The Complete Aristotle (eng.)

number, that of the Forms and that which is
mathematical, neither have said nor can say how mathematical number
is to exist and of what it is to consist. For they place it between
ideal and sensible number. If (i) it consists of the great and
small, it will be the same as the other-ideal-number (he makes
spatial magnitudes out of some other small and great). And if (ii)
he names some other element, he will be making his elements rather
many. And if the principle of each of the two kinds of number is a
1, unity will be something common to these, and we must inquire how
the one is these many things, while at the same time number,
according to him, cannot be generated except from one and an
indefinite dyad.
    All this is absurd, and conflicts both with itself and with the
probabilities, and we seem to see in it Simonides ‘long rigmarole’
for the long rigmarole comes into play, like those of slaves, when
men have nothing sound to say. And the very elements-the great and
the small-seem to cry out against the violence that is done to
them; for they cannot in any way generate numbers other than those
got from 1 by doubling.
    It is strange also to attribute generation to things that are
eternal, or rather this is one of the things that are impossible.
There need be no doubt whether the Pythagoreans attribute
generation to them or not; for they say plainly that when the one
had been constructed, whether out of planes or of surface or of
seed or of elements which they cannot express, immediately the
nearest part of the unlimited began to be constrained and limited
by the limit. But since they are constructing a world and wish to
speak the language of natural science, it is fair to make some
examination of their physical theorics, but to let them off from
the present inquiry; for we are investigating the principles at
work in unchangeable things, so that it is numbers of this kind
whose genesis we must study.
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    These thinkers say there is no generation of the odd number,
which evidently implies that there is generation of the even; and
some present the even as produced first from unequals-the great and
the small-when these are equalized. The inequality, then, must
belong to them before they are equalized. If they had always been
equalized, they would not have been unequal before; for there is
nothing before that which is always. Therefore evidently they are
not giving their account of the generation of numbers merely to
assist contemplation of their nature.
    A difficulty, and a reproach to any one who finds it no
difficulty, are contained in the question how the elements and the
principles are related to the good and the beautiful; the
difficulty is this, whether any of the elements is such a thing as
we mean by the good itself and the best, or this is not so, but
these are later in origin than the elements. The theologians seem
to agree with some thinkers of the present day, who answer the
question in the negative, and say that both the good and the
beautiful appear in the nature of things only when that nature has
made some progress. (This they do to avoid a real objection which
confronts those who say, as some do, that the one is a first
principle. The objection arises not from their ascribing goodness
to the first principle as an attribute, but from their making the
one a principle-and a principle in the sense of an element-and
generating number from the one.) The old poets agree with this
inasmuch as they say that not those who are first in time, e.g.
Night and Heaven or Chaos or Ocean, reign and rule, but Zeus. These
poets, however, are led to speak thus only because they think of
the rulers of the world as changing; for those of them who combine
the two characters in that they do not use mythical language
throughout, e.g. Pherecydes and some others, make the original
generating agent the Best, and so do the Magi, and some of the
later sages also, e.g. both Empedocles and Anaxagoras, of whom one
made love an element, and the other made reason a principle. Of
those who maintain the existence of the unchangeable substances
some say the One itself is the good itself; but they thought its
substance lay mainly in its unity.
    This, then, is the problem,-which of the two ways of speaking is
right. It would be strange if to that which is primary and eternal
and most self-sufficient this very quality—self-sufficiency and
self-maintenance—belongs primarily in some other way