¹ Cornford, F.M., Plato and Parmenides (London: Routledge & Kegan Paul, 1939).Google Scholar

² Ryle, G., ‘Plato's Parmenides’, Mind N.S. 48 (1939), 129–51, 303–25CrossRefGoogle Scholar (reprinted with an Afterword in Studies in Plato's Metaphysics, ed. Allen, R.E. (London: Routledge & Kegan Paul, 1965),Google Scholar and without it in Ryle, G., Collected Papers, Vol. 1 (London: Hutchinson, 1971)).Google Scholar

³ Ryle, G., Critical Notice of Cornford, Plato and Parmenides, in Mind N.S. 48 (1939), 536–43.CrossRefGoogle Scholar

⁴ Robinson, R., ‘Plato's Parmenides’, CPh 37 (1942), 51–76, 159–86Google Scholar (reprinted in his Plato's Earlier Dialectic² (Oxford: Clarendon Press, 1953)).Google Scholar

⁵ Crombie, I.M., An Examination of Plato's Doctrines, Vol. 2 (London: Routledge & Kegan Paul, 1963), pp. 325–53.Google Scholar

⁶ Owen, G.E.L., ‘Notes on Ryle's Plato’, in Ryle: A Collection of Critical Essays, ed. Wood, O.P. and Pitcher, G. (London: Macmillan, 1971).Google Scholar

⁷ See in particular Mind N.S. 48 (1939), 312–14, 542–3.Google Scholar

⁸ See especially Plato and Parmenides, pp. 109–15.Google Scholar

⁹ As in the second movement (op. cit., pp. 135–6, 146, 150–4, etc.).

¹⁰ As in the fifth movement, at 162 b (op. cit., pp. 227–8).

¹¹ Owen, G.E.L., ‘Plato on Not-Being’, in Plato: A Collection of Critical Essays, Vol. 1, ed. Vlastos, G. (London: Macmillan, 1972), pp. 223–67, at 230.Google Scholar

¹² Cf. Ryle, , Mind N.S. 48 (1939), 538.Google Scholar

¹³ Ryle would disagree, holding as he does that Plato's operation is designed to show only that formal concepts like unity cannot be the subject of existential propositions. I shall dispute this interpretation below. Nor can it be maintained, consistently with an interpretation which takes the structure of antinomies seriously, that ‘one’ is ambiguous from one antinomy to the next (even though taken in the same sense in a given antinomy), and that in this way the charge of total scepticism can be rebutted. Although ‘one’ does shift its use in the second part of the dialogue, it will become evident that in the crucial at the heart of each antinomy Plato does not significantly exploit any potential ambiguity, neither within one antinomy nor from one to the next.

¹⁴ See in particular Robinson, , Plato's Early Dialectic ², pp. 248–64;Google ScholarPeck, A.L., ‘Plato's Parmenides: Some Suggestions for its Interpretation’, CQ N.S. 3 (1953), 142–50, 4 (1954), 31–45.CrossRefGoogle Scholar Peck's subtle discussion of the second part of the dialogue is very close to Robinson's in its general estimate of Plato's intentions. But Peck couples recognition of a gymnastic purpose with the suggestion that this primer of fallacies is meant to be an illustration of the perils of verbal sophistry, and yet also (his detailed proposals here were timely, although superceded by more recent scholarship) ‘to start trains of thought in the mind of Socrates and of the attentive reader which may lead them to sound and valuable results’ (op. cit., p. 150).Google Scholar

¹⁵ The most notable and successful attempt is by Owen, , in Ryle, pp. 341–72. His whole enterprise is designed to show that the second part of the Parmenides ‘is the first systematic exercise in the logic of aporematic and not demonstrative argument’ (p. 348); and it is an immediate corollary that fallacies are very much to be expected, and by no means a cause for alarm, in , although not in proofs.Google Scholar

¹⁶ Plato's Earlier Dialectic ², pp. 264–8.Google Scholar

¹⁷ Ryle, pp. 348–66, and especially pp. 366–8.Google Scholar

¹⁸ See Plato and Parmenides, p. 107.Google Scholar

¹⁹ See above all Robinson, , Plato's Earlier Dialectic ¹, pp. 268–74.Google Scholar

¹ Mind N.S. 48 (1939), 313.Google Scholar

²¹ Ryle, pp. 344–8.Google Scholar

²² Cf. Barnes, J., The Ontological Argument (London: Macmillan, 1972), Ch. 3, to which I am much indebted in this section.CrossRefGoogle Scholar

¹³ Plato, Vol. 1 (op. cit., note 11), p. 247.Google Scholar

²⁴ Plato and Parmenides, p. 115.Google Scholar

²⁵ Ibid., p. 135.

²⁶ Ibid., pp. 203–4 etc.

²⁷ With the argument of this paragraph cf. my article ‘Plato on Unity and Sameness’, CQ N.S. 24 (1974), 40–1.Google Scholar

²⁸ I have discussed the assumption at some length in CQ N.S. 24 (1974), 33–45.CrossRefGoogle Scholar

²⁹ Much of the argument of this section relies heavily on Owen's analyses in Ryle, pp. 349–53; I am also indebted to discussion in a class on the Parmenides given by Professor Owen in Cambridge in 1974–5.Google Scholar

³⁰ This was recognized as a problem for advocates of the genuineness of the antinomies by Ryle, , Mind N.S. 48 (1939), 543.Google Scholar

³¹ For the idea of conceptual exploration upon which I rely in this section I must refer to Ryle's work: see Mind N.S. 48 (1939), 150–1, 312–25;Google Scholar also ‘Letters and Syllables in Plato’, Philosophical Review 69 (1960), 431–51 (reprinted in his Collected Papers, Vol. 1).CrossRefGoogle Scholar

³² Cf. Owen, G.E.L., ‘Tithenai ta Phainomena’, in Articles on Aristotle, Vol. 1, ed. Barnes, J., Schofield, M., and Sorabji, R. (London: Duckworth, 1975), pp. 118–21Google Scholar (reprinted from Aristote et les problèmes de méthode (Louvain: Publications Universitaires de Louvain, and Paris: Éditions Béatrice-Nauwelaerts, 1961)).Google Scholar

³³ Note the connections of in Parmenides' poem with the inconsistencies of mortal thought (D.-K. 28 B 6.6, 16.1).

³⁴ Discussed by Allen, R.E., ‘The Generation of Numbers in Plato's Parmenides’, CPh 65 (1970), 30–4.Google Scholar

³⁵ See further on this section of the second movement Allen, R.E., ‘Unity and Infinity: Parmenides 142b–145a’, Review of Metaphysics 27 (1973–1974), 697–725.Google Scholar

³⁶ See my article ‘A Neglected Regress Argument in the Parmenides’, CQ N.S. 23 (1973), 29–44.CrossRefGoogle Scholar

³⁷ For discussion of this argument see Owen in Ryle, pp. 354–5;Google ScholarArticles on Aristotle, pp. 119–20.Google Scholar

³⁸ Cf. Robinson, , Plato's Earlier Dialectic ², p. 249;Google Scholar but not Cornford, , Plato and Parmenides, pp. 164–5.Google Scholar

³⁹ For one diagnosis see Owen in Ryle, p. 356.Google Scholar

⁴⁰ An Examination of Plato's Doctrines, Vol. 2, p. 342.Google Scholar

⁴¹ Ibid., p. 340.

⁴² Ibid., p. 343.

⁴³ Ibid., p. 344.

⁴⁴ Ryle, pp. 359–60, 368–9.Google Scholar

⁴⁵ Op. cit., p. 341.Google Scholar

⁴⁶ Cf. e.g. 146 d 1–5, 147 a 3–4, 152 e 10–153 a 5.

⁴⁷ So e.g. Owen, , in Articles on Aristotle, p. 125 n.33.Google Scholar

⁴⁸ On mass terms see e.g. Cartwright, H., ‘Quantities’, Philosophical Review 79 (1970), 25–42;CrossRefGoogle Scholar H. Laycock, ‘Some Questions of Ontology’, ibid. 81 (1972), 3–42.

⁴⁹ Cf. e.g. Owen, , in Plato, Vol. 1 (op. cit., note 11 above), 226 n.8.Google Scholar

⁵⁰ I am grateful for the criticism and encouragement of Mr. M.F. Bumyeat, Professor W.K.C. Guthrie, Dr. G.E.R. Lloyd, and Mr. R.R.K. Sorabji, each of whom read a draft of this paper. Professor G.E.L. Owen first stimulated and encouraged my researches on the Parmenides ten years ago: my debt to him will have been evident at every turn.