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7
First, then, let us inquire if the units are associable or
inassociable, and if inassociable, in which of the two ways we
distinguished. For it is possible that any unity is inassociable
with any, and it is possible that those in the 'itself' are
inassociable with those in the 'itself', and, generally, that those in
each ideal number are inassociable with those in other ideal
numbers. Now (1) all units are associable and without difference, we
get mathematical number-only one kind of number, and the Ideas
cannot be the numbers. 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
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