For
the objects of astronomy will similarly be distinct from sensible
things, and so will those of geometry; but how can a heaven and its
parts (or anything else which has motion) exist apart from the
sensible heaven? And similarly the objects of optics and of harmonics
will be distinct, for there will be sound and sight apart from the
sensible and particular objects.Hence clearly the other senses and objects of
sense will exist separately; for why should one class of objects do so
rather than another? And if this is so, animals too will exist
separately, inasmuch as the senses will.Again, there are certain general mathematical theorems which are not
restricted to these substances.Here, then, we shall have yet another kind of
substance intermediate between and distinct from the Ideas and the
intermediates, which is neither number nor points nor spatial
magnitude nor time. And if this is impossible, clearly it is also
impossible that the aforesaid substances should exist separately from
sensible objects. In general, consequences result which
are contrary both to the truth and to received opinion if we thus
posit the objects of mathematics as definite separately-existent
entities. For if they exist in this way, they must be prior to
sensible spatial magnitudes, whereas in truth they must be posterior
to them; for the incomplete spatial magnitude is in point of
generation prior, but in point of substantiality posterior,as the inanimate is to the
animate. Again, in virtue of what can we
possibly regard mathematical magnitudes as one? Things in this world
of ours may be reasonably supposed to be one in virtue of soul or part
of the soul, or some other influence; apart from this they are a
plurality and are disintegrated. But inasmuch as the former are
divisible and quantitative, what is the cause of their unity and
cohesion?Again, the ways in which
the objects of mathematics are generated prove our point;for they are generated first
in the dimension of length, then in that of breadth, and finally in
that of depth, whereupon the process is complete. Thus if that which
is posterior in generationi.e.,
in the natural order of development. Thus "generation" (γένεσις) is used in two different
senses in this argument, which therefore becomes invalid
(Bonitz). is prior in substantiality, body will be prior
to plane and line, and in this sense it will also be more truly
complete and whole, because it can become animate; whereas how could a
line or plane be animate? The supposition is beyond our powers of
apprehension. Further, body is a kind of substance,
since it already in some sense possesses completeness; but in what
sense are lines substances? Neither as being a kind of form or shape,
as perhaps the soul is, nor as being matter, like the body; for it
does not appear that anything can be composed either of lines or of
planes or of points,whereas if they were a kind of material substance it would be
apparent that things can be so composed.