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1 Cf. on 508 C, p. 103. note b.
2 Cf. my Idea of good in Plato's republic, pp. 230-234, for the ἀνυπόθετον. Ultimately, the ἀνυπόθετον is the Idea of Good so far as we assume that idea to be attainable either in ethics or in physics. But it is the Idea of Good, not as a transcendental ontological mystery, but in the ethical sense already explained. The ideal dialectician is the man who can, if challenged, run his reasons for any given proposition back, not to some assumed axioma medium, but to its relation to ultimate Good, To call the ἀνυπόθετον the Unconditioned or Absolute introduces metaphysical associations foreign to the passage. Cf. also Introd. pp. xxxiii-xxxiv.
3 The practical meaning of this is independent of the disputed metaphysics. Cf. Introd. pp. xvi-xviii.
4 Cf. Vol. I. p. 79, note c on 347 A and p. 47, not f on 338 D; What Plato Said, p. 503 on Gorg. 463 D.
5 Aristot.top. 100 b 2-3οὐ δεῖ γὰρ ἐν ταῖς ἐπιστημονικαῖς ἀρχαῖς ἐπιζητεῖσθαι τὸ διὰ τί, exactly expresses Plato's thought and the truth, though Aristotle may have meant it mainly for the principle of non-contradiction and other first principles of logic. Cf. the mediaeval “contra principium negantem non est disputandum.” A teacher of geometry will refuse to discuss the psychology of the idea of space, a teacher of chemistry will not permit the class to ask whether matter is “real.”
6 Cf. 527 A-B. This explanation of mathematical reasoning does not differ at all from that of Aristotle and Berkely and the moderns who praise Aristotle, except that the metaphysical doctrine of ideas is in the background to be asserted if challenged.
7 i.e. a bronze sphere would be the original of its imitative reflection in water, but it is in turn only the imperfect imitation of the mathematical idea of a sphere.
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