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. 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.
One might discuss the question whether the science we are
seeking should be said to deal with the principles which are by some
called elements; all men suppose these to be present in composite
things. But it might be thought that the science we seek should
treat rather of universals; for every definition and every science
is of universals and not of infimae species, so that as far as this
goes it would deal with the highest genera
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