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Metaphysics   


heavens can do what they do.
Further, if one either granted them that spatial magnitude
consists of these elements, or this were proved, still how would
some bodies be light and others have weight? To judge from what they
assume and maintain they are speaking no more of mathematical bodies
than of perceptible; hence they have said nothing whatever about
fire or earth or the other bodies of this sort, I suppose because they
have nothing to say which applies peculiarly to perceptible things.
Further, how are we to combine the beliefs that the attributes
of number, and number itself, are causes of what exists and happens in
the heavens both from the beginning and now, and that there is no
other number than this number out of which the world is composed? When
in one particular region they place opinion and opportunity, and, a
little above or below, injustice and decision or mixture, and
allege, as proof, that each of these is a number, and that there
happens to be already in this place a plurality of the extended bodies
composed of numbers, because these attributes of number attach to
the various places,-this being so, is this number, which we must
suppose each of these abstractions to be, the same number which is
exhibited in the material universe, or is it another than this?
Plato says it is different; yet even he thinks that both these
bodies and their causes are numbers, but that the intelligible numbers
are causes, while the others are sensible.
9

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'.
And in general the arguments for the Forms destroy the things
for whose existence we are more zealous than for the existence of
the Ideas; for it follows that not the dyad but number is first,
i.e. that the relative is prior to the absolute,-besides all the other
points on which certain people by following out the opinions held
about the Ideas have come into conflict with the principles of the
theory.
Further, according to the assumption on which our belief in the
Ideas rests, there will be Forms not only of substances but also of
many other things (for the concept is single not only in the case of
substances but also in the other cases, and there are sciences not
only of substance but also of other things, and a thousand other
such difficulties confront them). But according to the necessities
of the case and the opinions held about the Forms, if Forms can be
shared in there must be Ideas of substances only. For they are not
shared in incidentally, but a thing must share in its Form as in

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