Semantics and Self-Predication in Plato

TLDR: In this article, it is argued that the use of eponymy and homonymy is not sufficient to disallow self-predication in the theory of forms and hence the evidence for or against the latter must be sought elsewhere.

Abstract: It is crucial to the notorious Third Man argument (Parmenides 132a 1 -b2, 132d 1I 33a6), where an infinite regress is alleged to ensue from the adoption of Plato's Theory of Forms, that the Form and its instances be grouped together in the same class and this by virtue of the so-called Self-Predication of the Forms. In other words, a given Form, e.g., Beauty, or the Beautiful, is itself beautiful and this fact allows this Form to be included along with the beautiful particulars in the class of beautiful things. In general, not only is a certain predicate "F" true of a group of particulars, but the Form, F-ness, in virtue of which this is so, is F as well assuring the truth of the formulation "F-ness is F." Some scholars have convinced themselves that an examination of Plato's concepts of eponymy and homonymy is sufficient to disallow self-predication' and so free Plato from the questionable clutches of the Third Man. I propose to challenge this contention and shall maintain that Plato's use of eponymy and homonymy is inconclusive as regards selfpredication and hence the evidence for or against the latter must be sought elsewhere. I hope, in passing, to cast new light on an interesting passage in Plato (Parmenides 133d) and, finally, to offer some considerations on the relation between predicate adjectives and Platonic Forms. Let me begin with eponymy. Plato's account of the eponymous relation between particulars and Forms, whereby the particulars get their name from the Form, is given at Parmenides 130e13 la. The passage reads: "'There seem to you, as you say, to be certain Forms from which the other things that partake of them get their names ('ras E'nWvv1ics ... LoXeLv). For example, those partaking of Likeness (6Iot6T-q-Tos) become like (bou[ot), of Greatness great, of Beauty and Justice beautiful and just." (One may compare Phaedo 102b and 102c.) Eponymy, here, is the relation of a particular to a Form. Socrates, for example, gets the derivative designation "just" by partaking of the Form named "Justice." But these passages have been taken to give us much more. Bestor (PS, pp. 38-40; CPE, p. 190) assumes that, by virtue of the eponymous relation as it is presented by Plato, the same general word "F" has a primary referent, or Form, of which it is the proper name and also secondary referents, the many particulars, which are named after the Form.2 Since the application of the term "F" to the Form is not of the secondary or "named after" variety, we do not require another Form for a corresponding primary referent and hence the infinite regress proposed by the Third Man does not obtain. Allen, PP, p. 170, distinguishes "F" as a common name, when applied to particulars, from "F" as a proper name when applied to the Form. With respect to the use of "F" as the proper name of a Form, he maintains, p. 170, "When 'F' is used in primary designation it is a synonym of 'the F itself' and 'F-ness,' therefore to say that F-ness is F is to state an identity. It follows that it is invalid to infer self-predication from Plato's apparently self-predicative language." For both thinkers self-predication is blocked because "F" when applied to a Form is a proper name ( = "the F") and so "F-ness is F" is really equivalent to "F-ness is the F" or, indeed, "The F is the F" (cf. Bestor, PS, p. 58) and this gives us no license to