. 89. S ellars ( 1 974a), p . 298. Similarly John Bigelow ( 1 9 88), pp. 1 5 9-65. (Bigelow ' s favourite formula, 'There is somehow that so-and-so is' , is n o t a well-formed English dummy sentence, I dare say.) Williamson ( 1 999), p . 26 1 . Frege ( 1 892), p . 1 94. Wiggins ( 1 984), p p . 3 1 8, 326. Here is what Yablo says about sentences like (E2): ' Consider now statements like "there's something Jones is that Smith isn 't: happy" . . . Taken at face value, [such] sentences do indeed commit themselves [sic] to entities called "happy" . . . But . . . what on earth could [such entities] be?' (2000a, p . 298/2000b , p. 2 1 9). Yablo seems to think that one can only avoid commitment to such odd objects if one takes s entences

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Universals, Concepts and Qualities like (E2) to be metaphorical. (For this he is rightly taken to task in Stanley,200 1 , pp. 5 1 -2.) The alleged commitment is rather due to a misconstrual of such quantifications . Incidentally, the characterization o f Frege's Begriffe a s ' things that are incomplete' would hardly have been to Frege' s liking. Wiggins ( 1 984), pp. 320, 323. Cf. Strawson ( 1 990), p . 3 1 8 ; ( 1 997), p . 5 ; KUnne (2003) , p p . 362-3 . I f you want t o reserve the title 'second-order quantification' for quantification into predicate position (in a language that is certainly not English ! ) , call it non-nominal quantification. When B oolos defends the assumption that sentences like (E2) are second-order quantifications over sets against Quine' s reproach that it amounts to mistreating predicates as names, he explains that assumption in a structurally perfectly analogous w ay (Boolos, 1 97 5 , p. 5 1 1 ) . B oolos himself construes monadic second-order quantifications as plural quantifications : he reads (E2) as ' There are some things such that Socrates is one of them' . The availability of the extension of his technique to polyadic predications that was subsequently proposed by Lewis and Hazen is dependent on cosmological facts (Rayo and Yablo, 200 1 , pp. 76-7). Such predications are not embarrassing for my reading: 'There is something Socrates is with respect to Plato [namely older, a source of inspiration, . . . ] ' . In any case, B oolos ' s proposal is rather artificial even in the monadic case (as was pointed out in Simons , 1 997, p. 258 and Williamson, 2003 , p. 456). What Socrates is if he is courageous, is certainly not those who are courageous, and although he can be said to be one of those who are courageous, the sentence ' S ocrates is one of those who are courageous ' has a more complex structure than our plain (E). Somebody who has not yet learned to use plural terms and the dyadic predicate 'is one of' may have no trouble in comprehending (E) and 'There is something Socrates is (namely courageous) ' . Cf. Czeslaw Lejewski ( 1 970) , pp. 176, 1 84, 1 86-7; Prior ( 1 97 1 ) , p . 43 ; KUnne ( 1 9 8 3 ) , pp. 1 02, 126; Van Cleve ( 1 994), p. 5 8 7 ; Simons ( 1 997), pp. 262-7 0 ; Rayo and Yablo (200 1), pp. 79-80. Stanislaw Lesniewski may have been the first who emphasized this (cf. Simons, 1 997). Gareth Evans ( 1 976), p. 74. A similar remark on this meeting of the extremes in KUnne ( 1 9 8 3 ) , pp. 109- 1 0 was recently taken by . Tobias .Rosefeldt as a . starJing7point for an illuminating Fregean reconstruction of some of the things Heidegger says about the 'ontological differenc e ' (Rosefeldt, 2003) . Dummett h a s emphasized Frege' s opposition to the Quinean presupposition a long time ago: ' Quine's assumption that the question, "What obj ects are there?" , exhausts the content of the general ontological query, "What is there?", is . . . in sharp contrast with Frege' s view' (Dummett, 1 97 3 , p. 479). Quine ( 1 95 1 ), p . 204. Philosophers who got used to Quine' s idiom tend to say of a theory � or a sentence s that it is ontologically committed to Fs. I take that to be a case of metonymy ( ,The crown prefers . . . ' ) : � or s is committed to Fs, iff people would be (at least prima facie) committed to Fs if they were to endorse � or to utter s assertively. (In Quine, 1 95 3 , pp. 1 03-4 the priority is reversed.) The s ame kind of reductio argument establishes the conceptual impossibility of there being an object that satisfies the open sentence '.,:3<1> (x is <1>) ' : if there were it would be such that there is nothing it is. Husser! ( 1 9 1 3) , p . 1 3 5 (for further references see KUnne, 1983, p . 99). Strawson ( 1 959), p . 1 8 3 ; ( 1 979), pp. 54, 63; ( 1 994), p . 32; ( 1 995). Aristotle, Cat. 1 1 : 14a7 ff. ; cf. Anal. Post. II, 7 : 92b7 ff. Armstrong ( 1 978), II, p. 8 . Ibid. , p . 1 8 ; cf. his ( 1 992), p. 166.

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Dummett calls 'those abstract objects whose existence Frege takes to be analytic pure abstract obj ects' . In S ection II above I have argued that the claim that properties exist is analytic (conceptually true) . If Dummett agrees with this, he anticipates Armstrong when he says: 'Pure abstract objects are no more than the reflections of certain linguistic expressions ' (Dummett, 1973 , pp. 502, 505). The existence of reflections , like that o f shadows, is dependent o n what they are of Schlifer ( 1 996), p. 1 60; (2003) , p . 66. I am not saying that all . abstract obj ects exist necess arily. Many of them don 't. Witness the game of chess, The Art of the Fugue , the Union Jack, and the singleton { Big Ben } . Not even all properties exist necessarily. Witness the relati onal property of being a pupil of Socrates. HusserI distinguished such abstract objects as 'bound , idealities (gebundene Idealitiiten) , from 'free idealities ifreie Idealitiiten) (HusserI, 1 948, §65 ; cf. Kiinne, 1 9 8 3 , pp. 47, 92-3 ) . Cf. Kiinne (2003), c h . 2 . Lewis ( 1 9 86), p . 1 7 8 . Considered in the light of the considerations that follow above, ch. 5 . 2 of Searle ( 1 969) can be accused of prodigality. Cf. Durnmett ( 1 973), pp. 1 69 , 22 1 ; ( 1 98 1 ) , p. 479 (appealing to the Fregean notion of

Bedeutung).

It does not matter here whether it is false or ·neither true nor false. (Le Verrier hypothesized Vulcan to explain an irregularity in the orbit of Mercury, which was eventually explained by the general theory of relativity.) Dummett contends that 'the presence of a name which lacks a reference deprives any sentence of a truth-value' ( 1 97 3 , p. 1 70, cf. 220) . But what is s aid by 'King Jeroboam worshipped B aal' may be true in spite of the emptiness of 'Baal ' , and an utterance of 'That is a nineteenth-century celestial atlas which shows Vulcan in Mercury' s orbit' may very well express a truth. In neither case is the non-denoting name mentioned, nor is it embedded in oratio recta or oratio obliqua , and I cannot see that either s entence could be paraphrased salvo sensu in such a way that the rephrasal has ' B aal ' or 'Vulcan' in any such position. The general term 'a nineteenth-century celestial atlas which shows Vulcan in Mercury's orbit' contains the s ame empty name as (M), and yet it does connote a property. So whether a property is connoted or not depends on .the way in which. the non"de.noting· name is embedded in the. genera), Jerm; which is just to label the problem. Russell himself realized that the concepts class and membership are not essentially involved in the paradox, and the property variant is hinted at in Russell ( 1 906), pp. 1 40-4 1 . See also Prior ( 1 954). To say that there i s n o such property a s F-ness i s not the s ame thing a s saying that F­ ness is not (or cannot) be exemplified. Pripr embraces the generous conception of properties when he writes : 'The property of being a fire-breathing serpent, and the property of being at once ten feet tall and not ten feet tall, are neither of them exemplified, but I do 110t know of any reason for saying or believing that there are no such properties as these two. (That the second of them is self-contradictory is of course a reason for saying that it is unexemplified, but only its having contradictory properties . . . would be a reason for believing that it didn' t exist' (Prior, 1 954, p. 30). In Section IV we have examined S chiffer' s claim that the step from ' Socrates is courageous ' to ' Socrates has the property of being courageous ' is a ' something-from­ nothing transformation' . When Schlifer generalizes this contention he heeds the Russellian danger: 'Every predicate [general term] "F' determines . . . the property of being F, except when that leads to absurdity' (Schlifer, 1 996, p. 1 6 5 ; cf. 200 3 , pp. 623, 66). Examples like (M) show, I think, that the generalization needs a further restriction. (A somewhat cryptical remark in S chlifer, 1 996, p. 1 66, n. 2 may be an

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1 60 161

1 62 163 1 64

Universals, Concepts and Qualities allusion to the kind of problem I illustrated with (M), but no trace of this is left in Schiffer, 2003 . ) B oolos ( 1 9 84), p . 442; Van Cleve ( 1 994), p . 582; Rayo and Yablo (200 1 ) , p p . 8 1-2. (Only Van Cleve uses the property version of Russell ' s paradox.) Cf. Prior ( 1 9 7 1 ) , ch. 3 ; Boolos ( 1 9 84), p . 449 ; Van Cleve ( 1 994) , p . 5 8 8 ; S imons ( 1 997); and the authors mentioned in the next note. Following Prior, I opted for this position in Kunne ( 1 983), pp. 1 1 8�23 , and I followed Prior also in remaining silent on semantical issues . Richard ( 1 996), pp. 43 8-42 complains that Prior makes non­ nominal quantification 'unduly mysterious ' . This is correct, as far as it goes, for Prior only gives us, in substitutional terms, a sufficient condition for the truth of such quantifications. Cf. Bigelow ( 1 9 8 8 ) , pp. 163-4; Rayo and Yablo (200 1 ) , p. 7 8 ; Williamson ( 1 999), pp. 260-63 and (2003) . Could o n e understand them a s substitutional quantifications? ' I a m sceptical about the role of the substitutional quantifier for interpreting natural language' , Kripke s ays ( 1 976, p . 3 8 0) . In Kunne (2003) , pp. 359-60, I explain why I find this reserve wise. This is not to deny that a paradox-engendering general term expresses a concept (see S ection III) . S o my reaction to the Russellian antinomy is not parallel to (vain) attempts at shielding off semantic antinomies by denying that paradox-inducing sentences express propositions.

References Alston, WP. ( 1 958), ' Ontological Commitment' , Philosophical Studies, 9: 8-1 7 . Anderson, A . R . ( 1 959), 'Church on Ontological Commitment' , Journal of Philosophy, 5 6 : 448-52. Anderson, A.R. ( 1 9 6 1 ) , 'What Do Symbols Symbolize? ' , in B. B aumrin (ed.) , Philosophy of Science - The Delaware Seminar, vol. 1 . New York and London: John Wiley, pp. 1 3 7-5 1 . Armstrong, D.M. ( 1 97 8 ) , Universals & Scientifi c Realism. 2 vols. Cambridge: Cambridge University Press . Armstrong, D.M. ( 1 992), 'Properties ' , i n D.H. Mellor and A . Oliver (eds), Properties. Oxford: OXford University Press , pp. 1 60'--7 2 : " Arnauld, A. and Nicole, P. , ( 1 685), La Logique ou L'Art de penser. Stuttgart: Frommann­ Holzboog, 1 9 6 5 . Bealer, G. ( 1 99 8 ) , 'Universals and Properties' , i n S . Lawrence and C . Macdonald (eds), Contemporary Readings in the Foundations of Metaphysics. Oxford: Blackwell, pp. 1 3 147. B ernays , P. ( 1 93 5 ) , 'Sur Ie platonisme dans les mathematiques ' , trans. in P. B enacerraf and H. Putnam (eds), Philosophy of Mathematics. Englewood Cliffs, NJ: Prentice-Hall, 1 964. Bigelow, J. ( 1 9 8 8 ) , The Reality of Numbers. Oxford: Clarendon Press . B olzano, B . ( 1 8 3 7 ) , Wissenschaftslehre. 4 vols . S ulzbach : S eidel. Reprinted i n Gesamtausgabe, vols 1 . 1 1-1. 1 4. Stuttgart: Frommann-Holzboog, 1 9 8 5 . Partially trans. a s Theory of Science, OXford: Blackwell, 1 972; and Dordrecht: Reidel, 1 9 7 3 . (Quoted after orginal pagination.) B oolos, G. ( 1 975), 'On Second-Order Logic' , Journal of Philosophy, 72: 509-27. B oolos, G. ( 1 9 84) , 'To be is to be a value of a variable (or to be some values of some variables)" Journal of Philosophy, 8 1 : 430-49. B oolos, G. ( 1 9 85), 'Nominalist Platonism' , Philosophical Review, 94: 327-44. Carnap , R. ( 1 950), 'Empiricism, Semantics , and Ontology' , in his Meaning and Necesssity, 2nd edn, Chicago: University of Chicago Press, 1 956, pp. 205-2 1 .

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Cook Wilson, J. ( 1 926), Statement and Inference. Oxford: Clarendon Press. Davies, M. ( 1 9 8 1 ) , Meaning, Quantification, Necessity. London: Routledge. Devitt, M. ( 1 980), ' ''Ostrich Nominalism" or "Mirage Realism" ? ' , in D.H. Mellor and A. Oliver (eds) , Properties. Oxford: Oxford University Press, pp. 93-100. Dudman, V. ( 1 976), 'Bedeutung for Predicates' , in M. Schiro (ed.), Studien zu Frege, III. Stuttgart: Frommann-Holzboog, pp. 7 1-84. Dummett, M. ( 1 973), Frege - Philosophy of Language. London: Duckworth. Dummett, M. ( 1 9 8 1 ), The Interpretation of Frege 's Philosophy. London: Duckworth. Egan, A. (2004), ' S econd-Order Predication and the Metaphysics of Properties' . , Australian Journal of Philosophy, 82 : 48-66. Evans, G. ( 1 976), ' Semantic Structure and Logical Form ' , in his Collected Papers. Oxford: Clarendon Press, 1 982, pp. 49-7 5 . Field, H. (1 980), Science Without Numbers. Oxford: Blackwell. Frege, G. ( 1 89 1 ) , '{Auseinandersetzung mit Kerry]" in his ( 1 969), pp. 97-1 22. Frege, G. ( 1 8 92), ' Uber Begriff und Gegenstand' , in his ( 1 967/ 1 9 84, quoted according to original pagination). Frege, G. ( 1 903), ' Uber die Grundlagen der Geometrie, (II) ' , in his ( 1 96711 9 84, quoted according to original pagination). Frege, G. ( 1 906a), ' Uber Schoenflies: Die logischen Paradoxien der Mengenlehre ' , in his ( 1 969), pp. 1 9 1-9 . Frege, G. ( 1 906b), 'Einleitung i n die Logik' , i n his ( 1 969), pp. 20 1-12. Frege, G. ( 1 9 14), 'Logik in der Mathematik' , in his ( 1 969), pp. 2 1 9-70 . Frege, G. ( 1 9 1 8) , 'Der Gedanke' , i n his ( 1 967/1984, quoted according t o original pagination). Frege, G. ( 1 9 1 9) , Brief an Paul F. Linke, in his ( 1 976), pp. 1 5 3-6. Frege, G. ( 1 967), Kleine Schriften. Hildesheim: Olms. Frege, G. ( 1 969), Nachgelassene Schriften. Hamburg: Meiner. Trans. as Posthumous Writings. Oxford: Blackwell, 1 97 9 . Frege, G. ( 1 976), Wissenschaftlicher Briefwechsel. Hamburg: Meiner. Trans . as Philosophical and Mathematical Correspondence. Oxford: B lackwell, 1 979. Frege, G. ( 1 9 84), Collected Papers on Mathematics, Logic, and Philosophy. Oxford: Blackwell. Geach, P. ( 1 9 5 1 ) , 'On What There Is ' , Proceedings of the Aristotelian Society, SV 25: 1 3748. Geach, P. ( 1 975), 'Names and Identity' , i n S . Guttenplan (ed.) , Mind and Language. Oxford: Clarendon Press, pp. 1 3 9-5 8 . Geyer, B . ( 1 9 1 9-27), Peter Abaelards Philosophische Schriften, i n Beitrage zur Philosophie des Mittelalters, XXI, 1-4. MUnster: Aschendorff. Goodman, N. ( 1 9 5 1 ), The Structure ofAppearance. Dordrecht: Reidel, 3rd edn 1 97 7 . Goodman, N. ( 1 977), 'Predicates without Properties ' , i n his Of Mind and Other Matters. Cambridge, MA: Harvard University Press, 1 9 84, pp. 48-50. Goodman, N. and Quine, W.V. O . ( 1 947), ' S teps Toward a Constructive Nominalism' , in Goodman, Problems and Projects. Indianapolis, IN: B obbs-Merrill, 1 972, pp. 173-9 8 . Hale, B . ( 1 987), Abstract Objects. Oxford: B lackwell. Horwich, P. ( 1 998), Meaning. Oxford: Clarendon Press. Husserl, E. ( 1 9 1 3) , Logische Untersuchungen, vol. Ull . TUbingen: Niemeyer. Husserl, E. ( 1 948), Erfahrung und Urteil. Hamburg: Meiner. Jackson, F. ( 1 977), ' Statements about Universals ' , in D .H. Mellor and A. Oliver (eds), Properties. Oxford: Oxford University Press, pp. 89-92 . Jubien, M. ( 1 997), Contemporary Metaphysics. Oxford: Blackwell. Kemmerling, A. ( 1 990), 'Gedanken und ihre Teile' , Grazer Philosophische Studien, 37: pp. 1-30.

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Kripke, S . ( 1 976), 'Is There a Problem About Substitutional Quantification? ' , in .G. Evans and J. McDowell (eds), Truth and Meaning. Oxford: Clarendon Press, pp. 3 25-4 1 9 . Kunne, W. ( 1 983), Abstrakte Gegenstiinde. FrankfurtJM: Suhrkamp. Kunne, W. (2003), Conceptions of Truth. Oxford: Clarendon Press . Kunne, W. (2004), 'Die Gigantomachie in Platons Sophistes' , Archiv fo r Geschichte der Philosophie, 86: 1-1 8 . Lejewski, C . ( 1 970), 'Quantification and Ontological Commitment' , i n W. Yourgrau and . A.D. Breck (eds ) , Physics, Logic, and History. New York: Plenum, pp. 1 73-90. Lewis, D. ( 1 983), 'New Work for a Theory of Universals ' , in D .H. Mellor and A. Oliver (eds), Properties. Oxford: Oxford University Press, pp. 1 8 8-227. Lewis, D. ( 1 9 86), 'Modal Realism at Work: Properties ' , in D.H. Mellor and A. Oliver (eds), Properties. Oxford: Oxford University Press, pp. 1 73-87. Lewis, D. ( 1 9 87), On the Plurality of Worlds. Oxford: Blackwell. Loux, M. ( 1 998), Metaphysics, A Contemporary Introduction. London: Routledge. McGinn, C. (2000), Logical Properties. Oxford: Clarendon Press. Mill, J . S . ( 1 843 ) , System of Logic , in Collected Works , vols Vll-VIII. London: Routledge, 1 97 3 . Pap, A. ( 1 959), 'Nominalism, Empiricism and Universals, 1 ' , Philosophical Quarterly , 9 : 3 3 0-40. Peacocke, C. ( 1 992), A Study of Concepts. Cambridge, MA: MIT Press. Prior, A.N. ( 1 954), 'Entities' , in his Papers in Logic and Ethics. London: Duckworth, 1 976, pp. 25-3 2 . Prior, A . N . ( 1 97 1 ) , Objects of Thought. Oxford: Clarendon Press . Prior, A.N. ( 1 976), Th e Doctrine of Propositions and Terms. London: Duckworth. Putnam, H. ( 1 970), ' On Properties ' , in his Philosophical Papers , vol. 1 . Cambridge: Cambridge University Press, 1 975, pp. 3 05-22. Putnam, H. ( 1 975), 'The Meaning of "Meaning" ' , in his Philosophical Papers , vol. 2. Cambridge: Cambridge University Press, 1 975, pp. 2 1 5-7 1 . Qnine, w.V.O. ( 1 939), 'A Logistical Approach to the Ontological Problem' , i n his ( 1 976), pp. 1 97-202. Quine, w.V.O. ( 1 948), 'On What There Is ' , in his ( 1 9 6 1 ) , and in Mellor and Oliver (eds), Properties. Oxford: Oxford University Press, pp. 74--88 . Quine, W.V. O . ( 1950), Method,s of Logic. London: .Routledge, 3rd ed.n 1 974. , ' Quine, W.V.O . ( 1 9 5 1 ) , ' On Carnap ' s Views on Ontology' , in his ( 1 976), pp. 203-1 1 . Qnine, W.V. O . ( 1 953), 'Logic and the Reification of Universals ' , in his ( 1 9 6 1 ) , pp. 1 02-29. Quine, w.V.O. ( 1 960), Word and Object. Cambridge, MA: MIT Press . Quine, w.V.O. ( 1 96 1 ) , From a Logical Point of View. 2nd edn, New York: Harper & Row. Quine, W.V. O . ( 1 963), Set Theory and Its Logic. Cambridge, MA: Harvard University Press. Quine , w.V.O. ( 1 968), ' Existence and Quantification ' , in his Ontological Relativity and Other Essays. New York: Columbia University Press, 1 969, pp. 9 1-1 1 3 . Quine, W.V. O . ( 1 970), Philosophy of Logic. Englewood Cliffs, NJ: Prentice-Hall. Quine, w.V.O. ( 1 974), The Roots of Reference. La S alle, IL: Open Court. Quine, W.V. O . ( 1 976), The Ways of Paradox and Other Essays. Revd and enlarged edn. Cambridge, MA: Harvard University Press. Quine, w.V.O. ( 1 980), 'The Variable and Its Place in Reference' , in Z. Van Straaten (ed.) , Philosophical Subjects. Oxford: Clarendon Press, p p . 1 64--7 3. Quine, w.V.O. ( 1 9 86), 'Reply to Nelson Goodman ' , in L. Hahn and P. Schilpp (eds) , The Philosophy of W. V. O. Quine. La Salle, IL: Open Court, pp. 1 62-3 . Quine, w.v.o. ( 1 9 87), Quiddities. Cambridge, MA: Harvard University Press. Quinton, A. ( 1 973), The Nature of Things. London: Routledge. Ramsey, EP. ( 1 925), 'Universals ' , in D.H. Mellor and A. Oliver (eds), Properties. Oxford: Oxford University Press, pp. 57-7 3 . .

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Chapter 1 5

A Category of Particulars P.P.

Strawson

I should say, first, that the central notion of this chapter is by no means new. It has a long history, and has been variously interpreted and exploited at different times by different philosophers, as will become clear later. My own use of it will be to make a relatively unambitious attempt at a modest simplification in the theory of universals and particulars. But it may strike others as a gratuitous complication, with more than a whiff of scholasticism about it. To begin with a few familiar points. It is generally accepted that ontological categories include that of individual substances, that is, relatively enduring space­ occupying items with, at least normally, some internal principle of organization. Such items belong to the more comprehensive ontological category of particulars; and by 'particulars ' I understand individual things which have at any time some spatial location. (A minor qualification to that last provision is required in some cases.) Particulars come into, and go out of, existence, can have causal efficacy, and unless they are instantaneous particulars, are generally subj ect to change. Of those particulars which are individual substances, it is also generally accepted that any one such falls under some sortal concept, a sortal concept being a concept such that no two different individuals falling under the same sortal concept can occupy exactly the same space at exactly the same time. A given substantial individual will normally fall under a number of different sortal concepts at different times - as 'boy ' ; 'laWyer' , 'old-l:i.ge pensi6ner' and so on. B ut such different concepts will normally cluster round a certain central sorta! concept, with reference to which the others are explained, which applies to the given individual throughout its or his existence - which, indeed, is sometimes said to give the essential nature of the individual in question: in the cases mentioned the concept ' man' or, better, 'human being' . Of any substantial particulars falling under such a sortal concept, central or non-central, I shall say that it is an instance of the universal of which the concept in question is a concept; and I shall, without argument, take universals to be abstract objects, that is, non-spatio-temporal items without causal · efficacy, objects sometimes of thought but never, themselves , of sense-perception. Substances are not the only particulars which fall under sortal concepts. The same would generally be allowed to be true of particular events and processes births, deaths, explosions, parliamentary elections, battles and so on. Each particular such event is an instance of the appropriate sortal universal. What I want to argue for - or call attention to - is the existence of another class or category of particulars. 'Argue for' is appropriate because philosophical claims on behalf of this category have sometimes been philosophically derided; 'call

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attention to' is appropriate because there is evidence that the category in question is already and unreflectively recognized and acknowledged in our ordinary thought and speech. So what is this category? Its characterization can perhaps be best, that is, most p ersuasively, approached by referring to a certain sub-class of the already acknowledged category of events . Particular members of this sub-class include, for example, particular smiles, blushes, grimaces, sneezes, gestures . Each such event is a unique individual particular, with its own spatio-temporal position, a particular instance of its appropriate sortal. Of course the word 'particular' has its own invariably bothering ambiguity here. It may be pointed out, for example, that a particular gesture may be repeated a hundred times , that a daughter may reproduce her mother's smile, but these repeated gestures or shared smiles are not the particulars I am speaking of; indeed they are not particulars at all; they are the rather specific universals - if you like, the general patterns - of which the particulars I am speaking of are instances . All the . examples of this sub-class of particular events that I have so far given have a distinctive feature in common: the identity of each such particular is intimately linked to the identity of a particular, indeed personal, substance. A standard way of specifying the identity of any particular smile or gesture, for example, would consist in specifying the identity of the person in question, and the time at which he smiled that particular smile or made that particular gesture. This standard way is not an invariably available way. A particular gesture, for example, could be identified by the occasion, the time and place, of its being made without any knowledge of who exactly made it; if it was a profoundly offensive gesture, it might subsequently be referred to as the triggering cause of ensuing hostilities between two sects or nations . Nevertheless the peculiarly intimate link between substance and event in any such case is in fact exclusive even if unknown. If a particular smile is smiled at a certain time by John, no one else can smile that very smile, nor can John smile that very smile at another time (though, of course, he or others may smile an exactly similar smile) . All the abQ'�e has been to emphasize the particular,ity of particular events . Among the examples I mentioned I choose one which may help to ease the transition to the category of particulars which is my topic . The example I choose is that of a blush - a particular event which is an instance of the event-sortal blushing. It took a relatively short, though noticeable, time-interval. The subj ect blushed. Her face became red, and remained red for the interval in question. I shall s ay that the red with which her face is suffused during that interval is itself a perceptible particular: it has a short history during which it is itself subj ect to change, for it may grow less deep or less brilliant before it fades away completely. It is a particular instance of the property redness ; and I shall call all particulars of the s ame type or category as this one 'property-instances ' . It may help to reduce resistance to the particular example I have just given if we notice a feature of the word ' blush' . It is both a verb and a noun. In either cap acity it may refer to an event, an event of blushing. But it may also, as a noun, refer to what I have ' already called a particular instance of redness, to the red which suffuses the subj ect's face. The particular visual appearance of the surface of her skin is the blush which first grows deeper, then grows less deep and fades gradually away. It would seem perverse not to acknowledge the existence of this particular perceptible

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item - a particular instance of redness - as it c omes into exis tence , undergoes change and finally disappears. I remarked at the outset that the general notion I want to promote has nothing new about it. Indeed I myself referred to items of the type in question some forty years ago, describing them as 'particularised qualities ' ; and others have given them other names. More of that later. First I want to promote the idea a bit further with the help of other examples; and among them I shall unblushingly include some I have already used elsewhere. Here they are: ' Her happ iness shone in her eyes ' ; 'His hatred was visible in his whole countenance and demeanour' ; 'John loved to gaze on the brilliant blue of her eyes and the crimson of her lips' . The emphasized items are particulars : they have spatial location - directly and simply in the case of the colour-property-instances; loosely, and derivatively, from the identity and location of their subjects, in the case of particular states of mind like her happiness and his hatred. They all have duration and are subject to change : her happiness, alas, was short-lived; his anger cooled quite rapidly and with it his hatred dwindled; the blue of her eyes dimmed. So they are sharply to be distinguished from the universals the general properties - of which they are instances. For it does not make sense to say of the universal itself that it dims or is short-lived. One might indeed say 'happiness is generally short-lived' ; but that would be merely a brachylogy for saying that most particular cases or instances of happiness are of short duration. Further examples of such particulars could be multiplied au plaisir. Different particular instances of the same property can be compared with each other. S omeone is on record as having remarked that the pride of Wordsworth was equal to that of Lucifer; and few would dispute that the ambitiousness of C aesar or that of Napoleon exceeded those of most, perhaps of all, of their contemporaries. Of course I am ready to admit that for most remarks in which reference is explicitly made to such particulars, equivalent paraphrases could easily be framed which are free of such references. Thus 'Wordsworth was as proud as Lucifer' , ' She was not happy for long ' and so on. But this, by itself, is a feeble weapon to use against claims made on behalf of a maj or ontological . category, when there are no good independent reasons for disputing those claims and adequate reasons for accepting them. I have said more than once that there is nothing new about the central idea I am advocating. It figures in the Nyaya analytical stream in classical Indian philosophy. This was brought home to me initially when, in a train in B engal, I was talking about universals with a young Indian philosopher and remarked that a brown table would be an instance of brownness . He corrected me sharply, maintaining that, not the table but the brownness of the table, was the instance of brownness. Though disinclined at the time to accept this restriction on the use of the expression 'instance ' , I do now see the point and value of it. The notion of property-instance has also been attributed to Aristotle - I think (though I haven't the scholarship to support this) by some medieval and renaissance scholars, more recently by B olzano, and, more recently still, by some modern scholars. The correctness of the attribution to Aristotle has been strongly disputed by at least one heavyweight Aristotelian scholar. In any c ase, however, it might be with attributions to Aristotle, B olzano himself certainly accepted the idea of the items in question, though he called them not, as I have done, 'property-instances' or 'particularized qualities ' , but rather ' adherences ' or ' conditions ' or 'individual accidents ' . But he was emphatic that

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each could belong to or be a condition or adherence of only one substance, that none could belong to more than one. (This must be modified, and is by B olzano modified, to allow for the case of particular relational adherences or conditions, which could clearly be of, or belong to, a pair of substances, but, again, not to more than one such pair or trio.) For simplicity 's sake I shall not further consider the relational case.] Recent twentieth-century advocates of the notion include John B acon, Heath Campbell, C.B . Martin, Peter Simons and C.C. Williams . But the locus classicus for that century is probably the work of G.P' Stout, in his British Academy lecture of 1 923 and his contribution in the s ame year to the symposium, 'Are the characteristics of particular things universal or particular? ' , published in the Proceedings of the Aristotelian Society. Stout's case, somewhat carelessly stated, was, in the same symposium, rubbished by G.E. Moore - an exercise applauded by Ramsey, who declared that Stout had been ' sufficiently answered' . But I think this was a case of uncharacteristic blindness or conservatism on Moore's part and of a certain lofty indifference on Ramsey ' s . As for terminology, I have mentioned a number o f variations o n 'property­ instance' , such as my own 'particularized quality' , and B olzano' s ' adherence ' or ' condition' . There are yet others : for example, 'individual accident (or moment or case) ' . Less happy seems to me the phrase ' abstract particular' , which to my ear has an oxymoronic ring - though it may just be passable in certain very special cases as that of the equator, which is certainly a spatio-temporal item of a sort, though not sensorily perceptible or causally efficacious or in any relevant w ay embodied. Least happy of all, to my mind, though it has recently gained quite extensive currency, is the expression 'trope' , which has been used to convey either the very idea that it is in question or at least one very closely related to it. While acknowledging the currency of this expression, I personally refuse to embrace it in the present connection, since the vocable has a well-established and correct use in application to literature and rhetoric: tropes are nothing other than figures of speech in Beneral, such as metaphor, metonomy and the like. In the" present connection the -­ expression either has no relevant suggestiveness at all or, if it has any, the suggestion it carries is entirely inappropriate. As I earlier hinted, some of the authors I have mentioned, not content with recording and advocating recognition of the ontological category of property­ instances, proceed to make large metaphysical claims on their behalf. They have been described as 'the elements of being' or 'the building blocks of the universe ' ; such phrases are indicative of attempts to show that things generally or often regarded as belonging to some self-standing major ontological categories can, and should, be seen as reducible to, or constructed out of, these elements . The good S tout himself presents one example of this ambition, aiming to represent every property universal - say, wisdom - as what he slightly mysteriously calls the ' distributive unity' of the members of the class of particular wisdoms such as the wisdom of S ocrates . The principle of this unity remains a little opaque, though some relation of more-or-less resemblance must presumably play some part in it. Other more recent writers more simply and straightforwardly identify the universal property with the resemblance class of instances. A different, though comparable, reductive-constructive enterprise is undertaken by some authors who wish to

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represent individual substances as some sort of quasi-mereological sums of property­ instances. All such attempts, whether directed at universals or at substances, seem to me misguided and generative of gratuitous problems, calling for equally gratuitous exercises of ingenuity, but bringing no genuine illumination. For this reason I shall not bother you or myself with a list of exact references for these last remarks. If we set aside these ambitious metaphysical aims, we are left with two questions : what advantages if any, and what problems if any, come along with acceptance of the ontological category of property-instances? The two questions can be considered together. In earlier work, among univers als applicable to individual substances I distinguished sharply between the sortal universals which such substances, as I said, instantiate and the property or quality universals by which, as I then said, they can be characterized or which they exemplify; and correspondingly, with reference to the bonding of universal and particular, I spoke, in the first case, of an instantial tie and in the second, of a characterizing or exemplifying tie, taking care to emphasize that these expressions were not to be seen as themselves naming relational universals . But given the recognition of the category of property-instances, we see that we need not two different types, but only one type, of bonding between particular and universal, namely that of instantiation. For whenever, as we correctly say, a particular substance X is characterized by a universal 0, this is no more than to say that X has a particular instance, say Y, that is, a property-instance, of O. So a modest reduction is achieved: X' s exemplifying or being characterized by 0 is no more than the logical product of X's having Y and Y being an instance of 0 The point is elegantly made by Pranab Sen in the first chapter in this volume. It might now be said: have you not purchased one simplification at the cost of raising a fresh problem? What of the bond (? relation) between Y and X, between the particular property-instance and the particular substance that 'has ' it? Well, in ordinary discourse we habitually use a possessive or genitive form: her happiness, his anger, the deepening redness of her cheeks, the wisdom of Socrates - or, again, in a non-substantial case, the wisdom of so · and- so ' s decision. Philosophers , generalizing, tend towards more elaborate terminology. Thus, B olzano, as I have remarked, speaks of ' adherence ' . I, myself, in the work earlier referred to, spoke of another non-relational tie, the ' attributive' . Some have been tempted to think that Aristotle' s 'being present in' was meant to fulfIl just this role. (Aristotle might have made a better job of The Categories if he had intended this.) But, whatever the terminology, it is clear that no relational universals or instances thereof are called for here. It is the very nature of the substantial individual both to be an instance of some sortal universals and to exemplify some general properties, that is, to ' have' particular instances of those properties. A substance must necessarily both be a something or other and be some way or other, that is, have some property-instance or other. So am I saying, inter alia, that property-universals applicable to particulars are themselves sortal universals just as are the universals of the kinds or sorts to which substantial individuals belong? Yes, I am. It is equally true of sortals of both species that no two different individual instances of a given sortal of either kind can occupy exactly the same space at exactly the same time; though in the case of property universals this might be more lucidly expressed by saying that no two different .

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individual instances of the same property-sortal can be 'of' or 'had by' the s ame individual substance (or event or process) at exactly the same time. Of course there are s ome differences . Of some individual-substance sortals it is contingent that their instances do instantiate them. Thus it is contingent that Horatio Nelson is a naval officer; whereas it is essential to his existence and identity that he is a human being. But it is essential to any particular instance of a property that it is an instance of that property. It is contingent, let us say, that Nelson is brave or that Mary is, at some time, happy. Nelson's bravery or Mary's happiness might not have existed. But Nelson' s bravery could not be anything but a particular instance of bravery nor Mary ' s happiness anything but a particular instance of happiness . S ortals of either variety easily yield criteria of identity and principles o f individuation for their instances . Concepts o f central substance-sortals, man or horse, are themselves individuative. The case of properties which may characterize individual substances is a little more complicated: as indicated above, individuation of their particular instances is normally secured by specifying the individual substance in question and the time at which it 'has ' the property-instance in question; or, if this is not available, by the (spatio-temporal) occasion of their appearance. The case for regarding properties applicable to particulars as sortal universals is complete. What holds for such properties holds also, mutatis mutandis, for such relations . The particular instance of the relation of loving is adequately specified in the old S cottish ballad, which, having mentioned the principals in question, goes on, 'And deep and heavy was the love that fell the twa' between' . That particular instance of love can ' t fall or lie between any other couple. I would go so far as to say that the s ame holds of any universal whatever that has, or may have, application to particulars. Thus the property of being three in number has one particular instance which belongs to, or is of, the members of some particular trio of musicians, and another particular instance which belongs to the members of some particular family of two parents and one child. S ome may object to treating being three in number as a universal, a property; but I see no reason why. Now for some other questioI'�s. I have asserted that particular instances -of the , universals I am concerned with are in general and in principle perceptible, possible obj ects of sense-perception; whereas this is not so with the universals themselves, which I declared to be non-spatio-temporal abstract entities, obj ects of thought perhaps but not of perception. But here, in this negative contention, I run contrary to some other traditions , notably the Nyaya tradition in classical Indian philosophy, to which I have referred with respect; and contrary not only to respectable philosophical traditions, but also, it seems, to the accuracy of common speech; for the names of universals can often figure as the grammatical objects of verbs of perception. Thus we can correctly speak of witnessing brutality, observing courage in action, tasting sweetness or saltines s ; or, to repeat my earlier examples while deleting the particularizing possessives before the abstract nouns , we can properly say ' Happiness shone in her eyes ' or 'Hatred was visible in his whole countenance ' . One may even say 'I have just seen beauty itself' and not be misunderstood. These are all legitimate idioms ; but what we really sensibly perceive in all these cases is not the general thing itself, but a particular instance of the general thing, located in a particular substance or action. Given the acknowledged legitimacy of the idioms, this last comment may sound like a merely dogmatic rej ection of the claim that the

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general property is itself perceptible. But perhaps we can at least come close to an accommodation here. For we could not rightly be s aid to perceive the particular substance or action at all except as somewhat and as somehow, that is, except as of some sort and as qualified in some way. We see the particular action as courageous, we see the particular woman as beautiful, we taste the particular mouthful as sweet. How much difference does it make whether we say we see the universal in the particular, courage in the action, beauty in the woman or say that w e see his courage, her beauty? In so far as the answer is 'Very little ' , the difference between the two positions seems minimal, seems perhaps merely verbal. So a compromise is available. We can accept that locutions which have us s aying that we perceive the universal itself in the particular as a legitimate shorthand for the metaphysically more precise and literally correct claim that we perceive the particular instance of the universal and recognize it as what it is, that is, an instance of that universal. Yet, this concession made, we must of course still maintain the distinction between property-universals and their instances . For we must, as already illustrated; be able to say things about the particular property-instance that it wouldn ' t make sense to say about the property itself. And again we can think about the property or universal itself in total abstraction from all actual instances ; and indeed can think about a universal or property, given that we can form a coherent concept of it, even if it has no instances at all. But now a final question may be raised. Do I really need that initial un argued assumption that properties, and universals in general, unlike their particular instances, are non-spatio-temporal items without causal efficacy? Couldn' t I settle for general concepts instead, equally abstract items indeed, but less generally disputed? I think the answer is 'No ' . Property and concept, though closely related, are clean different things . The difference becomes clear if we consider what it is to possess, as we say, or exemplify, a property and what it is to possess, as we also say, or grasp, a concept. It is perfectly possible for someone, or something, to have a property and lack the concept of it; it is equally possible for someone to grasp the concept and ··· lack the .property. All · substantial ·things, ' animate, ' inanimate . of abstract" havf.C properties ; only conscious beings and cultures can be said to possess concepts . In this sense concepts are mind-dependent; but the properties they are concepts of are not - nor mind-dependent either in the sense that much of the natural world is. If to exist is to be part of the natural world, then universals do not exist, though their instances, if any, may do. The natural world consists of particulars . Universals, by contrast, are essences, intelligibilia. They exist as such; and as such, are possible obj ects of coherent thought, obj ects which may, or may not, have naturally existing, and possibly, sensibly perceptible, instances.

Note The source of my reference to Bolzano is an article by Wolfgang Kiinne, entitled ' S ubstances and Adherences ' , which deals with the ontology in B olzano' s 'Athanasia' . Kiinne's article appears in the first volume of a new series, Logical Analysis and History of Philosophy, ed. Neuwen and Meixner, pub. Schoningh ( 1 99 8 ) .

Chapter 1 6

On Perceiving Properties .Arindam Chakrabarti

'Although one perceives a particular, perception is of the universal' Aristotle, Posterior Analytics 1 00a. 1 7 'Do w e taste universals i n particulars too? ' J.L. Austin, footnote t o 'Are There Apriori Concepts? ' i n Philosophical Papers.

1.

Introduction

In his chapter on universals in this volume, Pranab Kumar Sen raises some hard questions regarding the alleged incompatibility between realism about universals and a robust naturalism. Unless universals take part in causation, and unless some of them are obj ects of ordinary sense-experience, insistence on the existence of universals would always smell of a kind of fictionalism, as if the existence-claim were in need of the qualifier: 'in a manner of speaking' . S en ends the essay dramatically with what I take to be a rhetorical question, suggesting some serious disagreement with Strawson whose views he was mainly discussing. He also whets our appetite for a more incisive treatment of this ' sensitive' issue by a longish note that alludes to the work of Locke, Kant, Austin, and of the Nyaya epistemologists . In this chapter I would like to take up his bold suggestion: 'if all our present theories bf peicepticin are inc'ajJable 'of accommodating the p()ssibility' or a perception of generalities , c an ' t we think of revising our theories of perception themselves ? ' and defend the thesis that universals can b e perceived a s directly a s the particulars in which they reside, My method of defending this perceptualism about our knowledge of universals will be, first, to raise the strongest imaginable obj ections against that thesis, and then to answer them, working out, in the process, some required changes in our theory of perception, I shall not argue against the nominalist who could simply insist that we can never see general properties because there aren't any. In an earlier essay ! I have tried to prove the following conditional claim: If realism concerning ordinary external objects ojperception is true, then realism concerning some universals must be true. Thus, if (even after being cautioned by physics and neuroscience) we claim to perceive the particular material obj ects that common sense undeniably feels that we do, then, in so far as our perception of these ordinary objects is irreducibly predicative in structure, we need to perceive the properties meant by those predicates as well. Even if we are often mistaken in ascribing the properties we seem to see in the external particulars, the detection of these mistakes presupposes that these mis-

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characterized particulars have real properties other than or incompatible with the ones we ascribe on those unlucky occasions . A normal nominalist is usually a believer in the mind-independent existence of particular obj ects (or particular insensible parts or causes of the obj ects) of perception. Such believers in the external world, I have tried to show in that earlier essay, would face an inconsistency if they denied the existence of language-independent and mind-independent universals . But of course, it is possible to be an idealist or phenomenalist about the external world and go on to deny the existence of both ordinary material particulars and universals . That was the consistent but highly revisionary Yogacara Buddhist (B erkeleyan, s ans God) package of wholesale anti-realism. In this chapter I am not engaging with that position, though I shall addres s some arguments against the perceivability of universals put forward by the Yogacara B uddhists . Just to make it explicit: I am not concerned here with a defence of realism about universals. B ut, assuming that there are universals, I am concerned with the question whether we can only reason about them or also experience them; whether we can encounter them with our sense-organs or have to access them only through thinking; whether they are only conceived or, indeed, perceived as well. I recently asked a British music composer whether he thinks people hear the 'musical work' . He was unambiguous that the work itself is a universal that could be multiply exemplified in actual particular performances during the long gaps between which it 'is there' as a performable abstract entity, not to be equated with the scores, but merely represented by them. He said quite spontaneously that although it is not his work that people hear if the performance deviates so badly from what he had in mind that he would disown it, none the les s , on a good day, in hearing an authentic performance of it, the audience, especially a well-trained audience, would most certainly hear the work, as well as hear that ephemeral sequence of sounds produced in the auditorium by the musicians on that occasion. That is why he said that when the critics write a review the next day, they should make two separate sets of comments, one about the work and another about the particular rendition of it the night .before. Tbe distinction between these t\VO targets of criticism would be clearer if the critic had heard more than one performance of the same musical composition. The discriminating critics ' remarks are based on the experience of both, not on their experience of the performance(s) and their thought or imagination of the work. But, against this extremely intuitive theory that we perceive universals when we perceive one or more instances of them in the appropriate way, the following arguments could be given .

2.

T h e First-Sight Argument

Only that sort of thing can be said to be genuinely perceived which can be perceived in our relevant sense-organ's very initial encounter with it. But on the occasion of our sighting of the first particular exemplifier of a property we can never see the property it shares with other such particulars , because we have not yet seen those other particulars. Therefore, a property is never genuinely perceived by the senses unaided by abstract thinking. Even Russell (in The Problems of Philosophy), who believes that we can have direct acquaintance with universals, admits that whiteness

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or horseness can be seen only after several experiences of white patches or horses. We need to abstract the common property out of the instances, and thus, to use Russell's tell-tale phrase, 'learn to be acquainted with' these properties . But a learnt acquaintance is no direct acquaintance, so goes this anti-perceptualist argument. S o , universals cannot be perceived at the untrained fIrst sighting. It requires learning, training - often learning the word for it - or at least some repeated experience of the resembling particulars to begin to see those particulars as falling under or manifesting some generality, the property with respect to which they resemble one another. Since the initial non-conceptual perception does not ever grasp a universal, a universal is not an obj ect of pure sense-perception. Concept-application, which is a non-sensory activity of thought, masquerades as perception when we seem to feel introspectively that we are hearing the common pitch across a regular interval between several strikes on the piano keyboard, or that, besides and along with the several ants, we are seeing the essence ant-hood. A further argument is sometimes given to bolster this first-sight argument. A perception only grasps what is presented to the subj ect at the present moment of time. No one can claim to perceive the past or the future. The universal birdness is something that all past, present and future birds have in common. The person who thinks he sees birdness must experience it as something belonging at least to all the birds that he had seen in the past and expects to see in the future. But to claim to see such a past- and future-involving entity is to mix up memory and expectation with what one is currently exposed to perceptually. Therefore, the so-called ' direct experience' of a universal is never a perception proper. There are many things that are wrong with the above line of argument. First, it is not clear at all where the fIrst premiss derives its strength from. Even about particular concrete physical objects we cannot claim that we do not perceive them unless we notice them the first time they are presented to our senses. I am pretty sure that as a child, the fIrst bird or ant I set my eyes on or the fIrst immobile stone on the mantelpiece to cross my visual path went unnoticed by me. A lot of tutoring, attention-drmving, and even learning the linguistic conventions governing names and demonstratives may have been required before I started noticing birds and ants and tiny stationary items in nature or the household or telling them apart - and I am not even talking about noticing them as birds, as ants and as stones or spoons and so on. The argument not only assumes that there is something like a pure non­ conceptual perception of real particulars ; it basically denies the status of proper perception to any subsequent experience which is due to trained attention, abstraction, comparison and concept-application. Though this picture of real perception being untainted by concepts is popular among a certain stripe of philosophers, the ones who subscribe to the view that genuine perception is untouched by imagination, memory, concepts and words like the baby's fIrst experiences of the world, the average intelligent person takes the very fIrst sighting of something to be a rather impoverished and vague experience of it. To see all aspects of it with care, to bring it under several classifIcation schemes and to exclude it from some of those kinds or classes, and even to know what it is called and how it is described from different points of view is to get a better view of it, and enrich our perception of it, rather than move away from genuine perception. Imagine a child saying 'Where is it? I can ' t see it' after the fIrst attempt at noticing something faint, distant, or easily

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confused with the background. 'Try · again' , s ays the teacher, supplying s ome more clues and cues. 'Ah ! Now I see it' , says the child. S uch an assisted triumph of careful descrying should not be discredited as just an intellectually adulterated non­ sensory perception. The habit-honed experiences of an 'experienced' perceiver are more, not less, genuinely experiential. The very idea of pre-conceptual non-predicative perception is highly suspect. Even if we accept a variety of sense-experience which is totally ineffable and free from any characterization of its own object, the vast maj ority of our adult perceptions are not like that, because we regularly tell each other what we saw. We learn to see, hear, smell and taste things better from what others tell us. To announce that only this first variety (what I have called elsewhere 'immaculate perception ' ) is genuinely sensory and all the rest is non-perceptual is intolerably hasty. Let me rehearse here some five or six responses that Jayanta Bhatta (ninth­ century philosopher of the Nyaya school) 2 makes on behalf of the theory of real perceptible universals , after presenting the Buddhist nominalist arguments against it.

o

•

(i) Is it a 'Royal Decree' that only the first awareness authentically touches the objects and is truly visual, whereas any subsequent ones are not s o ? (ii) Even i f that first sight alone is the proof of something, how is one to ascertain that the unique specificity of a particular alone figures in such initial experience and not its shared properties as well? The duration of a non-conceptual perception, even if it happens in adult life before our experience gets structured into a judgement, is unobservably short. You (the nominalist) are s aying that only the propertyless particular constitutes its content. I am saying that even the shared features are included in that very initial content. We cannot decide who is right by mere swearing. So we must carefully analyse the content of the subsequent fully developed experience of particulars that we can talk about, and infer what must have been seen in that initial moment. (iii) The . f�t ..thah upoD, our second and tl).ircJ. e!i!Countel'S with. the ·same sort of particular we recognize them to be of the same sort shows that we must have seen the sort-making properties initially, though not as sort-making properties . If our first experience of a fruit were totally innocent of any fruity character, then suddenly out of the blue how and when would our grasp of the fruit-universal arise through our subsequent experience? This point is worth pondering over. Hume and Kant have been puzzled about the secret art of concept-formation, because it has been always taken for granted that at first there is only acquaintance with bare particulars. It has been taken as uncontroversial that even if they actually possess general features , those features could not be perceived at first. But once we start from this perception of the bare particular, our account of learning to acquaint ourselves with the shared properties or seeing similarities is never going to get off the ground. If the first sight shows only the propertyless particular, the second sight of another such particular is not a 'second' sight of anything. And similarly the third sight of another instance of that as-yet unperceived universal must fail to arouse any sense of resemblance or the feeling: 'Ah ! Another one of that kind' , because one has never yet seen that kind, or that kind-making property, so that one could recall it. No amount of multiple encounters with individual dogs would then generate any . .

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sense of similarity or thought of shared property, because these initial allegedly pre-conceptual encounters would not be recognized as more than one encounter with the same object of perception, since the only obj ect that can claim to be recognizably the same . across them would have to be the property which, upon this account of concept-acquisition, is not perceived at all in these initial encounters. But we do see similarities and do experience individuals richly endowed with properties that we see that they share with other individuals experienced at other times and places. Therefore, this myth of the first encounter shorn of all properties must be dropped, and along with that the myth of imperceptibility of properties would be dropped too . (iv) You may s ay that generalities are mere imaginary constructions out o f words (and their meanings) and do not owe their origin in any experience. 'But that is not so. Even when the word for it is unknown, one sees the common form running through multiple instances, just as . when a person from south India sees a convoy of camels for the first time.' Similarly, when for the first time one's eyes fall on four fingers (this is Jayanta's example but we now know from experimental studies of newborns ' imitation behaviour and other evidences that human children are born with basic face-recognition and body-part representation schemata), such visual perception already comes with a sense that those are four body-parts of the same sort - even if four is not recognized as four nor fingers as fingers . Here an extremely insightful remark made by S alikanatha, an earlier philosopher of a distinct realist school (Prabhakara Mlmarp.sa) , must be recalled: 'What has been said (by the nominalist) : individual cows (let's call them: "the black-eyed-one", "the peaceful­ one") are seen one at a time, but the universal cowness is not seen in any one of them, that is unproven. The universal is the form. Even when it is seen it need not be seen as a universal form. Until the other individuals are seen, recalled and compared, that the same form runs through them is not perceived. But the universal is what is actually uniformly seen and seen again among many particulars, not its uniform presence. Even when that characteristic of the universal - that it runs like a thread across many instances is not g-rasped, that which possesses this characteristic; namely the universal itself, can be grasped.' (v) Although, strictly speaking, a mere recalling of a past encounter with another instance of a universal would not be a perception, the seeing of a universal is not remembering but recognizing. B oth remembering and recognizing depend on memory. But the former talces the form: 'That past a was F' , whereas the latter takes the form: ' This present b is the same F as that' . The former is not a perception but the latter is. Otherwise none of our perceptual recognition of a familiar creature would count as perceptual, because familiarity with a type involves the memory traces of previously seen samples of the same kind. When I come back after a long absence to my own room, I may see it with nostalgia and warm hope. Does that show that I am not seeing my room as my oId room but only thinking about the absent past and expected future? (vi) Finally, when we see a huge heap of tiny grains of the same natural kind, such as a mountain of beans or sesame seeds , notice that here the compared particulars are co-present to the senses. It is only the common form shared by each individual grain which strikes the senses, not their unique individualities at all. It is nearly impossible for us to visually identify and re-identify the same grain in the -"

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same heap after a gap in looking. ' Just as there we are compelled to say that, although the heap is seen generally as 'a collection of some sesame seeds ' , the eyes must be seeing the particular grains as well, though not one by one as that very particular distinct from this other one; similarly we are compelled to say that even in the so-called fIrst sight the universal is seen, though not as a recognized universal because the question of recognizing it as running through many instances does not yet arise.

3.

The Cause-Obj ect Argumeut

The second most important argument against my view that some universals can be seen in seeing their instances is given by Strawson, who is sympathetic to realism about universals but fails to understand how the ordinary talk about perceiving properties could be taken literally. Strawson's qualms can be formulated in the form of the following apparently valid argument: A. B.

If something has to be perceived, it must be the sort of thing that can cause an experience by interacting with our senses. A universal being an abstract entity is not in time or space, hence it cannot cause an experience or interact with our senses. Therefore, universals cannot be perceived.

Let us examine the premisses of this argument. S alikanatha anticipates this argument while critically defending the Prabhakara MlmliIp.sa claim that universals are accessible to sensory perception. He rebuts it by simply questioning the fIrst premiss . Every obj ect of a perceptual experience need not be its cause. If x is known from the experience y, then x is the obj ect revealed by y, he asserts, being committed to the rather pecutlar" viev,� that all Qur awal'enesses ·are correct fu'1d self-illuminating. · · · Errors are explained in Prabhakara MlmliIp.sa as failing to see the distinction between a correct perception and a correct memory, as cases of non-awareness rather than instances of awareness gone astray. Thus, if an awareness certifIes itself to be a visual awareness of a shared essence, then it must be so, because nothing can be a better j udge of what exactly is the object of a cognition than the cognition itself. However, we need not take this infallibilist approach. B ut when I perceive the absence of my daughter at home, or see a big gap in the bookshelf, the absence or gap is surely something that somehow is registered by my senses. Yet, it sounds odd to say that the absence or gap - a negative entity - causes my perception in the same sense as a running dog would. On a different note, this insistence on the obj ect being the cause has always made way for the 'scientific ' rej ection of direct realisms even about ordinary concrete macroscopic particulars . Yet, it seems initially plausible to hold that just as not all that causes a perception is its obj ect (take the blood-circulation or oxygen breathed in by the perceiver) , similarly, not all that is its obj ect is a cause . Under a certain interpretation o f physics, what causes the optic nerves t o carry the neural mess age that the brain processes as ' s eeing a dog' are some wave-

On Perceiving Properties

3 15

particles roughly in the area where the dog is seen to be. B ut the wave-particles are not seen but reasoned and thought about, whereas the dog, which is strictly speaking causally inefficacious, is undeniably the obj ect of visual perception. If we deny perceivability to properties because of their causal inefficacy under a certain 'scientific image' , we have to strip particular middle-sized concrete continuants also of their intuitively obvious perceivability under that s ame image. B oth will be reduced to ' constructs of thought' under such a scientistic breaking down of real causal interaction. Under the 'manifest image ' both are equally obj ects of perception. Even if we let A stand as a premiss, B surely cannot be accepted so easily. True, the universal by itself is not there in space or time, because it is not there 'by itself' . We are not arguing here about the High Platonic universals which do not need their exemplifiers in order to exist and indeed are more real than them. We are talking about seeing a universal as inherent in each one of its many instances. If the instances are in space and time, then through them the universal can be indirectly c ausally operative. Here we must remind ourselves that one of the most important philosophical grounds for postulating the existence of universals, at least in Nyaya­ Vaise�ika, was their explanatory role,as those generalities in virtue of which certain things and events cause other things and events ( ,limitors of cause-hood' , to use the technical j argon of New Nyaya) . Now, just as the causal law that an a-type event causes a b-type event itself does not cause anything because it is not an event, but unless that causal law were operative those events would not cause one another, similarly the property in virtue of which one event is a cause of another has a definite causal role to play, even if it is an abstract property present fully in many instances located in many different times and places. One way of thus rejecting the second premiss of the cause-obj ect argument would be to construe the causal role of a universal in the following fashion: the particular cat is supposed to be an obj ect of the total perceptual (audio-visual) experience of 'a grey cat jumping on the piano and the note C-sharp being heard' because unless that particular cat were there, that p311:icular experience would not happen� Similarly the cat's grey colour, 'as well as the catness of the cat, must be objects of that experience because unless the cat was that shade of grey and unless it was a cat (unless, that is, it had catness), again, that specific experience would not have the content that it does . The general recognizable pitch-property of being C-sharp is also causally indispensable for the specific phenomenological content of that total experience. Thus the visually accessible universal catness , and the auditorily accessible universal C-sharpness, are both causally necessary for the perceptual experience described above, and it is not correct that properties are causally idle.3

4.

The Reference Argument

The last argument I shall consider has its roots in Frege's fear that to mention the meaning of a predicate with a name-like expression is to make a complete self­ standing object out of it, when, in reality it was an unsaturated functional entity. A.

Whatever can be perceived must be an object of perception.

316

B. C.

Universals, Concepts and Qualities

An obj ect is something which can be the referent of a singular term. B ut a property can never be the referent of a singular term. Therefore, a property can never be perceived.

This argument has all the lure and all the weakness of a Kantian paralogism. Just as the paralogism of rational psychology skids over an ambiguity in the term 'subject ' , this argument turn s o n an equivocation with the term ' object' . Whatever i s the intentional accusative of a cognitive state is an obj ect, in one sense. When I am reflecting on the shape called helix or on the moral virtue called honesty, that shape or that virtue is the object of my imagination. But there is another sense of the term ' object' : a substance or thing. A stone is an object but that the stone is rolling is not an obj ect. In this sense, the shape helix is not an obj ect but something shaped that way would be. In this latter sense, in which Frege draws the contrast between objects and concepts, Michelangelo 's David is an object; that it is in Florence is a fact or true thought, and the property by virtue of which filling up the blank in ' . . . is made of a single piece of marble' with the name ' David' yields a true sentence, is a concept. That property is not an object because, we could remark in Fregean vein, it is a function from objects to truth-values. But these two senses of the term ' object' are totally distinct. Frege considered the realm of reference and the realm of sense to be utterly disjoint realms with no possible overlap. His objects, as against concepts, belong squarely to the realm of reference. B ut he routinely admits the possibility of making thoughts or senses of expressions the object (intentional accusative) of thinking or apprehension. The reference argument would succeed only if it could use the term ' object' in A and B in exactly the same sense. But there is no non-question-begging way of establishing that only a substantial particular referent of a singular term could ever be the intentional object of perception. I just found out by touch that my computer monitor is colder than the surface of my palm. Must this fact be referred to by a name or singular term (formed with that ·prefixing device: ; 'The fact that :: .!)· beforeT.can.claim that that i;<; exactly what I · have perceived? And if a non-common-sensical affirmative answer is insisted upon, then we can simply forget about the Fregean complications and rej ect premiss C. Yes, a property can be the referent of a singular term. As Pranab Kumar Sen has ably demonstrated, we can cut through a lot of Fregean confusions if we allow the meaning of the open sentence 'x is wise' , the intension of the predicate ' . . . is wise' , the property of being wise and the universal wisdom to be ontically all the same. Though he resolutely refuses to think of any complete or incomplete entity as a referent of a predicate, Sen has no problem assigning the obj ect wisdom ( ' a property a s an obj ect' ) as the extension o f the abstract name ' wisdom' . A property can be the referent of a singular term; it just cannot be a reference of a predicate, because a predicate-expression does not do the j ob of referring, according to S en. So he rejects premiss C . Notice his remarks (in response to Amita Chatterj ee) bringing out the subtleties of his views on this issue: .

Going back to my favoured notion of a property, the possibility of translating a sentence with a predicate having a property as its intension into a s entence in which the predicate is replaced by a singular term having the same property as its reference - together, of

On Perceiving Pmperties

3 17

course, with a two-place relational predicate like ' . . . is possessed of . . . ' - unmistakably shows this. Although a property in this sense, i.e. a property as an object, is an 'intensional' entity, it can behave as an extensional entity in the context of the sentence which results from the translation: It does so for, first, in that sentence the singular term standing for the property would be' interchangeable salva veritate with all other co-referential singular terms. Now, once this extensionality is established, there would be no difficulty in having a Tarski-type of truth theory for the so-called 'intensional ' sentences. The development of the truth-theory would not be easy, but it would be possible. (Replies, p. 5 7 1 ) (my emphasis)

5.

On Tasting Immanent Universals

In a profound but somewhat puzzling passage in the Posterior Analytics (quoted as an epigraph for this chapter) , Aristotle had made a distinction between perception, memories generated by perceptions and experience generated by consolidation of memories. But he also remarked rather mysteriously that perception is of the universal. For example, he remarks, perception would be of man but not of Callias , the man. Of course, our initial perception of an arbitrarily chosen man would not clearly isolate the humanity inherent in him as a universal, distinct from his animality or dark-skinnednes s . B ut the same humanity which must have been noticed by me in the very fIrst instance later on is recognized in other specimens of humanity, since otherwise no amount of perceptions would make me ' experienced' in what it is to be human. But subsequent Western theories of perception have never faced this challenge of accommodating this fact that with our eyes and ears and skin and tongue we come across general properties with which we characterize, classify, distinguish and cluster together our particular obj ects of experience. Of course, in one sense, we extract these empirical concepts - our recognitional capacities to detect universals as those very universals - from repeated perceptual encounters. B ut notice how we cannot-ever- get to · acquire · a col1ccpt bY 'repeated encounter with bare partictilats . While encountering many particulars, what we really need to repeat is our sensory encounter with the same attributes, ways, features, structures, patterns, relations and so on. Only a universal is repeatable, because it remains indivisibly the same while being found in many instances. Even if we manage to establish some apriori truths by reflecting upon, for example, the empirical concepts of sound and colour, such as the truth that no sound has a colour, our acquaintance with the property of being a sound, or with the property of being a colour need not be a non-sensory acquaintance. Unfortunately, even Austin, who considered a couple of transcendental arguments in favour of the existence of universals and vindicated naIve realism of a sort in a hostile atmosphere of phenomenalism and scientifIc realism, says dismissively : 'The "universal" is emphatically not anything we stumble across ' .4 He also puts a strange and loose argument in the mouth of the realist about universals : 'Since it is admitted that the things we sense are many or different, it follows that this "universal", which is single and identical, is not sensed.' Actually, as we have seen before, this is a very bad argument. As Jayanta has pointed out, the things that we sense are known to be many and different, thanks to general properties (many

Universals, Concepts and Qualities

318

what? Many flowers, many bees) which they are seen to share or not to share. S o our theory o f perception must make room for the appropriate complex o f relations through which a universal (which is inherent, let us say, in a particular material substance which, in its turn, is in contact with the sense-organ) can get directly linked to the appropriate sense-organ. As long as we understand how the operative link between the olfactory organ and the foul smell in the air is a logical product of the relation between the smelling inhalation and the air (contact) and between the particular whiff of air and its foul smell (inherence) and that smell-quality and the general foulness which it shares with other distinct foul smells (inherence), there is no harm recognizing that we can smell ( 1 ) the general property of foulness as much as smell (2) the particular quality (odour) of that air as well as smell (3) the air. Such a detailed theory of distinct varieties of operative sense-obj ect relations through which we perceive substances , tropes, events , event-universals resident in events, general properties of tropes and so on is what S en was gesturing towards when, in the last note to his chapter in this volume, he commented : [TJhe Nyaya philosophers showed n o hesitation i n admitting the possibility o f a perceptual access to universals, but rather tried to figure out what our perception has got to be to give us this access .

I have a dispositional memory of the taste o f a mango. M y brain only remembers those tastes that my tongue has experienced once or more. I don ' t remember any particular mango or its specific taste. If I now eat an apple, I perceive that it does not have the taste of a mango . When I eat a particular mango I clearly recognize that besides its own unique determinate taste - this one may be a bit tart, with a sweet aftertaste - it does have a generic determinable mango-taste. In that case, I must be tasting a universal in a particular too. Why not? S omehow, though, I expect that my two teachers, Professor Strawson and Professor Sen, would have had a philosophically juicy disagreement about this.

Notes

2 3 4

'Non-Particular Individuals ' , in Philosophy of PF Strawson, edited by P.K. S en and R.R.Verma, Delhi: Indian Council of Philosophical Research, 1 995. Jayanta Bhatta in Nyayamanjari, vol. 2, Ahnika 5 , p . 30 (Mysore edition, 1 98 3 ) . I am grateful to Simon Blackburn for helping me formulate this point, although he himself has no stake in any metaphysical or epistemological thesis about univers als . J.L. Austin, Philosophical Papers, Oxford: Clarendon Press, 1 96 1 , p. 3 .

Index

actualism 1 0 1 Alexander (c.200 AD), on universals 10810, 1 22 anti-realism 9, 3 1 0 see also realism apoha semantics 7, 95, 98, 1 00 Aristotle 50 categories 1 05-6 constructio periphrastica 250-5 1 Criterion 193, 1 95 , 196-9 qualities, contrasts 1 9 1-3 , 1 94 universal concepts 1 1 4-1 8 , 1 2 1 on universals 1 05, 106 works Categories 105, 106, 1 0 8 , 1 2 1 , 1 3 0 , 305 de Interpretatione 105 Metaphysics 105, 106, 1 2 1 Posterior Analytics 1 0 6 , 1 14, 3 17 Armstrong, D.M. 1 2- 1 3 , 9 1 , 23 9-47 on properties 280 universals 67 ascription notion, Wright's 1 6 9-70 atomism, roneepttla1 145attributes 14, 29, 33 B axter, Donald 242 Bealer, George 12, 1 3 , 225-3 8 behaviourism 127, 128 B oethius 109, i 3 0 on universals 1 1 3 B olzano, Bernard 267, 303-4 B oole, George, On the Laws o/ Thought 131 Bradley regress 9 3 Buddhist Nominalism 7 , 94, 95, 1 00, 1 0 1 , 312 Buddhist Nominalists 9 1 , 9 3 , 94, 9 5 , 96, 97, 98, 1 00, 1 0 1 bundle theories , properties 239-40 Carnap, Rudolf 36, 8 3 , 1 3 0 , 144, 261

Caston, Victor 1 07 , 1 22 categories , Aristotle 1 05-6 see also universals causality B uddhist 97 role of universals 39, 4 1 n47, 1 2 1 Chakrabarti, Arindam 1-1 5 , 309- 1 8 Chiaradonna, Riccardo 1 1 3 , 1 14 Chrysippus 8, 1 07 , 1 22 cognition animal 129 and concepts 1 3 3 and epistemology 149-50 cognitive science 1 2 8 colour, and universals 92 concept horse paradox 155, 1 5 6 , 1 6 1 , 1 623, 1 65 , 1 66, 1 67 concepts 9 anchoring role 147 atomism, for and against 1 45 classical model 1 4 1 -2 for and against 142 for classification 1 3 8 -and c0gIDtion 1 3 3 cognitive functions 1 3 8-9, 1 47 context 1 3 6-7 descriptive content 1 34, 1 3 6 direct reference 1 3 4 exemplar theories 144 existence of 1 00 features 1 3 2-40 formation 1 16- 1 7 , 3 1 2- 1 3 and imagination 1 1 7-1 8 and general terms 263-6 generality 1 2 8-9 and inductive learning 1 49-50 and inference 1 3 8-9, 147 and information processing 1 2 8 intensionality 1 5 0-5 1 kinds of 1 3 7 lexical intuitions 140 and mathematics 1 5 1

3 20

Index

as mental entities 1 3 3 naturalness 1 3 5 and obj ects, distinction 1 6 1 , 1 62, 1 7 1 and ontology 14S-9 Peacocke on 99-100 for perception 1 3 8 Platonist, and Aristotelian 1 1 8-20 and predicates 1 6 6-7 productivity 1 40 projectibility 1 3 9 proj ection 1 20 prototype theories 143-4 semantic role 1 45-6 semantic values 1 29-30, 150 similarities 142-4 stability 1 3 5 systematicity 1 40 theories of 7, 1 4 1-S theory theory 1 44-5 typicality effects 1 3 9-40, 1 47 and universals 14, 1 29-30, 14S-5 1 universals as l O S , 1 1 4 use 1 39-40 usefulness 1 2 8-30 vagueness 1 33 see also conceptualism; ideas conceptualism 8, 9 case for 1 27-32 demise 1 27-8 origins 1 3 0-3 1 revival 1 2 8 themes 1 3 1 see also concepts connotation 3 6 constructio periphrastica, Aristotle 250-5 1 copula 249-53 Diogenes Laertius 1 07 Discernibility of Non�identicals, principle 11 distinctness and individuators 92 and resemblance 96-7 , 97-8 Dudman, Victor 261 Dummett, Michael 10, 1 1 , 74, 75, 155, 1 9 3 , 1 94, 1 9 5 , 1 9 6 , 1 9 8-9, 249 epistemology, and cognition 1 49-50 'Error Theorists' 258 extension 3 6 Extensionality, Axiom of 85-6

facts, as universals 24, 47 Fodor, Jerry 9 Forms, Platonic 7, 1 0 5 , 1 06, 1 07 Proclus on I I I Simplicius on 1 1 0-1 1 Frege, Gottlob 8, 9, 1 0 , 1 1 , 3 1 , 3 5 , 7 8 , 1 7 7 , 252, 254, 3 1 5 , 3 1 6 concept horse 1 5 5 criterion o f identity 86 on functions 1 5 6-65 , 177 ontology 1 5 5 , 177 on predicates 40n32, 77 works Conceptual Notation 1 5 6 , 1 60 Foundations 1 5 9 'Function and Concept' 1 5 6 , 1 5 9 , 1 606 1 , 1 64, 1 65 'Logic and Mathematics ' 1 60 ' On Concept and Obj ect' 156, 1 6 1 , 1 62 , 1 64, 1 69 'What is a function? ' 156, 1 59, 1 6 1 functions Frege on 1 5 6-65 , 1 7 7 linguistic 1 5 8 mathematical 1 5 6-8, 1 5 9-60 vs objects 1 5 5 Ganeri, Ionardon 5-6, 5 1-65 Geach, Peter 156, 1 6 5 , 1 6 6 general terms and concepts 263-6 and properties 253-63 general thi.ngs see universals generalities 8 non-universals 62-3 generality, concepts 1 2 8-9 Gettier intuitions 226 grue concept 1 3 9 , 235 Hale, B ob 10, 177-203 Heil, John 24 1 ideas 1 3 1 innate 1

see also concepts identity, and s ameness 92 identity criterion, Frege 86 Identity of Indiscernibles, Principle 1 1 meaning 205 non-trivial versions 206 trivializing properties 205, 207- 1 9 imagination, and concept formation 1 17-1 8

Index Indian Realists 92, 9 3 , 97 individuators, and distinctness 92 inductive learning, and concepts 1 49-50 inference, and concepts 1 3 8-9, 147 infonnation processing, and concepts 1 2 8 inherence category 92-3 instantial tie 49, 305 instantiation 21, 28-9, 67, 305 explanatory value 26-7 intensionality 3 6 concepts 150-5 1 and predicates 8 3 intuitions 226-7 invocation 59 Johnson, W.E. 179, 1 80, 1 8 3 Kant, lnimanue1

Critique of Pure Reason 8 on thinking 1 8 transcendental idealism 4 , 1 8 Katz, Bernard 2 1 1 - 1 2 Kerry, B enno 156, 1 6 1 , 1 66 Kripke, SauI 36, 1 3 4 Kiinne, Wolfgang 1 3-14, 249-300 language, and thought 1 29 Leibniz, Gottfried 2 1 0 Lewis, David 1 0 1 o n properties 28 1 theory of possibility 240 linguistic tnm, philosophy 1 27-8 Locke, John 1 3 1 , J 44

321

verbally bound 9 5 Neoplatonists, and universals 1 1 0-13 nominalism 8 , 91, 94-5 , 1 3 0 , 3 1 0 realism, opposition 1 8 , 3 5 , 9 3 , 226 see also B uddhist Nominalism nominalists 1 2 see also Buddhist Nominalists ; , Ostrich Nominalists non-universal generality 6 Noonan, Harry 9-10, 1 5 5-76 numbers, as universals 23, 46, 49-50 Nyaya tradition 49, 64, 1 02n 1 , 303, 306, 312 objects actual, vs non-actual 1 5 5 concepts, distinction 1 6 1 , 1 62, 1 7 1 vs functions 1 5 5 one-over-many 9 1 , 94 vs many-over-one 3 ontology and concepts 148-9 Frege's 1 5 5 , 177 Strawson's contribution 17 Ostrich Nominalists 9 1 , 9 3 , 94 particularism kinds 255-7 non-reductive 255, 256-7 reductive 255-6, 259 particulars examples 1 5 5 higher-order relation1\ 24,5,.,{J meaning 3 0 1 properties of 239 relational properties 245 relations 243-5 Strawson on 30 1-7 universals, distinction 1 5 5 , 177, 303 Peacocke, Christopher, on concepts 99-100 perception concepts use 1 3 8 non-conceptual 3 12 of universal concepts 1 14- 1 6 o f universals 39, 42n48, 50, 3 0 9 , 3 1 0-14, 3 1 7-1 8 philosophers, analytical 3 philosophical problems features 1 universals, comparison 1 -2 philosophy, linguistic tum 1 27-8 place-markers 68 '

MacBride, Fraser 6, 67-90 manifestation notion 1 70-7 1 many-over-one, vs one-over-many 3 Martin, C.B . 24 1 mathematics, and concepts 1 5 1 Matilal, B .K. 5 9 , 60, 6 1-2, 95 metaphysics conceptualist 1 3 1 -2 revival 3-4, 17, 1 2 8 Strawson's contribution 1 7 Mill, J . S . 3 6 Mirage Realist 9 1 Moore, G . B . 304 Mulligan, Kevin, Language, Truth, and Ontology 1 4 negation nominally bound 95-6

.

322 Plato 50 Forms, as universals 1 05 works Cratylus 1 05 Meno 96 Parmenides 105 Phaedo 1 0 5 , 1 06, 1 14 Republic 105, 1 20 Statesman 1 05 Timaeus 1 05 , 1 10 Platonism, Strawson's 3 5 Plotinus 1 05 on universals 1 1 3- 1 4 Porphyry 1 3 0-3 1 on universals 1 1 2- 1 3 Porphyry' s Tree 3 0 predicates complex 8 3 and concepts 1 66-7 Frege on 40n32, 77 and intensionality 83 meaning 6 and properties 73-4, 7 8 , 83-5 quantification 37 Quine on 3 5 , 36, 3 7 , 80-82 Sen on 73-8 , 79-80, 83 simple 8 3 trivializing 2 1 1-12 types 28 predication deflected 6, 57-8 delimitors 62 elementary, and quasi-Platonic counterparts 266-72 examples 249-53 Strawson's 30, 3 1-2, 3 5-9, 5 8-9 Wright on 1 66-7 1 Proclus , on Platonic Forms 1 1 1 properties abstract 1 2 9 ante rem 129, 1 3 2 Armstrong on 280 bundle theories 239-40 cause-object argument 3 14-1 5 characterizing universals 30-3 1 designation 1 9 differences 3 1 expression o f 6 8 firs t-sight argument 3 1 0-14 and general terms 253-63 generous conception of 279-8 1 imposed 6 1-2

Index in re 1 29, 1 3 0 Lewis o n 2 8 1 'natural' 226 nature of 1 3 need for 1 1 number of 6 parsimonious conception of 280 of particulars 239 and predicates 73-4, 78, 83-5 property of 1 1 reference argument 3 1 5- 1 7 Schiffer on 1 2 , 2 7 1 -2 Sen on 6 8 and their particulars 1 3 theory o f 4, 6 trivializing 205, 207- 1 9 definitions 2 1 1-1 3 , 2 1 9 unexemplified 279-80 as universals 225-6 property, titular 6 property-instances, S trawson on 49, 302, 303, 3 04-7 propositions 4, 23 1-4 Fregean 99 Russellian 99 sentences, distinction 1 6 3 a s universals 2 4 , 47 quantification nominallnon-nomina1 272-9, 282 Sen on 8 1-2 Quine, Willard 6, 7, 8 , 32, 49, 6 8 , 8 3 , 8 6 , 226, 258, 274, .275 eliminative naturalism 25 on predicates 3 5 , 3 6 , 37, 80-82 Ramsey, F.P. 267 universals theory, scepticism 1 0-1 1 , 1 7 8-86 response to 1 87-200 Rashed, Marwan 1 0 8 realism 9 , 1 3 0 , 309 nominalism, opposition 1 8, 3 5 , 93, 226 see also anti-realism realists 2, 7 see also Indian Realists recollection, myth of 9 6 reference, S en on 7 4 relations, as universals 24, 3 3-4 resemblance, and distinctness 96-7 Rodriguez-Pereyra, Gonzalo 3, 1 1-12, 20523

Index; Russell, Bertrand 1 80, 1 83 , 1 8 5 , 267-8 The Problems of Philosophy 3 1 0-1 1 sameness, and identity 92 Sanskrit 59-60 saying/showing distinction 1 5 6 , 1 65-6 schematic letters 68 Schiffer, Stephen, on properties 1 2 , 27 1-2 Sellars, Wilfrid 268 semantic values, concepts 1 29-30, 150 Sen, Pranab Kumar 10, 1 1 , 1 7-47, 49, 309, 3 16 on predicates 73-8 , 79-80 and properties 83-5 on properties 68 on quantification 8 1-2 on reference 74 on Strawson 3-5 , 1 7-47, 5 1-4 universals, theory of 67-87 on variables 68-9, 7 1-2 works The Philosophy of P.F. Strawson 5 1 'Universals and Concepts ' 67-8, 80, 85 'Variables and Quantification' 68 sentence frames 68 sentences closed 69, 70 intensional 230 open 68, 69, 70 propositions, distinction 1 6 3 sets, a s universals 23, 45-6 Siderits, M.arl< 7, 9 1-103 , Simplicius 1 07 on Platonic Forms 1 1 0-1 1 Sorabji, Richard 8, 1 05-25 sorites paradox 1 00- 1 0 1 sortal concepts 3 0 1 mechanisms 1 3 1-2 Stobaeus 107, 1 1 0-1 1 Stoics, on universals 1 06-8, 1 22 Stout, G.F. 304 S trawson, Peter 267, 274, 30 1-7 metaphysics, contribution 1 7 ontology, contribution 1 7 on particulars 301-7 Platonism 35 on property-instances 49, 302, 303, 3 047 Sen on 3-5, 1 7-47, 5 1-4 universals 14-15 , 1 7-47, 5 1

323 attributes 29, 3 3 , 5 1 characterizing 2 1-2, 25, 27, 28-9, 30, 5 1 , 52, 5 3 , 305 classification 1 9-22 definition 2 8 1 exemplification 2 9 existence of 34-9 feature-universals 22, 23 , 42-7, 50, 5 1 , 52, 5 3 , 5 9 instantiation 2 1 , 26-7 , 28-9 , 3 3 mass-terms 5 9 , 6 1 non-examples o f 23-5 and particulars 20-2 1 , 26, 54-7 predication 3 1-2, 3 5-9, 5 8-9 reality of 3 5 relationship 29-30 sortal 2 1 , 22, 25, 2 8 , 29-30 , 32, 3 3 , 3 8 , 5 1 , 52, 5 3 , 1 1 6 , 305 theory of 22-3 , 28-34 works 'Arindam Chakrabarti on Non­ Particular Individuals ' 1 8 , 34 'Entity and Identity' 1 8 , 34 Individuals 1 7 , 18, 1 9 , 2 1 , 22, 2 3 , 24, 27, 2 8 , 3 3 , 34, 42, 54 'Particular and General ' 1 8 , 1 9 , 22, 23, 24, 25 , 27, 2 8 , 3 0 , 3 3 , 34, 42 Skepticism and Naturalism 1 8 , 34

Subject and Predicate in Logic and Grammar 5 1 , 5 9

'Two Conceptions of Philosophy ' 1 8 , 3 1 , 34 " " 'Uuiver.sals' 1 8 , 29, �4_ . subjecthittribute tropes 241-2 universals 242-3 substances complex 94 primary 1 1 2, 1 9 1 and universals 1 9 , 20, 92 substitutionalism 230-3 1 Swoyer, Chris 8-9, 1 27-54 Syrianus 106, 1 20 thinking Kant on 1 8 and universals 1 7 Third Man argument 9 3 thought, without language 1 29 transcendental idealism, Kant 4, 1 8 trope-theory 1 4 tropes 5 , 1 3 , 49, 6 1 , 62, 70, 304

324 subject/attribute 24 1-2 see also property-instances truth-makers 3 types meaning 23-4 as universals 24, 46-7 universal concepts Aristotle 1 1 4-1 8 , 1 2 1 perception o f 1 1 4- 1 6 universals abstract entities as 25 Alexander (c.200 AD) on 1 08-10, 1 22 arguments for 1 2 Aristotelian 7 Aristotle on 105, 106 Armstrong' s 67 B oethius on 1 1 3 causality, role in 3 9 , 4 1 n47, 1 2 1 and colour 9 2 a s concepts 1 0 8 , 1 14 and concepts 14, 1 29-30, 1 48-5 1 existence 227-34 facts as 24, 47 features 2-3 materials 1 9 'natural' 235 and Neoplatonists 1 1 0- 1 3 numbers as 23 , 4 6 , 49-50 particulars, distinction 1 5 5 , 177, 303 perceptibility 1 4- 1 5 perception of 3 9 , 42n48, 50, 3 0 9 , 3 1 01 4, 3 1 7-1 8 philosophical problems, comparison 1-2 Plato on 1 05 Platonic Forms as 1 05 Plotinus on 1 1 3-1 4

Index Porphyry on 1 1 2- 1 3 and predicates 6 7 properties 3 properties as 225-6 propositions as 24, 47 qualities 1 9-20 relations as 24, 3 3-4 scope 225 Sen's 67-90 sets as 23, 45-6 S toics on 1 06-8 , 1 22 Strawson ' s 1 4-1 5 , 1 7-47, 5 1 subj ect/attribute 242-3 and substances 1 9 , 20, 92 theory 7-8 and thinking 1 7 types a s 24, 46-7 WestemJIndian differences 7 see also under Strawson upildhi 6 1 -2 Vaisesika metaphysics 53-4 variables, Sen on 68-9, 7 1-2 Verma, R.R. , The Philosophy ofP. F Strawson 5 1 Whitehead, A.N. 1 7 9 , 200 Wiggins , David 252 Wittgenstein, Ludwig saying/showing distinction 1 56, 1 65 Tractatus Logico-Philosophicus 1 65 Wright, Crispin 1 5 6 ascription notion 1 69-70 on predication 1 66-7 1 Reference Principle 1 67 Zeno 107