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that there are other substances besides the sensible must be
considered next after those we have been mentioning. 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. This in
itself, then, would be one difficulty in the view we have mentioned.

Let us now mention a point which presents a certain difficulty
both to those who believe in the Ideas and to those who do not, and
which was stated before, at the beginning, among the problems. If we
do not suppose substances to be separate, and in the way in which
individual things are said to be separate, we shall destroy
substance in the sense in which we understand 'substance'; but if we
conceive substances to be separable, how are we to conceive their
elements and their principles?
If they are individual and not universal, (a) real things will
be just of the same number as the elements, and (b) the elements
will not be knowable. For (a) let the syllables in speech be
substances, and their elements elements of substances; then there must
be only one 'ba' and one of each of the syllables, since they are
not universal and the same in form but each is one in number and a
'this' and not a kind possessed of a common name (and again they
suppose that the 'just what a thing is' is in each case one). And if
the syllables are unique, so too are the parts of which they
consist; there will not, then, be more a's than one, nor more than one
of any of the other elements, on the same principle on which an
identical syllable cannot exist in the plural number. But if this is
so, there will not be other things existing besides the elements,
but only the elements.
(b) Again, the elements will not be even knowable; for they are
not universal, and knowledge is of universals. This is clear from
demonstrations and from definitions; for we do not conclude that
this triangle has its angles equal to two right angles, unless every
triangle has its angles equal to two right angles, nor that this man
is an animal, unless every man is an animal.
But if the principles are universal, either the substances
composed of them are also universal, or non-substance will be prior to
substance; for the universal is not a substance, but the element or
principle is universal, and the element or principle is prior to the
things of which it is the principle or element.

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