Written circa 350 B.C.
Translated by J. L. Stocks
Book III.4
There is, further, another view-that of Leucippus and Democritus
of Abdera-the implications of which are also unacceptable. The primary
masses, according to them, are infinite in number and indivisible in
mass: one cannot turn into many nor many into one; and all things
are generated by their combination and involution. Now this view in
a sense makes things out to be numbers or composed of numbers. The
exposition is not clear, but this is its real meaning. And further,
they say that since the atomic bodies differ in shape, and there is an
infinity of shapes, there is an infinity of simple bodies. But they
have never explained in detail the shapes of the various elements,
except so far to allot the sphere to fire. Air, water, and the rest
they distinguished by the relative size of the atom, assuming that the
atomic substance was a sort of master-seed for each and every element.
Now, in the first place, they make the mistake already noticed. The
principles which they assume are not limited in number, though such
limitation would necessitate no other alteration in their theory.
Further, if the differences of bodies are not infinite, plainly the
elements will not be an infinity. Besides, a view which asserts atomic
bodies must needs come into conflict with the mathematical sciences,
in addition to invalidating many common opinions and apparent data
of sense perception. But of these things we have already spoken in our
discussion of time and movement. They are also bound to contradict
themselves. For if the elements are atomic, air, earth, and water
cannot be differentiated by the relative sizes of their atoms, since
then they could not be generated out of one another. The extrusion
of the largest atoms is a process that will in time exhaust the
supply; and it is by such a process that they account for the
generation of water, air, and earth from one another. Again, even on
their own presuppositions it does not seem as if the clements would be
infinite in number. The atoms differ in figure, and all figures are
composed of pyramids, rectilinear the case of rectilinear figures,
while the sphere has eight pyramidal parts. The figures must have
their principles, and, whether these are one or two or more, the
simple bodies must be the same in number as they. Again, if every
element has its proper movement, and a simple body has a simple
movement, and the number of simple movements is not infinite,
because the simple motions are only two and the number of places is
not infinite, on these grounds also we should have to deny that the
number of elements is infinite.