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Let us leave the Pythagoreans for the present; for it is enough to
have touched on them as much as we have done. But as for those who
posit the Ideas as causes, firstly, in seeking to grasp the causes
of the things around us, they introduced others equal in number to
these, as if a man who wanted to count things thought he would not
be able to do it while they were few, but tried to count them when
he had added to their number. For the Forms are practically equal
to-or not fewer than-the things, in trying to explain which these
thinkers proceeded from them to the Forms. For to each thing there
answers an entity which has the same name and exists apart from the
substances, and so also in the case of all other groups there is a one
over many, whether the many are in this world or are eternal.
Further, of the ways in which we prove that the Forms exist,
none is convincing; for from some no inference necessarily follows,
and from some arise Forms even of things of which we think there are
no Forms. For according to the arguments from the existence of the
sciences there will be Forms of all things of which there are sciences
and according to the 'one over many' argument there will be Forms even
of negations, and according to the argument that there is an object
for thought even when the thing has perished, there will be Forms of
perishable things; for we have an image of these. Further, of the more
accurate arguments, some lead to Ideas of relations, of which we say
there is no independent class, and others introduce the 'third man'.
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