Various Works

  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

  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.

  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.