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seem not to exist, if there were no void, since what is full cannot

  contain anything more. If it could, and there were two bodies in the

  same place, it would also be true that any number of bodies could be

  together; for it is impossible to draw a line of division beyond which

  the statement would become untrue. If this were possible, it would

  follow also that the smallest body would contain the greatest; for

  'many a little makes a mickle': thus if many equal bodies can be

  together, so also can many unequal bodies.

  Melissus, indeed, infers from these considerations that the All is

  immovable; for if it were moved there must, he says, be void, but void

  is not among the things that exist.

  This argument, then, is one way in which they show that there is a

  void.

  (2) They reason from the fact that some things are observed to

  contract and be compressed, as people say that a cask will hold the

  wine which formerly filled it, along with the skins into which the

  wine has been decanted, which implies that the compressed body

  contracts into the voids present in it.

  Again (3) increase, too, is thought to take always by means of void,

  for nutriment is body, and it is impossible for two bodies to be

  together. A proof of this they find also in what happens to ashes,

  which absorb as much water as the empty vessel.

  The Pythagoreans, too, (4) held that void exists and that it

  enters the heaven itself, which as it were inhales it, from the

  infinite air. Further it is the void which distinguishes the natures

  of things, as if it were like what separates and distinguishes the

  terms of a series. This holds primarily in the numbers, for the void

  distinguishes their nature.

  These, then, and so many, are the main grounds on which people

  have argued for and against the existence of the void.

  7

  As a step towards settling which view is true, we must determine the

  meaning of the name.

  The void is thought to be place with nothing in it. The reason for

  this is that people take what exists to be body, and hold that while

  every body is in place, void is place in which there is no body, so

  that where there is no body, there must be void.

  Every body, again, they suppose to be tangible; and of this nature

  is whatever has weight or lightness.

  Hence, by a syllogism, what has nothing heavy or light in it, is

  void.

  This result, then, as I have said, is reached by syllogism. It would

  be absurd to suppose that the point is void; for the void must be

  place which has in it an interval in tangible body.

  But at all events we observe then that in one way the void is

  described as what is not full of body perceptible to touch; and what

  has heaviness and lightness is perceptible to touch. So we would raise

  the question: what would they say of an interval that has colour or

  sound-is it void or not? Clearly they would reply that if it could

  receive what is tangible it was void, and if not, not.

  In another way void is that in which there is no 'this' or corporeal

  substance. So some say that the void is the matter of the body (they

  identify the place, too, with this), and in this they speak

  incorrectly; for the matter is not separable from the things, but they

  are inquiring about the void as about something separable.

  Since we have determined the nature of place, and void must, if it

  exists, be place deprived of body, and we have stated both in what

  sense place exists and in what sense it does not, it is plain that

  on this showing void does not exist, either unseparated or

  separated; the void is meant to be, not body but rather an interval in

  body. This is why the void is thought to be something, viz. because

  place is, and for the same reasons. For the fact of motion in

  respect of place comes to the aid both of those who maintain that

  place is something over and above the bodies that come to occupy it,

  and of those who maintain that the void is something. They state

  that the void is the condition of movement in the sense of that in

  which movement takes place; and this would be the kind of thing that

  some say place is.

  But there is no necessity for there being a void if there is

  movement. It is not in the least needed as a condition of movement

  in general, for a reason which, incidentally, escaped Melissus; viz.

  that the full can suffer qualitative change.

  But not even movement in respect of place involves a void; for

  bodies may simultaneously make room for one another, though there is

  no interval separate and apart from the bodies that are in movement.

  And this is plain even in the rotation of continuous things, as in

  that of liquids.

  And things can also be compressed not into a void but because they

  squeeze out what is contained in them (as, for instance, when water is

  compressed the air within it is squeezed out); and things can increase

  in size not only by the entrance of something but also by

  qualitative change; e.g. if water were to be transformed into air.

  In general, both the argument about increase of size and that

  about water poured on to the ashes get in their own way. For either

  not any and every part of the body is increased, or bodies may be

  increased otherwise than by the addition of body, or there may be

  two bodies in the same place (in which case they are claiming to solve

  a quite general difficulty, but are not proving the existence of

  void), or the whole body must be void, if it is increased in every

  part and is increased by means of void. The same argument applies to

  the ashes.

  It is evident, then, that it is easy to refute the arguments by

  which they prove the existence of the void.

  8

  Let us explain again that there is no void existing separately, as

  some maintain. If each of the simple bodies has a natural

  locomotion, e.g. fire upward and earth downward and towards the middle

  of the universe, it is clear that it cannot be the void that is the

  condition of locomotion. What, then, will the void be the condition

  of? It is thought to be the condition of movement in respect of place,

  and it is not the condition of this.

  Again, if void is a sort of place deprived of body, when there is

  a void where will a body placed in it move to? It certainly cannot

  move into the whole of the void. The same argument applies as

  against those who think that place is something separate, into which

  things are carried; viz. how will what is placed in it move, or

  rest? Much the same argument will apply to the void as to the 'up' and

  'down' in place, as is natural enough since those who maintain the

  existence of the void make it a place.

  And in what way will things be present either in place-or in the

  void? For the expected result does not take place when a body is

  placed as a whole in a place conceived of as separate and permanent;

  for a part of it, unless it be placed apart, will not be in a place

  but in the whole. Further, if separate place does not exist, neither

  wi
ll void.

  If people say that the void must exist, as being necessary if

  there is to be movement, what rather turns out to be the case, if

  one the matter, is the opposite, that not a single thing can be

  moved if there is a void; for as with those who for a like reason

  say the earth is at rest, so, too, in the void things must be at rest;

  for there is no place to which things can move more or less than to

  another; since the void in so far as it is void admits no difference.

  The second reason is this: all movement is either compulsory or

  according to nature, and if there is compulsory movement there must

  also be natural (for compulsory movement is contrary to nature, and

  movement contrary to nature is posterior to that according to

  nature, so that if each of the natural bodies has not a natural

  movement, none of the other movements can exist); but how can there be

  natural movement if there is no difference throughout the void or

  the infinite? For in so far as it is infinite, there will be no up

  or down or middle, and in so far as it is a void, up differs no whit

  from down; for as there is no difference in what is nothing, there

  is none in the void (for the void seems to be a non-existent and a

  privation of being), but natural locomotion seems to be

  differentiated, so that the things that exist by nature must be

  differentiated. Either, then, nothing has a natural locomotion, or

  else there is no void.

  Further, in point of fact things that are thrown move though that

  which gave them their impulse is not touching them, either by reason

  of mutual replacement, as some maintain, or because the air that has

  been pushed pushes them with a movement quicker than the natural

  locomotion of the projectile wherewith it moves to its proper place.

  But in a void none of these things can take place, nor can anything be

  moved save as that which is carried is moved.

  Further, no one could say why a thing once set in motion should stop

  anywhere; for why should it stop here rather than here? So that a

  thing will either be at rest or must be moved ad infinitum, unless

  something more powerful get in its way.

  Further, things are now thought to move into the void because it

  yields; but in a void this quality is present equally everywhere, so

  that things should move in all directions.

  Further, the truth of what we assert is plain from the following

  considerations. We see the same weight or body moving faster than

  another for two reasons, either because there is a difference in

  what it moves through, as between water, air, and earth, or because,

  other things being equal, the moving body differs from the other owing

  to excess of weight or of lightness.

  Now the medium causes a difference because it impedes the moving

  thing, most of all if it is moving in the opposite direction, but in a

  secondary degree even if it is at rest; and especially a medium that

  is not easily divided, i.e. a medium that is somewhat dense. A,

  then, will move through B in time G, and through D, which is

  thinner, in time E (if the length of B is egual to D), in proportion

  to the density of the hindering body. For let B be water and D air;

  then by so much as air is thinner and more incorporeal than water, A

  will move through D faster than through B. Let the speed have the same

  ratio to the speed, then, that air has to water. Then if air is

  twice as thin, the body will traverse B in twice the time that it does

  D, and the time G will be twice the time E. And always, by so much

  as the medium is more incorporeal and less resistant and more easily

  divided, the faster will be the movement.

  Now there is no ratio in which the void is exceeded by body, as

  there is no ratio of 0 to a number. For if 4 exceeds 3 by 1, and 2

  by more than 1, and 1 by still more than it exceeds 2, still there

  is no ratio by which it exceeds 0; for that which exceeds must be

  divisible into the excess + that which is exceeded, so that will be

  what it exceeds 0 by + 0. For this reason, too, a line does not exceed

  a point unless it is composed of points! Similarly the void can bear

  no ratio to the full, and therefore neither can movement through the

  one to movement through the other, but if a thing moves through the

  thickest medium such and such a distance in such and such a time, it

  moves through the void with a speed beyond any ratio. For let Z be

  void, equal in magnitude to B and to D. Then if A is to traverse and

  move through it in a certain time, H, a time less than E, however, the

  void will bear this ratio to the full. But in a time equal to H, A

  will traverse the part O of A. And it will surely also traverse in

  that time any substance Z which exceeds air in thickness in the

  ratio which the time E bears to the time H. For if the body Z be as

  much thinner than D as E exceeds H, A, if it moves through Z, will

  traverse it in a time inverse to the speed of the movement, i.e. in

  a time equal to H. If, then, there is no body in Z, A will traverse

  Z still more quickly. But we supposed that its traverse of Z when Z

  was void occupied the time H. So that it will traverse Z in an equal

  time whether Z be full or void. But this is impossible. It is plain,

  then, that if there is a time in which it will move through any part

  of the void, this impossible result will follow: it will be found to

  traverse a certain distance, whether this be full or void, in an equal

  time; for there will be some body which is in the same ratio to the

  other body as the time is to the time.

  To sum the matter up, the cause of this result is obvious, viz. that

  between any two movements there is a ratio (for they occupy time,

  and there is a ratio between any two times, so long as both are

  finite), but there is no ratio of void to full.

  These are the consequences that result from a difference in the

  media; the following depend upon an excess of one moving body over

  another. We see that bodies which have a greater impulse either of

  weight or of lightness, if they are alike in other respects, move

  faster over an equal space, and in the ratio which their magnitudes

  bear to each other. Therefore they will also move through the void

  with this ratio of speed. But that is impossible; for why should one

  move faster? (In moving through plena it must be so; for the greater

  divides them faster by its force. For a moving thing cleaves the

  medium either by its shape, or by the impulse which the body that is

  carried along or is projected possesses.) Therefore all will possess

  equal velocity. But this is impossible.

  It is evident from what has been said, then, that, if there is a

  void, a result follows which is the very opposite of the reason for

  which those who believe in a void set it up. They think that if

  movement in respect of place is to exist, the void cannot exist,

  separated all by itself; but this is the same as to say that place

  is a separate cavity; and this has already been stated to be

  impossible.

  But even if we consider it on its own merits the so-calle
d vacuum

  will be found to be really vacuous. For as, if one puts a cube in

  water, an amount of water equal to the cube will be displaced; so

  too in air; but the effect is imperceptible to sense. And indeed

  always in the case of any body that can be displaced, must, if it is

  not compressed, be displaced in the direction in which it is its

  nature to be displaced-always either down, if its locomotion is

  downwards as in the case of earth, or up, if it is fire, or in both

  directions-whatever be the nature of the inserted body. Now in the

  void this is impossible; for it is not body; the void must have

  penetrated the cube to a distance equal to that which this portion

  of void formerly occupied in the void, just as if the water or air had

  not been displaced by the wooden cube, but had penetrated right

  through it.

  But the cube also has a magnitude equal to that occupied by the

  void; a magnitude which, if it is also hot or cold, or heavy or light,

  is none the less different in essence from all its attributes, even if

  it is not separable from them; I mean the volume of the wooden cube.

  So that even if it were separated from everything else and were

  neither heavy nor light, it will occupy an equal amount of void, and

  fill the same place, as the part of place or of the void equal to

  itself. How then will the body of the cube differ from the void or

  place that is equal to it? And if there can be two such things, why

  cannot there be any number coinciding?

  This, then, is one absurd and impossible implication of the

  theory. It is also evident that the cube will have this same volume

  even if it is displaced, which is an attribute possessed by all

  other bodies also. Therefore if this differs in no respect from its

  place, why need we assume a place for bodies over and above the volume

  of each, if their volume be conceived of as free from attributes? It