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1 Always avoid “faith” in translating Plato.
2 Cf. on 508 C, p. 103, note b.
3 That is the meaning, though some critics will object to the phrase. Lit. “the things over which these (mental states) are set, or to which they apply.”
4 There are two probable reasons for this: (1) The objective classification is nothing to Plato's present purpose; (2) The second member of the proportion is lacking in the objective correlates. Numbers are distinguished from ideas not in themselves but only by the difference of method in dialectics and in mathematics. Cf. on 525 D, 526 A, Unity of Plato's Thought, pp. 83-84, and Class. Phil. xxii. (1927) pp. 213-218. The explicit qualifications of my arguments there have been neglected and the arguments misquoted but not answered. They can be answered only by assuming the point at issue and affirming that Plato did assign an intermediate place to mathematical conceptions, for which there is no evidence in Plato's own writings.
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