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. Since, then, some
say that the Ideas and the numbers are such substances, and that the
elements of these are elements and principles of real things, we
must inquire regarding these what they say and in what sense they
say it.
Those who posit numbers only, and these mathematical, must be
considered later; but as regards those who believe in the Ideas one
might survey at the same time their way of thinking and the difficulty
into which they fall. For they at the same time make the Ideas
universal and again treat them as separable and as individuals. That
this is not possible has been argued before. The reason why those
who described their substances as universal combined these two
characteristics in one thing, is that they did not make substances
identical with sensible things. They thought that the particulars in
the sensible world were a state of flux and none of them remained, but
that the universal was apart from these and something different. And
Socrates gave the impulse to this theory, as we said in our earlier
discussion, by reason of his definitions, but he did not separate
universals from individuals; and in this he thought rightly, in not
separating them. This is plain from the results; for without the
universal it is not possible to get knowledge, but the separation is
the cause of the objections that arise with regard to the Ideas. His
successors, however, treating it as necessary, if there are to be
any substances besides the sensible and transient substances, that
they must be separable, had no others, but gave separate existence
to these universally predicated substances, so that it followed that
universals and individuals were almost the same sort of thing
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