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.