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Self-Predication and the "Third Man"

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Self-Predication and the SELF-PREDICATION AND THE "THIRD MAN" Arnold CUSMARIU Columbia The passage at Parmenides 132A-B has attracted a great deal of attention. Here Plato raises a deep and powerful objection, the "Third Man" argument (TMA), aimed directly at an essential constituent of his own Theory of Forms.' I. The following is only a partial list of discussions of this problem: Ryle, G: "Plato's 'Paramenides', I", Mind 48 (1939), 129-51. Cornford, F.M.: Plato and Parmenides (London, 1939). Cherniss, H.: Aristotle's Criticism of Plato and the Academy, I (Baltimore, 1944). Ross, D.: Plato's Theory of Ideas (Oxford, 1951). VIastos, G. [A): "The Third Man Argument in the Parmenides". Philosophical Review 63 (1954), 319-49. Reprinted in R.E. Allen (ed.) Studies in Plato's Metaphysics (London. 1965). 231-63. VIastos. G. [B]: "A Reply to Mr. Geach", reprinted in Allen, 279-91. VIastos. G. [C]: "Plato's 'Third Man' Argument: Text and Logic", Philosophical Quarterly 19 (1969), 289-30 I. Wedberg, A.: Plato's Philosophy of Mathematics (Stockholm, 1955). Ch. III reprinted in G. VIastos (ed.) Plato: A collection ofCritical Essays, Vol. I (Garden City. 1970). 28-52. Geach, P.T.: "The Third Man Again':, Philosophical Review 65 (1956), 72- 82. Reprinted in Allen. 265-77. Allen, R.E.: "Participation and Predication in Plato's Middle Dialogues", Philosophical Review 59 (1960), 147-64. Reprinted in Allen, 43-60, and in VIastos, 167-83. Moravcsik, J.M.E.: "The 'Third Man' Argument and Plato's Theory of Forms", Phronesis 8 (1963), 50-62. Strang, c.: "Plato and the Third Man", Proceedings of the Aristotelian Society, Suppl. Vol. 37 (1963), 147-64. Reprinted in VIastos, 184-200. Sellars. W.: "VIastos and the 'Third Man' ", and "A Rejoinder", both in his Phi/osophical Papers (Springfield. 1967),23-72. Cohen, S.M.: "The Logic of the Third Man", Philosophical Review 80 (l97\). 448-75. 106 Considerable effort has gone into c1arifying the structure and the content of the TMA. Though progress has been made, I will show in this paper that apremise crucial to the argument has yet to be stated openly. This premise holds the way out of the predicament which, happily, enables Plato to retain intact the foundations of the Theory of Forms. The solution I shall propose allows us in addition to look beyond the TMA and place this ancient argument in the context of an important modern insight. I I begin with the famous passage itself: How do you feel about this? I imagine your ground for believing in a single form in each case is this. When it seems to you that a number of things are large, there seems, I suppose, to be a certain single character which is the same when you look at them all; hence you think that largeness is a single thing. True, he replied. But now take largeness and the other things which are large. Suppose you look at all these in the same way in your mind's eye, will not yet another unity make its appearance - a largeness by virtue of which they all appear large? So it would seem. If so, a second form of largeness will present itself, over and above largeness itself and the things that share in it, and again, covering these, yet another, wh ich will make all ofthem large. So each one ofyourforms will no longer be one, but an indefinite number. (F.M. Cornford translation). As is weil known, this passage does not contain all the premises necessary to have a valid argument. Two additional premises, both important elements of the Theory of Forms, must be brought forward to reconstruct the TMA: (SP) Plato seems to have held that all forms are predicable of themselves.2 Thus, Beauty is itself beautiful, lustice is itself just, 2. Many passages suggest that Plato thought forms were self-predicable, though he nowhere asserts that aII of them are. Cf., Protagoras330C3-E2; Hippias Major 29101-?; Phaedo 74A-750, WOB-lOSE; Symposium 21OE- 212A; Parmenides 129BI-2, 129B6-7; Euthyphro 6E3-6. Issues of inter­ pretation here are discussed by S. Peterson, HA Reasonable Self-Predication Premise for the Third Man Argument", Philosophical Review 82 (1973),451- 70. .
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