By H.W.B. Joseph
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Extra info for Knowledge and the Good in Plato's Republic
1927), p. 12. But again Aristotle seems to think Plato was concerned with the derivation of integers, not of irrationals. , or temporal-these may have, I am convinced is illusory. But if it is true, they are dispensing with any reference to objects that we need to think of by the help of sensible models and diagrams, precisely as Plato thought the dialectician would. For if we can think at all of objects belonging to a 4-dimensional or a nonEuclidean space, we certainly cannot do it by the help of visible bodies like them.
They are rather mere accidents. We mean by calling something accidental not that it occurs uncaused, but that it is not purposed. It occurs in the course of executing a purpose, perhaps owing to the nature of the material in which the purpose has to be executed; and Plato seems to have put down much of the disorder found in the sensible world to the fact that the Ideas manifest themselves in a material not completely subdued to them. And hair perhaps he conceived as accidental too; its biological significance was not recognized, and it was counted by Aristotle as a product of superfluous nutriment.
He is discussing not the Idea-numbers indeed, but mathematical number. 2 But the many units of arithmetic are not each allT6 T6