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. Now (1)
the accumulation becomes absurd; for we find ourselves with one set of
solids apart from the sensible solids; three sets of planes apart from
the sensible planes-those which exist apart from the sensible
planes, and those in the mathematical solids, and those which exist
apart from those in the mathematical solids; four sets of lines, and
five sets of points. With which of these, then, will the
mathematical sciences deal? Certainly not with the planes and lines
and points in the motionless solid; for science always deals with what
is prior. And (the same account will apply also to numbers; for
there will be a different set of units apart from each set of
points, and also apart from each set of realities, from the objects of
sense and again from those of thought; so that there will be various
classes of mathematical numbers.
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
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