The Complete Aristotle (eng.)

same-in words, since in fact mathematical
number has been destroyed; for they state hypotheses peculiar to
themselves and not those of mathematics. And he who first supposed
that the Forms exist and that the Forms are numbers and that the
objects of mathematics exist, naturally separated the two.
Therefore it turns out that all of them are right in some respect,
but on the whole not right. And they themselves confirm this, for
their statements do not agree but conflict. The cause is that their
hypotheses and their principles are false. And it is hard to make a
good case out of bad materials, according to Epicharmus: ‘as soon
as ‘tis said, ‘tis seen to be wrong.’
    But regarding numbers the questions we have raised and the
conclusions we have reached are sufficient (for while he who is
already convinced might be further convinced by a longer
discussion, one not yet convinced would not come any nearer to
conviction); regarding the first principles and the first causes
and elements, the views expressed by those who discuss only
sensible substance have been partly stated in our works on nature,
and partly do not belong to the present inquiry; but the views of
those who assert 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.
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10
    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