If with others, it must deal either with the
Forms or with the objects of mathematics. Now (a) evidently the
Forms do not exist. (But it is hard to say, even if one suppose them
to exist, why in the world the same is not true of the other things of
which there are Forms, as of the objects of mathematics. I mean that
these thinkers place the objects of mathematics between the Forms
and perceptible things, as a kind of third set of things apart both
from the Forms and from the things in this world; but there is not a
third man or horse besides the ideal and the individuals. If on the
other hand it is not as they say, with what sort of things must the
mathematician be supposed to deal? Certainly not with the things in
this world; for none of these is the sort of thing which the
mathematical sciences demand.) Nor (b) does the science which we are
now seeking treat of the objects of mathematics; for none of them
can exist separately. But again it does not deal with perceptible
substances; for they are perishable.
In general one might raise the question, to what kind of science
it belongs to discuss the difficulties about the matter of the objects
of mathematics. Neither to physics (because the whole inquiry of the
physicist is about the things that have in themselves a principle.
of movement and rest), nor yet to the science which inquires into
demonstration and science; for this is just the subject which it
investigates. It remains then that it is the philosophy which we
have set before ourselves that treats of those subjects.
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