The Context of the Third Man Argument in Plato's Parmenides

The Context of the Third Man Argument in Plato's Parmenides ROBERT BARFORD IN 1957 HAROLD CHERNISS SPOKE OF a "still-rising flood of literature" on the Third Man argument (henceforth TMA) in Plato's Parmenides. 1 The waters went on to rather great heights, abating somewhat in recent years, although the argument continues to attract attention. To stay with the flood analogy for a moment, the flow of interest has clearly been in the direction of the logical analysis of the argument . 2 What has received less attention and remains unclear is Plato's own evaluation of the TMA. This is the question of the context in which the TMA appears in the Parmenides. The relation of logic and context can be seen in the following. Those who believe that the TMA is unsound (e.g., Cherniss, R. E. Allen) have argued that the theory of Forms has the necessary resources to prevent the regress from starting. 3 Specifically, they have denied that the Forms are self-predicational, an assumption thought to be necessary to the TMA. The question can be raised, however, whether Plato was aware of these resources, and if so, why he did not utilize them to expose the TMA as unsound. In terms of context it is at this point that the "puzzlement" theory makes its entry. 4 Vlastos (followed by Booth, Nerlich, Moravcsik, and Geach, among others) has argued that Plato did not expose the TMA as unsound because he himself was probably not aware of all of its necessary premises, for which reason Plato could not determine whether or not the TMA is sound. According to Vlastos, Plato was never really able to discover the exact source "The Relation of the Timaeus to Plato's Later Dialogues," in R. E. Allen, ed., Studies in Plato's Metaphysics (London: Routledge and Kegan Paul, 1965), p. 369. 2 In our century the logical tradition on the TMA begins with the excellent contribution of A. E. Taylor, "Parmenides, Zeno, and Socrates," Proceedings of the Aristotelian Society 16 (1916):234-289. But it undoubtedly received its most provocative presentation in the article by G. Vlastos, "The Third Man Argument in the Parmenides," Philosophical Review 63 (1954): 319-349; reprinted with addenda, 1963, in Allen, Studies, pp. 231-263. Since then numerous articles have appeared (too numerous to mention here) dealing with the logic of the TMA in the Parmenides. 3 Cherniss, "Relation," and Allen, "Participation and Predication in Plato's Middle Dialogues," Philosophical Review 69 (1960):147-164; reprinted in Allen, Studies, pp. 43-60. 4 In his 1916 article Taylor points out that the "solution" to the TMA is the necessity of denying the "tacit premise" of Parmenides, namely, "that a universal can be predicated of itself as it is predicated of its 'instances'" (p. 253). Taylor explains this by pointing out that a white thing has whiteness or white color, but whiteness does not have the color white; it is the color white. Logically speaking, this is to distinguish an 'is' of identity and an 'is' of predication. Taylor says, "The solution of Parmenides' puzzle, then, is simply that identity and the relation of predicate to subject are different and disparate ..." (p. 254). But was Plato aware of the ambiguity? Taylor writes: "It is perhaps important to note that the source of the apparent fallacy, the ambiguity of 'is', is also, as Plato was to show in the Sophistes, the source of all the old 'eristic' difficulties about negative propositions. Since as everyone admits, Plato saw and explained the ambiguity so far as it affects the possibility of significant denial, it is only reasonable to suppose he was aware of the presence of the same ambiguity in the argument we have just analyzed [the TMA]" (p. 255). However, by 1934 Taylor had come to have second thoughts on this latter point. In The "'Parmenides" of Plato (Oxford, 1934), Taylor repeats his 1916 analysis of the TMA, but he now claims that "it is more than we can say" whether Plato was alive to the ambiguity upon which he believes the TMA rests (p. 21). [1] 2 HISTORY OF PHILOSOPHY of the difficulties raised by the...