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offer are abstract,-with this exception, that if the exceeding and the
exceeded are the principles, and not the great and the small,
consistency requires that number should come from the elements
before does; for number is more universal than as the exceeding and
the exceeded are more universal than the great and the small. But as
it is, they say one of these things but do not say the other. Others
oppose the different and the other to the One, and others oppose
plurality to the One. But if, as they claim, things consist of
contraries, and to the One either there is nothing contrary, or if
there is to be anything it is plurality, and the unequal is contrary
to the equal, and the different to the same, and the other to the
thing itself, those who oppose the One to plurality have most claim to
plausibility, but even their view is inadequate, for the One would
on their view be a few; for plurality is opposed to fewness, and the
many to the few.
'The one' evidently means a measure. And in every case there is
some underlying thing with a distinct nature of its own, e.g. in the
scale a quarter-tone, in spatial magnitude a finger or a foot or
something of the sort, in rhythms a beat or a syllable; and
similarly in gravity it is a definite weight; and in the same way in
all cases, in qualities a quality, in quantities a quantity (and the
measure is indivisible, in the former case in kind, and in the
latter to the sense); which implies that the one is not in itself
the substance of anything. And this is reasonable; for 'the one' means
the measure of some plurality, and 'number' means a measured plurality
and a plurality of measures. (Thus it is natural that one is not a
number; for the measure is not measures, but both the measure and
the one are starting-points.) The measure must always be some
identical thing predicable of all the things it measures, e.g. if
the things are horses, the measure is 'horse', and if they are men,
'man'. If they are a man, a horse, and a god, the measure is perhaps
'living being', and the number of them will be a number of living
beings. If the things are 'man' and 'pale' and 'walking', these will
scarcely have a number, because all belong to a subject which is one
and the same in number, yet the number of these will be a number of
'kinds' or of some such term.
Those who treat the unequal as one thing, and the dyad as an
indefinite compound of great and small, say what is very far from
being probable or possible. For (a) these are modifications and
accidents, rather than substrata, of numbers and magnitudes-the many
and few of number, and the great and small of magnitude-like even
and odd, smooth and rough, straight and curved. Again, (b) apart
from this mistake, the great and the small, and so on, must be
relative to something; but what is relative is least of all things a
kind of entity or substance, and is posterior to quality and quantity;
and the relative is an accident of quantity, as was said, not its
matter, since something with a distinct nature of its own must serve
as matter both to the relative in general and to its parts and
kinds. For there is nothing either great or small, many or few, or, in
general, relative to something else, which without having a nature
of its own is many or few, great or small, or relative to something
else. A sign that the relative is least of all a substance and a
real thing is the fact that it alone has no proper generation or
destruction or movement, as in respect of quantity there is increase
and diminution, in respect of quality alteration, in respect of
place locomotion, in respect of substance simple generation and
destruction. In respect of relation there is no proper change; for,
without changing, a thing will be now greater and now less or equal,
if that with which it is compared has changed in quantity. And (c) the
matter of each thing, and therefore of substance, must be that which
is potentially of the nature in question; but the relative is
neither potentially nor actually substance. It is strange, then, or
rather impossible, to make not-substance an element in, and prior
to, substance; for all the categories are posterior to substance.

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