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a sense both mentions, and is the first to mention, the bad and the
good as principles, we should perhaps be right, since the cause of all
goods is the good itself.
These thinkers, as we say, evidently grasped, and to this
extent, two of the causes which we distinguished in our work on
nature-the matter and the source of the movement-vaguely, however, and
with no clearness, but as untrained men behave in fights; for they
go round their opponents and often strike fine blows, but they do
not fight on scientific principles, and so too these thinkers do not
seem to know what they say; for it is evident that, as a rule, they
make no use of their causes except to a small extent. For Anaxagoras
uses reason as a deus ex machina for the making of the world, and when
he is at a loss to tell from what cause something necessarily is, then
he drags reason in, but in all other cases ascribes events to anything
rather than to reason. And Empedocles, though he uses the causes to
a greater extent than this, neither does so sufficiently nor attains
consistency in their use. At least, in many cases he makes love
segregate things, and strife aggregate them. For whenever the universe
is dissolved into its elements by strife, fire is aggregated into one,
and so is each of the other elements; but whenever again under the
influence of love they come together into one, the parts must again be
segregated out of each element.
Empedocles, then, in contrast with his precessors, was the first
to introduce the dividing of this cause, not positing one source of
movement, but different and contrary sources. Again, he was the
first to speak of four material elements; yet he does not use four,
but treats them as two only; he treats fire by itself, and its
opposite-earth, air, and water-as one kind of thing. We may learn this
by study of his verses.
This philosopher then, as we say, has spoken of the principles
in this way, and made them of this number. Leucippus and his associate
Democritus say that the full and the empty are the elements, calling
the one being and the other non-being-the full and solid being
being, the empty non-being (whence they say being no more is than
non-being, because the solid no more is than the empty); and they make
these the material causes of things. And as those who make the
underlying substance one generate all other things by its
modifications, supposing the rare and the dense to be the sources of
the modifications, in the same way these philosophers say the
differences in the elements are the causes of all other qualities.
These differences, they say, are three-shape and order and position.
For they say the real is differentiated only by 'rhythm and
'inter-contact' and 'turning'; and of these rhythm is shape,
inter-contact is order, and turning is position; for A differs from
N in shape, AN from NA in order, M from W in position. The question of
movement-whence or how it is to belong to things-these thinkers,
like the others, lazily neglected.
Regarding the two causes, then, as we say, the inquiry seems to
have been pushed thus far by the early philosophers.
5

Contemporaneously with these philosophers and before them, the
so-called Pythagoreans, who were the first to take up mathematics, not
only advanced this study, but also having been brought up in it they
thought its principles were the principles of all things. Since of
these principles numbers are by nature the first, and in numbers
they seemed to see many resemblances to the things that exist and come
into being-more than in fire and earth and water (such and such a
modification of numbers being justice, another being soul and
reason, another being opportunity-and similarly almost all other
things being numerically expressible); since, again, they saw that the
modifications and the ratios of the musical scales were expressible in
numbers;-since, then, all other things seemed in their whole nature to
be modelled on numbers, and numbers seemed to be the first things in

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