13. Now why should we not posit quantity among the primary genera? And
why not also quality? Quantity is not one of the primary genera like
those we have posited, because the primary genera coexist with essence
(which is not the case with quantity). Indeed, movement is inseparable
from essence; being its actualization and life. Stability is implied in
being; while identity and difference are still more inseparable from
essence; so that all these (categories) appear to us simultaneously. As
to number (which is discrete quantity), it is something posterior. As
to (mathematical) numbers, far more are they posterior both to these
genera, and themselves; for the numbers follow each other; the second
depends on the first, and so forth; the last are contained within the
first. Number, therefore, cannot be posited among the primary genera.
Indeed, it is permissible to doubt whether quantity may be posited
as any kind of a genus. More even than number, extension (which is
continuous quantity), shows the characteristics of compositeness, and
of posteriority. Along with number, the line enters into the idea of
extension. This would make two elements. Then comes surface, which
makes three. If then it be from number that continuous dimension
derives its quantitativeness, how could this dimension be a genus, when
number is not? On the other hand, anteriority and posteriority exist
in dimension as well as in numbers. But if both kinds of quantities
have in common this, that they are quantities, it will be necessary to
discover the nature of quantity. When this will have been found, we
shall be able to make of it a secondary genus; but it could not rank
with the primary genera. If, then, quantity be a genus without being a
primary one, it will still remain for us to discover to which higher
genus, whether primary or secondary, it should be subsumed.
NUMBER AND DIMENSION DIFFER SO MUCH AS TO SUGGEST DIFFERENT
CLASSIFICATION.
It is evident that quantity informs us of the amount of a thing,
and permits us to measure this; therefore itself must be an amount.
This then is the element common to number (the discrete quantity),
and to continuous dimension. But number is anterior, and continuous
dimension proceeds therefrom; number consists in a certain blending
of movement and stability; continuous dimension is a certain movement
or proceeds from some movement; movement produces it in its progress
towards infinity, but stability arrests it in its progress, limits
it, and creates unity. Besides, we shall in the following explain the
generation of number and dimension; and, what is more, their mode of
existence, and how to conceive of it rightly. It is possible that we
might find that number should be posited among the primary genera, but
that, because of its composite nature, continuous dimension should
be posited among the posterior or later genera; that number is to be
posited among stable things, while dimension belongs among those in
movement. But, as said above, all this will be treated of later.