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1 φιλοχρήματον is a virtual synonym of ἐπιθυμητικόν. Cf. 580 E and Phaedo 68 C, 82 C.
2 In Laws 747 C, Plato tells that for this or some other cause the mathematical education of the Phoenicians and Egyptians, which he commends, developed in them πανουργία rather than σοφία.
3 The questions debated by psychologists from Aristotle (Eth. Nic. 1102 a 31) to the present day is still a matter of rhetoric, poetry, and point of view rather than of strict science. For some purposes we must treat the “faculties” of the mind as distinct entities, for others we must revert to the essential unity of the soul. Cf. Arnold's “Lines on Butler's Sermons” and my remarks in The Assault on Humanism. Plato himself is well aware of this, and in different dialogues emphasizes the aspect that suits his purpose. There is no contradiction between this passage and Phaedo 68 C, 82 C, and Republic x. 611-12. Cf. Unity of Plato's Thought, pp. 42-43.
4 The first formulation of the law of contradiction. Cf. Phaedo 102 E, Theaetetus 188 A, Soph. 220 B, 602 E. Sophistical objections are anticipated here and below (436 E) by attaching to it nearly all the qualifying distinctions of the categories which Aristotle wearily observes are necessary πρὸς τὰς σοφιστικὰς ἐνοχλήσεις(De interp. 17 a 36-37). Cf. Met. 1005 b 22πρὸς τὰς λογικὰς δυσχερείας, and Rhet. ii. 24. Plato invokes the principle against Heraclitism and other philosophies of relativity and the sophistries that grew out of them or played with their formulas. Cf. Unity of Plato's Thought, pp. 50 ff., 53, 58, 68. Aristotle follows Plato in this, pronouncing it πασῶν βεβαιοτάτη ἀρχή.
5 κατὰ ταὐτόν=in the same part or aspect of itself;πρὸς ταὐτόν=in relation to the same (other) thing. Cf. Sophist 230 Bἅμα περὶ τῶν αὐτῶν πρὸς τὰ αὐτὰ κατὰ ταὐτὰ ἐναντίας.
6 For this method of reasoning cf. 478 D, 609 B, Laws 896 C, Charmides 168 B-C, Gorgias 496 C, Philebus 11 D-E.
8 The maxim is applied to the antithesis of rest and motion, so prominent in the dialectics of the day. Cf. Sophist 249 C-D, Parmenides 156 D and passim.
9 Cf. Theaetetus 181 E.
10 The argumentative γε is controversial. For the illustration of the top cf. Spencer, First Principle, 170, who analyzes “certain oscillations described by the expressive though inelegant word 'wobbling'” and their final dissipation when the top appears stationary in the equilibrium mobile.
11 The meaning is plain, the alleged rest and motion do not relate to the same parts of the objects. But the syntax of τὰ τοιαῦτα is difficult. Obvious remedies are to expunge the words or to read τῶν τοιούτων, the cacophony of which in the context Plato perhaps rejected at the cost of leaving his syntax to our conjectures.
12 Cf. Aristotle Met. 1022 a 23ἔτι δὲ τὸ καθὸ τὸ κατὰ θέσιν λέγεται, καθὸ ἕστηκεν, etc,
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