There are some who think that the existence of rarity and density
shows that there is a void. If rarity and density do not exist, they
say, neither can things contract and be compressed. But if this were
not to take place, either there would be no movement at all, or the
universe would bulge, as Xuthus said, or air and water must always
change into equal amounts (e.g. if air has been made out of a cupful
of water, at the same time out of an equal amount of air a cupful of
water must have been made), or void must necessarily exist; for
compression and expansion cannot take place otherwise.

    Now, if they mean by the rare that which has many voids existing
separately, it is plain that if void cannot exist separate any more
than a place can exist with an extension all to itself, neither can
the rare exist in this sense. But if they mean that there is void, not
separately existent, but still present in the rare, this is less
impossible, yet, first, the void turns out not to be a condition of
all movement, but only of movement upwards (for the rare is light,
which is the reason why they say fire is rare); second, the void turns
out to be a condition of movement not as that in which it takes place,
but in that the void carries things up as skins by being carried up
themselves carry up what is continuous with them. Yet how can void
have a local movement or a place? For thus that into which void
moves is till then void of a void.

    Again, how will they explain, in the case of what is heavy, its
movement downwards? And it is plain that if the rarer and more void
a thing is the quicker it will move upwards, if it were completely
void it would move with a maximum speed! But perhaps even this is
impossible, that it should move at all; the same reason which showed
that in the void all things are incapable of moving shows that the
void cannot move, viz. the fact that the speeds are incomparable.

    Since we deny that a void exists, but for the rest the problem has
been truly stated, that either there will be no movement, if there
is not to be condensation and rarefaction, or the universe will bulge,
or a transformation of water into air will always be balanced by an
equal transformation of air into water (for it is clear that the air
produced from water is bulkier than the water): it is necessary
therefore, if compression does not exist, either that the next portion
will be pushed outwards and make the outermost part bulge, or that
somewhere else there must be an equal amount of water produced out
of air, so that the entire bulk of the whole may be equal, or that
nothing moves. For when anything is displaced this will always happen,
unless it comes round in a circle; but locomotion is not always
circular, but sometimes in a straight line.

    These then are the reasons for which they might say that there is
a void; our statement is based on the assumption that there is a
single matter for contraries, hot and cold and the other natural
contrarieties, and that what exists actually is produced from a
potential existent, and that matter is not separable from the
contraries but its being is different, and that a single matter may
serve for colour and heat and cold.

    The same matter also serves for both a large and a small body.
This is evident; for when air is produced from water, the same
matter has become something different, not by acquiring an addition to
it, but has become actually what it was potentially, and, again, water
is produced from air in the same way, the change being sometimes
from smallness to greatness, and sometimes from greatness to
smallness. Similarly, therefore, if air which is large in extent comes
to have a smaller volume, or becomes greater from being smaller, it is
the matter which is potentially both that comes to be each of the two.

    For as the same matter becomes hot from being cold, and cold from
being hot, because it was potentially both, so too from hot it can
become more hot, though nothing in the matter has become hot that
was not hot when the thing was less hot; just as, if the arc or
curve of a greater circle becomes that of a smaller, whether it
remains the same or becomes a different curve, convexity has not
come to exist in anything that was not convex but straight (for
differences of degree do not depend on an intermission of the
quality); nor can we get any portion of a flame, in which both heat
and whiteness are not present. So too, then, is the earlier heat
related to the later. So that the greatness and smallness, also, of
the sensible volume are extended, not by the matter's acquiring
anything new, but because the matter is potentially matter for both
states; so that the same thing is dense and rare, and the two
qualities have one matter.

    The dense is heavy, and the rare is light. [Again, as the arc of a
circle when contracted into a smaller space does not acquire a new
part which is convex, but what was there has been contracted; and as
any part of fire that one takes will be hot; so, too, it is all a
question of contraction and expansion of the same matter.] There are
two types in each case, both in the dense and in the rare; for both
the heavy and the hard are thought to be dense, and contrariwise
both the light and the soft are rare; and weight and hardness fail
to coincide in the case of lead and iron.

    From what has been said it is evident, then, that void does not
exist either separate (either absolutely separate or as a separate
element in the rare) or potentially, unless one is willing to call the
condition of movement void, whatever it may be. At that rate the
matter of the heavy and the light, qua matter of them, would be the
void; for the dense and the rare are productive of locomotion in
virtue of this contrariety, and in virtue of their hardness and
softness productive of passivity and impassivity, i.e. not of
locomotion but rather of qualitative change.

    So much, then, for the discussion of the void, and of the sense in
which it exists and the sense in which it does not exist.