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and if it cannot exist in any of these, evidently number has no such
nature as those who make it separable set up for it.
"Again, does each unit come from the great and the small, equalized,
or one from the small, another from the great? (a) If the latter,
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METAPHYSICS 166
neither does each thing contain all the elements, nor are the units
without difference; for in one there is the great and in another the
small, which is contrary in its nature to the great. Again, how is
it with the units in the 3-itself? One of them is an odd unit. But
perhaps it is for this reason that they give 1-itself the middle place
in odd numbers. (b) But if each of the two units consists of both
the great and the small, equalized, how will the 2 which is a single
thing, consist of the great and the small? Or how will it differ from
the unit? Again, the unit is prior to the 2; for when it is destroyed
the 2 is destroyed. It must, then, be the Idea of an Idea since it
is prior to an Idea, and it must have come into being before it. From
what, then? Not from the indefinite dyad, for its function was to
double.
"Again, number must be either infinite or finite; for these thinkers
think of number as capable of existing separately, so that it is not
possible that neither of those alternatives should be true. Clearly
it cannot be infinite; for infinite number is neither odd nor even,
but the generation of numbers is always the generation 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
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METAPHYSICS 167
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 [ Pobierz całość w formacie PDF ]