contributes nothing to the situation if there is an equal interval
attached to it as well. [Further it ought to be clear by the study
of moving things what sort of thing void is. But in fact it is found
nowhere in the world. For air is something, though it does not seem to
be so-nor, for that matter, would water, if fishes were made of
iron; for the discrimination of the tangible is by touch.]
It is clear, then, from these considerations that there is no
separate void.
9
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
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.
10
Next for discussion after the subjects mentioned is Time. The best
plan will be to begin by working out the difficulties connected with
it, making use of the current arguments. First, does it belong to
the class of things that exist or to that of things that do not exist?
Then secondly, what is its nature? To start, then: the following
considerations would make one suspect that it either does not exist at
all
or barely, and in an obscure way. One part of it has been and is
not, while the other is going to be and is not yet. Yet time-both
infinite time and any time you like to take-is made up of these. One
would naturally suppose that what is made up of things which do not
exist could have no share in reality.
Further, if a divisible thing is to exist, it is necessary that,
when it exists, all or some of its parts must exist. But of time
some parts have been, while others have to be, and no part of it is
though it is divisible. For what is 'now' is not a part: a part is a
measure of the whole, which must be made up of parts. Time, on the
other hand, is not held to be made up of 'nows'.
Again, the 'now' which seems to bound the past and the future-does
it always remain one and the same or is it always other and other?
It is hard to say.
(1) If it is always different and different, and if none of the
parts in time which are other and other are simultaneous (unless the
one contains and the other is contained, as the shorter time is by the
longer), and if the 'now' which is not, but formerly was, must have
ceased-to-be at some time, the 'nows' too cannot be simultaneous
with one another, but the prior 'now' must always have ceased-to-be.
But the prior 'now' cannot have ceased-to-be in itself (since it
then existed); yet it cannot have ceased-to-be in another 'now'. For
we may lay it down that one 'now' cannot be next to another, any
more than point to point. If then it did not cease-to-be in the next
'now' but in another, it would exist simultaneously with the
innumerable 'nows' between the two-which is impossible.
Yes, but (2) neither is it possible for the 'now' to remain always
the same. No determinate divisible thing has a single termination,
whether it is continuously extended in one or in more than one
dimension: but the 'now' is a termination, and it is possible to cut
off a determinate time. Further, if coincidence in time (i.e. being
neither prior nor posterior) means to be 'in one and the same
"now"', then, if both what is before and what is after are in this
same 'now', things which happened ten thousand years ago would be
simultaneous with what has happened to-day, and nothing would be
before or after anything else.
This may serve as a statement of the difficulties about the
attributes of time.
As to what time is or what is its nature, the traditional accounts
give us as little light as the preliminary problems which we have
worked through.
Some assert that it is (1) the movement of the whole, others that it
is (2) the sphere itself.
(1) Yet part, too, of the revolution is a time, but it certainly
is not a revolution: for what is taken is part of a revolution, not
a revolution. Besides, if there were more heavens than one, the
movement of any of them equally would be time, so that there would
be many times at the same time.
(2) Those who said that time is the sphere of the whole thought
so, no doubt, on the ground that all things are in time and all things
are in the sphere of the whole. The view is too naive for it to be
worth while to consider the impossibilities implied in it.
But as time is most usually supposed to be (3) motion and a kind
of change, we must consider this view.
Now (a) the change or movement of each thing is only in the thing
which changes or where the thing itself which moves or changes may
chance to be. But time is present equally everywhere and with all
things.
Again, (b) change is always faster or slower, whereas time is not:
for 'fast' and 'slow' are defined by time-'fast' is what moves much in
a short time, 'slow' what moves little in a long time; but time is not
defined by time, by being either a certain amount or a certain kind of
it.
Clearly then it is not movement. (We need not distinguish at present
between 'movement' and 'change'.)
11
But neither does time exist without change; for when the state of
our own minds does not change at all, or we have not noticed its
changing, we do not realize that time has elapsed, any more than those
who are fabled to sleep among the heroes in Sardinia do when they
are awakened; for they connect the earlier 'now' with the later and
make them one, cutting out the interval because of their failure to
notice it. So, just as, if the 'now' were not different but one and
the same, there would not have been time, so too when its difference
escapes our notice the interval does not seem to be time. If, then,
the non-realization of the existence of time happens to us when we
do not distinguish any change, but the soul seems to stay in one
indivisible state, and when we perceive and distinguish we say time
has elapsed, evidently time is not independent of movement and change.
It is evident, then, that time is neither movement nor independent
of movement.
We must take this as our starting-point and try to discover-since we
wish to know what time is-what exactly it has to do with movement.
Now we perceive movement and time together: for even when it is dark
and we are not being affected through the body, if any movement
takes place in the mind we at once suppose that some time also has
elapsed; and not only that but also, when some time is thought to have
passed, some movement also along with it seems to have taken place.
Hence time is either movement or something that belongs to movement.
Since then it is not movement, it must be the other.
But what is moved is moved from something to something, and all
magnitude is continuous. Therefore the movement goes with the
magnitude. Because the magnitude is continuous, the movement too
must be continuous, and if the movement, then the time; for the time
that has passed is always thought to be in proportion to the movement.
The distinction of 'before' and 'after' holds primarily, then, in
place; and there in virtue of relative position. Since then 'before'
and 'after' hold in magnitude, they must hold also in movement,
these corresponding to those. But also in time the distinction of
'before' and 'after' must hold, for time and movement always
correspond with each other. The 'before' and 'after' in motion is
identical in substratum with motion yet differs from it in definition,
and is not identical with motion.
But we apprehend time only when we have marked motion, marking it by
'before' and 'after'; and it is only when we have perceived 'before'
and 'after' in motion that we say that time has elapsed. Now we mark
them by judging that A and B are different, and that some third
thing is intermediate to them. When we think of the extremes as
different from the middle and the mind pronounces that the 'nows'
are two, one before and one after, it is then that we say that there
is time, and this that we say is time. For what is bounded by the
'now' is thought to be time-we may assume this.
When, therefore, we perceive the 'now' one, and neither as befo
re
and after in a motion nor as an identity but in relation to a 'before'
and an 'after', no time is thought to have elapsed, because there
has been no motion either. On the other hand, when we do perceive a
'before' and an 'after', then we say that there is time. For time is
just this-number of motion in respect of 'before' and 'after'.
Hence time is not movement, but only movement in so far as it admits
of enumeration. A proof of this: we discriminate the more or the
less by number, but more or less movement by time. Time then is a kind
of number. (Number, we must note, is used in two senses-both of what
is counted or the countable and also of that with which we count. Time
obviously is what is counted, not that with which we count: there
are different kinds of thing.) Just as motion is a perpetual
succession, so also is time. But every simultaneous time is
self-identical; for the 'now' as a subject is an identity, but it
accepts different attributes. The 'now' measures time, in so far as
time involves the 'before and after'.
The 'now' in one sense is the same, in another it is not the same.
In so far as it is in succession, it is different (which is just
what its being was supposed to mean), but its substratum is an
identity: for motion, as was said, goes with magnitude, and time, as
we maintain, with motion. Similarly, then, there corresponds to the
point the body which is carried along, and by which we are aware of
the motion and of the 'before and after' involved in it. This is an
identical substratum (whether a point or a stone or something else
of the kind), but it has different attributes as the sophists assume
that Coriscus' being in the Lyceum is a different thing from Coriscus'
being in the market-place. And the body which is carried along is
different, in so far as it is at one time here and at another there.