Physics
By Aristotle
Written 350 B.C.E
Translated by R. P. Hardie and R. K. Gaye
Part 1
It remains to consider the following question. Was there ever a becoming
of motion before which it had no being, and is it perishing again so as
to leave nothing in motion? Or are we to say that it never had any becoming
and is not perishing, but always was and always will be? Is it in fact
an immortal never-failing property of things that are, a sort of life as
it were to all naturally constituted things?
Now the existence of motion is asserted by all who have anything
to say about nature, because they all concern themselves with the construction
of the world and study the question of becoming and perishing, which processes
could not come about without the existence of motion. But those who say
that there is an infinite number of worlds, some of which are in process
of becoming while others are in process of perishing, assert that there
is always motion (for these processes of becoming and perishing of the
worlds necessarily involve motion), whereas those who hold that there is
only one world, whether everlasting or not, make corresponding assumptions
in regard to motion. If then it is possible that at any time nothing should
be in motion, this must come about in one of two ways: either in the manner
described by Anaxagoras, who says that all things were together and at
rest for an infinite period of time, and that then Mind introduced motion
and separated them; or in the manner described by Empedocles, according
to whom the universe is alternately in motion and at rest-in motion, when
Love is making the one out of many, or Strife is making many out of one,
and at rest in the intermediate periods of time-his account being as
follows:
'Since One hath learned to spring from Manifold, And
One disjoined makes manifold arise, Thus they Become, nor stable
is their life: But since their motion must alternate be, Thus
have they ever Rest upon their round': for we must suppose that he
means by this that they alternate from the one motion to the other. We
must consider, then, how this matter stands, for the discovery of the truth
about it is of importance, not only for the study of nature, but also for
the investigation of the First Principle.
Let us take our start from what we have already laid down in our
course on Physics. Motion, we say, is the fulfilment of the movable in
so far as it is movable. Each kind of motion, therefore, necessarily involves
the presence of the things that are capable of that motion. In fact, even
apart from the definition of motion, every one would admit that in each
kind of motion it is that which is capable of that motion that is in motion:
thus it is that which is capable of alteration that is altered, and that
which is capable of local change that is in locomotion: and so there must
be something capable of being burned before there can be a process of being
burned, and something capable of burning before there can be a process
of burning. Moreover, these things also must either have a beginning before
which they had no being, or they must be eternal. Now if there was a becoming
of every movable thing, it follows that before the motion in question another
change or motion must have taken place in which that which was capable
of being moved or of causing motion had its becoming. To suppose, on the
other hand, that these things were in being throughout all previous time
without there being any motion appears unreasonable on a moment's thought,
and still more unreasonable, we shall find, on further consideration. For
if we are to say that, while there are on the one hand things that are
movable, and on the other hand things that are motive, there is a time
when there is a first movent and a first moved, and another time when there
is no such thing but only something that is at rest, then this thing that
is at rest must previously have been in process of change: for there must
have been some cause of its rest, rest being the privation of motion. Therefore,
before this first change there will be a previous change. For some things
cause motion in only one way, while others can produce either of two contrary
motions: thus fire causes heating but not cooling, whereas it would seem
that knowledge may be directed to two contrary ends while remaining one
and the same. Even in the former class, however, there seems to be something
similar, for a cold thing in a sense causes heating by turning away and
retiring, just as one possessed of knowledge voluntarily makes an error
when he uses his knowledge in the reverse way. But at any rate all things
that are capable respectively of affecting and being affected, or of causing
motion and being moved, are capable of it not under all conditions, but
only when they are in a particular condition and approach one another:
so it is on the approach of one thing to another that the one causes motion
and the other is moved, and when they are present under such conditions
as rendered the one motive and the other movable. So if the motion was
not always in process, it is clear that they must have been in a condition
not such as to render them capable respectively of being moved and of causing
motion, and one or other of them must have been in process of change: for
in what is relative this is a necessary consequence: e.g. if one thing
is double another when before it was not so, one or other of them, if not
both, must have been in process of change. It follows then, that there
will be a process of change previous to the first.
(Further, how can there be any 'before' and 'after' without the
existence of time? Or how can there be any time without the existence of
motion? If, then, time is the number of motion or itself a kind of motion,
it follows that, if there is always time, motion must also be eternal.
But so far as time is concerned we see that all with one exception are
in agreement in saying that it is uncreated: in fact, it is just this that
enables Democritus to show that all things cannot have had a becoming:
for time, he says, is uncreated. Plato alone asserts the creation of time,
saying that it had a becoming together with the universe, the universe
according to him having had a becoming. Now since time cannot exist and
is unthinkable apart from the moment, and the moment a kind of middle-point,
uniting as it does in itself both a beginning and an end, a beginning of
future time and an end of past time, it follows that there must always
be time: for the extremity of the last period of time that we take must
be found in some moment, since time contains no point of contact for us
except the moment. Therefore, since the moment is both a beginning and
an end, there must always be time on both sides of it. But if this is true
of time, it is evident that it must also be true of motion, time being
a kind of affection of motion.)
The same reasoning will also serve to show the imperishability
of motion: just as a becoming of motion would involve, as we saw, the existence
of a process of change previous to the first, in the same way a perishing
of motion would involve the existence of a process of change subsequent
to the last: for when a thing ceases to be moved, it does not therefore
at the same time cease to be movable-e.g. the cessation of the process
of being burned does not involve the cessation of the capacity of being
burned, since a thing may be capable of being burned without being in process
of being burned-nor, when a thing ceases to be movent, does it therefore
at the same time cease to a be motive. Again, the destructive agent will
have to be destroyed, after what it destroys has been destroyed, and then
that which has the capacity of destroying it will have to be destroyed
afterwards, (so that there will be a process of change subsequent to the
last,) for being destroyed also is a kind of change. If, then, view which
we are criticizing involves these impossible consequences, it is clear
that motion is eternal and cannot have existed at one time and not at another:
in fact such a view can hardly be described as anythling else than
fantastic.
And much the same may be said of the view that such is the ordinance
of nature and that this must be regarded as a principle, as would seem
to be the view of Empedocles when he says that the constitution of the
world is of necessity such that Love and Strife alternately predominate
and cause motion, while in the intermediate period of time there is a state
of rest. Probably also those who like like Anaxagoras, assert a single
principle (of motion) would hold this view. But that which is produced
or directed by nature can never be anything disorderly: for nature is everywhere
the cause of order. Moreover, there is no ratio in the relation of the
infinite to the infinite, whereas order always means ratio. But if we say
that there is first a state of rest for an infinite time, and then motion
is started at some moment, and that the fact that it is this rather than
a previous moment is of no importance, and involves no order, then we can
no longer say that it is nature's work: for if anything is of a certain
character naturally, it either is so invariably and is not sometimes of
this and sometimes of another character (e.g. fire, which travels upwards
naturally, does not sometimes do so and sometimes not) or there is a ratio
in the variation. It would be better, therefore, to say with Empedocles
and any one else who may have maintained such a theory as his that the
universe is alternately at rest and in motion: for in a system of this
kind we have at once a certain order. But even here the holder of the theory
ought not only to assert the fact: he ought to explain the cause of it:
i.e. he should not make any mere assumption or lay down any gratuitous
axiom, but should employ either inductive or demonstrative reasoning. The
Love and Strife postulated by Empedocles are not in themselves causes of
the fact in question, nor is it of the essence of either that it should
be so, the essential function of the former being to unite, of the latter
to separate. If he is to go on to explain this alternate predominance,
he should adduce cases where such a state of things exists, as he points
to the fact that among mankind we have something that unites men, namely
Love, while on the other hand enemies avoid one another: thus from the
observed fact that this occurs in certain cases comes the assumption that
it occurs also in the universe. Then, again, some argument is needed to
explain why the predominance of each of the two forces lasts for an equal
period of time. But it is a wrong assumption to suppose universally that
we have an adequate first principle in virtue of the fact that something
always is so or always happens so. Thus Democritus reduces the causes that
explain nature to the fact that things happened in the past in the same
way as they happen now: but he does not think fit to seek for a first principle
to explain this 'always': so, while his theory is right in so far as it
is applied to certain individual cases, he is wrong in making it of universal
application. Thus, a triangle always has its angles equal to two right
angles, but there is nevertheless an ulterior cause of the eternity of
this truth, whereas first principles are eternal and have no ulterior cause.
Let this conclude what we have to say in support of our contention that
there never was a time when there was not motion, and never will be a time
when there will not be motion.
Part 2
The arguments that may be advanced against this position are not
difficult to dispose of. The chief considerations that might be thought
to indicate that motion may exist though at one time it had not existed
at all are the following:
First, it may be said that no process of change is eternal: for
the nature of all change is such that it proceeds from something to something,
so that every process of change must be bounded by the contraries that
mark its course, and no motion can go on to infinity.
Secondly, we see that a thing that neither is in motion nor contains
any motion within itself can be set in motion; e.g. inanimate things that
are (whether the whole or some part is in question) not in motion but at
rest, are at some moment set in motion: whereas, if motion cannot have
a becoming before which it had no being, these things ought to be either
always or never in motion.
Thirdly, the fact is evident above all in the case of animate beings:
for it sometimes happens that there is no motion in us and we are quite
still, and that nevertheless we are then at some moment set in motion,
that is to say it sometimes happens that we produce a beginning of motion
in ourselves spontaneously without anything having set us in motion from
without. We see nothing like this in the case of inanimate things, which
are always set in motion by something else from without: the animal, on
the other hand, we say, moves itself: therefore, if an animal is ever in
a state of absolute rest, we have a motionless thing in which motion can
be produced from the thing itself, and not from without. Now if this can
occur in an animal, why should not the same be true also of the universe
as a whole? If it can occur in a small world it could also occur in a great
one: and if it can occur in the world, it could also occur in the infinite;
that is, if the infinite could as a whole possibly be in motion or at
rest.
Of these objections, then, the first-mentioned motion to opposites
is not always the same and numerically one a correct statement; in fact,
this may be said to be a necessary conclusion, provided that it is possible
for the motion of that which is one and the same to be not always one and
the same. (I mean that e.g. we may question whether the note given by a
single string is one and the same, or is different each time the string
is struck, although the string is in the same condition and is moved in
the same way.) But still, however this may be, there is nothing to prevent
there being a motion that is the same in virtue of being continuous and
eternal: we shall have something to say later that will make this point
clearer.
As regards the second objection, no absurdity is involved in the
fact that something not in motion may be set in motion, that which caused
the motion from without being at one time present, and at another absent.
Nevertheless, how this can be so remains matter for inquiry; how it comes
about, I mean, that the same motive force at one time causes a thing to
be in motion, and at another does not do so: for the difficulty raised
by our objector really amounts to this-why is it that some things are not
always at rest, and the rest always in motion?
The third objection may be thought to present more difficulty than
the others, namely, that which alleges that motion arises in things in
which it did not exist before, and adduces in proof the case of animate
things: thus an animal is first at rest and afterwards walks, not having
been set in motion apparently by anything from without. This, however,
is false: for we observe that there is always some part of the animal's
organism in motion, and the cause of the motion of this part is not the
animal itself, but, it may be, its environment. Moreover, we say that the
animal itself originates not all of its motions but its locomotion. So
it may well be the case-or rather we may perhaps say that it must necessarily
be the case-that many motions are produced in the body by its environment,
and some of these set in motion the intellect or the appetite, and this
again then sets the whole animal in motion: this is what happens when animals
are asleep: though there is then no perceptive motion in them, there is
some motion that causes them to wake up again. But we will leave this point
also to be elucidated at a later stage in our discussion.
Part 3
Our enquiry will resolve itself at the outset into a consideration
of the above-mentioned problem-what can be the reason why some things in
the world at one time are in motion and at another are at rest again? Now
one of three things must be true: either all things are always at rest,
or all things are always in motion, or some things are in motion and others
at rest: and in this last case again either the things that are in motion
are always in motion and the things that are at rest are always at rest,
or they are all constituted so as to be capable alike of motion and of
rest; or there is yet a third possibility remaining-it may be that some
things in the world are always motionless, others always in motion, while
others again admit of both conditions. This last is the account of the
matter that we must give: for herein lies the solution of all the difficulties
raised and the conclusion of the investigation upon which we are
engaged.
To maintain that all things are at rest, and to disregard sense-perception
in an attempt to show the theory to be reasonable, would be an instance
of intellectual weakness: it would call in question a whole system, not
a particular detail: moreover, it would be an attack not only on the physicist
but on almost all sciences and all received opinions, since motion plays
a part in all of them. Further, just as in arguments about mathematics
objections that involve first principles do not affect the mathematician-and
the other sciences are in similar case-so, too, objections involving the
point that we have just raised do not affect the physicist: for it is a
fundamental assumption with him that motion is ultimately referable to
nature herself.
The assertion that all things are in motion we may fairly regard
as equally false, though it is less subversive of physical science: for
though in our course on physics it was laid down that rest no less than
motion is ultimately referable to nature herself, nevertheless motion is
the characteristic fact of nature: moreover, the view is actually held
by some that not merely some things but all things in the world are in
motion and always in motion, though we cannot apprehend the fact by sense-perception.
Although the supporters of this theory do not state clearly what kind of
motion they mean, or whether they mean all kinds, it is no hard matter
to reply to them: thus we may point out that there cannot be a continuous
process either of increase or of decrease: that which comes between the
two has to be included. The theory resembles that about the stone being
worn away by the drop of water or split by plants growing out of it: if
so much has been extruded or removed by the drop, it does not follow that
half the amount has previously been extruded or removed in half the time:
the case of the hauled ship is exactly comparable: here we have so many
drops setting so much in motion, but a part of them will not set as much
in motion in any period of time. The amount removed is, it is true, divisible
into a number of parts, but no one of these was set in motion separately:
they were all set in motion together. It is evident, then, that from the
fact that the decrease is divisible into an infinite number of parts it
does not follow that some part must always be passing away: it all passes
away at a particular moment. Similarly, too, in the case of any alteration
whatever if that which suffers alteration is infinitely divisible it does
not follow from this that the same is true of the alteration itself, which
often occurs all at once, as in freezing. Again, when any one has fallen
ill, there must follow a period of time in which his restoration to health
is in the future: the process of change cannot take place in an instant:
yet the change cannot be a change to anything else but health. The assertion.
therefore, that alteration is continuous is an extravagant calling into
question of the obvious: for alteration is a change from one contrary to
another. Moreover, we notice that a stone becomes neither harder nor softer.
Again, in the matter of locomotion, it would be a strange thing if a stone
could be falling or resting on the ground without our being able to perceive
the fact. Further, it is a law of nature that earth and all other bodies
should remain in their proper places and be moved from them only by violence:
from the fact then that some of them are in their proper places it follows
that in respect of place also all things cannot be in motion. These and
other similar arguments, then, should convince us that it is impossible
either that all things are always in motion or that all things are always
at rest.
Nor again can it be that some things are always at rest, others
always in motion, and nothing sometimes at rest and sometimes in motion.
This theory must be pronounced impossible on the same grounds as those
previously mentioned: viz. that we see the above-mentioned changes occurring
in the case of the same things. We may further point out that the defender
of this position is fighting against the obvious, for on this theory there
can be no such thing as increase: nor can there be any such thing as compulsory
motion, if it is impossible that a thing can be at rest before being set
in motion unnaturally. This theory, then, does away with becoming and perishing.
Moreover, motion, it would seem, is generally thought to be a sort of becoming
and perishing, for that to which a thing changes comes to be, or occupancy
of it comes to be, and that from which a thing changes ceases to be, or
there ceases to be occupancy of it. It is clear, therefore, that there
are cases of occasional motion and occasional rest.
We have now to take the assertion that all things are sometimes
at rest and sometimes in motion and to confront it with the arguments previously
advanced. We must take our start as before from the possibilities that
we distinguished just above. Either all things are at rest, or all things
are in motion, or some things are at rest and others in motion. And if
some things are at rest and others in motion, then it must be that either
all things are sometimes at rest and sometimes in motion, or some things
are always at rest and the remainder always in motion, or some of the things
are always at rest and others always in motion while others again are sometimes
at rest and sometimes in motion. Now we have said before that it is impossible
that all things should be at rest: nevertheless we may now repeat that
assertion. We may point out that, even if it is really the case, as certain
persons assert, that the existent is infinite and motionless, it certainly
does not appear to be so if we follow sense-perception: many things that
exist appear to be in motion. Now if there is such a thing as false opinion
or opinion at all, there is also motion; and similarly if there is such
a thing as imagination, or if it is the case that anything seems to be
different at different times: for imagination and opinion are thought to
be motions of a kind. But to investigate this question at all-to seek a
reasoned justification of a belief with regard to which we are too well
off to require reasoned justification-implies bad judgement of what is
better and what is worse, what commends itself to belief and what does
not, what is ultimate and what is not. It is likewise impossible that all
things should be in motion or that some things should be always in motion
and the remainder always at rest. We have sufficient ground for rejecting
all these theories in the single fact that we see some things that are
sometimes in motion and sometimes at rest. It is evident, therefore, that
it is no less impossible that some things should be always in motion and
the remainder always at rest than that all things should be at rest or
that all things should be in motion continuously. It remains, then, to
consider whether all things are so constituted as to be capable both of
being in motion and of being at rest, or whether, while some things are
so constituted, some are always at rest and some are always in motion:
for it is this last view that we have to show to be
true.
Part 4
Now of things that cause motion or suffer motion, to some the motion
is accidental, to others essential: thus it is accidental to what merely
belongs to or contains as a part a thing that causes motion or suffers
motion, essential to a thing that causes motion or suffers motion not merely
by belonging to such a thing or containing it as a part.
Of things to which the motion is essential some derive their motion
from themselves, others from something else: and in some cases their motion
is natural, in others violent and unnatural. Thus in things that derive
their motion from themselves, e.g. all animals, the motion is natural (for
when an animal is in motion its motion is derived from itself): and whenever
the source of the motion of a thing is in the thing itself we say that
the motion of that thing is natural. Therefore the animal as a whole moves
itself naturally: but the body of the animal may be in motion unnaturally
as well as naturally: it depends upon the kind of motion that it may chance
to be suffering and the kind of element of which it is composed. And the
motion of things that derive their motion from something else is in some
cases natural, in other unnatural: e.g. upward motion of earthy things
and downward motion of fire are unnatural. Moreover the parts of animals
are often in motion in an unnatural way, their positions and the character
of the motion being abnormal. The fact that a thing that is in motion derives
its motion from something is most evident in things that are in motion
unnaturally, because in such cases it is clear that the motion is derived
from something other than the thing itself. Next to things that are in
motion unnaturally those whose motion while natural is derived from themselves-e.g.
animals-make this fact clear: for here the uncertainty is not as to whether
the motion is derived from something but as to how we ought to distinguish
in the thing between the movent and the moved. It would seem that in animals,
just as in ships and things not naturally organized, that which causes
motion is separate from that which suffers motion, and that it is only
in this sense that the animal as a whole causes its own
motion.
The greatest difficulty, however, is presented by the remaining
case of those that we last distinguished. Where things derive their motion
from something else we distinguished the cases in which the motion is unnatural:
we are left with those that are to be contrasted with the others by reason
of the fact that the motion is natural. It is in these cases that difficulty
would be experienced in deciding whence the motion is derived, e.g. in
the case of light and heavy things. When these things are in motion to
positions the reverse of those they would properly occupy, their motion
is violent: when they are in motion to their proper positions-the light
thing up and the heavy thing down-their motion is natural; but in this
latter case it is no longer evident, as it is when the motion is unnatural,
whence their motion is derived. It is impossible to say that their motion
is derived from themselves: this is a characteristic of life and peculiar
to living things. Further, if it were, it would have been in their power
to stop themselves (I mean that if e.g. a thing can cause itself to walk
it can also cause itself not to walk), and so, since on this supposition
fire itself possesses the power of upward locomotion, it is clear that
it should also possess the power of downward locomotion. Moreover if things
move themselves, it would be unreasonable to suppose that in only one kind
of motion is their motion derived from themselves. Again, how can anything
of continuous and naturally connected substance move itself? In so far
as a thing is one and continuous not merely in virtue of contact, it is
impassive: it is only in so far as a thing is divided that one part of
it is by nature active and another passive. Therefore none of the things
that we are now considering move themselves (for they are of naturally
connected substance), nor does anything else that is continuous: in each
case the movent must be separate from the moved, as we see to be the case
with inanimate things when an animate thing moves them. It is the fact
that these things also always derive their motion from something: what
it is would become evident if we were to distinguish the different kinds
of cause.
The above-mentioned distinctions can also be made in the case of
things that cause motion: some of them are capable of causing motion unnaturally
(e.g. the lever is not naturally capable of moving the weight), others
naturally (e.g. what is actually hot is naturally capable of moving what
is potentially hot): and similarly in the case of all other things of this
kind.
In the same way, too, what is potentially of a certain quality
or of a certain quantity in a certain place is naturally movable when it
contains the corresponding principle in itself and not accidentally (for
the same thing may be both of a certain quality and of a certain quantity,
but the one is an accidental, not an essential property of the other).
So when fire or earth is moved by something the motion is violent when
it is unnatural, and natural when it brings to actuality the proper activities
that they potentially possess. But the fact that the term 'potentially'
is used in more than one sense is the reason why it is not evident whence
such motions as the upward motion of fire and the downward motion of earth
are derived. One who is learning a science potentially knows it in a different
sense from one who while already possessing the knowledge is not actually
exercising it. Wherever we have something capable of acting and something
capable of being correspondingly acted on, in the event of any such pair
being in contact what is potential becomes at times actual: e.g. the learner
becomes from one potential something another potential something: for one
who possesses knowledge of a science but is not actually exercising it
knows the science potentially in a sense, though not in the same sense
as he knew it potentially before he learnt it. And when he is in this condition,
if something does not prevent him, he actively exercises his knowledge:
otherwise he would be in the contradictory state of not knowing. In regard
to natural bodies also the case is similar. Thus what is cold is potentially
hot: then a change takes place and it is fire, and it burns, unless something
prevents and hinders it. So, too, with heavy and light: light is generated
from heavy, e.g. air from water (for water is the first thing that is potentially
light), and air is actually light, and will at once realize its proper
activity as such unless something prevents it. The activity of lightness
consists in the light thing being in a certain situation, namely high up:
when it is in the contrary situation, it is being prevented from rising.
The case is similar also in regard to quantity and quality. But, be it
noted, this is the question we are trying to answer-how can we account
for the motion of light things and heavy things to their proper situations?
The reason for it is that they have a natural tendency respectively towards
a certain position: and this constitutes the essence of lightness and heaviness,
the former being determined by an upward, the latter by a downward, tendency.
As we have said, a thing may be potentially light or heavy in more senses
than one. Thus not only when a thing is water is it in a sense potentially
light, but when it has become air it may be still potentially light: for
it may be that through some hindrance it does not occupy an upper position,
whereas, if what hinders it is removed, it realizes its activity and continues
to rise higher. The process whereby what is of a certain quality changes
to a condition of active existence is similar: thus the exercise of knowledge
follows at once upon the possession of it unless something prevents it.
So, too, what is of a certain quantity extends itself over a certain space
unless something prevents it. The thing in a sense is and in a sense is
not moved by one who moves what is obstructing and preventing its motion
(e.g. one who pulls away a pillar from under a roof or one who removes
a stone from a wineskin in the water is the accidental cause of motion):
and in the same way the real cause of the motion of a ball rebounding from
a wall is not the wall but the thrower. So it is clear that in all these
cases the thing does not move itself, but it contains within itself the
source of motion-not of moving something or of causing motion, but of suffering
it.
If then the motion of all things that are in motion is either natural
or unnatural and violent, and all things whose motion is violent and unnatural
are moved by something, and something other than themselves, and again
all things whose motion is natural are moved by something-both those that
are moved by themselves and those that are not moved by themselves (e.g.
light things and heavy things, which are moved either by that which brought
the thing into existence as such and made it light and heavy, or by that
which released what was hindering and preventing it); then all things that
are in motion must be moved by something.
Part 5
Now this may come about in either of two ways. Either the movent
is not itself responsible for the motion, which is to be referred to something
else which moves the movent, or the movent is itself responsible for the
motion. Further, in the latter case, either the movent immediately precedes
the last thing in the series, or there may be one or more intermediate
links: e.g. the stick moves the stone and is moved by the hand, which again
is moved by the man: in the man, however, we have reached a movent that
is not so in virtue of being moved by something else. Now we say that the
thing is moved both by the last and by the first movent in the series,
but more strictly by the first, since the first movent moves the last,
whereas the last does not move the first, and the first will move the thing
without the last, but the last will not move it without the first: e.g.
the stick will not move anything unless it is itself moved by the man.
If then everything that is in motion must be moved by something, and the
movent must either itself be moved by something else or not, and in the
former case there must be some first movent that is not itself moved by
anything else, while in the case of the immediate movent being of this
kind there is no need of an intermediate movent that is also moved (for
it is impossible that there should be an infinite series of movents, each
of which is itself moved by something else, since in an infinite series
there is no first term)-if then everything that is in motion is moved by
something, and the first movent is moved but not by anything else, it much
be moved by itself.
This same argument may also be stated in another way as follows.
Every movent moves something and moves it with something, either with itself
or with something else: e.g. a man moves a thing either himself or with
a stick, and a thing is knocked down either by the wind itself or by a
stone propelled by the wind. But it is impossible for that with which a
thing is moved to move it without being moved by that which imparts motion
by its own agency: on the other hand, if a thing imparts motion by its
own agency, it is not necessary that there should be anything else with
which it imparts motion, whereas if there is a different thing with which
it imparts motion, there must be something that imparts motion not with
something else but with itself, or else there will be an infinite series.
If, then, anything is a movent while being itself moved, the series must
stop somewhere and not be infinite. Thus, if the stick moves something
in virtue of being moved by the hand, the hand moves the stick: and if
something else moves with the hand, the hand also is moved by something
different from itself. So when motion by means of an instrument is at each
stage caused by something different from the instrument, this must always
be preceded by something else which imparts motion with itself. Therefore,
if this last movent is in motion and there is nothing else that moves it,
it must move itself. So this reasoning also shows that when a thing is
moved, if it is not moved immediately by something that moves itself, the
series brings us at some time or other to a movent of this
kind.
And if we consider the matter in yet a third wa Ly we shall get
this same result as follows. If everything that is in motion is moved by
something that is in motion, ether this being in motion is an accidental
attribute of the movents in question, so that each of them moves something
while being itself in motion, but not always because it is itself in motion,
or it is not accidental but an essential attribute. Let us consider the
former alternative. If then it is an accidental attribute, it is not necessary
that that is in motion should be in motion: and if this is so it is clear
that there may be a time when nothing that exists is in motion, since the
accidental is not necessary but contingent. Now if we assume the existence
of a possibility, any conclusion that we thereby reach will not be an impossibility
though it may be contrary to fact. But the nonexistence of motion is an
impossibility: for we have shown above that there must always be
motion.
Moreover, the conclusion to which we have been led is a reasonable
one. For there must be three things-the moved, the movent, and the instrument
of motion. Now the moved must be in motion, but it need not move anything
else: the instrument of motion must both move something else and be itself
in motion (for it changes together with the moved, with which it is in
contact and continuous, as is clear in the case of things that move other
things locally, in which case the two things must up to a certain point
be in contact): and the movent-that is to say, that which causes motion
in such a manner that it is not merely the instrument of motion-must be
unmoved. Now we have visual experience of the last term in this series,
namely that which has the capacity of being in motion, but does not contain
a motive principle, and also of that which is in motion but is moved by
itself and not by anything else: it is reasonable, therefore, not to say
necessary, to suppose the existence of the third term also, that which
causes motion but is itself unmoved. So, too, Anaxagoras is right when
he says that Mind is impassive and unmixed, since he makes it the principle
of motion: for it could cause motion in this sense only by being itself
unmoved, and have supreme control only by being unmixed.
We will now take the second alternative. If the movement is not
accidentally but necessarily in motion-so that, if it were not in motion,
it would not move anything-then the movent, in so far as it is in motion,
must be in motion in one of two ways: it is moved either as that is which
is moved with the same kind of motion, or with a different kind-either
that which is heating, I mean, is itself in process of becoming hot, that
which is making healthy in process of becoming healthy, and that which
is causing locomotion in process of locomotion, or else that which is making
healthy is, let us say, in process of locomotion, and that which is causing
locomotion in process of, say, increase. But it is evident that this is
impossible. For if we adopt the first assumption we have to make it apply
within each of the very lowest species into which motion can be divided:
e.g. we must say that if some one is teaching some lesson in geometry,
he is also in process of being taught that same lesson in geometry, and
that if he is throwing he is in process of being thrown in just the same
manner. Or if we reject this assumption we must say that one kind of motion
is derived from another; e.g. that that which is causing locomotion is
in process of increase, that which is causing this increase is in process
of being altered by something else, and that which is causing this alteration
is in process of suffering some different kind of motion. But the series
must stop somewhere, since the kinds of motion are limited; and if we say
that the process is reversible, and that that which is causing alteration
is in process of locomotion, we do no more than if we had said at the outset
that that which is causing locomotion is in process of locomotion, and
that one who is teaching is in process of being taught: for it is clear
that everything that is moved is moved by the movent that is further back
in the series as well as by that which immediately moves it: in fact the
earlier movent is that which more strictly moves it. But this is of course
impossible: for it involves the consequence that one who is teaching is
in process of learning what he is teaching, whereas teaching necessarily
implies possessing knowledge, and learning not possessing it. Still more
unreasonable is the consequence involved that, since everything that is
moved is moved by something that is itself moved by something else, everything
that has a capacity for causing motion has as such a corresponding capacity
for being moved: i.e. it will have a capacity for being moved in the sense
in which one might say that everything that has a capacity for making healthy,
and exercises that capacity, has as such a capacity for being made healthy,
and that which has a capacity for building has as such a capacity for being
built. It will have the capacity for being thus moved either immediately
or through one or more links (as it will if, while everything that has
a capacity for causing motion has as such a capacity for being moved by
something else, the motion that it has the capacity for suffering is not
that with which it affects what is next to it, but a motion of a different
kind; e.g. that which has a capacity for making healthy might as such have
a capacity for learn. the series, however, could be traced back, as we
said before, until at some time or other we arrived at the same kind of
motion). Now the first alternative is impossible, and the second is fantastic:
it is absurd that that which has a capacity for causing alteration should
as such necessarily have a capacity, let us say, for increase. It is not
necessary, therefore, that that which is moved should always be moved by
something else that is itself moved by something else: so there will be
an end to the series. Consequently the first thing that is in motion will
derive its motion either from something that is at rest or from itself.
But if there were any need to consider which of the two, that which moves
itself or that which is moved by something else, is the cause and principle
of motion, every one would decide the former: for that which is itself
independently a cause is always prior as a cause to that which is so only
in virtue of being itself dependent upon something else that makes it
so.
We must therefore make a fresh start and consider the question;
if a thing moves itself, in what sense and in what manner does it do so?
Now everything that is in motion must be infinitely divisible, for it has
been shown already in our general course on Physics, that everything that
is essentially in motion is continuous. Now it is impossible that that
which moves itself should in its entirety move itself: for then, while
being specifically one and indivisible, it would as a Whole both undergo
and cause the same locomotion or alteration: thus it would at the same
time be both teaching and being taught (the same thing), or both restoring
to and being restored to the same health. Moreover, we have established
the fact that it is the movable that is moved; and this is potentially,
not actually, in motion, but the potential is in process to actuality,
and motion is an incomplete actuality of the movable. The movent on the
other hand is already in activity: e.g. it is that which is hot that produces
heat: in fact, that which produces the form is always something that possesses
it. Consequently (if a thing can move itself as a whole), the same thing
in respect of the same thing may be at the same time both hot and not hot.
So, too, in every other case where the movent must be described by the
same name in the same sense as the moved. Therefore when a thing moves
itself it is one part of it that is the movent and another part that is
moved. But it is not self-moving in the sense that each of the two parts
is moved by the other part: the following considerations make this evident.
In the first place, if each of the two parts is to move the other, there
will be no first movent. If a thing is moved by a series of movents, that
which is earlier in the series is more the cause of its being moved than
that which comes next, and will be more truly the movent: for we found
that there are two kinds of movent, that which is itself moved by something
else and that which derives its motion from itself: and that which is further
from the thing that is moved is nearer to the principle of motion than
that which is intermediate. In the second place, there is no necessity
for the movent part to be moved by anything but itself: so it can only
be accidentally that the other part moves it in return. I take then the
possible case of its not moving it: then there will be a part that is moved
and a part that is an unmoved movent. In the third place, there is no necessity
for the movent to be moved in return: on the contrary the necessity that
there should always be motion makes it necessary that there should be some
movent that is either unmoved or moved by itself. In the fourth place we
should then have a thing undergoing the same motion that it is causing-that
which is producing heat, therefore, being heated. But as a matter of fact
that which primarily moves itself cannot contain either a single part that
moves itself or a number of parts each of which moves itself. For, if the
whole is moved by itself, it must be moved either by some part of itself
or as a whole by itself as a whole. If, then, it is moved in virtue of
some part of it being moved by that part itself, it is this part that will
be the primary self-movent, since, if this part is separated from the whole,
the part will still move itself, but the whole will do so no longer. If
on the other hand the whole is moved by itself as a whole, it must be accidentally
that the parts move themselves: and therefore, their self-motion not being
necessary, we may take the case of their not being moved by themselves.
Therefore in the whole of the thing we may distinguish that which imparts
motion without itself being moved and that which is moved: for only in
this way is it possible for a thing to be self-moved. Further, if the whole
moves itself we may distinguish in it that which imparts the motion and
that which is moved: so while we say that AB is moved by itself, we may
also say that it is moved by A. And since that which imparts motion may
be either a thing that is moved by something else or a thing that is unmoved,
and that which is moved may be either a thing that imparts motion to something
else or a thing that does not, that which moves itself must be composed
of something that is unmoved but imparts motion and also of something that
is moved but does not necessarily impart motion but may or may not do so.
Thus let A be something that imparts motion but is unmoved, B something
that is moved by A and moves G, G something that is moved by B but moves
nothing (granted that we eventually arrive at G we may take it that there
is only one intermediate term, though there may be more). Then the whole
ABG moves itself. But if I take away G, AB will move itself, A imparting
motion and B being moved, whereas G will not move itself or in fact be
moved at all. Nor again will BG move itself apart from A: for B imparts
motion only through being moved by something else, not through being moved
by any part of itself. So only AB moves itself. That which moves itself,
therefore, must comprise something that imparts motion but is unmoved and
something that is moved but does not necessarily move anything else: and
each of these two things, or at any rate one of them, must be in contact
with the other. If, then, that which imparts motion is a continuous substance-that
which is moved must of course be so-it is clear that it is not through
some part of the whole being of such a nature as to be capable of moving
itself that the whole moves itself: it moves itself as a whole, both being
moved and imparting motion through containing a part that imparts motion
and a part that is moved. It does not impart motion as a whole nor is it
moved as a whole: it is A alone that imparts motion and B alone that is
moved. It is not true, further, that G is moved by A, which is
impossible.
Here a difficulty arises: if something is taken away from A (supposing
that that which imparts motion but is unmoved is a continuous substance),
or from B the part that is moved, will the remainder of A continue to impart
motion or the remainder of B continue to be moved? If so, it will not be
AB primarily that is moved by itself, since, when something is taken away
from AB, the remainder of AB will still continue to move itself. Perhaps
we may state the case thus: there is nothing to prevent each of the two
parts, or at any rate one of them, that which is moved, being divisible
though actually undivided, so that if it is divided it will not continue
in the possession of the same capacity: and so there is nothing to prevent
self-motion residing primarily in things that are potentially
divisible.
From what has been said, then, it is evident that that which primarily
imparts motion is unmoved: for, whether the series is closed at once by
that which is in motion but moved by something else deriving its motion
directly from the first unmoved, or whether the motion is derived from
what is in motion but moves itself and stops its own motion, on both suppositions
we have the result that in all cases of things being in motion that which
primarily imparts motion is unmoved.
Part 6
Since there must always be motion without intermission, there must
necessarily be something, one thing or it may be a plurality, that first
imparts motion, and this first movent must be unmoved. Now the question
whether each of the things that are unmoved but impart motion is eternal
is irrelevant to our present argument: but the following considerations
will make it clear that there must necessarily be some such thing, which,
while it has the capacity of moving something else, is itself unmoved and
exempt from all change, which can affect it neither in an unqualified nor
in an accidental sense. Let us suppose, if any one likes, that in the case
of certain things it is possible for them at different times to be and
not to be, without any process of becoming and perishing (in fact it would
seem to be necessary, if a thing that has not parts at one time is and
at another time is not, that any such thing should without undergoing any
process of change at one time be and at another time not be). And let us
further suppose it possible that some principles that are unmoved but capable
of imparting motion at one time are and at another time are not. Even so,
this cannot be true of all such principles, since there must clearly be
something that causes things that move themselves at one time to be and
at another not to be. For, since nothing that has not parts can be in motion,
that which moves itself must as a whole have magnitude, though nothing
that we have said makes this necessarily true of every movent. So the fact
that some things become and others perish, and that this is so continuously,
cannot be caused by any one of those things that, though they are unmoved,
do not always exist: nor again can it be caused by any of those which move
certain particular things, while others move other things. The eternity
and continuity of the process cannot be caused either by any one of them
singly or by the sum of them, because this causal relation must be eternal
and necessary, whereas the sum of these movents is infinite and they do
not all exist together. It is clear, then, that though there may be countless
instances of the perishing of some principles that are unmoved but impart
motion, and though many things that move themselves perish and are succeeded
by others that come into being, and though one thing that is unmoved moves
one thing while another moves another, nevertheless there is something
that comprehends them all, and that as something apart from each one of
them, and this it is that is the cause of the fact that some things are
and others are not and of the continuous process of change: and this causes
the motion of the other movents, while they are the causes of the motion
of other things. Motion, then, being eternal, the first movent, if there
is but one, will be eternal also: if there are more than one, there will
be a plurality of such eternal movents. We ought, however, to suppose that
there is one rather than many, and a finite rather than an infinite number.
When the consequences of either assumption are the same, we should always
assume that things are finite rather than infinite in number, since in
things constituted by nature that which is finite and that which is better
ought, if possible, to be present rather than the reverse: and here it
is sufficient to assume only one movent, the first of unmoved things, which
being eternal will be the principle of motion to everything
else.
The following argument also makes it evident that the first movent
must be something that is one and eternal. We have shown that there must
always be motion. That being so, motion must also be continuous, because
what is always is continuous, whereas what is merely in succession is not
continuous. But further, if motion is continuous, it is one: and it is
one only if the movent and the moved that constitute it are each of them
one, since in the event of a thing's being moved now by one thing and now
by another the whole motion will not be continuous but
successive.
Moreover a conviction that there is a first unmoved something may
be reached not only from the foregoing arguments, but also by considering
again the principles operative in movents. Now it is evident that among
existing things there are some that are sometimes in motion and sometimes
at rest. This fact has served above to make it clear that it is not true
either that all things are in motion or that all things are at rest or
that some things are always at rest and the remainder always in motion:
on this matter proof is supplied by things that fluctuate between the two
and have the capacity of being sometimes in motion and sometimes at rest.
The existence of things of this kind is clear to all: but we wish to explain
also the nature of each of the other two kinds and show that there are
some things that are always unmoved and some things that are always in
motion. In the course of our argument directed to this end we established
the fact that everything that is in motion is moved by something, and that
the movent is either unmoved or in motion, and that, if it is in motion,
it is moved either by itself or by something else and so on throughout
the series: and so we proceeded to the position that the first principle
that directly causes things that are in motion to be moved is that which
moves itself, and the first principle of the whole series is the unmoved.
Further it is evident from actual observation that there are things that
have the characteristic of moving themselves, e.g. the animal kingdom and
the whole class of living things. This being so, then, the view was suggested
that perhaps it may be possible for motion to come to be in a thing without
having been in existence at all before, because we see this actually occurring
in animals: they are unmoved at one time and then again they are in motion,
as it seems. We must grasp the fact, therefore, that animals move themselves
only with one kind of motion, and that this is not strictly originated
by them. The cause of it is not derived from the animal itself: it is connected
with other natural motions in animals, which they do not experience through
their own instrumentality, e.g. increase, decrease, and respiration: these
are experienced by every animal while it is at rest and not in motion in
respect of the motion set up by its own agency: here the motion is caused
by the atmosphere and by many things that enter into the animal: thus in
some cases the cause is nourishment: when it is being digested animals
sleep, and when it is being distributed through the system they awake and
move themselves, the first principle of this motion being thus originally
derived from outside. Therefore animals are not always in continuous motion
by their own agency: it is something else that moves them, itself being
in motion and changing as it comes into relation with each several thing
that moves itself. (Moreover in all these self-moving things the first
movent and cause of their self-motion is itself moved by itself, though
in an accidental sense: that is to say, the body changes its place, so
that that which is in the body changes its place also and is a self-movent
through its exercise of leverage.) Hence we may confidently conclude that
if a thing belongs to the class of unmoved movents that are also themselves
moved accidentally, it is impossible that it should cause continuous motion.
So the necessity that there should be motion continuously requires that
there should be a first movent that is unmoved even accidentally, if, as
we have said, there is to be in the world of things an unceasing and undying
motion, and the world is to remain permanently self-contained and within
the same limits: for if the first principle is permanent, the universe
must also be permanent, since it is continuous with the first principle.
(We must distinguish, however, between accidental motion of a thing by
itself and such motion by something else, the former being confined to
perishable things, whereas the latter belongs also to certain first principles
of heavenly bodies, of all those, that is to say, that experience more
than one locomotion.)
And further, if there is always something of this nature, a movent
that is itself unmoved and eternal, then that which is first moved by it
must be eternal. Indeed this is clear also from the consideration that
there would otherwise be no becoming and perishing and no change of any
kind in other things, which require something that is in motion to move
them: for the motion imparted by the unmoved will always be imparted in
the same way and be one and the same, since the unmoved does not itself
change in relation to that which is moved by it. But that which is moved
by something that, though it is in motion, is moved directly by the unmoved
stands in varying relations to the things that it moves, so that the motion
that it causes will not be always the same: by reason of the fact that
it occupies contrary positions or assumes contrary forms at different times
it will produce contrary motions in each several thing that it moves and
will cause it to be at one time at rest and at another time in
motion.
The foregoing argument, then, has served to clear up the point
about which we raised a difficulty at the outset-why is it that instead
of all things being either in motion or at rest, or some things being always
in motion and the remainder always at rest, there are things that are sometimes
in motion and sometimes not? The cause of this is now plain: it is because,
while some things are moved by an eternal unmoved movent and are therefore
always in motion, other things are moved by a movent that is in motion
and changing, so that they too must change. But the unmoved movent, as
has been said, since it remains permanently simple and unvarying and in
the same state, will cause motion that is one and simple.
Part 7
This matter will be made clearer, however, if we start afresh from
another point. We must consider whether it is or is not possible that there
should be a continuous motion, and, if it is possible, which this motion
is, and which is the primary motion: for it is plain that if there must
always be motion, and a particular motion is primary and continuous, then
it is this motion that is imparted by the first movent, and so it is necessarily
one and the same and continuous and primary.
Now of the three kinds of motion that there are-motion in respect
of magnitude, motion in respect of affection, and motion in respect of
place-it is this last, which we call locomotion, that must be primary.
This may be shown as follows. It is impossible that there should be increase
without the previous occurrence of alteration: for that which is increased,
although in a sense it is increased by what is like itself, is in a sense
increased by what is unlike itself: thus it is said that contrary is nourishment
to contrary: but growth is effected only by things becoming like to like.
There must be alteration, then, in that there is this change from contrary
to contrary. But the fact that a thing is altered requires that there should
be something that alters it, something e.g. that makes the potentially
hot into the actually hot: so it is plain that the movent does not maintain
a uniform relation to it but is at one time nearer to and at another farther
from that which is altered: and we cannot have this without locomotion.
If, therefore, there must always be motion, there must also always be locomotion
as the primary motion, and, if there is a primary as distinguished from
a secondary form of locomotion, it must be the primary form. Again, all
affections have their origin in condensation and rarefaction: thus heavy
and light, soft and hard, hot and cold, are considered to be forms of density
and rarity. But condensation and rarefaction are nothing more than combination
and separation, processes in accordance with which substances are said
to become and perish: and in being combined and separated things must change
in respect of place. And further, when a thing is increased or decreased
its magnitude changes in respect of place.
Again, there is another point of view from which it will be clearly
seen that locomotion is primary. As in the case of other things so too
in the case of motion the word 'primary' may be used in several senses.
A thing is said to be prior to other things when, if it does not exist,
the others will not exist, whereas it can exist without the others: and
there is also priority in time and priority in perfection of existence.
Let us begin, then, with the first sense. Now there must be motion continuously,
and there may be continuously either continuous motion or successive motion,
the former, however, in a higher degree than the latter: moreover it is
better that it should be continuous rather than successive motion, and
we always assume the presence in nature of the better, if it be possible:
since, then, continuous motion is possible (this will be proved later:
for the present let us take it for granted), and no other motion can be
continuous except locomotion, locomotion must be primary. For there is
no necessity for the subject of locomotion to be the subject either of
increase or of alteration, nor need it become or perish: on the other hand
there cannot be any one of these processes without the existence of the
continuous motion imparted by the first movent.
Secondly, locomotion must be primary in time: for this is the only
motion possible for things. It is true indeed that, in the case of any
individual thing that has a becoming, locomotion must be the last of its
motions: for after its becoming it first experiences alteration and increase,
and locomotion is a motion that belongs to such things only when they are
perfected. But there must previously be something else that is in process
of locomotion to be the cause even of the becoming of things that become,
without itself being in process of becoming, as e.g. the begotten is preceded
by what begot it: otherwise becoming might be thought to be the primary
motion on the ground that the thing must first become. But though this
is so in the case of any individual thing that becomes, nevertheless before
anything becomes, something else must be in motion, not itself becoming
but being, and before this there must again be something else. And since
becoming cannot be primary-for, if it were, everything that is in motion
would be perishable-it is plain that no one of the motions next in order
can be prior to locomotion. By the motions next in order I mean increase
and then alteration, decrease, and perishing. All these are posterior to
becoming: consequently, if not even becoming is prior to locomotion, then
no one of the other processes of change is so either.
Thirdly, that which is in process of becoming appears universally
as something imperfect and proceeding to a first principle: and so what
is posterior in the order of becoming is prior in the order of nature.
Now all things that go through the process of becoming acquire locomotion
last. It is this that accounts for the fact that some living things, e.g.
plants and many kinds of animals, owing to lack of the requisite organ,
are entirely without motion, whereas others acquire it in the course of
their being perfected. Therefore, if the degree in which things possess
locomotion corresponds to the degree in which they have realized their
natural development, then this motion must be prior to all others in respect
of perfection of existence: and not only for this reason but also because
a thing that is in motion loses its essential character less in the process
of locomotion than in any other kind of motion: it is the only motion that
does not involve a change of being in the sense in which there is a change
in quality when a thing is altered and a change in quantity when a thing
is increased or decreased. Above all it is plain that this motion, motion
in respect of place, is what is in the strictest sense produced by that
which moves itself; but it is the self-movent that we declare to be the
first principle of things that are moved and impart motion and the primary
source to which things that are in motion are to be
referred.
It is clear, then, from the foregoing arguments that locomotion
is the primary motion. We have now to show which kind of locomotion is
primary. The same process of reasoning will also make clear at the same
time the truth of the assumption we have made both now and at a previous
stage that it is possible that there should be a motion that is continuous
and eternal. Now it is clear from the following considerations that no
other than locomotion can be continuous. Every other motion and change
is from an opposite to an opposite: thus for the processes of becoming
and perishing the limits are the existent and the non-existent, for alteration
the various pairs of contrary affections, and for increase and decrease
either greatness and smallness or perfection and imperfection of magnitude:
and changes to the respective contraries are contrary changes. Now a thing
that is undergoing any particular kind of motion, but though previously
existent has not always undergone it, must previously have been at rest
so far as that motion is concerned. It is clear, then, that for the changing
thing the contraries will be states of rest. And we have a similar result
in the case of changes that are not motions: for becoming and perishing,
whether regarded simply as such without qualification or as affecting something
in particular, are opposites: therefore provided it is impossible for a
thing to undergo opposite changes at the same time, the change will not
be continuous, but a period of time will intervene between the opposite
processes. The question whether these contradictory changes are contraries
or not makes no difference, provided only it is impossible for them both
to be present to the same thing at the same time: the point is of no importance
to the argument. Nor does it matter if the thing need not rest in the contradictory
state, or if there is no state of rest as a contrary to the process of
change: it may be true that the non-existent is not at rest, and that perishing
is a process to the non-existent. All that matters is the intervention
of a time: it is this that prevents the change from being continuous: so,
too, in our previous instances the important thing was not the relation
of contrariety but the impossibility of the two processes being present
to a thing at the same time. And there is no need to be disturbed by the
fact that on this showing there may be more than one contrary to the same
thing, that a particular motion will be contrary both to rest and to motion
in the contrary direction. We have only to grasp the fact that a particular
motion is in a sense the opposite both of a state of rest and of the contrary
motion, in the same way as that which is of equal or standard measure is
the opposite both of that which surpasses it and of that which it surpasses,
and that it is impossible for the opposite motions or changes to be present
to a thing at the same time. Furthermore, in the case of becoming and perishing
it would seem to be an utterly absurd thing if as soon as anything has
become it must necessarily perish and cannot continue to exist for any
time: and, if this is true of becoming and perishing, we have fair grounds
for inferring the same to be true of the other kinds of change, since it
would be in the natural order of things that they should be uniform in
this respect.
Part 8
Let us now proceed to maintain that it is possible that there should
be an infinite motion that is single and continuous, and that this motion
is rotatory motion. The motion of everything that is in process of locomotion
is either rotatory or rectilinear or a compound of the two: consequently,
if one of the former two is not continuous, that which is composed of them
both cannot be continuous either. Now it is plain that if the locomotion
of a thing is rectilinear and finite it is not continuous locomotion: for
the thing must turn back, and that which turns back in a straight line
undergoes two contrary locomotions, since, so far as motion in respect
of place is concerned, upward motion is the contrary of downward motion,
forward motion of backward motion, and motion to the left of motion to
the right, these being the pairs of contraries in the sphere of place.
But we have already defined single and continuous motion to be motion of
a single thing in a single period of time and operating within a sphere
admitting of no further specific differentiation (for we have three things
to consider, first that which is in motion, e.g. a man or a god, secondly
the 'when' of the motion, that is to say, the time, and thirdly the sphere
within which it operates, which may be either place or affection or essential
form or magnitude): and contraries are specifically not one and the same
but distinct: and within the sphere of place we have the above-mentioned
distinctions. Moreover we have an indication that motion from A to B is
the contrary of motion from B to A in the fact that, if they occur at the
same time, they arrest and stop each other. And the same is true in the
case of a circle: the motion from A towards B is the contrary of the motion
from A towards G: for even if they are continuous and there is no turning
back they arrest each other, because contraries annihilate or obstruct
one another. On the other hand lateral motion is not the contrary of upward
motion. But what shows most clearly that rectilinear motion cannot be continuous
is the fact that turning back necessarily implies coming to a stand, not
only when it is a straight line that is traversed, but also in the case
of locomotion in a circle (which is not the same thing as rotatory locomotion:
for, when a thing merely traverses a circle, it may either proceed on its
course without a break or turn back again when it has reached the same
point from which it started). We may assure ourselves of the necessity
of this coming to a stand not only on the strength of observation, but
also on theoretical grounds. We may start as follows: we have three points,
starting-point, middle-point, and finishing-point, of which the middle-point
in virtue of the relations in which it stands severally to the other two
is both a starting-point and a finishing-point, and though numerically
one is theoretically two. We have further the distinction between the potential
and the actual. So in the straight line in question any one of the points
lying between the two extremes is potentially a middle-point: but it is
not actually so unless that which is in motion divides the line by coming
to a stand at that point and beginning its motion again: thus the middle-point
becomes both a starting-point and a goal, the starting-point of the latter
part and the finishing-point of the first part of the motion. This is the
case e.g. when A in the course of its locomotion comes to a stand at B
and starts again towards G: but when its motion is continuous A cannot
either have come to be or have ceased to be at the point B: it can only
have been there at the moment of passing, its passage not being contained
within any period of time except the whole of which the particular moment
is a dividing-point. To maintain that it has come to be and ceased to be
there will involve the consequence that A in the course of its locomotion
will always be coming to a stand: for it is impossible that A should simultaneously
have come to be at B and ceased to be there, so that the two things must
have happened at different points of time, and therefore there will be
the intervening period of time: consequently A will be in a state of rest
at B, and similarly at all other points, since the same reasoning holds
good in every case. When to A, that which is in process of locomotion,
B, the middle-point, serves both as a finishing-point and as a starting-point
for its motion, A must come to a stand at B, because it makes it two just
as one might do in thought. However, the point A is the real starting-point
at which the moving body has ceased to be, and it is at G that it has really
come to be when its course is finished and it comes to a stand. So this
is how we must meet the difficulty that then arises, which is as follows.
Suppose the line E is equal to the line Z, that A proceeds in continuous
locomotion from the extreme point of E to G, and that, at the moment when
A is at the point B, D is proceeding in uniform locomotion and with the
same velocity as A from the extremity of Z to H: then, says the argument,
D will have reached H before A has reached G for that which makes an earlier
start and departure must make an earlier arrival: the reason, then, for
the late arrival of A is that it has not simultaneously come to be and
ceased to be at B: otherwise it will not arrive later: for this to happen
it will be necessary that it should come to a stand there. Therefore we
must not hold that there was a moment when A came to be at B and that at
the same moment D was in motion from the extremity of Z: for the fact of
A's having come to be at B will involve the fact of its also ceasing to
be there, and the two events will not be simultaneous, whereas the truth
is that A is at B at a sectional point of time and does not occupy time
there. In this case, therefore, where the motion of a thing is continuous,
it is impossible to use this form of expression. On the other hand in the
case of a thing that turns back in its course we must do so. For suppose
H in the course of its locomotion proceeds to D and then turns back and
proceeds downwards again: then the extreme point D has served as finishing-point
and as starting-point for it, one point thus serving as two: therefore
H must have come to a stand there: it cannot have come to be at D and departed
from D simultaneously, for in that case it would simultaneously be there
and not be there at the same moment. And here we cannot apply the argument
used to solve the difficulty stated above: we cannot argue that H is at
D at a sectional point of time and has not come to be or ceased to be there.
For here the goal that is reached is necessarily one that is actually,
not potentially, existent. Now the point in the middle is potential: but
this one is actual, and regarded from below it is a finishing-point, while
regarded from above it is a starting-point, so that it stands in these
same two respective relations to the two motions. Therefore that which
turns back in traversing a rectilinear course must in so doing come to
a stand. Consequently there cannot be a continuous rectilinear motion that
is eternal.
The same method should also be adopted in replying to those who
ask, in the terms of Zeno's argument, whether we admit that before any
distance can be traversed half the distance must be traversed, that these
half-distances are infinite in number, and that it is impossible to traverse
distances infinite in number-or some on the lines of this same argument
put the questions in another form, and would have us grant that in the
time during which a motion is in progress it should be possible to reckon
a half-motion before the whole for every half-distance that we get, so
that we have the result that when the whole distance is traversed we have
reckoned an infinite number, which is admittedly impossible. Now when we
first discussed the question of motion we put forward a solution of this
difficulty turning on the fact that the period of time occupied in traversing
the distance contains within itself an infinite number of units: there
is no absurdity, we said, in supposing the traversing of infinite distances
in infinite time, and the element of infinity is present in the time no
less than in the distance. But, although this solution is adequate as a
reply to the questioner (the question asked being whether it is possible
in a finite time to traverse or reckon an infinite number of units), nevertheless
as an account of the fact and explanation of its true nature it is inadequate.
For suppose the distance to be left out of account and the question asked
to be no longer whether it is possible in a finite time to traverse an
infinite number of distances, and suppose that the inquiry is made to refer
to the time taken by itself (for the time contains an infinite number of
divisions): then this solution will no longer be adequate, and we must
apply the truth that we enunciated in our recent discussion, stating it
in the following way. In the act of dividing the continuous distance into
two halves one point is treated as two, since we make it a starting-point
and a finishing-point: and this same result is also produced by the act
of reckoning halves as well as by the act of dividing into halves. But
if divisions are made in this way, neither the distance nor the motion
will be continuous: for motion if it is to be continuous must relate to
what is continuous: and though what is continuous contains an infinite
number of halves, they are not actual but potential halves. If the halves
are made actual, we shall get not a continuous but an intermittent motion.
In the case of reckoning the halves, it is clear that this result follows:
for then one point must be reckoned as two: it will be the finishing-point
of the one half and the starting-point of the other, if we reckon not the
one continuous whole but the two halves. Therefore to the question whether
it is possible to pass through an infinite number of units either of time
or of distance we must reply that in a sense it is and in a sense it is
not. If the units are actual, it is not possible: if they are potential,
it is possible. For in the course of a continuous motion the traveller
has traversed an infinite number of units in an accidental sense but not
in an unqualified sense: for though it is an accidental characteristic
of the distance to be an infinite number of half-distances, this is not
its real and essential character. It is also plain that unless we hold
that the point of time that divides earlier from later always belongs only
to the later so far as the thing is concerned, we shall be involved in
the consequence that the same thing is at the same moment existent and
not existent, and that a thing is not existent at the moment when it has
become. It is true that the point is common to both times, the earlier
as well as the later, and that, while numerically one and the same, it
is theoretically not so, being the finishing-point of the one and the starting-point
of the other: but so far as the thing is concerned it belongs to the later
stage of what happens to it. Let us suppose a time ABG and a thing D, D
being white in the time A and not-white in the time B. Then D is at the
moment G white and not-white: for if we were right in saying that it is
white during the whole time A, it is true to call it white at any moment
of A, and not-white in B, and G is in both A and B. We must not allow,
therefore, that it is white in the whole of A, but must say that it is
so in all of it except the last moment G. G belongs already to the later
period, and if in the whole of A not-white was in process of becoming and
white of perishing, at G the process is complete. And so G is the first
moment at which it is true to call the thing white or not white respectively.
Otherwise a thing may be non-existent at the moment when it has become
and existent at the moment when it has perished: or else it must be possible
for a thing at the same time to be white and not white and in fact to be
existent and non-existent. Further, if anything that exists after having
been previously non-existent must become existent and does not exist when
it is becoming, time cannot be divisible into time-atoms. For suppose that
D was becoming white in the time A and that at another time B, a time-atom
consecutive with the last atom of A, D has already become white and so
is white at that moment: then, inasmuch as in the time A it was becoming
white and so was not white and at the moment B it is white, there must
have been a becoming between A and B and therefore also a time in which
the becoming took place. On the other hand, those who deny atoms of time
(as we do) are not affected by this argument: according to them D has become
and so is white at the last point of the actual time in which it was becoming
white: and this point has no other point consecutive with or in succession
to it, whereas time-atoms are conceived as successive. Moreover it is clear
that if D was becoming white in the whole time A, the time occupied by
it in having become white in addition to having been in process of becoming
white is no more than all that it occupied in the mere process of becoming
white.
These and such-like, then, are the arguments for our conclusion
that derive cogency from the fact that they have a special bearing on the
point at issue. If we look at the question from the point of view of general
theory, the same result would also appear to be indicated by the following
arguments. Everything whose motion is continuous must, on arriving at any
point in the course of its locomotion, have been previously also in process
of locomotion to that point, if it is not forced out of its path by anything:
e.g. on arriving at B a thing must also have been in process of locomotion
to B, and that not merely when it was near to B, but from the moment of
its starting on its course, since there can be, no reason for its being
so at any particular stage rather than at an earlier one. So, too, in the
case of the other kinds of motion. Now we are to suppose that a thing proceeds
in locomotion from A to G and that at the moment of its arrival at G the
continuity of its motion is unbroken and will remain so until it has arrived
back at A. Then when it is undergoing locomotion from A to G it is at the
same time undergoing also its locomotion to A from G: consequently it is
simultaneously undergoing two contrary motions, since the two motions that
follow the same straight line are contrary to each other. With this consequence
there also follows another: we have a thing that is in process of change
from a position in which it has not yet been: so, inasmuch as this is impossible,
the thing must come to a stand at G. Therefore the motion is not a single
motion, since motion that is interrupted by stationariness is not
single.
Further, the following argument will serve better to make this
point clear universally in respect of every kind of motion. If the motion
undergone by that which is in motion is always one of those already enumerated,
and the state of rest that it undergoes is one of those that are the opposites
of the motions (for we found that there could be no other besides these),
and moreover that which is undergoing but does not always undergo a particular
motion (by this I mean one of the various specifically distinct motions,
not some particular part of the whole motion) must have been previously
undergoing the state of rest that is the opposite of the motion, the state
of rest being privation of motion; then, inasmuch as the two motions that
follow the same straight line are contrary motions, and it is impossible
for a thing to undergo simultaneously two contrary motions, that which
is undergoing locomotion from A to G cannot also simultaneously be undergoing
locomotion from G to A: and since the latter locomotion is not simultaneous
with the former but is still to be undergone, before it is undergone there
must occur a state of rest at G: for this, as we found, is the state of
rest that is the opposite of the motion from G. The foregoing argument,
then, makes it plain that the motion in question is not
continuous.
Our next argument has a more special bearing than the foregoing
on the point at issue. We will suppose that there has occurred in something
simultaneously a perishing of not-white and a becoming of white. Then if
the alteration to white and from white is a continuous process and the
white does not remain any time, there must have occurred simultaneously
a perishing of not-white, a becoming of white, and a becoming of not-white:
for the time of the three will be the same.
Again, from the continuity of the time in which the motion takes
place we cannot infer continuity in the motion, but only successiveness:
in fact, how could contraries, e.g. whiteness and blackness, meet in the
same extreme point?
On the other hand, in motion on a circular line we shall find singleness
and continuity: for here we are met by no impossible consequence: that
which is in motion from A will in virtue of the same direction of energy
be simultaneously in motion to A (since it is in motion to the point at
which it will finally arrive), and yet will not be undergoing two contrary
or opposite motions: for a motion to a point and a motion from that point
are not always contraries or opposites: they are contraries only if they
are on the same straight line (for then they are contrary to one another
in respect of place, as e.g. the two motions along the diameter of the
circle, since the ends of this are at the greatest possible distance from
one another), and they are opposites only if they are along the same line.
Therefore in the case we are now considering there is nothing to prevent
the motion being continuous and free from all intermission: for rotatory
motion is motion of a thing from its place to its place, whereas rectilinear
motion is motion from its place to another place.
Moreover the progress of rotatory motion is never localized within
certain fixed limits, whereas that of rectilinear motion repeatedly is
so. Now a motion that is always shifting its ground from moment to moment
can be continuous: but a motion that is repeatedly localized within certain
fixed limits cannot be so, since then the same thing would have to undergo
simultaneously two opposite motions. So, too, there cannot be continuous
motion in a semicircle or in any other arc of a circle, since here also
the same ground must be traversed repeatedly and two contrary processes
of change must occur. The reason is that in these motions the starting-point
and the termination do not coincide, whereas in motion over a circle they
do coincide, and so this is the only perfect motion.
This differentiation also provides another means of showing that
the other kinds of motion cannot be continuous either: for in all of them
we find that there is the same ground to be traversed repeatedly; thus
in alteration there are the intermediate stages of the process, and in
quantitative change there are the intervening degrees of magnitude: and
in becoming and perishing the same thing is true. It makes no difference
whether we take the intermediate stages of the process to be few or many,
or whether we add or subtract one: for in either case we find that there
is still the same ground to be traversed repeatedly. Moreover it is plain
from what has been said that those physicists who assert that all sensible
things are always in motion are wrong: for their motion must be one or
other of the motions just mentioned: in fact they mostly conceive it as
alteration (things are always in flux and decay, they say), and they go
so far as to speak even of becoming and perishing as a process of alteration.
On the other hand, our argument has enabled us to assert the fact, applying
universally to all motions, that no motion admits of continuity except
rotatory motion: consequently neither alteration nor increase admits of
continuity. We need now say no more in support of the position that there
is no process of change that admits of infinity or continuity except rotatory
locomotion.
Part 9
It can now be shown plainly that rotation is the primary locomotion.
Every locomotion, as we said before, is either rotatory or rectilinear
or a compound of the two: and the two former must be prior to the last,
since they are the elements of which the latter consists. Moreover rotatory
locomotion is prior to rectilinear locomotion, because it is more simple
and complete, which may be shown as follows. The straight line traversed
in rectilinear motion cannot be infinite: for there is no such thing as
an infinite straight line; and even if there were, it would not be traversed
by anything in motion: for the impossible does not happen and it is impossible
to traverse an infinite distance. On the other hand rectilinear motion
on a finite straight line is if it turns back a composite motion, in fact
two motions, while if it does not turn back it is incomplete and perishable:
and in the order of nature, of definition, and of time alike the complete
is prior to the incomplete and the imperishable to the perishable. Again,
a motion that admits of being eternal is prior to one that does not. Now
rotatory motion can be eternal: but no other motion, whether locomotion
or motion of any other kind, can be so, since in all of them rest must
occur and with the occurrence of rest the motion has perished. Moreover
the result at which we have arrived, that rotatory motion is single and
continuous, and rectilinear motion is not, is a reasonable one. In rectilinear
motion we have a definite starting-point, finishing-point, middle-point,
which all have their place in it in such a way that there is a point from
which that which is in motion can be said to start and a point at which
it can be said to finish its course (for when anything is at the limits
of its course, whether at the starting-point or at the finishing-point,
it must be in a state of rest). On the other hand in circular motion there
are no such definite points: for why should any one point on the line be
a limit rather than any other? Any one point as much as any other is alike
starting-point, middle-point, and finishing-point, so that we can say of
certain things both that they are always and that they never are at a starting-point
and at a finishing-point (so that a revolving sphere, while it is in motion,
is also in a sense at rest, for it continues to occupy the same place).
The reason of this is that in this case all these characteristics belong
to the centre: that is to say, the centre is alike starting-point, middle-point,
and finishing-point of the space traversed; consequently since this point
is not a point on the circular line, there is no point at which that which
is in process of locomotion can be in a state of rest as having traversed
its course, because in its locomotion it is proceeding always about a central
point and not to an extreme point: therefore it remains still, and the
whole is in a sense always at rest as well as continuously in motion. Our
next point gives a convertible result: on the one hand, because rotation
is the measure of motions it must be the primary motion (for all things
are measured by what is primary): on the other hand, because rotation is
the primary motion it is the measure of all other motions. Again, rotatory
motion is also the only motion that admits of being regular. In rectilinear
locomotion the motion of things in leaving the starting-point is not uniform
with their motion in approaching the finishing-point, since the velocity
of a thing always increases proportionately as it removes itself farther
from its position of rest: on the other hand rotatory motion is the only
motion whose course is naturally such that it has no starting-point or
finishing-point in itself but is determined from elsewhere.
As to locomotion being the primary motion, this is a truth that
is attested by all who have ever made mention of motion in their theories:
they all assign their first principles of motion to things that impart
motion of this kind. Thus 'separation' and 'combination' are motions in
respect of place, and the motion imparted by 'Love' and 'Strife' takes
these forms, the latter 'separating' and the former 'combining'. Anaxagoras,
too, says that 'Mind', his first movent, 'separates'. Similarly those who
assert no cause of this kind but say that 'void' accounts for motion-they
also hold that the motion of natural substance is motion in respect of
place: for their motion that is accounted for by 'void' is locomotion,
and its sphere of operation may be said to be place. Moreover they are
of opinion that the primary substances are not subject to any of the other
motions, though the things that are compounds of these substances are so
subject: the processes of increase and decrease and alteration, they say,
are effects of the 'combination' and 'separation' of atoms. It is the same,
too, with those who make out that the becoming or perishing of a thing
is accounted for by 'density' or 'rarity': for it is by 'combination' and
'separation' that the place of these things in their systems is determined.
Moreover to these we may add those who make Soul the cause of motion: for
they say that things that undergo motion have as their first principle
'that which moves itself': and when animals and all living things move
themselves, the motion is motion in respect of place. Finally it is to
be noted that we say that a thing 'is in motion' in the strict sense of
the term only when its motion is motion in respect of place: if a thing
is in process of increase or decrease or is undergoing some alteration
while remaining at rest in the same place, we say that it is in motion
in some particular respect: we do not say that it 'is in motion' without
qualification.
Our present position, then, is this: We have argued that there
always was motion and always will be motion throughout all time, and we
have explained what is the first principle of this eternal motion: we have
explained further which is the primary motion and which is the only motion
that can be eternal: and we have pronounced the first movent to be
unmoved.
Part 10
We have now to assert that the first movent must be without parts
and without magnitude, beginning with the establishment of the premisses
on which this conclusion depends.
One of these premisses is that nothing finite can cause motion
during an infinite time. We have three things, the movent, the moved, and
thirdly that in which the motion takes place, namely the time: and these
are either all infinite or all finite or partly-that is to say two of them
or one of them-finite and partly infinite. Let A be the movement, B the
moved, and G the infinite time. Now let us suppose that D moves E, a part
of B. Then the time occupied by this motion cannot be equal to G: for the
greater the amount moved, the longer the time occupied. It follows that
the time Z is not infinite. Now we see that by continuing to add to D,
I shall use up A and by continuing to add to E, I shall use up B: but I
shall not use up the time by continually subtracting a correspon | |
