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. Things of this other sort, then, he called
Ideas, and sensible things, he said, were all named after these, and
in virtue of a relation to these; for the many existed by
participation in the Ideas that have the same name as they. Only the
name 'participation' was new; for the Pythagoreans say that things
exist by 'imitation' of numbers, and Plato says they exist by
participation, changing the name. But what the participation or the
imitation of the Forms could be they left an open question.
Further, besides sensible things and Forms he says there are the
objects of mathematics, which occupy an intermediate position,
differing from sensible things in being eternal and unchangeable, from
Forms in that there are many alike, while the Form itself is in each
case unique.
Since the Forms were the causes of all other things, he thought
their elements were the elements of all things. As matter, the great
and the small were principles; as essential reality, the One; for from
the great and the small, by participation in the One, come the
Numbers.
But he agreed with the Pythagoreans in saying that the One is
substance and not a predicate of something else; and in saying that
the Numbers are the causes of the reality of other things he agreed
with them; but positing a dyad and constructing the infinite out of
great and small, instead of treating the infinite as one, is
peculiar to him; and so is his view that the Numbers exist apart
from sensible things, while they say that the things themselves are
Numbers, and do not place the objects of mathematics between Forms and
sensible things
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