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. But those who wished to make the
Forms at the same time also numbers, but did not see, if one assumed
these principles, how mathematical number was to exist apart from
ideal, made ideal and mathematical number the 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
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