Again, how is it possible to solve the questions which we have
already enumerated in our discussion of difficulties? For the
objects of astronomy will exist apart from sensible things just as the
objects of geometry will; but how is it possible that a heaven and its
parts-or anything else which has movement-should exist apart?
Similarly also the objects of optics and of harmonics will exist
apart; for there will be both voice and sight besides the sensible
or individual voices and sights. Therefore it is plain that the
other senses as well, and the other objects of sense, will exist
apart; for why should one set of them do so and another not? And if
this is so, there will also be animals existing apart, since there
will be senses.
Again, there are certain mathematical theorems that are universal,
extending beyond these substances. Here then we shall have another
intermediate substance separate both from the Ideas and from the
intermediates,-a substance which is neither number nor points nor
spatial magnitude nor time. And if this is impossible, plainly it is
also impossible that the former entities should exist separate from
sensible things.
And, in general, conclusion contrary alike to the truth and to the
usual views follow, if one is to suppose the objects of mathematics to
exist thus as separate entities. For because they exist thus they must
be prior to sensible spatial magnitudes, but in truth they must be
posterior; for the incomplete spatial magnitude is in the order of
generation prior, but in the order of substance posterior, as the
lifeless is to the living.
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