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One might fix one's attention also on the question, regarding
the numbers, what justifies the belief that they exist. To the
believer in Ideas they provide some sort of cause for existing things,
since each number is an Idea, and the Idea is to other things
somehow or other the cause of their being; for let this supposition be
granted them. But as for him who does not hold this view because he
sees the inherent objections to the Ideas (so that it is not for
this reason that he posits numbers), but who posits mathematical
number, why must we believe his statement that such number exists, and
of what use is such number to other things? Neither does he who says
it exists maintain that it is the cause of anything (he rather says it
is a thing existing by itself), nor is it observed to be the cause
of anything; for the theorems of arithmeticians will all be found true
even of sensible things, as was said before.
3
As for those, then, who suppose the Ideas to exist and to be
numbers, by their assumption in virtue of the method of setting out
each term apart from its instances-of the unity of each general term
they try at least to explain somehow why number must exist. Since
their reasons, however, are neither conclusive nor in themselves
possible, one must not, for these reasons at least, assert the
existence of number. Again, the Pythagoreans, because they saw many
attributes of numbers belonging te sensible bodies, supposed real
things to be numbers-not separable numbers, however, but numbers of
which real things consist
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