[1059b]
[1]
or not with sensible substances, but with some
other kind.1 If with another kind, it must
be concerned either with the Forms or with mathematical objects. Now
clearly the Forms do not exist. (But nevertheless, even if we posit
them, it is a difficult question as to why the same rule does not
apply to the other things of which there are Forms as applies to the
objects of mathematics.I
mean that they posit the objects of mathematics as intermediate
between the Forms and sensible things, as a third class besides the
Forms and the things of our world; but there is no "third man"2
or "horse" besides the Ideal one and the particulars. If on the other
hand it is not as they make out, what sort of objects are we to
suppose to be the concern of the mathematician? Not surely the things
of our world; for none of these is of the kind which the mathematical
sciences investigate.)Nor
indeed is the science which we are now seeking concerned with the
objects of mathematics; for none of them can exist separately. But it
does not deal with sensible substances either; for they are
perishable.In general the
question might be raised, to what science it pertains to discuss the
problems concerned with the matter3 of mathematical objects.It is not the province of physics,
because the whole business of the physicist is with things which
contain in themselves a principle of motion and rest; nor yet of the
science which inquires into demonstration andscientific knowledge,
[20]
for it is simply this sort of thing which forms the
subject of its inquiry. It remains, therefore, that it is the science
which we have set ourselves to find that treats of these
subjects. One might consider the question
whether we should regard the science which we are now seeking as
dealing with the principles which by some are called elements.4 But everyone assumes that these are
present in composite things; and it would seem rather that the science
which we are seeking must be concerned with universals, since every
formula and every science is of universals and not of ultimate
species; so that in this case it must deal with the primary
genera.These would
be Being and Unity; for these, if any, might best be supposed to
embrace all existing things, and to be most of the nature of first
principles, because they are by nature primary; for if they are
destroyed, everything else is destroyed with them, since everything
exists and is one.But
inasmuch as, if Being and Unity are to be regarded as genera, they
must be predicable of their differentiae, whereas no genus is
predicable of any of its differentiae, from this point of view it
would seem that they should be regarded neither as genera nor as
principles.Further,
since the more simple is more nearly a principle than the less simple,
and the ultimate subdivisions of the genus are more simple than the
genera (because they are indivisible), and the genera are divided into
a number of different species, it would seem that species are more
nearly a principle than genera.On the other hand, inasmuch as species are
destroyed together with their genera, it seems more likely that the
genera are principles;
1 Cf. Aristot. Met. 3.1.7, Aristot. Met.3.2.20-30.
2 This phrase has no technical sense here; cf. Aristot. Met. 1.9.4.
3 i.e., intelligible matter (cf. Aristot. Met. 7.10.18). This problem is not raised in Book 3.
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