9. It must therefore be granted that in the things of which we
first spoke, such as knowing and doing (active being), there is an
actualization, an habituation, and an actualizing reason; while in the
other things there is a participation in form and reason. For indeed,
if the bodies were the only essences, the relative habituations would
bear no reality. If, on the contrary, we assign the first rank in
existence to incorporeal things, and to the reasons, and if we define
the habituations as reasons that participate in the forms, we should
say that what is double has the double for its cause, and what is
half, has the half as its cause; and that other things are what they
are named because of the presence of the same, or of the contrary
form. Now either two things simultaneously receive one the double,
and the other the half, and one greatness, and the other smallness;
or contraries such as resemblance and dissimilarity are to be found
in each thing, as well as identity and difference; and everything
finds itself simultaneously similar and dissimilar, identical and
different. It might be objected that if one object were ugly, and
another uglier still, they are such because they participate in a form.
Not so; for if these two objects be equally ugly, they are equal in
the absence of the form. If they be unequally ugly, the least ugly is
such because it participates in a form which does not sufficiently
subdue matter, and the uglier is such because it participates in a
form which does so still less. They could, besides, be judged from the
standpoint of deprivation, comparing them to each other as if they
contained some form. The sensation is a form that results from two
things (of that which feels, and that which is felt); so also with
knowledge. In respect to the thing possessed, possession is an act
which contains, which has a kind of efficacy. As to mensuration, which
is an actualization of measure, in respect of the measured object, it
consists in a reason.
WHILE SOME ARISTOTELIAN CATEGORIES ARE LOGICALLY POSSIBLE, THE OBJECTS
SUBSUMED ARE IMPOSSIBLE.
If then, considering the constitution of the relative relations as a
generic form, it be admitted that it constitutes an unity, it forms
a classification; consequently it constitutes an existence and a
form in all things. But if the reasons (or, relations) be opposed to
each other, if the above-mentioned differences obtain among them,
they do not constitute a class, and everything must be reduced to a
resemblance, or category. Now, even if we admit that the things of
which we have spoken can be reduced to a unity, it does not follow that
all the things gathered under the same category by the Aristotelians,
could be reduced to a single sort. Indeed, they lump together into
the same classification, both objects and mere statements of their
absence, as well as the objects which derive their appellation from
them; as, for instance, doubleness itself, and the double object.
Now how is it possible to reduce to the same classification both a
thing and the mere lack of it, as, for instance, doubleness and the
non-double, the relative and the non-relative? This is as absurd as it
would be to gather into the same classification the living "being,"
and the non-living "being." Worse yet, how could one assort together
duplication and the double object, whiteness and the white object? Such
things could not possibly be identical.