So that the subject of our discussion will be not
whether they exist but how they exist.
2
That it is impossible for mathematical objects to exist in
sensible things, and at the same time that the doctrine in question is
an artificial one, has been said already in our discussion of
difficulties we have pointed out that it is impossible for two
solids to be in the same place, and also that according to the same
argument the other powers and characteristics also should exist in
sensible things and none of them separately. This we have said
already. But, further, it is obvious that on this theory it is
impossible for any body whatever to be divided; for it would have to
be divided at a plane, and the plane at a line, and the line at a
point, so that if the point cannot be divided, neither can the line,
and if the line cannot, neither can the plane nor the solid. What
difference, then, does it make whether sensible things are such
indivisible entities, or, without being so themselves, have
indivisible entities in them? The result will be the same; if the
sensible entities are divided the others will be divided too, or
else not even the sensible entities can be divided.
But, again, it is not possible that such entities should exist
separately. For if besides the sensible solids there are to be other
solids which are separate from them and prior to the sensible
solids, it is plain that besides the planes also there must be other
and separate planes and points and lines; for consistency requires
this.
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