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1 This passage is often taken as another example of Plato's hostility to science and the experimental method. It is of course not that, but the precise interpretation is difficult. Glaucon at first misapprehends (cf. p. 180, note a, on 529 A) and gives an amusing description of the mere empiricist in music. But Socrates says he does not mean these, but those who try to apply mathematics to the perception of sound instead of developing a (Kantian)a priori science of harmony to match the mathematical science of astronomy. Cf. also p. 193, note g, on 531 B, W. Whewell, Transaction of the Cabridge Philos. Soc. vol. ix. p. 389, and for music A. Rivaud, “Platon et la musique,”Rev. d’Histoire de la Philos. 1929, pp. 1-30; also Stallbaum ad loc., and E. Frank, Platon u. d. sog. Pyth.,Anhang, on the history of Greek music. He expresses surprise (p. 199) that Glaucon knows nothing of Pythagorean theories of music. Others use this to prove Socrates' ignorance of music.
2 This hints at the distinction developed in the Politicus between relative measurement of one thing against another and measurement by a standard. Cf. Polit. 283 E, 284 B-C, Theat. 186 A.
3 πυκνώματα(condensed notes). The word is technical. Cf. Adam ad loc.But, as ἄττα shows, Plato is using it loosely to distinguish a measure of sense perception from a mathematically determined interval.
4 Cf. Pater, Renaissance, p. 157. The phrase,ἐκ γειτόνων, is colloquial and, despite the protest of those who insist that it only means in the neighborhood, suggests overhearing what goes on next door—as often in the New Comedy.
5 Cf. Aldous Huxley, Jesting Pilate, p. 152: “Much is enthusiastically taught about the use of quarter tones in Indian music. I listened attentively at Lucknow in the hope of hearing some new and extraordinary kind of melody based on these celebrated fractions. But I listened in vain.” Gomprez, Greek Thinkers, iii. pp. 334-335, n. 85, thinks that Plato “shrugs his shoulders at experiments.” He refers to Plutarch, Life of Marcellus, xiv. 65, and Quaest. Conv. viii. 2. 1, 7, where Plato is represented as “having been angry with Eudoxus and Archytas because they employed instruments and apparatus for the solution of a problem, instead of relying solely on reasoning.”
6 So Malebranche, Entretiens sur la métaphysique, 3, x.: “Je pense que nous vous moquez de moi. C’est la raison et non les sens qu'il faut consulter.”
8 The language of the imagery confounds the torture of slaves giving evidence on the rack with the strings and pegs of a musical instrument. For the latter cf. Horace, A.P. 348, “nam neque chorda sonum reddit quem vult manus et mens Poscentique gravem persaepe remittit acutum.” Stallbaum says that Plato here was imitated by Aristaenetus, Epist. xiv. libr. 1τί πράγματα παρέχετε χορδαῖς;
9 This also may suggest a reluctant and a too willing witness.
10 Cf. on 489 A, p. 23, note d.
11 He distinguishes from the pure empirics just satirized those who apply their mathematics only to the data of observation. This is perhaps one of Plato's rare errors. For though there may be in some sense a Kantian a priori mechanics of astronomy, there can hardly be a purely a priori mathematics of acoustics. What numbers are consonantly harmonious must always remain a fact of direct experience. Cf. my Platonism and the History of Science, p. 176.
12 Cf. Friedländer, Platon, p. 108, n. 1.
13 Cf. Tim. 47 C-D. Plato always keeps to his point—cf. 349 B-C, 564 A-B—or returns to it after a digression. Cf. on 572 B, p. 339, note e.
14 Cf. on 505 B, p. 88, note a.
16 Cf. on 537 C, Epin. 991 E.
17 Plato is fond of this image. It suggests here also the preamble of a law, as the translation more explicitly indicates. Cf. 532 D, anticipated in 457 C, and Laws 722 D-E, 723 A-B and E, 720 D-E, ;772 E, 870 D, 854 A, 932 A and passim.
18 Cf. Theaet. 146 B, and perhaps Euthyd. 290 C. Though mathematics quicken the mind of the student, it is, apart from metaphysics, a matter of common experience that mathematicians are not necessarily good reasoners on other subjects. Jowett's wicked jest, “I have hardly ever known a mathematician who could reason,” misled an eminent professor of education who infers that Plato disbelieved in “mental discipline” (Yale Review,July 1917). Cf. also Taylor, Note in Reply to Mr. A. W. Benn, Mind, xii. (1903) p. 511; Charles Fox, Educational Psychology pp. 187-188: “ . . . a training in the mathematics may produce exactness of thought . . . provided that the training is of such a kind as to inculcate an ideal which the pupil values and strives to attain. Failing this, Glaucon's observation that he had ‘hardly ever known a mathematician who was capable of reasoning’ is likely to be repeated.” On the text cf. Wilamowitz, Platon, ii. pp. 384-385, and Adam ad loc.
19 λόγον . . . δοῦναιA commonplace Platonic plea for dialectics. Cf. 534 B, Prot. 336 C, Polit. 286 A, Theaet. 202 C, 175 C, 183 D, Soph. 230 A, Phaedo 78 C-D, 95 D, Charm. 165 B, Xen.Oecon. 11. 22. Cf. also λόγον λαβεῖνRep. 402 A, 534 B, Soph. 246 C, Theaet. 208 D, and Thompson on Meno 76 D.
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