But this is not possible, if there is a first and a second
number.
Nor will the Ideas be numbers. For in this particular point they
are right who claim that the units must be different, if there are
to be Ideas; as has been said before. For the Form is unique; but if
the units are not different, the 2's and the 3's also will not be
different. This is also the reason why they must say that when we
count thus-'1,2'-we do not proceed by adding to the given number;
for if we do, neither will the numbers be generated from the
indefinite dyad, nor can a number be an Idea; for then one Idea will
be in another, and all Forms will be parts of one Form. 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.
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