Various Works

to deny that KM is moved by anything on the ground that it is not

  evident which is the part that is moving it and which the part that is

  moved. In the second place that which is in motion without being moved

  by anything does not necessarily cease from its motion because

  something else is at rest, but a thing must be moved by something if

  the fact of something else having ceased from its motion causes it

  to be at rest. Thus, if this is accepted, everything that is in motion

  must be moved by something. For AB, which has been taken to

  represent that which is in motion, must be divisible since

  everything that is in motion is divisible. Let it be divided, then, at

  G. Now if GB is not in motion, then AB will not be in motion: for if

  it is, it is clear that AG would be in motion while BG is at rest, and

  thus AB cannot be in motion essentially and primarily. But ex

  hypothesi AB is in motion essentially and primarily. Therefore if GB

  is not in motion AB will be at rest. But we have agreed that that

  which is at rest if something else is not in motion must be moved by

  something. Consequently, everything that is in motion must be moved by

  something: for that which is in motion will always be divisible, and

  if a part of it is not in motion the whole must be at rest.

  Since everything that is in motion must be moved by something, let

  us take the case in which a thing is in locomotion and is moved by

  something that is itself in motion, and that again is moved by

  something else that is in motion, and that by something else, and so

  on continually: then the series cannot go on to infinity, but there

  must be some first movent. For let us suppose that this is not so

  and take the series to be infinite. Let A then be moved by B, B by

  G, G by D, and so on, each member of the series being moved by that

  which comes next to it. Then since ex hypothesi the movent while

  causing motion is also itself in motion, and the motion of the moved

  and the motion of the movent must proceed simultaneously (for the

  movent is causing motion and the moved is being moved

  simultaneously) it is evident that the respective motions of A, B,

  G, and each of the other moved movents are simultaneous. Let us take

  the motion of each separately and let E be the motion of A, Z of B,

  and H and O respectively the motions of G and D: for though they are

  all moved severally one by another, yet we may still take the motion

  of each as numerically one, since every motion is from something to

  something and is not infinite in respect of its extreme points. By a

  motion that is numerically one I mean a motion that proceeds from

  something numerically one and the same to something numerically one

  and the same in a period of time numerically one and the same: for a

  motion may be the same generically, specifically, or numerically: it

  is generically the same if it belongs to the same category, e.g.

  substance or quality: it is specifically the same if it proceeds

  from something specifically the same to something specifically the

  same, e.g. from white to black or from good to bad, which is not of

  a kind specifically distinct: it is numerically the same if it

  proceeds from something numerically one to something numerically one

  in the same period of time, e.g. from a particular white to a

  particular black, or from a particular place to a particular place, in

  a particular period of time: for if the period of time were not one

  and the same, the motion would no longer be numerically one though

  it would still be specifically one.

  We have dealt with this question above. Now let us further take

  the time in which A has completed its motion, and let it be

  represented by K. Then since the motion of A is finite the time will

  also be finite. But since the movents and the things moved are

  infinite, the motion EZHO, i.e. the motion that is composed of all the

  individual motions, must be infinite. For the motions of A, B, and the

  others may be equal, or the motions of the others may be greater:

  but assuming what is conceivable, we find that whether they are

  equal or some are greater, in both cases the whole motion is infinite.

  And since the motion of A and that of each of the others are

  simultaneous, the whole motion must occupy the same time as the motion

  of A: but the time occupied by the motion of A is finite: consequently

  the motion will be infinite in a finite time, which is impossible.

  It might be thought that what we set out to prove has thus been

  shown, but our argument so far does not prove it, because it does

  not yet prove that anything impossible results from the contrary

  supposition: for in a finite time there may be an infinite motion,

  though not of one thing, but of many: and in the case that we are

  considering this is so: for each thing accomplishes its own motion,

  and there is no impossibility in many things being in motion

  simultaneously. But if (as we see to be universally the case) that

  which primarily is moved locally and corporeally must be either in

  contact with or continuous with that which moves it, the things

  moved and the movents must be continuous or in contact with one

  another, so that together they all form a single unity: whether this

  unity is finite or infinite makes no difference to our present

  argument; for in any case since the things in motion are infinite in

  number the whole motion will be infinite, if, as is theoretically

  possible, each motion is either equal to or greater than that which

  follows it in the series: for we shall take as actual that which is

  theoretically possible. If, then, A, B, G, D form an infinite

  magnitude that passes through the motion EZHO in the finite time K,

  this involves the conclusion that an infinite motion is passed through

  in a finite time: and whether the magnitude in question is finite or

  infinite this is in either case impossible. Therefore the series

  must come to an end, and there must be a first movent and a first

  moved: for the fact that this impossibility results only from the

  assumption of a particular case is immaterial, since the case

  assumed is theoretically possible, and the assumption of a

  theoretically possible case ought not to give rise to any impossible

  result.

  2

  That which is the first movement of a thing-in the sense that it

  supplies not 'that for the sake of which' but the source of the

  motion-is always together with that which is moved by it by 'together'

  I mean that there is nothing intermediate between them). This is

  universally true wherever one thing is moved by another. And since

  there are three kinds of motion, local, qualitative, and quantitative,

  there must also be three kinds of movent, that which causes

  locomotion, that which causes alteration, and that which causes

  increase or decrease.

  Let us begin with locomotion, for this is the primary motion.

  Everything that is in locomotion is moved either by itself or by

  something else. In the case of things that are moved by themselves

  it is evident that the moved and the movent are tog
ether: for they

  contain within themselves their first movent, so that there is nothing

  in between. The motion of things that are moved by something else must

  proceed in one of four ways: for there are four kinds of locomotion

  caused by something other than that which is in motion, viz.

  pulling, pushing, carrying, and twirling. All forms of locomotion

  are reducible to these. Thus pushing on is a form of pushing in

  which that which is causing motion away from itself follows up that

  which it pushes and continues to push it: pushing off occurs when

  the movent does not follow up the thing that it has moved: throwing

  when the movent causes a motion away from itself more violent than the

  natural locomotion of the thing moved, which continues its course so

  long as it is controlled by the motion imparted to it. Again,

  pushing apart and pushing together are forms respectively of pushing

  off and pulling: pushing apart is pushing off, which may be a motion

  either away from the pusher or away from something else, while pushing

  together is pulling, which may be a motion towards something else as

  well as the puller. We may similarly classify all the varieties of

  these last two, e.g. packing and combing: the former is a form of

  pushing together, the latter a form of pushing apart. The same is true

  of the other processes of combination and separation (they will all be

  found to be forms of pushing apart or of pushing together), except

  such as are involved in the processes of becoming and perishing. (At

  same time it is evident that there is no other kind of motion but

  combination and separation: for they may all be apportioned to one

  or other of those already mentioned.) Again, inhaling is a form of

  pulling, exhaling a form of pushing: and the same is true of

  spitting and of all other motions that proceed through the body,

  whether secretive or assimilative, the assimilative being forms of

  pulling, the secretive of pushing off. All other kinds of locomotion

  must be similarly reduced, for they all fall under one or other of our

  four heads. And again, of these four, carrying and twirling are to

  pulling and pushing. For carrying always follows one of the other

  three methods, for that which is carried is in motion accidentally,

  because it is in or upon something that is in motion, and that which

  carries it is in doing so being either pulled or pushed or twirled;

  thus carrying belongs to all the other three kinds of motion in

  common. And twirling is a compound of pulling and pushing, for that

  which is twirling a thing must be pulling one part of the thing and

  pushing another part, since it impels one part away from itself and

  another part towards itself. If, therefore, it can be shown that

  that which is pushing and that which is pushing and pulling are

  adjacent respectively to that which is being pushed and that which

  is being pulled, it will be evident that in all locomotion there is

  nothing intermediate between moved and movent. But the former fact

  is clear even from the definitions of pushing and pulling, for pushing

  is motion to something else from oneself or from something else, and

  pulling is motion from something else to oneself or to something else,

  when the motion of that which is pulling is quicker than the motion

  that would separate from one another the two things that are

  continuous: for it is this that causes one thing to be pulled on along

  with the other. (It might indeed be thought that there is a form of

  pulling that arises in another way: that wood, e.g. pulls fire in a

  manner different from that described above. But it makes no difference

  whether that which pulls is in motion or is stationary when it is

  pulling: in the latter case it pulls to the place where it is, while

  in the former it pulls to the place where it was.) Now it is

  impossible to move anything either from oneself to something else or

  something else to oneself without being in contact with it: it is

  evident, therefore, that in all locomotion there is nothing

  intermediate between moved and movent.

  Nor again is there anything intermediate between that which

  undergoes and that which causes alteration: this can be proved by

  induction: for in every case we find that the respective extremities

  of that which causes and that which undergoes alteration are adjacent.

  For our assumption is that things that are undergoing alteration are

  altered in virtue of their being affected in respect of their

  so-called affective qualities, since that which is of a certain

  quality is altered in so far as it is sensible, and the

  characteristics in which bodies differ from one another are sensible

  characteristics: for every body differs from another in possessing a

  greater or lesser number of sensible characteristics or in

  possessing the same sensible characteristics in a greater or lesser

  degree. But the alteration of that which undergoes alteration is

  also caused by the above-mentioned characteristics, which are

  affections of some particular underlying quality. Thus we say that a

  thing is altered by becoming hot or sweet or thick or dry or white:

  and we make these assertions alike of what is inanimate and of what is

  animate, and further, where animate things are in question, we make

  them both of the parts that have no power of sense-perception and of

  the senses themselves. For in a way even the senses undergo

  alteration, since the active sense is a motion through the body in the

  course of which the sense is affected in a certain way. We see,

  then, that the animate is capable of every kind of alteration of which

  the inanimate is capable: but the inanimate is not capable of every

  kind of alteration of which the animate is capable, since it is not

  capable of alteration in respect of the senses: moreover the inanimate

  is unconscious of being affected by alteration, whereas the animate is

  conscious of it, though there is nothing to prevent the animate also

  being unconscious of it when the process of the alteration does not

  concern the senses. Since, then, the alteration of that which

  undergoes alteration is caused by sensible things, in every case of

  such alteration it is evident that the respective extremities of

  that which causes and that which undergoes alteration are adjacent.

  Thus the air is continuous with that which causes the alteration,

  and the body that undergoes alteration is continuous with the air.

  Again, the colour is continuous with the light and the light with

  the sight. And the same is true of hearing and smelling: for the

  primary movent in respect to the moved is the air. Similarly, in the

  case of tasting, the flavour is adjacent to the sense of taste. And it

  is just the same in the case of things that are inanimate and

  incapable of sense-perception. Thus there can be nothing

  intermediate between that which undergoes and that which causes

  alteration.

  Nor, again, can there be anything intermediate between that which

  suffers and that which causes increase: for the part of the latter

  that starts the increase doe
s so by becoming attached in such a way to

  the former that the whole becomes one. Again, the decrease of that

  which suffers decrease is caused by a part of the thing becoming

  detached. So that which causes increase and that which causes decrease

  must be continuous with that which suffers increase and that which

  suffers decrease respectively: and if two things are continuous with

  one another there can be nothing intermediate between them.

  It is evident, therefore, that between the extremities of the

  moved and the movent that are respectively first and last in reference

  to the moved there is nothing intermediate.

  3

  Everything, we say, that undergoes alteration is altered by sensible

  causes, and there is alteration only in things that are said to be

  essentially affected by sensible things. The truth of this is to be

  seen from the following considerations. Of all other things it would

  be most natural to suppose that there is alteration in figures and

  shapes, and in acquired states and in the processes of acquiring and

  losing these: but as a matter of fact in neither of these two

  classes of things is there alteration.

  In the first place, when a particular formation of a thing is

  completed, we do not call it by the name of its material: e.g. we do

  not call the statue 'bronze' or the pyramid 'wax' or the bed 'wood',

  but we use a derived expression and call them 'of bronze', 'waxen',

  and 'wooden' respectively. But when a thing has been affected and

  altered in any way we still call it by the original name: thus we

  speak of the bronze or the wax being dry or fluid or hard or hot.

  And not only so: we also speak of the particular fluid or hot

  substance as being bronze, giving the material the same name as that

  which we use to describe the affection.

  Since, therefore, having regard to the figure or shape of a thing we

  no longer call that which has become of a certain figure by the name

  of the material that exhibits the figure, whereas having regard to a

  thing's affections or alterations we still call it by the name of

  its material, it is evident that becomings of the former kind cannot

  be alterations.