The Basic Works of Aristotle (Modern Library Classics) (51 page)

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,
(25)
or the universe would bulge, as Xuthus
¹²
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,
(30)
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,
(35)
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.
[217a]
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,
(5)
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,
(10)
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,
(15)
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,
(20)
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,
(25)
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,
(30)
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,
(5)
in which both heat and whiteness are not present.
[217b]
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,
(10)
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.
(15)
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,
(20)
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,
(25)
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,
(30)
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.
[218a]
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,
(5)
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.
(10)

(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,
(15)
but the prior ‘now’ must always have ceased-to-be. But the prior ‘now’ cannot have ceased-to-be in
¹³
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.
(20)

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.
(25)
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.
(30)

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.
¹⁴
[218b]

(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,
(5)
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.
(10)

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,
(15)
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’.
(20)
)

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,
(25)
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,
(30)
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.
[219a]

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,
(5)
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,
(10)
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,
(15)
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 identical in substratum with motion yet differs from it in definition, and is not identical with motion.
(20)

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.
(25)
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,
(30)
therefore, we perceive the ‘now’ as one, and neither as before 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.
[219b]
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.
(5)
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: these are different kinds of thing.)

Just as motion is a perpetual succession, so also is time.
(10)
But every simultaneous time is self-identical; for the ‘now’ as a subject is an identity, but it accepts different attributes.
¹⁵
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 now was supposed to mean), but its substratum is an identity: for motion,
(15)
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),
(20)
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. But the ‘now’ corresponds to the body that is carried along, as time corresponds to the motion. For it is by means of the body that is carried along that we become aware of the ‘before and after’ in the motion,
(25)
and if we regard these as countable we get the ‘now’. Hence in these also the ‘now’ as substratum remains the same (for it is what is before and after in movement), but what is predicated of it is different; for it is
in so far as the ‘before and after’ is numerable that we get the ‘now’. This is what is most knowable: for, similarly, motion is known because of that which is moved, locomotion because of that which is carried. For what is carried is a real thing, the movement is not.
(30)
Thus what is called ‘now’ in one sense is always the same; in another it is not the same: for this is true also of what is carried.

Clearly, too, if there were no time, there would be no ‘now’, and vice versa. Just as the moving body and its locomotion involve each other mutually, so too do the number of the moving body and the number of its locomotion.
[220a]
For the number of the locomotion is time, while the ‘now’ corresponds to the moving body, and is like the unit of number.

Time, then, also is both made continuous by the ‘now’ and divided at it.
(5)
For here too there is a correspondence with the locomotion and the moving body. For the motion or locomotion is made one by the thing which is moved, because
it
is one—not because it is one in its own nature (for there might be pauses in the movement of such a thing)—but because it is one in definition: for this determines the movement as ‘before’ and ‘after’. Here, too, there is a correspondence with the point; for the point also both connects and terminates the length—it is the beginning of one and the end of another.
(10)
But when you take it in this way, using the one point as two, a pause is necessary, if the same point is to be the beginning and the end. The ‘now’ on the other hand, since the body carried is moving, is always different.

Hence time is not number in the sense in which there is ‘number’ of the same point because it is beginning and end, but rather as the extremities of a line form a number, and not as the parts of the line do so,
(15)
both for the reason given (for we can use the middle point as two, so that on that analogy time might stand still), and further because obviously the ‘now’ is no
part
of time nor the section any part of the movement, any more than the points are parts of the line—for it is two
lines
that are
parts
of one line.
(20)

In so far then as the ‘now’ is a boundary, it is not time, but an attribute of it; in so far as it numbers, it is number; for boundaries belong only to that which they bound, but number (e. g. ten) is the number of these horses, and belongs also elsewhere.

It is clear, then, that time is ‘number of movement in respect of the before and after’, and is continuous since it is an attribute of what is continuous.
(25)