The Complete Aristotle (eng.)

matter, assert that number is substance? How are we to think
of ‘two’, and each of the other numbers composed of units, as one?
On this point neither do they say anything nor is it easy to say
anything. But if we are to suppose lines or what comes after these
(I mean the primary surfaces) to be principles, these at least are
not separable substances, but sections and divisions-the former of
surfaces, the latter of bodies (while points are sections and
divisions of lines); and further they are limits of these same
things; and all these are in other things and none is separable.
Further, how are we to suppose that there is a substance of unity
and the point? Every substance comes into being by a gradual
process, but a point does not; for the point is a division.
    A further difficulty is raised by the fact that all knowledge is
of universals and of the ‘such’, but substance is not a universal,
but is rather a ‘this’-a separable thing, so that if there is
knowledge about the first principles, the question arises, how are
we to suppose the first principle to be substance?
    Further, is there anything apart from the concrete thing (by
which I mean the matter and that which is joined with it), or not?
If not, we are met by the objection that all things that are in
matter are perishable. But if there is something, it must be the
form or shape. Now it is hard to determine in which cases this
exists apart and in which it does not; for in some cases the form
is evidently not separable, e.g. in the case of a house.
    Further, are the principles the same in kind or in number? If
they are one in number, all things will be the same.
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3
    Since the science of the philosopher treats of being qua being
universally and not in respect of a part of it, and ‘being’ has
many senses and is not used in one only, it follows that if the
word is used equivocally and in virtue of nothing common to its
various uses, being does not fall under one science (for the
meanings of an equivocal term do not form one genus); but if the
word is used in virtue of something common, being will fall under
one science. The term seems to be used in the way we have
mentioned, like ‘medical’ and ‘healthy’. For each of these also we
use in many senses. Terms are used in this way by virtue of some
kind of reference, in the one case to medical science, in the other
to health, in others to something else, but in each case to one
identical concept. For a discussion and a knife are called medical
because the former proceeds from medical science, and the latter is
useful to it. And a thing is called healthy in a similar way; one
thing because it is indicative of health, another because it is
productive of it. And the same is true in the other cases.
Everything that is, then, is said to ‘be’ in this same way; each
thing that is is said to ‘be’ because it is a modification of being
qua being or a permanent or a transient state or a movement of it,
or something else of the sort. And since everything that is may be
referred to something single and common, each of the contrarieties
also may be referred to the first differences and contrarieties of
being, whether the first differences of being are plurality and
unity, or likeness and unlikeness, or some other differences; let
these be taken as already discussed. It makes no difference whether
that which is be referred to being or to unity. For even if they
are not the same but different, at least they are convertible; for
that which is one is also somehow being, and that which is being is
one.
    But since every pair of contraries falls to be examined by one
and the same science, and in each pair one term is the privative of
the other though one might regarding some contraries raise the
question, how they can be privately related, viz. those which have
an intermediate, e.g. unjust and just-in all such cases one must
maintain that the privation is not of the whole definition, but of
the infima species. if the just man is ‘by virtue of some permanent
disposition obedient to the laws’, the unjust man will not in every
case have the whole definition denied of him, but may be merely ‘in
some respect deficient in obedience to the laws’, and in this
respect the privation will attach to him; and similarly in all
other cases.
    As the mathematician investigates abstractions (for before
beginning his investigation he strips off all the sensible
qualities,