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. And so with
a view to their hypothesis their statements are right, but as a
whole they are wrong; for their view is very destructive, since they
will admit that this question itself affords some
difficulty-whether, when we count and say -1,2,3-we count by
addition or by separate portions. But we do both; and so it is
absurd to reason back from this problem to so great a difference of
essence.
8
First of all it is well to determine what is the differentia of
a number-and of a unit, if it has a differentia. Units must differ
either in quantity or in quality; and neither of these seems to be
possible. But number qua number differs in quantity. And if the
units also did differ in quantity, number would differ from number,
though equal in number of units. Again, are the first units greater or
smaller, and do the later ones increase or diminish? All these are
irrational suppositions. But neither can they differ in quality. For
no attribute can attach to them; for even to numbers quality is said
to belong after quantity. Again, quality could not come to them either
from the 1 or the dyad; for the former has no quality, and the
latter gives quantity; for this entity is what makes things to be
many. If the facts are really otherwise, they should state this
quite at the beginning and determine if possible, regarding the
differentia of the unit, why it must exist, and, failing this, what
differentia they mean
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