Journal of the History of Philosophy

Self-Predication and the "Third Man" Argument ROGER A. SHINER 1.1. IN COMMPm'mO on the 'Third Man' Argument (TMA), Proclus z produces the following line of thought. He argues that. if the relation of resemblance between Form and particular were symmetrical, the argument in question would be valid; the relation is not, however, symmetrical. Where a Form and particular are both alike, have the quality of likeness, the likeness of that which is derived is not the same as the likeness of that from which it is derived, just because of the former's derivatory nature. Consequently, ~k tt~v ala01]x~ bttotoi3c0at ~re[vot~ (sc. xo~ ~Semv), abx~ 8~ xo6~ot~ oSr~xt, 'the sensible particulars resemble the Forms, but they are not in the same relation of resemblance to the particulars' (ibid., 913.29-30). That is to say, the bare relation of similarity may be symmetrical , but the relation of a similar copy to a similar original is not; the copy is 'a copy of' the original, but the original/s not 'a copy of' the copy. This way of defending the Theory of Forms against the TMA I shall for purposes of identification call the 'Ontological Defence'. It lays stress on the ontological difference between Form and particular in order to avoid the fatal implication that the relation between them is symmetrical. If we use the language of predication, the point is as follows: the TMA is valid, if the Forms have a given term predicated of them severally in exactly the same sense as it is predicated of their respective dependent particulars. This, however, is not the case, for the quality in virtue of which a given term is predicated of a given Form differs in ontological status from the quality in virtue of which that term is predicated of that Form's dependent particulars. Thus we see that underlying the Ontological x I am grateful for helpful comments on an earlier version of this paper to Professor Gilbert Ryle, Professor John F. Malcolm and two anonymous readers for this Journal. Since this paper went to press, the following relevant articles have appeared: G. Vlastos, "'Self Predication' in Plato's Later Period," Philosophical Review, LXXVIII (1969), 74-78, and "Plato's 'Third Man' Argument (Parm. 132al-b2): Text and Logic," Philosophical Quarterly , XIX (1969), 289-301; K. W. Rankin, "The Duplicity of Plato's Third Man," Mind, LXXVIII (1969), 178-197; T. O. Smith, "'The Theory of Forms, Relations and Infinite Regress," Dialogue, VIII (1969), 116-123. 2 Proelus, In Platonis Parmenidem, ed. V. Cousin, Paris, 1864; 912.27 ft. [3711 372 HISTORY OF PHILOSOPHY Defence is the following assumption--the fact that the Forms are self-predicating only causes problems for the Theory of Forms, if a given Form F and its corresponding particulars, a set of f things, have 'F' predicated of them univocally , are F in precisely the same sense. My thesis in this paper is that this latter assumption is false, it is, rather, quite sufficient for the Self-Predication Assumption (SPA) to be vicious, if 'F' is predicated of both Form and particular not equivocally. This is not the same as 'univocally', and furthermore it is not possible that Plato could have thought of the predication of a term of both Form and particular as equivocal, the only alternative left to him to escape the TMA. The SPA, therefore, is required for the Theory of Forms to make sense, and leads to an ineradicable defect in that Theory. 1.2. One minor terminological point must be noted before we proceed. There are two versions of the TMA in the Parmenides; the first runs from 131eS-132b2, and the second from 132c11-133a7. The second of these explicitly employs the language of copy-resemblance, 7mpdS~tytm ('paradigm'), 6lxoio)tta ('likeness'), ~tKao0~vat ('resemble') as an explication of ~t~0e~tq ('participation'): the first employs the lan~.,uage of cttx6 ~ xai3xa.., eIvat ('that by which things are . . .'), which, as Plato has already indicated (Phaedo 100d6-8), is deliberatety noncommittal as to the relation between Forms and particulars. I shall refer to the first argument as TMA(1) and the second...