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Aristotle - Metaphysics
Atec Февраль 16 2008 19:57:08
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. (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. And
similarly 2 will consist of the 1-itself and another 1; but if this is
so, the other element cannot be an indefinite 2; for it generates
one unit, not, as the indefinite 2 does, a definite 2.
Again, besides the 3-itself and the 2-itself how can there be
other 3's and 2's? And how do they consist of prior and posterior
units? All this is absurd and fictitious, and there cannot be a
first 2 and then a 3-itself
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