[
992b]
[1]
Further, one might regard the substance
which they make the material substrate as too mathematical, and as
being a predicate and differentia of substance or matter rather than
as matter itself, I mean the "Great and Small," which is like the
"Rare and Dense" of which the physicists speak,
1 holding that they are the
primary differentiae of the substrate; because these qualities are a
species of excess and defect.Also with regard to motion, if the "Great and
Small" is to constitute motion, obviously the Forms will be moved; if
not, whence did it come? On this view the whole study of physics is
abolished. And what is supposed to be easy, to prove that everything
is One, does not follow; because from their exposition
2 it
does not follow, even if you grant them all their assumptions that
everything is One, but only that there is an absolute
One—and
not even this, unless you grant that the universal is a class; which
is impossible in some cases.
3 Nor
is there any explanation of the lines, planes and solids which "come
after" the Numbers
4: neither as to how they exist or can exist, nor as
to what their importance is. They cannot be Forms (since they are not
numbers) or Intermediates (which are the objects of mathematics) or
perishables; clearly they form yet another fourth class.
In general, to investigate the elements of existing things without
distinguishing the various senses in which things are said to exist is
a hopeless task;
[20]
especially
when one inquires along these lines into the nature of the elements of
which things are composed. For (a) we cannot surely conceive of the
elements of activity or passivity or straightness; this is possible,
if at all, only in the case of substances. Hence to look for, or to
suppose that one has found, the elements of
everything
that exists, is a mistake.(b) How
can one apprehend the elements of
everything ? Obviously one could not have any
previous knowledge of anything; because just as a man who is beginning
to learn geometry can have previous knowledge of other facts, but no
previous knowledge of the principles of that science or of the things
about which he is to learn, so it is in the case of all other branches
of knowledge.Hence if
there is a science which embraces everything
5(as
some say), the student of it can have no previous knowledge at all.
But all learning proceeds, wholly or in part, from what is already
known; whether it is through demonstration or through
definition—since the parts of the definition must be already
known and familiar. The same is true of induction.