The Complete Aristotle (eng.)
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, Book IV
Translated by R. P. Hardie and R. K. Gaye
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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 different from both.
Further, the typical locomotions of the elementary natural
bodies-namely, fire, earth, and the like-show not only that place
is something, but also that it exerts a certain influence. Each is
carried to its own place, if it is not hindered, the one up, the
other down. Now these are regions or kinds of place-up and down and
the rest of the six directions. Nor do such distinctions (up and
down and right and left, &c.) hold only in relation to us. To
us they are not always the same but change with the direction in
which we are turned: that is why the same thing may be both right
and left, up and down, before and behind. But in nature each is
distinct, taken apart by itself. It is not every chance direction
which is ‘up’, but where fire and what is light are carried;
similarly, too, ‘down’ is not any chance direction but where what
has weight and what is made of earth are carried-the implication
being that these places do not differ merely in relative position,
but also as possessing distinct potencies. This is made plain also
by the objects studied by mathematics. Though they have no real
place, they nevertheless, in respect of their position relatively
to us, have a right and left as attributes ascribed to them only in
consequence of their relative position, not having by nature these
various characteristics. Again, the theory that the void exists
involves the existence of place: for one would define void as place
bereft of body.
These considerations then would lead us to suppose that place is
something distinct from bodies, and that every sensible body is in
place. Hesiod too might be held to have given a correct account of
it when he made chaos
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