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Again, (d) elements are not predicated of the things of which they are
elements, but many and few are predicated both apart and together of
number, and long and short of the line, and both broad and narrow
apply to the plane. If there is a plurality, then, of which the one
term, viz. few, is always predicated, e.g. 2 (which cannot be many,
for if it were many, 1 would be few), there must be also one which
is absolutely many, e.g. 10 is many (if there is no number which is
greater than 10), or 10,000. How then, in view of this, can number
consist of few and many? Either both ought to be predicated of it,
or neither; but in fact only the one or the other is predicated.

We must inquire generally, whether eternal things can consist of
elements. If they do, they will have matter; for everything that
consists of elements is composite. Since, then, even if a thing exists
for ever, out of that of which it consists it would necessarily
also, if it had come into being, have come into being, and since
everything comes to be what it comes to be out of that which is it
potentially (for it could not have come to be out of that which had
not this capacity, nor could it consist of such elements), and since
the potential can be either actual or not,-this being so, however
everlasting number or anything else that has matter is, it must be
capable of not existing, just as that which is any number of years old
is as capable of not existing as that which is a day old; if this is
capable of not existing, so is that which has lasted for a time so
long that it has no limit. They cannot, then, be eternal, since that
which is capable of not existing is not eternal, as we had occasion to
show in another context. If that which we are now saying is true
universally-that no substance is eternal unless it is actuality-and if
the elements are matter that underlies substance, no eternal substance
can have elements present in it, of which it consists.
There are some who describe the element which acts with the One as
an indefinite dyad, and object to 'the unequal', reasonably enough,
because of the ensuing difficulties; but they have got rid only of
those objections which inevitably arise from the treatment of the
unequal, i.e. the relative, as an element; those which arise apart
from this opinion must confront even these thinkers, whether it is
ideal number, or mathematical, that they construct out of those
There are many causes which led them off into these
explanations, and especially the fact that they framed the
difficulty in an obsolete form. For they thought that all things
that are would be one (viz. Being itself), if one did not join issue
with and refute the saying of Parmenides:

'For never will this he proved, that things that are not are.'

They thought it necessary to prove that that which is not is;
for only thus-of that which is and something else-could the things
that are be composed, if they are many.
But, first, if 'being' has many senses (for it means sometimes
substance, sometimes that it is of a certain quality, sometimes that
it is of a certain quantity, and at other times the other categories),
what sort of 'one', then, are all the things that are, if non-being is
to be supposed not to be? Is it the substances that are one, or the
affections and similarly the other categories as well, or all
together-so that the 'this' and the 'such' and the 'so much' and the
other categories that indicate each some one class of being will all
be one? But it is strange, or rather impossible, that the coming
into play of a single thing should bring it about that part of that
which is is a 'this', part a 'such', part a 'so much', part a 'here'.
Secondly, of what sort of non-being and being do the things that
are consist? For 'nonbeing' also has many senses, since 'being' has;
and 'not being a man' means not being a certain substance, 'not

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