(for water and fire and such things are bodies), and of whom some
suppose that there is one corporeal principle, others that there are
more than one, but both put these under the head of matter; and on the
other hand from some who posit both this cause and besides this the
source of movement, which we have got from some as single and from
others as twofold.

    Down to the Italian school, then, and apart from it,
philosophers have treated these subjects rather obscurely, except
that, as we said, they have in fact used two kinds of cause, and one
of these-the source of movement-some treat as one and others as two.
But the Pythagoreans have said in the same way that there are two
principles, but added this much, which is peculiar to them, that
they thought that finitude and infinity were not attributes of certain
other things, e.g. of fire or earth or anything else of this kind, but
that infinity itself and unity itself were the substance of the things
of which they are predicated. This is why number was the substance
of all things. On this subject, then, they expressed themselves
thus; and regarding the question of essence they began to make
statements and definitions, but treated the matter too simply. For
they both defined superficially and thought that the first subject
of which a given definition was predicable was the substance of the
thing defined, as if one supposed that 'double' and '2' were the same,
because 2 is the first thing of which 'double' is predicable. But
surely to be double and to be 2 are not the same; if they are, one
thing will be many-a consequence which they actually drew. From the
earlier philosophers, then, and from their successors we can learn
thus much.

                                   6

    After the systems we have named came the philosophy of Plato,
which in most respects followed these thinkers, but had
pecullarities that distinguished it from the philosophy of the
Italians. For, having in his youth first become familiar with Cratylus
and with the Heraclitean doctrines (that all sensible things are
ever in a state of flux and there is no knowledge about them), these
views he held even in later years. Socrates, however, was busying
himself about ethical matters and neglecting the world of nature as
a whole but seeking the universal in these ethical matters, and
fixed thought for the first time on definitions; Plato accepted his
teaching, but held that the problem applied not to sensible things but
to entities of another kind-for this reason, that the common
definition could not be a definition of any sensible thing, as they
were always changing. 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. His divergence from the Pythagoreans in making the
One and the Numbers separate from things, and his introduction of
the Forms, were due to his inquiries in the region of definitions (for
the earlier thinkers had no tincture of dialectic), and his making the
other entity besides the One a dyad was due to the belief that the
numbers, except those which were prime, could be neatly produced out
of the dyad as out of some plastic material. Yet what happens is the
contrary; the theory is not a reasonable one. For they make many
things out of the matter, and the form generates only once, but what
we observe is that one table is made from one matter, while the man
who applies the form, though he is one, makes many tables. And the
relation of the male to the female is similar; for the latter is
impregnated by one copulation, but the male impregnates many
females; yet these are analogues of those first principles.

    Plato, then, declared himself thus on the points in question; it
is evident from what has been said that he has used only two causes,
that of the essence and the material cause (for the Forms are the
causes of the essence of all other things, and the One is the cause of
the essence of the Forms); and it is evident what the underlying
matter is, of which the Forms are predicated in the case of sensible
things, and the One in the case of Forms, viz. that this is a dyad,
the great and the small. Further, he has assigned the cause of good
and that of evil to the elements, one to each of the two, as we say
some of his predecessors sought to do, e.g. Empedocles and Anaxagoras.

                                   7