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[525d] that there is something fine in it, and that it is useful for our purpose in many ways, provided it is pursued for the sake of knowledge1 and not for huckstering.” “In what respect?” he said. “Why, in respect of the very point of which we were speaking, that it strongly directs the soul upward and compels it to discourse about pure numbers,2 never acquiescing if anyone proffers to it in the discussion numbers attached to visible and tangible bodies. For you are doubtless aware

1 Cf. Aristot. Met. 982 a 15τοῦ εἰδέναι χάριν, and Laws 741 C. Montesquieu apud Arnold, Culture and Anarchy, p. 6: “The first motive which ought to impel us to study is the desire to augment the excellence of our nature and to render an intelligent being more intelligent.”

2 Lit. “numbers (in) themselves,” i.e. ideal numbers or the ideas of numbers. For this and the following as one of the sources of the silly notion that mathematical numbers are intermediate between ideal and concrete numbers, cf. my De Platonis Idearum Doctrina, p. 33, Unity of Plato's Thought, pp. 83-84, Class. Phil. xxii. (1927) pp. 213-218.

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