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Aristotle

"Metaphysics"

g. there will be a third unit in 2 before 3 exists, and a fourth and
a fifth in 3 before the numbers 4 and 5 exist.-Now none of these
thinkers has said the units are inassociable in this way, but
according to their principles it is reasonable that they should be
so even in this way, though in truth it is impossible. For it is
reasonable both that the units should have priority and posteriority
if there is a first unit or first 1, and also that the 2's should if
there is a first 2; for after the first it is reasonable and necessary
that there should be a second, and if a second, a third, and so with
the others successively. (And to say both things at the same time,
that a unit is first and another unit is second after the ideal 1, and
that a 2 is first after it, is impossible.) But they make a first unit
or 1, but not also a second and a third, and a first 2, but not also a
second and a third. Clearly, also, it is not possible, if all the
units are inassociable, that there should be a 2-itself and a
3-itself; and so with the other numbers. For whether the units are
undifferentiated or different each from each, number must be counted
by addition, e.g. 2 by adding another 1 to the one, 3 by adding
another 1 to the two, and similarly. This being so, numbers cannot
be generated as they generate them, from the 2 and the 1; for 2
becomes part of 3 and 3 of 4 and the same happens in the case of the
succeeding numbers, but they say 4 came from the first 2 and the
indefinite which makes it two 2's other than the 2-itself; if not, the
2-itself will be a part of 4 and one other 2 will be added.


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