The Complete Aristotle (eng.)

centre, but because this is its nature. Yet in this
case also we may say that it fixes itself. If then in the case of
the earth, supposed to be infinite, it is at rest, not because it
is infinite, but because it 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.
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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 the infinite has this mode of existence: one thing is
always being taken after another, and each thing that is taken is
always finite, but always different. Again, ‘being’ has more than
one sense, so that we must not regard the infinite as a ‘this’,
such as a man or a horse, but must suppose it to exist in the