DUMMETT ON 'S 'IN' A ND FREGE'S O F

M. GLOUBERMAN

In Frege: Philosophy o f (Harper & Row, 1973), Michael Du mme tt analyzes A risto tle 's distinction between items belonging to, and those outside of, the category of sub- stance b y means o f Frege's dichotomisation o f objects in t o concrete a n d abstract. I w i l l argue th a t th e connection i s spurious. For Aristotle, non-substances (e.g. qualities such as colour) are 'in' substances; substances, b y contrast, are not 'in a n y - thing else: they exist in their own right o r are self-sufficient. This one-way dependence, according to Dummett, ois meant in the sense in which a direction is 'of' a line. (...) We cannot understand what a direction is unless we understand it as the o f the function f o r wh ich 'the direction o f x ' stands, for some line as argument» (pp. 257-258). On Frege's vie w, objects are abstract if, in order to grasp their names, they must be recognised as lyin g with in the ran- ge of functional expressions of the kind presented, i.e. if they must b e grasped as 'of' appropriate arguments. Du m- mett thus holds th a t this Fregean semantic dependence d u - plicates the dependence of non-substances on substances which Aristotle expresses b y means o f the 'in'. Several immediate demurs come to . I f an a is both red and blue, then, fo r Aristotle, both colours are 'in' it. But in this case the function 'the colour of x' lacks a value for a as argument. The way that 'in' and 'of' diverge here suggests that Aristotle is not concerned with the o f abstract names. Fo r he does not argue that in such cases the colours 'in' a would have to be identified independently, b y reference to monochrome objects, b u t this is cle a rly implied b y Du m- mett's Fregean account. 160 M. GLOUBERMAN

Such a possibility can be exploited further t o argue th a t Frege's distinction between is not whol- ly semantic. I f our grasp of a colour's name requires that its nominatum be recognised as a value fo r a suitable argument, and i f — as seems p rima facie possible — we could learn colour words in a wo rld o f multi-coloured objects, then the indefinite ' a co lo u r o f x', wh ich has a va lu e e ve n f o r th e latter, would not capture a ll that is essential to grasping na- mes of colours. The question 'Wh ich colour of a?' wo u ld a l- ways arise, and whatever is used to pin a specific colour down would b e p a rt o f th e crite rio n f o r differentiating concrete from abstract objects. To block the problem, it may be insisted that it is a necessary condition for a name's being introduced into a speaker's repertoire that arguments exist which give a unique value to 'a colour of x', hence that in a world of multi- coloured objects colour words could not be introduced system- atically at all. But plainly, even in a wo rld of multi-coloured objects, parts o f these objects a re monochrome. So suitable arguments do exist. Hence, the problem concerns the manner in wh ich the la tte r are specified. Consider a case in wh ich the question 'Which colour of a?' is answered by 'The one on its rig h t side'. I t is reasonable to see the success o f the speci- fication in this case as requiring abilities o f selective atten- tion to aspects of objects. But to introduce an epistemological like selective attention is t o augment the p u re ly se- mantic character of the abstract/concrete distinction. Moreover, though colours are non-substances f o r Aristotle, and hence are 'in' substances, 'red', as a proper name, can be introduced by ostension, without reliance on phrases like 'the colour of the table'. So 'in' and 'of' diverge again. True, Dum- mett's re ma rk that in this respect «Colours are.., on the bor- derline between concrete and abstract objects» (p. 486) mig h t be used t o ju st if y a moderately reconstructive ra th e r than slavishly exegetical linkage o f th e prepositions: Aristo tle 's specific categorisations w i l l thus b e treated a s provisional, due to a p rimitive semantics wh ich Frege makes good t wo millenia after. Note, however, that such a recategorisation o f colour as a substance throws the Aristotelian system askew. DUMMETT O N ARISTOTLE'S 'I N' A N D FREGE'S 'OF' 1 6 1

Colours would have to be definable Per genus et differentiam rather than as determinates o f a determinable range. Leaving these marginal objections, I w i l l n o w argue th at Aristotle's 'in has no straightforward connection with seman- tic issues, but embodies a specifically ontological thesis about existential self-sufficiency. The central clash between Aristotle and Frege becomes clear once the point is made th at Frege's semantic vie ws f a il t o duplicate the anti-Platonic point — to which, after all, A ris- totle's doctrine of categories gives expression — that univer- sals lack instances. Frege factors the 'The table is red' semantically into a functional component — wh ich we ma y represent as '( ) is red' — and a complementing object. The same function- al component reappears when we decompose different senten- ces in vo lvin g the same grammatical predicate, e.g. 'The flag is red'. This analysis is thus congenial to the Platonist. Wh ile the semantic analysans does not automatically elect his posi- tion, it makes it virtu a lly irresistable b y inclining us to state the -conditions o f sentences lik e these so that tru th in both cases depends o n the identical condition's being met. Given certain ontological assumptions concerning which and his disciple are n o t in dispute, the decision is clinched against Aristotle by the following two claims: (1) Frege's sem- antic analysans identifies the basic integral non-logical com- ponents o f sense (in standard /predicate sentences); (2) the senses of a sentence's components determine the char- acter of its truth-conditions. On this evidence, the spirit of Aristotle's doctrine rather than merely its details is contravened by Frege. Note how Aristotle might accept (1) and ye t hold, against (2), tha t wh a t makes 'The flag is red' true differs from what makes 'The table is red' true. Wh a t makes the former true is specified b y the phrase 'the redness o f the flag'; the latter is accordingly verified b y the redness o f the table. These remarks pinpoint an which Dummett mis- ses in the phrase 'the colour o f the table'. The ambiguity is resolved by the pair 162 M. GLOUBERMAN

the redness of the table and the colour of the table, viz. red.

Common usage, a s we see, sanctions the preposition 'of' i n both cases, and this feature of English may be responsible fo r Dummett's oversight. On ly the first phrase, taken as a whole, is true to Aristotle's 'in'; it specifies something which is pro- prietary to th e table: a co lo u r instance. Th e second phrase accurately duplicates Frege's 'of' ; it specifies something which may be had b y innumerable objects, and hence which, save by cosmic accident, is proprietary to none. Formally, Aristotle's 'the redness o f the table' stands to 'the colour of the table n o t as value to complemented function, as Dummett's interpretation requires, but as more precise to less precise specification. The pair 'boy' and 'youngster' are related in th e la tte r fashion. Plainly, there is n o argument f o r th e function 'th e youngster o f x ' su ch th a t 'b o y' specifies t h e value. This a mb ig u ity reemerges systematically. I f th e fla n kin g phrases in the equation the colour of the table = the colour of the flag identify items which are 'in' substances, it could not be true: the non-substance 'in ' th e table is numerically distinct fro m the one 'in' the flag, even if phenomenologically they are in - distinguishable. So the sentence is necessarily false fo r A ris- totle. I n Frege's sense o f 'of', however, th e sentence has a contingent truth-value. A genuine Aristotelian may be expressed by the colour of the table — the redness of the table. But in Frege's sense o f 'of', the sentence is ill-formed. 'What may be true for Frege is the colour of the table = red. Dummett's alignment o f the prepositions is thus unaccep- table. I f w e reformulate Aristotle's position i n a semantic idiom, the dependence he expresses b y 'in' wo u ld emerge in his denial that certain grammatical names specify elements of truth-conditions, e.g. 'red' as used in recognitional responses to DUMMETT O N ARISTOTLE'S 'I N' A N D FREGE'S 'OF' 1 6 3 ostensively presented somples. I t would be a of indif- ference to Aristotle that such names could be introduced d i- rectly into language; fo r he rejects (2); i.e. he holds that a l- though a linguistic element ma y be a n integral, basic, co m- ponent of sense, it ma y still fa il to isolate o r identify an in - tegral element of the truth-conditions o f a sentence to wh ich it contributes. B y polar contrast, Frege's classification o f a n object as abstract turns precisely on denying that its (proper) name is an unstructured component o f sense. A name is ab- stract, again, if a grasp of its sense is mediated by a grasp of the senses of the components of a structured functional expression, the referent of the name being 'of' the function's argument. How could Aristotle agree to (1) and ye t dispute (2) ? A - gain: B y claiming that the p rima ry elements o f sense do not provide a sufficient basis fo r specifying basic elements o f the truth-conditions o f sentences t o wh ich th e y contribute. Th is is n o t to cla im that sense and truth-conditions a re e n tire ly divorced fro m one another. The claim, rather, is that senses do not directly or isomorphically reflect the character of truth- conditions. An d this is f u lly compatible with the o f quite systematic connections between the structure o f senses and the ontological structure o f wh a t sentences represent. I think that such a vie w may we ll be correct, fo r the following reasons. Given that the truth-conditions o f the sentences o f a la n- guage mu st be systematically specifiable, e.g. re cu rsive ly a la Tarski, it is hard to see how (I), o r something ve ry like it, could be denied. But if we were indiscriminately to read Aris- totle's account of the p rima ry elements o f truth-conditions as a semantic account of the p rima ry components o f sense, this would co mmit us t o saying th at 'the redness o f the table', which wo u ld thus b e a p rima ry component o f sense, la cks structure. I f so, n o single explanation could b e supplied o f how we understand 'the redness o f the table' and 'the redness of the flag', and this, aside fro m falsifying the facts, would, per impossible, complicate the semantic specifications beyond toleration. It is essential to recognise therefore that Aristotle's account 164 M. =LIBERMAN focusses p rima rily o n truth-conditions and o n ly derivatively on sense. I t would be dogmatic to insist that such a vie w is simply unintelligible. W h y ma y one k e y factor determining the structure of sense in a language — viz, the mentioned re- quirement of system — be unsynchronised with the ontologi- cal character of the world represented by language ? Obvious- ly, a position would be rejectible if it sanctioned, let alone re- quired, total divergence between the two. But nothing com- mits Aristotle, o r any theorist who voices a simila r objection to (2), t o concede to ta l divergence. N o r is th e re anything magical about the la ck o f to ta l divergence. Fo r obviously, the of the world, with which we are extra-linguistically in contact, also plays a ro le in determining the structure o f senses. In vie w o f the outlined Aristotelian assessment o f (1) and (2), it is not surprising that Dummett, who accepts both, should misinterpret the phrase 'the colour o f the table' a s used t o formulate Aristotle's 'in'. On Aristotle's view, such a phrase is not a natural mode of expression; it is contrived fo r specify- ing an integral element of truth-conditions o f a sentence like 'The table is red'. The divergence between (1) and (2) f u lly explains wh y, as ontologists, we are thus obliged to contort ourselves linguistically and make do with a pis aller.

University of the Negev M. Glouberman