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Plato, Republic, Book 7, section 527a (search)
n. Cf. on 523 A, p. 152, note b; and Titchener, A Beginner's Psychology, pp. 265-266: “There are probably a good many of us whose abstract idea of ‘triangle’ is simply a mental picture of the little equilateral triangle that stands for the word in text-books of geometry.” There have been some attempts to prove (that of Mr. F. M. Cornford in Mind,April 1932, is the most recent) that Plato, if he could not anticipate in detail the modern reduction of mathematics to logic, did postulate something like it as an ideal, the realization of which would abolish his own sharp distinction between mathematics and dialectic. The argument rests on a remote and strained interpretation of two or three texts of the Rep