
On The Heavens
that any other natural conformation is composed of parts like
itself. Obviously then it would be better to assume a finite number of
principles. They should, in fact, be as few as possible,
consistently with proving what has to be proved. This is the common
demand of mathematicians, who always assume as principles things
finite either in kind or in number. Again, if body is distinguished
from body by the appropriate qualitative difference, and there is a
limit to the number of differences (for the difference lies in
qualities apprehended by sense, which are in fact finite in number,
though this requires proof), then manifestly there is necessarily a
limit to the number of elements.
There is, further, another viewthat of Leucippus and Democritus
of Abderathe 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 masterseed 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
