themselves, and there would be some one entity that became fire and
water, which Empedocles denies.

    As regards Anaxagoras, if one were to suppose that he said there
were two elements, the supposition would accord thoroughly with an
argument which Anaxagoras himself did not state articulately, but
which he must have accepted if any one had led him on to it. True,
to say that in the beginning all things were mixed is absurd both on
other grounds and because it follows that they must have existed
before in an unmixed form, and because nature does not allow any
chance thing to be mixed with any chance thing, and also because on
this view modifications and accidents could be separated from
substances (for the same things which are mixed can be separated); yet
if one were to follow him up, piecing together what he means, he would
perhaps be seen to be somewhat modern in his views. For when nothing
was separated out, evidently nothing could be truly asserted of the
substance that then existed. I mean, e.g. that it was neither white
nor black, nor grey nor any other colour, but of necessity colourless;
for if it had been coloured, it would have had one of these colours.
And similarly, by this same argument, it was flavourless, nor had it
any similar attribute; for it could not be either of any quality or of
any size, nor could it be any definite kind of thing. For if it
were, one of the particular forms would have belonged to it, and
this is impossible, since all were mixed together; for the
particular form would necessarily have been already separated out, but
he all were mixed except reason, and this alone was unmixed and
pure. From this it follows, then, that he must say the principles
are the One (for this is simple and unmixed) and the Other, which is
of such a nature as we suppose the indefinite to be before it is
defined and partakes of some form. Therefore, while expressing himself
neither rightly nor clearly, he means something like what the later
thinkers say and what is now more clearly seen to be the case.

    But these thinkers are, after all, at home only in arguments about
generation and destruction and movement; for it is practically only of
this sort of substance that they seek the principles and the causes.
But those who extend their vision to all things that exist, and of
existing things suppose some to be perceptible and others not
perceptible, evidently study both classes, which is all the more
reason why one should devote some time to seeing what is good in their
views and what bad from the standpoint of the inquiry we have now
before us.

    The 'Pythagoreans' treat of principles and elements stranger
than those of the physical philosophers (the reason is that they got
the principles from non-sensible things, for the objects of
mathematics, except those of astronomy, are of the class of things
without movement); yet their discussions and investigations are all
about nature; for they generate the heavens, and with regard to
their parts and attributes and functions they observe the phenomena,
and use up the principles and the causes in explaining these, which
implies that they agree with the others, the physical philosophers,
that the real is just all that which is perceptible and contained by
the so-called 'heavens'. But the causes and the principles which
they mention are, as we said, sufficient to act as steps even up to
the higher realms of reality, and are more suited to these than to
theories about nature. They do not tell us at all, however, how
there can be movement if limit and unlimited and odd and even are
the only things assumed, or how without movement and change there
can be generation and destruction, or the bodies that move through the
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.