On The Heavens
Moreover it would be necessary also that their places should be
infinite in extent, so that the movements too of all these bodies
would be infinite. But this is not possible, if we are to hold to
the truth of our original presuppositions and to the view that neither
that which moves downward, nor, by the same reasoning, that which
moves upward, can prolong its movement to infinity. For it is true
in regard to quality, quantity, and place alike that any process of
change is impossible which can have no end. I mean that if it is
impossible for a thing to have come to be white, or a cubit long, or
in Egypt, it is also impossible for it to be in process of coming to
be any of these. It is thus impossible for a thing to be moving to a
place at which in its motion it can never by any possibility arrive.
Again, suppose the body to exist in dispersion, it may be maintained
none the less that the total of all these scattered particles, say, of
fire, is infinite. But body we saw to be that which has extension
every way. How can there be several dissimilar elements, each
infinite? Each would have to be infinitely extended every way.
It is no more conceivable, again, that the infinite should exist
as a whole of similar parts. For, in the first place, there is no
other (straight) movement beyond those mentioned: we must therefore
give it one of them. And if so, we shall have to admit either infinite
weight or infinite lightness. Nor, secondly, could the body whose
movement is circular be infinite, since it is impossible for the
infinite to move in a circle. This, indeed, would be as good as saying
that the heavens are infinite, which we have shown to be impossible.
Moreover, in general, it is impossible that the infinite should move
at all. If it did, it would move either naturally or by constraint:
and if by constraint, it possesses also a natural motion, that is to
say, there is another place, infinite like itself, to which it will
move. But that is impossible.
That in general it is impossible for the infinite to be acted upon
by the finite or to act upon it may be shown as follows.