The Complete Aristotle (eng.)

it two 2’s other than the 2-itself; if
not, the 2-itself will be a part of 4 and one other 2 will be
added. And similarly 2 will consist of the 1-itself and another 1;
but if this is so, the other element cannot be an indefinite 2; for
it generates one unit, not, as the indefinite 2 does, a definite
2.
    Again, besides the 3-itself and the 2-itself how can there be
other 3’s and 2’s? And how do they consist of prior and posterior
units? All this is absurd and fictitious, and there cannot be a
first 2 and then a 3-itself. Yet there must, if the 1 and the
indefinite dyad are to be the elements. But if the results are
impossible, it is also impossible that these are the generating
principles.
    If the units, then, are differentiated, each from each, these
results and others similar to these follow of necessity. But (3) if
those in different numbers are differentiated, but those in the
same number are alone undifferentiated from one another, even so
the difficulties that follow are no less. E.g. in the 10-itself
their are ten units, and the 10 is composed both of them and of two
5’s. But since the 10-itself is not any chance number nor composed
of any chance 5’s—or, for that matter, units—the units in this 10
must differ. For if they do not differ, neither will the 5’s of
which the 10 consists differ; but since these differ, the units
also will differ. But if they differ, will there be no other 5’s in
the 10 but only these two, or will there be others? If there are
not, this is paradoxical; and if there are, what sort of 10 will
consist of them? For there is no other in the 10 but the 10 itself.
But it is actually necessary on their view that the 4 should not
consist of any chance 2’s; for the indefinite as they say, received
the definite 2 and made two 2’s; for its nature was to double what
it received.
    Again, as to the 2 being an entity apart from its two units, and
the 3 an entity apart from its three units, how is this possible?
Either by one’s sharing in the other, as ‘pale man’ is different
from ‘pale’ and ‘man’ (for it shares in these), or when one is a
differentia of the other, as ‘man’ is different from ‘animal’ and
‘two-footed’.
    Again, some things are one by contact, some by intermixture,
some by position; none of which can belong to the units of which
the 2 or the 3 consists; but as two men are not a unity apart from
both, so must it be with the units. And their being indivisible
will make no difference to them; for points too are indivisible,
but yet a pair of them is nothing apart from the two.
    But this consequence also we must not forget, that it follows
that there are prior and posterior 2 and similarly with the other
numbers. For let the 2’s in the 4 be simultaneous; yet these are
prior to those in the 8 and as the 2 generated them, they generated
the 4’s in the 8-itself. Therefore if the first 2 is an Idea, these
2’s also will be Ideas of some kind. And the same account applies
to the units; for the units in the first 2 generate the four in 4,
so that all the units come to be Ideas and an Idea will be composed
of Ideas. Clearly therefore those things also of which these happen
to be the Ideas will be composite, e.g. one might say that animals
are composed of animals, if there are Ideas of them.
    In general, to differentiate the units in any way is an
absurdity and a fiction; and by a fiction I mean a forced statement
made to suit a hypothesis. For neither in quantity nor in quality
do we see unit differing from unit, and number must be either equal
or unequal-all number but especially that which consists of
abstract units-so that if one number is neither greater nor less
than another, it is equal to it; but things that are equal and in
no wise differentiated we take to be the same when we are speaking
of numbers. If not, not even the 2 in the 10-itself will be
undifferentiated, though they are equal; for what reason will the
man who alleges that they are not differentiated be able to
give?
    Again, if every unit + another unit makes two, a unit from the
2-itself and one from the 3-itself will make a 2. Now (a) this will
consist of differentiated units; and will it be prior to the 3 or
posterior? It rather seems that it must be prior; for one of the
units is simultaneous with the 3 and the other is simultaneous with
the 2. And we, for our part, suppose that in general 1 and 1,
whether the things are equal or unequal, is 2, e.g. the good and
the bad, or