Physics   

has weight and what is heavy rests at the centre and the earth is at
the centre, similarly the infinite also would rest in itself, not
because it is infinite and fixes itself, but owing to some other
cause.
Another difficulty emerges at the same time. Any part of the infinite
body ought to remain at rest. Just as the infinite remains at rest in
itself because it fixes itself, so too any part of it you may take
will remain in itself. The appropriate places of the whole and of the
part are alike, e.g. of the whole earth and of a clod the appropriate
place is the lower region; of fire as a whole and of a spark, the
upper region. If, therefore, to be in itself is the place of the
infinite, that also will be appropriate to the part. Therefore it will
remain in itself.
In general, the view that there is an infinite body is plainly
incompatible with the doctrine that there is necessarily a proper
place for each kind of body, if every sensible body has either weight
or lightness, and if a body has a natural locomotion towards the
centre if it is heavy, and upwards if it is light. This would need to
be true of the infinite also. But neither character can belong to it:
it cannot be either as a whole, nor can it be half the one and half
the other. For how should you divide it? or how can the infinite have
the one part up and the other down, or an extremity and a centre?
Further, every sensible body is in place, and the kinds or differences
of place are up-down, before-behind, right-left; and these
distinctions hold not only in relation to us and by arbitrary
agreement, but also in the whole itself. But in the infinite body they
cannot exist. In general, if it is impossible that there should be an
infinite place, and if every body is in place, there cannot be an
infinite body.
Surely what is in a special place is in place, and what is in place is
in a special place. Just, then, as the infinite cannot be
quantity-that would imply that it has a particular quantity, e,g, two
or three cubits; quantity just means these-so a thing's being in place
means that it is somewhere, and that is either up or down or in some
other of the six differences of position: but each of these is a
limit.
It is plain from these arguments that there is no body which is
actually infinite.
Part 6
But on the other hand to suppose that the infinite does not exist in
any way leads obviously to many impossible consequences: there will be
a beginning and an end of time, a magnitude will not be divisible into
magnitudes, number will not be infinite. If, then, in view of the
above considerations, neither alternative seems possible, an arbiter
must be called in; and clearly there is a sense in which the infinite
exists and another in which it does not.
We must keep in mind that the word 'is' means either what potentially
is or what fully is. Further, a thing is infinite either by addition
or by division.
Now, as we have seen, magnitude is not actually infinite. But by
division it is infinite. (There is no difficulty in refuting the
theory of indivisible lines.) The alternative then remains that the
infinite has a potential existence.
But the phrase 'potential existence' is ambiguous. When we speak of
the potential existence of a statue we mean that there will be an
actual statue. It is not so with the infinite. There will not be an
actual infinite. The word 'is' has many senses, and we say that the
infinite 'is' in the sense in which we say 'it is day' or 'it is the
games', because one thing after another is always coming into
existence. For of these things too the distinction between potential
and actual existence holds. We say that there are Olympic games, both
in the sense that they may occur and that they are actually occurring.
The infinite exhibits itself in different ways-in time, in the
generations of man, and in the division of magnitudes. For generally