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Home , Platonic realism

RYLE'S PARADOX AND THE OF EXEMPLIFICATION*

Amold CUSMARIU - University of Rhode Island

Some years ago, in the first of two studies on 's , 1 Gilbert Ryle gave an to show that Plato's was a 'logically viciouS'2 doctrine. Two recent commentators on Ryle's argument, Alan Donagan3 ahd David Armstrong4, agree that the argument has this consequence. But I think that Ryle's argument does not succeed in showing Platonic to be 'logically vicious' although it does bring up an important, and deep, question which Platonic Realists should be able to answer satisfactorily. So I will do two things in this paper. First, I will reply to Ryle's argument and then I will reply to the question wh ich that argument raises.

1. Ryle's Argument

Ryle hopes to show that Platonic Realism is 'logically vicious' by showing that its account of predication (see (A) and (D) below) leads to absurdity. He states his argument rather loosely, in a passage in which he seems to be playing a kind of question-and-answer game. To make it easier to extrude an argument out of this passage, I will number the sentences which make it up, keeping their original order: (1) Now what of the alleged relation itself, which we are calling 'exemplification'?

*1 am indebted to Roderick M. Chisholm, Ernest Sosa and James Van Cleve for helpful comments on an earlier draft of this paper. 1. Plato's 'Parmenides", I,Mind, Vol. 48 (1939), pp. 129-151. 2. Ibid., p. 134. 3. 'Universalsand Metaphysical Realism', The Monist, Vol. 47, No. 2 (1963), pp. 211-246. Reprinted in Universals and Particulars, MJ. Loux (ed.), (Double• day, 1970), pp. 128-158. Donagan also attempts to solve Ryle's paradox; 1 con• sider his solution briefly in footnote 8 below. 4. 'Infmite Regress and the ' ,Australasian Journal of , Vol. 52 (1974), pp. 191-201, esp. pp. 197-8. 66 (2) Is this a F onn or an instance of a F onn? (3) Take the two propositions 'this is square' and 'that is circular'. (4) We have here two different cases of something exemplifying something else. (5) We have two different instances of the relation of being-an-in• stance-of. (6) What is the relation between them and that of which they are instances? (7) It will have to be exemplification Number 2. (8) The exemplification of P by S will be an instance of exemplifi• cation, and its being in that relation to exemplification will be an instance of a second-order exemplification, and that of a third, and so on ad infinitum. (9) This conc1usion is impossible. So there is no such relation as being-an-instance-of. 'This is green' is not a relational proposi• tion ... 5

Ryle's argument might be put as follows: 6 (A) For any x, x is F iff x exemplifies F*. (B) Exemplification is a genuine relation. That is, (C) For any x, x exemplifies F* iff x is related to F* by the exem• plification relation E*. But, (0) For any x, y and R, x bears R to y iff the ordered pair (x;y) exemplifies R *. Therefore, (E) a is related to F* by the exemplification relation E* iff the or• dered pair (a; F*) exemplifies F*. But then,

s. Ibid., p. 138. One minor point: unless he meant to be talking about sen• tences, Ryle should have said in (3) 'the two propositions expressed by 'this is square' and 'that is circular". Now one might deny these sentences express pro• positions - in view of the presence of referring expressions which cannot be paraphrased a la RusselI. But this does not matter, since Ryle could have chosen different examples to make his point. 6. The following shorthand will be used: (a) single capitals will be predicate letters, (b) starred single capitals will denote the expressed by the cor• responding predicate, and (c) italicized single lower case letters will be indivi• dual expressions, denoting individuals.