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Metaphysics   


either of an odd or of an even number; in one way, when 1 operates
on an even number, an odd number is produced; in another way, when 2
operates, the numbers got from 1 by doubling are produced; in
another way, when the odd numbers operate, the other even numbers
are produced. Again, if every Idea is an Idea of something, and the
numbers are Ideas, infinite number itself will be an Idea of
something, either of some sensible thing or of something else. Yet
this is not possible in view of their thesis any more than it is
reasonable in itself, at least if they arrange the Ideas as they do.
But if number is finite, how far does it go? With regard to this
not only the fact but the reason should be stated. But if number
goes only up to 10 as some say, firstly the Forms will soon run short;
e.g. if 3 is man-himself, what number will be the horse-itself? The
series of the numbers which are the several things-themselves goes
up to 10. It must, then, be one of the numbers within these limits;
for it is these that are substances and Ideas. Yet they will run
short; for the various forms of animal will outnumber them. At the
same time it is clear that if in this way the 3 is man-himself, the
other 3's are so also (for those in identical numbers are similar), so
that there will be an infinite number of men; if each 3 is an Idea,
each of the numbers will be man-himself, and if not, they will at
least be men. And if the smaller number is part of the greater
(being number of such a sort that the units in the same number are
associable), then if the 4-itself is an Idea of something, e.g. of
'horse' or of 'white', man will be a part of horse, if man is It is
paradoxical also that there should be an Idea of 10 but not of 11, nor
of the succeeding numbers. Again, there both are and come to be
certain things of which there are no Forms; why, then, are there not
Forms of them also? We infer that the Forms are not causes. Again,
it is paradoxical-if the number series up to 10 is more of a real
thing and a Form than 10 itself. There is no generation of the
former as one thing, and there is of the latter. But they try to
work on the assumption that the series of numbers up to 10 is a
complete series. At least they generate the derivatives-e.g. the void,
proportion, the odd, and the others of this kind-within the decade.
For some things, e.g. movement and rest, good and bad, they assign
to the originative principles, and the others to the numbers. This
is why they identify the odd with 1; for if the odd implied 3 how
would 5 be odd? Again, spatial magnitudes and all such things are
explained without going beyond a definite number; e.g. the first,
the indivisible, line, then the 2 &c.; these entities also extend only
up to 10.
Again, if number can exist separately, one might ask which is
prior- 1, or 3 or 2? Inasmuch as the number is composite, 1 is prior,
but inasmuch as the universal and the form is prior, the number is
prior; for each of the units is part of the number as its matter,
and the number acts as form. And in a sense the right angle is prior
to the acute, because it is determinate and in virtue of its
definition; but in a sense the acute is prior, because it is a part
and the right angle is divided into acute angles. As matter, then, the
acute angle and the element and the unit are prior, but in respect
of the form and of the substance as expressed in the definition, the
right angle, and the whole consisting of the matter and the form,
are prior; for the concrete thing is nearer to the form and to what is
expressed in the definition, though in generation it is later. How
then is 1 the starting-point? Because it is not divisiable, they
say; but both the universal, and the particular or the element, are
indivisible. But they are starting-points in different ways, one in
definition and the other in time. In which way, then, is 1 the
starting-point? As has been said, the right angle is thought to be
prior to the acute, and the acute to the right, and each is one.
Accordingly they make 1 the starting-point in both ways. But this is
impossible. For the universal is one as form or substance, while the
element is one as a part or as matter. For each of the two is in a

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