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[522a] that we seek.” “No.” “Is it, then, music, so far as we have already described it?1” “Nay, that,” he said, “was the counterpart of gymnastics, if you remember. It educated the guardians through habits, imparting by the melody a certain harmony of spirit that is not science,2 and by the rhythm measure and grace, and also qualities akin to these in the words of tales that are fables and those that are more nearly true. But it included no study that tended to any such good as [522b] you are now seeking.” “Your recollection is most exact,” I said; “for in fact it had nothing of the kind. But in heaven's name, Glaucon, what study could there be of that kind? For all the arts were in our opinion base and mechanical.3” “Surely; and yet what other study is left apart from music, gymnastics and the arts?” “Come,” said I, “if we are unable to discover anything outside of these, let us take [522c] something that applies to all alike.4” “What?” “Why, for example, this common thing that all arts and forms of thought5 and all sciences employ, and which is among the first things that everybody must learn.” “What?” he said. “This trifling matter,6” I said, “of distinguishing one and two and three. I mean, in sum, number and calculation. Is it not true of them that every art and science must necessarily partake of them?” “Indeed it is,” he said. “The art of war too?” said I. “Most necessarily,” he said. [522d] “Certainly, then,” said I, “Palamedes7 in the play is always making Agamemnon appear a most ridiculous8 general. Have you not noticed that he affirms that by the invention of number he marshalled the troops in the army at Troy in ranks and companies and enumerated the ships and everything else as if before that they had not been counted, and Agamemnon apparently did not know how many feet he had if he couldn't count? And yet what sort of a General do you think he would be in that case?” “A very queer one in my opinion,” he said, “if that was true.” [522e]

“Shall we not, then,” I said, “set down as a study requisite for a soldier the ability to reckon and number?” “Most certainly, if he is to know anything whatever of the ordering of his troops—or rather if he is to be a man at all.9” “Do you observe then,” said I, “in this study what I do?” “What?” “It seems likely

1 The ordinary study of music may cultivate and refine feeling. Only the mathematics of music would develop the power of abstract thought.

2 Knowledge in the true sense, as contrasted with opinion or habit.

3 Cf. supra, p. 49 note e on 495 E. This idea is the source of much modern prejudice against Plato.

4 Cf. Symp. 186 Bἐπὶ πᾶν τείνει.

5 διάνοιαι is not to be pressed in the special sense of 511 D-E.

6 A playful introduction to Plato's serious treatment of the psychology of number and the value of the study of mathematics.

7 Palamedes, like Prometheus, is a “culture hero,” who personifies in Greek tragedy the inventions and discoveries that produced civilization. Cf. the speech of Prometheus in Aesch.Prom. 459 ff. and Harvard Studies, xii. p. 208, n. 2.

8 Quoted by later writers in praise of mathematics. Cf. Theo Smyrn. p. 7 ed. Gelder. For the necessity of mathematics Cf. Laws 818 C.

9 Cf. Laws 819 D.

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