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991b]
[1]
Further, it would seem impossible that the
substance and the thing of which it is the substance exist in
separation; hence how can the Ideas, if they are the substances of
things, exist in separation from them?
1 It is stated in the
Phaedo2 that the
Forms are the causes both of existence and of generation.Yet, assuming that the Forms
exist, still the things which participate in them are not generated
unless there is something to impart motion; while many other things
are generated (e.g. house, ring) of which we hold
that there are no Forms. Thus it is clearly possible that all other
things may both exist and be generated for the same causes as the
things just mentioned.
Further, if the Forms are
numbers, in what sense will they be causes? Is it because things are
other numbers, e.g. such and such a number Man, such and such another
Socrates, such and such
another Callias? then why are those numbers the causes of these? Even
if the one class is eternal and the other not, it will make no
difference.And if
it is because the things of our world are ratios of numbers (e.g. a
musical concord), clearly there is some one class of things of which
they are ratios. Now if there is this something, i.e. their
matter , clearly the numbers themselves will be
ratios of one thing to another.I mean, e.g., that if Callias is a numerical
ratio of fire, earth, water and air, the corresponding Idea too will
be a number of certain other things which are its substrate. The Idea
of Man, too, whether it is in a sense a number or not, will yet be an
arithmetical ratio of certain things,
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and not a mere number; nor, on these grounds, will
any Idea be a number.
3Again,
one number can be composed of several numbers, but how can one Form be
composed of several Forms? And if the one number is not composed of
the other numbers themselves, but of their constituents (e.g. those of
the number 10,000), what is the relation of the units? If they are
specifically alike, many absurdities will result, and also if they are
not (whether (a) the units in a given number are unlike, or (b) the
units in each number are unlike those in every other number).
4 For in
what can they differ, seeing that they have no qualities? Such a view
is neither reasonable nor compatible with our conception of
units.
Further, it becomes necessary to set up
another kind of number (with which calculation deals), and all the
objects which are called "intermediate" by some thinkers.
5 But how or
from what principles can these be derived? or on what grounds are they
to be considered intermediate between things
here and
Ideal numbers? Further, each of the units in the number 2 comes from a
prior 2; but this is impossible.
6