For what sort of number will man-himself or
animal-itself or any other Form be? There is one Idea of each thing
e.g. one of man-himself and another one of animal-itself; but the
similar and undifferentiated numbers are infinitely many, so that
any particular 3 is no more man-himself than any other 3. But if the
Ideas are not numbers, neither can they exist at all. For from what
principles will the Ideas come? It is number that comes from the 1 and
the indefinite dyad, and the principles or elements are said to be
principles and elements of number, and the Ideas cannot be ranked as
either prior or posterior to the numbers.
But (2) if the units are inassociable, and inassociable in the
sense that any is inassociable with any other, number of this sort
cannot be mathematical number; for mathematical number consists of
undifferentiated units, and the truths proved of it suit this
character. Nor can it be ideal number. For 2 will not proceed
immediately from 1 and the indefinite dyad, and be followed by the
successive numbers, as they say '2,3,4' for the units in the ideal are
generated at the same time, whether, as the first holder of the theory
said, from unequals (coming into being when these were equalized) or
in some other way-since, if one unit is to be prior to the other, it
will be prior also to 2 the composed of these; for when there is one
thing prior and another posterior, the resultant of these will be
prior to one and posterior to the other. Again, since the 1-itself is
first, and then there is a particular 1 which is first among the
others and next after the 1-itself, and again a third which is next
after the second and next but one after the first 1,-so the units must
be prior to the numbers after which they are named when we count them;
e.
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