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. We must therefore
examine this argument too, and see whether it is not remarkably
weak. For (i) extremes are not substances, but rather all these things
are limits. For even walking, and movement in general, has a limit, so
that on their theory this will be a 'this' and a substance. But that
is absurd. Not but what (ii) even if they are substances, they will
all be the substances of the sensible things in this world; for it
is to these that the argument applied. Why then should they be capable
of existing apart?
Again, if we are not too easily satisfied, we may, regarding all
number and the objects of mathematics, press this difficulty, that
they contribute nothing to one another, the prior to the posterior;
for if number did not exist, none the less spatial magnitudes would
exist for those who maintain the existence of the objects of
mathematics only, and if spatial magnitudes did not exist, soul and
sensible bodies would exist. But the observed facts show that nature
is not a series of episodes, like a bad tragedy. As for the
believers in the Ideas, this difficulty misses them; for they
construct spatial magnitudes out of matter and number, lines out of
the number planes doubtless out of solids out of or they use other
numbers, which makes no difference. But will these magnitudes be
Ideas, or what is their manner of existence, and what do they
contribute to things? These contribute nothing, as the objects of
mathematics contribute nothing
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