Physics   

disproving the actual existence of the infinite in the direction of
increase, in the sense of the untraversable. In point of fact they do
not need the infinite and do not use it. They postulate only that the
finite straight line may be produced as far as they wish. It is
possible to have divided in the same ratio as the largest quantity
another magnitude of any size you like. Hence, for the purposes of
proof, it will make no difference to them to have such an infinite
instead, while its existence will be in the sphere of real magnitudes.
In the fourfold scheme of causes, it is plain that the infinite is a
cause in the sense of matter, and that its essence is privation, the
subject as such being what is continuous and sensible. All the other
thinkers, too, evidently treat the infinite as matter-that is why it
is inconsistent in them to make it what contains, and not what is
contained.
Part 8
It remains to dispose of the arguments which are supposed to support
the view that the infinite exists not only potentially but as a
separate thing. Some have no cogency; others can be met by fresh
objections that are valid.
(1) In order that coming to be should not fail, it is not necessary
that there should be a sensible body which is actually infinite. The
passing away of one thing may be the coming to be of another, the All
being limited.
(2) There is a difference between touching and being limited. The
former is relative to something and is the touching of something (for
everything that touches touches something), and further is an
attribute of some one of the things which are limited. On the other
hand, what is limited is not limited in relation to anything. Again,
contact is not necessarily possible between any two things taken at
random.
(3) To rely on mere thinking is absurd, for then the excess or defect
is not in the thing but in the thought. One might think that one of us
is bigger than he is and magnify him ad infinitum. But it does not
follow that he is bigger than the size we are, just because some one
thinks he is, but only because he is the size he is. The thought is an
accident.
(a) Time indeed and movement are infinite, and also thinking, in the
sense that each part that is taken passes in succession out of
existence.
(b) Magnitude is not infinite either in the way of reduction or of
magnification in thought.
This concludes my account of the way in which the infinite exists, and
of the way in which it does not exist, and of what it is.
Physics
By Aristotle
Written 350 B.C.E Part 1
The physicist must have a knowledge of Place, too, as well as of the
infinite-namely, whether there is such a thing or not, and the manner
of its existence and what it is-both because all suppose that things
which exist are somewhere (the non-existent is nowhere--where is the
goat-stag or the sphinx?), and because 'motion' in its most general
and primary sense is change of place, which we call 'locomotion'.
The question, what is place? presents many difficulties. An
examination of all the relevant facts seems to lead to divergent
conclusions. Moreover, we have inherited nothing from previous
thinkers, whether in the way of a statement of difficulties or of a
solution.
The existence of place is held to be obvious from the fact of mutual
replacement. Where water now is, there in turn, when the water has
gone out as from a vessel, air is present. When therefore another body
occupies this same place, the place is thought to be different from
all the bodies which come to be in it and replace one another. What
now contains air formerly contained water, so that clearly the place
or space into which and out of which they passed was something