Written ca. 350 B.C.
Translated by R. P. Hardie and R. K. Gaye
text file [458k]
Book IV - Part 1
THE physicist must have a knowledge of Place, too, as well as of the infinite-namely,
whether there is such a thing or not, and the manner of its existence and what it
is-both because all suppose that things which exist are somewhere (the non-existent
is nowhere--where is the goat-stag or the sphinx?), and because 'motion' in its most
general and primary sense is change of place, which we call 'locomotion'.
The question, what is place? presents many difficulties. An examination of all the
relevant facts seems to lead to divergent conclusions. Moreover, we have inherited
nothing from previous thinkers, whether in the way of a statement of difficulties or of
The existence of place is held to be obvious from the fact of mutual replacement.
Where water now is, there in turn, when the water has gone out as from a vessel, air
is present. When therefore another body occupies this same place, the place is
thought to be different from all the bodies which come to be in it and replace one
another. What now contains air formerly contained water, so that clearly the place or
space into which and out of which they passed was something different from both.
How does Aristotle prove the existence of place?
Further, the typical locomotions of the elementary natural bodies-namely, fire, earth,
and the like-show not only that place is something, but also that it exerts a certain
influence. Each is carried to its own place, if it is not hindered, the one up, the other
down. Now these are regions or kinds of place-up and down and the rest of the six
directions. Nor do such distinctions (up and down and right and left, &c.) hold only
in relation to us. To us they are not always the same but change with the direction in
which we are turned: that is why the same thing may be both right and left, up and
down, before and behind. But in nature each is distinct, taken apart by itself. It is not
every chance direction which is 'up', but where fire and what is light are carried;
similarly, too, 'down' is not any chance direction but where what has weight and
what is made of earth are carried-the implication being that these places do not differ
merely in relative position, but also as possessing distinct potencies. This is made
plain also by the objects studied by mathematics. Though they have no real place,
they nevertheless, in respect of their position relatively to us, have a right and left as
attributes ascribed to them only in consequence of their relative position, not having
by nature these various characteristics. Again, the theory that the void exists involves
the existence of place: for one would define void as place bereft of body.
These considerations then would lead us to suppose that place is something distinct
from bodies, and that every sensible body is in place. Hesiod too might be held to
have given a correct account of it when he made chaos first. At least he says:
'First of all things came chaos to being, then broad-breasted earth,' implying that
things need to have space first, because he thought, with most people, that everything
is somewhere and in place. If this is its nature, the potency of place must be a
marvellous thing, and take precedence of all other things. For that without which
nothing else can exist, while it can exist without the others, must needs be first; for
place does not pass out of existence when the things in it are annihilated.
True, but even if we suppose its existence settled, the question of its nature presents
difficulty-whether it is some sort of 'bulk' of body or some entity other than that, for
we must first determine its genus.
(1) Now it has three dimensions, length, breadth, depth, the dimensions by which all
body also is bounded. But the place cannot be body; for if it were there would be
two bodies in the same place.
(2) Further, if body has a place and space, clearly so too have surface and the other
limits of body; for the same statement will apply to them: where the bounding planes
of the water were, there in turn will be those of the air. But when we come to a point
we cannot make a distinction between it and its place. Hence if the place of a point is
not different from the point, no more will that of any of the others be different, and
place will not be something different from each of them.
(3) What in the world then are we to suppose place to be? If it has the sort of nature
described, it cannot be an element or composed of elements, whether these be
corporeal or incorporeal: for while it has size, it has not body. But the elements of
sensible bodies are bodies, while nothing that has size results from a combination of
(4) Also we may ask: of what in things is space the cause? None of the four modes
of causation can be ascribed to it. It is neither in the sense of the matter of existents
(for nothing is composed of it), nor as the form and definition of things, nor as end,
nor does it move existents.
(5) Further, too, if it is itself an existent, where will it be? Zeno's difficulty demands
an explanation: for if everything that exists has a place, place too will have a place,
and so on ad infinitum.
(6) Again, just as every body is in place, so, too, every place has a body in it. What
then shall we say about growing things? It follows from these premisses that their
place must grow with them, if their place is neither less nor greater than they are.
By asking these questions, then, we must raise the whole problem about place-not
only as to what it is, but even whether there is such a thing.
Summarize the six characteristics of place.
Book IV - Part 2
We may distinguish generally between predicating B of A because it (A) is itself, and
because it is something else; and particularly between place which is common and in
which all bodies are, and the special place occupied primarily by each. I mean, for
instance, that you are now in the heavens because you are in the air and it is in the
heavens; and you are in the air because you are on the earth; and similarly on the
earth because you are in this place which contains no more than you.
Now if place is what primarily contains each body, it would be a limit, so that the
place would be the form or shape of each body by which the magnitude or the
matter of the magnitude is defined: for this is the limit of each body.
If, then, we look at the question in this way the place of a thing is its form. But, if we
regard the place as the extension of the magnitude, it is the matter. For this is
different from the magnitude: it is what is contained and defined by the form, as by a
bounding plane. Matter or the indeterminate is of this nature; when the boundary and
attributes of a sphere are taken away, nothing but the matter is left.
This is why Plato in the Timaeus says that matter and space are the same; for the
'participant' and space are identical. (It is true, indeed, that the account he gives there
of the 'participant' is different from what he says in his so-called 'unwritten teaching'.
Nevertheless, he did identify place and space.) I mention Plato because, while all
hold place to be something, he alone tried to say what it is.
In view of these facts we should naturally expect to find difficulty in determining what
place is, if indeed it is one of these two things, matter or form. They demand a very
close scrutiny, especially as it is not easy to recognize them apart.
But it is at any rate not difficult to see that place cannot be either of them. The form
and the matter are not separate from the thing, whereas the place can be separated.
As we pointed out, where air was, water in turn comes to be, the one replacing the
other; and similarly with other bodies. Hence the place of a thing is neither a part nor
a state of it, but is separable from it. For place is supposed to be something like a
vessel-the vessel being a transportable place. But the vessel is no part of the thing.
In so far then as it is separable from the thing, it is not the form: qua containing, it is
different from the matter.
Also it is held that what is anywhere is both itself something and that there is a
different thing outside it. (Plato of course, if we may digress, ought to tell us why the
form and the numbers are not in place, if 'what participates' is place-whether what
participates is the Great and the Small or the matter, as he called it in writing in the
Further, how could a body be carried to its own place, if place was the matter or the
form? It is impossible that what has no reference to motion or the distinction of up
and down can be place. So place must be looked for among things which have these
If the place is in the thing (it must be if it is either shape or matter) place will have a
place: for both the form and the indeterminate undergo change and motion along with
the thing, and are not always in the same place, but are where the thing is. Hence the
place will have a place.
Further, when water is produced from air, the place has been destroyed, for the
resulting body is not in the same place. What sort of destruction then is that?
This concludes my statement of the reasons why space must be something, and again
of the difficulties that may be raised about its essential nature.
Book IV - Part 3
The next step we must take is to see in how many senses one thing is said to be 'in'
(1) As the finger is 'in' the hand and generally the part 'in' the whole.
(2) As the whole is 'in' the parts: for there is no whole over and above the parts.
(3) As man is 'in' animal and generally species 'in' genus.
(4) As the genus is 'in' the species and generally the part of the specific form 'in' the
definition of the specific form.
(5) As health is 'in' the hot and the cold and generally the form 'in' the matter.
(6) As the affairs of Greece centre 'in' the king, and generally events centre 'in' their
primary motive agent.
(7) As the existence of a thing centres 'in its good and generally 'in' its end, i.e. in
'that for the sake of which' it exists.
(8) In the strictest sense of all, as a thing is 'in' a vessel, and generally 'in' place.
One might raise the question whether a thing can be in itself, or whether nothing can
be in itself-everything being either nowhere or in something else.
The question is ambiguous; we may mean the thing qua itself or qua something else.
When there are parts of a whole-the one that in which a thing is, the other the thing
which is in it-the whole will be described as being in itself. For a thing is described in
terms of its parts, as well as in terms of the thing as a whole, e.g. a man is said to be
white because the visible surface of him is white, or to be scientific because his
thinking faculty has been trained. The jar then will not be in itself and the wine will not
be in itself. But the jar of wine will: for the contents and the container are both parts
of the same whole.
In this sense then, but not primarily, a thing can be in itself, namely, as 'white' is in
body (for the visible surface is in body), and science is in the mind.
It is from these, which are 'parts' (in the sense at least of being 'in' the man), that the
man is called white, &c. But the jar and the wine in separation are not parts of a
whole, though together they are. So when there are parts, a thing will be in itself, as
'white' is in man because it is in body, and in body because it resides in the visible
surface. We cannot go further and say that it is in surface in virtue of something other
than itself. (Yet it is not in itself: though these are in a way the same thing,) they differ
in essence, each having a special nature and capacity, 'surface' and 'white'.
Thus if we look at the matter inductively we do not find anything to be 'in' itself in any
of the senses that have been distinguished; and it can be seen by argument that it is
impossible. For each of two things will have to be both, e.g. the jar will have to be
both vessel and wine, and the wine both wine and jar, if it is possible for a thing to be
in itself; so that, however true it might be that they were in each other, the jar will
receive the wine in virtue not of its being wine but of the wine's being wine, and the
wine will be in the jar in virtue not of its being a jar but of the jar's being a jar. Now
that they are different in respect of their essence is evident; for 'that in which
something is' and 'that which is in it' would be differently defined.
Nor is it possible for a thing to be in itself even incidentally: for two things would at
the same time in the same thing. The jar would be in itself-if a thing whose nature it is
to receive can be in itself; and that which it receives, namely (if wine) wine, will be in
Obviously then a thing cannot be in itself primarily.
Zeno's problem-that if Place is something it must be in something-is not difficult to
solve. There is nothing to prevent the first place from being 'in' something else-not
indeed in that as 'in' place, but as health is 'in' the hot as a positive determination of it
or as the hot is 'in' body as an affection. So we escape the infinite regress.
What is Aristotle's solution to Zeno's paradox that "place must be at a place which must be at a place which...."?
Another thing is plain: since the vessel is no part of what is in it (what contains in the
strict sense is different from what is contained), place could not be either the matter
or the form of the thing contained, but must different-for the latter, both the matter
and the shape, are parts of what is contained.
This then may serve as a critical statement of the difficulties involved.
Book IV - Part 4
What then after all is place? The answer to this question may be elucidated as
Let us take for granted about it the various characteristics which are supposed
correctly to belong to it essentially. We assume then-
(1) Place is what contains that of which it is the place.
(2) Place is no part of the thing.
(3) The immediate place of a thing is neither less nor greater than the thing.
(4) Place can be left behind by the thing and is separable. In addition:
(5) All place admits of the distinction of up and down, and each of the bodies is
naturally carried to its appropriate place and rests there, and this makes the place
either up or down.
Having laid these foundations, we must complete the theory. We ought to try to
make our investigation such as will render an account of place, and will not only
solve the difficulties connected with it, but will also show that the attributes supposed
to belong to it do really belong to it, and further will make clear the cause of the
trouble and of the difficulties about it. Such is the most satisfactory kind of
First then we must understand that place would not have been thought of, if there
had not been a special kind of motion, namely that with respect to place. It is chiefly
for this reason that we suppose the heaven also to be in place, because it is in
constant movement. Of this kind of change there are two species-locomotion on the
one hand and, on the other, increase and diminution. For these too involve variation
of place: what was then in this place has now in turn changed to what is larger or
Again, when we say a thing is 'moved', the predicate either (1) belongs to it actually,
in virtue of its own nature, or (2) in virtue of something conjoined with it. In the latter
case it may be either (a) something which by its own nature is capable of being
moved, e.g. the parts of the body or the nail in the ship, or (b) something which is not
in itself capable of being moved, but is always moved through its conjunction with
something else, as 'whiteness' or 'science'. These have changed their place only
because the subjects to which they belong do so.
We say that a thing is in the world, in the sense of in place, because it is in the air,
and the air is in the world; and when we say it is in the air, we do not mean it is in
every part of the air, but that it is in the air because of the outer surface of the air
which surrounds it; for if all the air were its place, the place of a thing would not be
equal to the thing-which it is supposed to be, and which the primary place in which a
thing is actually is.
When what surrounds, then, is not separate from the thing, but is in continuity with it,
the thing is said to be in what surrounds it, not in the sense of in place, but as a part
in a whole. But when the thing is separate and in contact, it is immediately 'in' the
inner surface of the surrounding body, and this surface is neither a part of what is in it
nor yet greater than its extension, but equal to it; for the extremities of things which
touch are coincident.
Further, if one body is in continuity with another, it is not moved in that but with that.
On the other hand it is moved in that if it is separate. It makes no difference whether
what contains is moved or not.
Again, when it is not separate it is described as a part in a whole, as the pupil in the
eye or the hand in the body: when it is separate, as the water in the cask or the wine
in the jar. For the hand is moved with the body and the water in the cask.
It will now be plain from these considerations what place is. There are just four
things of which place must be one-the shape, or the matter, or some sort of
extension between the bounding surfaces of the containing body, or this boundary
itself if it contains no extension over and above the bulk of the body which comes to
be in it.
Three of these it obviously cannot be:
(1) The shape is supposed to be place because it surrounds, for the extremities of
what contains and of what is contained are coincident. Both the shape and the place,
it is true, are boundaries. But not of the same thing: the form is the boundary of the
thing, the place is the boundary of the body which contains it.
Explain the differences between place and form.
(2) The extension between the extremities is thought to be something, because what
is contained and separate may often be changed while the container remains the
same (as water may be poured from a vessel)-the assumption being that the
extension is something over and above the body displaced. But there is no such
extension. One of the bodies which change places and are naturally capable of being
in contact with the container falls in whichever it may chance to be.
If there were an extension which were such as to exist independently and be
permanent, there would be an infinity of places in the same thing. For when the water
and the air change places, all the portions of the two together will play the same part
in the whole which was previously played by all the water in the vessel; at the same
time the place too will be undergoing change; so that there will be another place
which is the place of the place, and many places will be coincident. There is not a
different place of the part, in which it is moved, when the whole vessel changes its
place: it is always the same: for it is in the (proximate) place where they are that the
air and the water (or the parts of the water) succeed each other, not in that place in
which they come to be, which is part of the place which is the place of the whole
(3) The matter, too, might seem to be place, at least if we consider it in what is at
rest and is thus separate but in continuity. For just as in change of quality there is
something which was formerly black and is now white, or formerly soft and now
hard-this is just why we say that the matter exists-so place, because it presents a
similar phenomenon, is thought to exist-only in the one case we say so because what
was air is now water, in the other because where air formerly was there a is now
water. But the matter, as we said before, is neither separable from the thing nor
contains it, whereas place has both characteristics.
Well, then, if place is none of the three-neither the form nor the matter nor an
extension which is always there, different from, and over and above, the extension of
the thing which is displaced-place necessarily is the one of the four which is left,
namely, the boundary of the containing body at which it is in contact with the
contained body. (By the contained body is meant what can be moved by way of
Place is thought to be something important and hard to grasp, both because the
matter and the shape present themselves along with it, and because the displacement
of the body that is moved takes place in a stationary container, for it seems possible
that there should be an interval which is other than the bodies which are moved. The
air, too, which is thought to be incorporeal, contributes something to the belief: it is
not only the boundaries of the vessel which seem to be place, but also what is
between them, regarded as empty. Just, in fact, as the vessel is transportable place,
so place is a non-portable vessel. So when what is within a thing which is moved, is
moved and changes its place, as a boat on a river, what contains plays the part of a
vessel rather than that of place. Place on the other hand is rather what is motionless:
so it is rather the whole river that is place, because as a whole it is motionless.
Hence we conclude that the innermost motionless boundary of what contains is
Why is place motionless?
This explains why the middle of the heaven and the surface which faces us of the
rotating system are held to be 'up' and 'down' in the strict and fullest sense for all
men: for the one is always at rest, while the inner side of the rotating body remains
always coincident with itself. Hence since the light is what is naturally carried up, and
the heavy what is carried down, the boundary which contains in the direction of the
middle of the universe, and the middle itself, are down, and that which contains in the
direction of the outermost part of the universe, and the outermost part itself, are up.
For this reason, too, place is thought to be a kind of surface, and as it were a vessel,
i.e. a container of the thing.
Further, place is coincident with the thing, for boundaries are coincident with the
Book IV - Part 5
If then a body has another body outside it and containing it, it is in place, and if not,
not. That is why, even if there were to be water which had not a container, the parts
of it, on the one hand, will be moved (for one part is contained in another), while, on
the other hand, the whole will be moved in one sense, but not in another. For as a
whole it does not simultaneously change its place, though it will be moved in a circle:
for this place is the place of its parts. (Some things are moved, not up and down, but
in a circle; others up and down, such things namely as admit of condensation and
As was explained, some things are potentially in place, others actually. So, when you
have a homogeneous substance which is continuous, the parts are potentially in
place: when the parts are separated, but in contact, like a heap, they are actually in
Again, (1) some things are per se in place, namely every body which is movable
either by way of locomotion or by way of increase is per se somewhere, but the
heaven, as has been said, is not anywhere as a whole, nor in any place, if at least, as
we must suppose, no body contains it. On the line on which it is moved, its parts
have place: for each is contiguous the next.
Why does the heaven not have a place?
But (2) other things are in place indirectly, through something conjoined with them,
as the soul and the heaven. The latter is, in a way, in place, for all its parts are: for on
the orb one part contains another. That is why the upper part is moved in a circle,
while the All is not anywhere. For what is somewhere is itself something, and there
must be alongside it some other thing wherein it is and which contains it. But
alongside the All or the Whole there is nothing outside the All, and for this reason all
things are in the heaven; for the heaven, we may say, is the All. Yet their place is not
the same as the heaven. It is part of it, the innermost part of it, which is in contact
with the movable body; and for this reason the earth is in water, and this in the air,
and the air in the aether, and the aether in heaven, but we cannot go on and say that
the heaven is in anything else.
It is clear, too, from these considerations that all the problems which were raised
about place will be solved when it is explained in this way:
(1) There is no necessity that the place should grow with the body in it,
(2) Nor that a point should have a place,
(3) Nor that two bodies should be in the same place,
(4) Nor that place should be a corporeal interval: for what is between the boundaries
of the place is any body which may chance to be there, not an interval in body.
Further, (5) place is also somewhere, not in the sense of being in a place, but as the
limit is in the limited; for not everything that is is in place, but only movable body.
Also (6) it is reasonable that each kind of body should be carried to its own place.
For a body which is next in the series and in contact (not by compulsion) is akin, and
bodies which are united do not affect each other, while those which are in contact
interact on each other.
Nor (7) is it without reason that each should remain naturally in its proper place. For
this part has the same relation to its place, as a separable part to its whole, as when
one moves a part of water or air: so, too, air is related to water, for the one is like
matter, the other form-water is the matter of air, air as it were the actuality of water,
for water is potentially air, while air is potentially water, though in another way.
These distinctions will be drawn more carefully later. On the present occasion it was
necessary to refer to them: what has now been stated obscurely will then be made
more clear. If the matter and the fulfilment are the same thing (for water is both, the
one potentially, the other completely), water will be related to air in a way as part to
whole. That is why these have contact: it is organic union when both become actually
one. This concludes my account of place-both of its existence and of its nature.
Book IV - Part 8
Let us explain again that there is no void existing separately, as some maintain. If
each of the simple bodies has a natural locomotion, e.g. fire upward and earth
downward and towards the middle of the universe, it is clear that it cannot be the
void that is the condition of locomotion. What, then, will the void be the condition
of? It is thought to be the condition of movement in respect of place, and it is not the
condition of this.
Again, if void is a sort of place deprived of body, when there is a void where will a
body placed in it move to? It certainly cannot move into the whole of the void. The
same argument applies as against those who think that place is something separate,
into which things are carried; viz. how will what is placed in it move, or rest? Much
the same argument will apply to the void as to the 'up' and 'down' in place, as is
natural enough since those who maintain the existence of the void make it a place.
Why cannot void be a place?
And in what way will things be present either in place-or in the void? For the
expected result does not take place when a body is placed as a whole in a place
conceived of as separate and permanent; for a part of it, unless it be placed apart,
will not be in a place but in the whole. Further, if separate place does not exist,
neither will void.
If people say that the void must exist, as being necessary if there is to be movement,
what rather turns out to be the case, if one the matter, is the opposite, that not a
single thing can be moved if there is a void; for as with those who for a like reason
say the earth is at rest, so, too, in the void things must be at rest; for there is no place
to which things can move more or less than to another; since the void in so far as it is
void admits no difference.
The second reason is this: all movement is either compulsory or according to nature,
and if there is compulsory movement there must also be natural (for compulsory
movement is contrary to nature, and movement contrary to nature is posterior to that
according to nature, so that if each of the natural bodies has not a natural movement,
none of the other movements can exist); but how can there be natural movement if
there is no difference throughout the void or the infinite? For in so far as it is infinite,
there will be no up or down or middle, and in so far as it is a void, up differs no whit
from down; for as there is no difference in what is nothing, there is none in the void
(for the void seems to be a non-existent and a privation of being), but natural
locomotion seems to be differentiated, so that the things that exist by nature must be
differentiated. Either, then, nothing has a natural locomotion, or else there is no void.
Further, in point of fact things that are thrown move though that which gave them
their impulse is not touching them, either by reason of mutual replacement, as some
maintain, or because the air that has been pushed pushes them with a movement
quicker than the natural locomotion of the projectile wherewith it moves to its proper
place. But in a void none of these things can take place, nor can anything be moved
save as that which is carried is moved.
Further, no one could say why a thing once set in motion should stop anywhere; for
why should it stop here rather than here? So that a thing will either be at rest or must
be moved ad infinitum, unless something more powerful get in its way.
Further, things are now thought to move into the void because it yields; but in a void
this quality is present equally everywhere, so that things should move in all directions.
Further, the truth of what we assert is plain from the following considerations. We
see the same weight or body moving faster than another for two reasons, either
because there is a difference in what it moves through, as between water, air, and
earth, or because, other things being equal, the moving body differs from the other
owing to excess of weight or of lightness.
Now the medium causes a difference because it impedes the moving thing, most of
all if it is moving in the opposite direction, but in a secondary degree even if it is at
rest; and especially a medium that is not easily divided, i.e. a medium that is
somewhat dense. A, then, will move through B in time G, and through D, which is
thinner, in time E (if the length of B is egual to D), in proportion to the density of the
hindering body. For let B be water and D air; then by so much as air is thinner and
more incorporeal than water, A will move through D faster than through B. Let the
speed have the same ratio to the speed, then, that air has to water. Then if air is
twice as thin, the body will traverse B in twice the time that it does D, and the time G
will be twice the time E. And always, by so much as the medium is more incorporeal
and less resistant and more easily divided, the faster will be the movement.
Now there is no ratio in which the void is exceeded by body, as there is no ratio of 0
to a number. For if 4 exceeds 3 by 1, and 2 by more than 1, and 1 by still more than
it exceeds 2, still there is no ratio by which it exceeds 0; for that which exceeds must
be divisible into the excess + that which is exceeded, so that will be what it exceeds
0 by + 0. For this reason, too, a line does not exceed a point unless it is composed
of points! Similarly the void can bear no ratio to the full, and therefore neither can
movement through the one to movement through the other, but if a thing moves
through the thickest medium such and such a distance in such and such a time, it
moves through the void with a speed beyond any ratio. For let Z be void, equal in
magnitude to B and to D. Then if A is to traverse and move through it in a certain
time, H, a time less than E, however, the void will bear this ratio to the full. But in a
time equal to H, A will traverse the part O of A. And it will surely also traverse in
that time any substance Z which exceeds air in thickness in the ratio which the time E
bears to the time H. For if the body Z be as much thinner than D as E exceeds H, A,
if it moves through Z, will traverse it in a time inverse to the speed of the movement,
i.e. in a time equal to H. If, then, there is no body in Z, A will traverse Z still more
quickly. But we supposed that its traverse of Z when Z was void occupied the time
H. So that it will traverse Z in an equal time whether Z be full or void. But this is
impossible. It is plain, then, that if there is a time in which it will move through any
part of the void, this impossible result will follow: it will be found to traverse a certain
distance, whether this be full or void, in an equal time; for there will be some body
which is in the same ratio to the other body as the time is to the time.
Why is 1/0 undefined?
How long would it take a body to traverse a void?
To sum the matter up, the cause of this result is obvious, viz. that between any two
movements there is a ratio (for they occupy time, and there is a ratio between any
two times, so long as both are finite), but there is no ratio of void to full.
These are the consequences that result from a difference in the media; the following
depend upon an excess of one moving body over another. We see that bodies which
have a greater impulse either of weight or of lightness, if they are alike in other
respects, move faster over an equal space, and in the ratio which their magnitudes
bear to each other. Therefore they will also move through the void with this ratio of
speed. But that is impossible; for why should one move faster? (In moving through
plena it must be so; for the greater divides them faster by its force. For a moving
thing cleaves the medium either by its shape, or by the impulse which the body that is
carried along or is projected possesses.) Therefore all will possess equal velocity.
But this is impossible.
It is evident from what has been said, then, that, if there is a void, a result follows
which is the very opposite of the reason for which those who believe in a void set it
up. They think that if movement in respect of place is to exist, the void cannot exist,
separated all by itself; but this is the same as to say that place is a separate cavity;
and this has already been stated to be impossible.
But even if we consider it on its own merits the so-called vacuum will be found to be
really vacuous. For as, if one puts a cube in water, an amount of water equal to the
cube will be displaced; so too in air; but the effect is imperceptible to sense. And
indeed always in the case of any body that can be displaced, must, if it is not
compressed, be displaced in the direction in which it is its nature to be
displaced-always either down, if its locomotion is downwards as in the case of earth,
or up, if it is fire, or in both directions-whatever be the nature of the inserted body.
Now in the void this is impossible; for it is not body; the void must have penetrated
the cube to a distance equal to that which this portion of void formerly occupied in
the void, just as if the water or air had not been displaced by the wooden cube, but
had penetrated right through it.
But the cube also has a magnitude equal to that occupied by the void; a magnitude
which, if it is also hot or cold, or heavy or light, is none the less different in essence
from all its attributes, even if it is not separable from them; I mean the volume of the
wooden cube. So that even if it were separated from everything else and were
neither heavy nor light, it will occupy an equal amount of void, and fill the same
place, as the part of place or of the void equal to itself. How then will the body of the
cube differ from the void or place that is equal to it? And if there can be two such
things, why cannot there be any number coinciding?
This, then, is one absurd and impossible implication of the theory. It is also evident
that the cube will have this same volume even if it is displaced, which is an attribute
possessed by all other bodies also. Therefore if this differs in no respect from its
place, why need we assume a place for bodies over and above the volume of each,
if their volume be conceived of as free from attributes? It contributes nothing to the
situation if there is an equal interval attached to it as well. [Further it ought to be clear
by the study of moving things what sort of thing void is. But in fact it is found
nowhere in the world. For air is something, though it does not seem to be so-nor, for
that matter, would water, if fishes were made of iron; for the discrimination of the
tangible is by touch.]
It is clear, then, from these considerations that there is no separate void.
Book III - Part 4
The science of nature is concerned with spatial magnitudes and motion and time, and
each of these at least is necessarily infinite or finite, even if some things dealt with by
the science are not, e.g. a quality or a point-it is not necessary perhaps that such
things should be put under either head. Hence it is incumbent on the person who
specializes in physics to discuss the infinite and to inquire whether there is such a
thing or not, and, if there is, what it is.
The appropriateness to the science of this problem is clearly indicated. All who have
touched on this kind of science in a way worth considering have formulated views
about the infinite, and indeed, to a man, make it a principle of things.
(1) Some, as the Pythagoreans and Plato, make the infinite a principle in the sense of
a self-subsistent substance, and not as a mere attribute of some other thing. Only the
Pythagoreans place the infinite among the objects of sense (they do not regard
number as separable from these), and assert that what is outside the heaven is
infinite. Plato, on the other hand, holds that there is no body outside (the Forms are
not outside because they are nowhere),yet that the infinite is present not only in the
objects of sense but in the Forms also.
Further, the Pythagoreans identify the infinite with the even. For this, they say, when
it is cut off and shut in by the odd, provides things with the element of infinity. An
indication of this is what happens with numbers. If the gnomons are placed round the
one, and without the one, in the one construction the figure that results is always
different, in the other it is always the same. But Plato has two infinites, the Great and
The physicists, on the other hand, all of them, always regard the infinite as an
attribute of a substance which is different from it and belongs to the class of the
so-called elements-water or air or what is intermediate between them. Those who
make them limited in number never make them infinite in amount. But those who
make the elements infinite in number, as Anaxagoras and Democritus do, say that the
infinite is continuous by contact-compounded of the homogeneous parts according to
the one, of the seed-mass of the atomic shapes according to the other.
Further, Anaxagoras held that any part is a mixture in the same way as the All, on the
ground of the observed fact that anything comes out of anything. For it is probably
for this reason that he maintains that once upon a time all things were together. (This
flesh and this bone were together, and so of any thing: therefore all things: and at the
same time too.) For there is a beginning of separation, not only for each thing, but for
all. Each thing that comes to be comes from a similar body, and there is a coming to
be of all things, though not, it is true, at the same time. Hence there must also be an
origin of coming to be. One such source there is which he calls Mind, and Mind
begins its work of thinking from some starting-point. So necessarily all things must
have been together at a certain time, and must have begun to be moved at a certain
Democritus, for his part, asserts the contrary, namely that no element arises from
another element. Nevertheless for him the common body is a source of all things,
differing from part to part in size and in shape.
It is clear then from these considerations that the inquiry concerns the physicist. Nor
is it without reason that they all make it a principle or source. We cannot say that the
infinite has no effect, and the only effectiveness which we can ascribe to it is that of a
principle. Everything is either a source or derived from a source. But there cannot be
a source of the infinite or limitless, for that would be a limit of it. Further, as it is a
beginning, it is both uncreatable and indestructible. For there must be a point at
which what has come to be reaches completion, and also a termination of all passing
away. That is why, as we say, there is no principle of this, but it is this which is held
to be the principle of other things, and to encompass all and to steer all, as those
assert who do not recognize, alongside the infinite, other causes, such as Mind or
Friendship. Further they identify it with the Divine, for it is 'deathless and
imperishable' as Anaximander says, with the majority of the physicists.
Belief in the existence of the infinite comes mainly from five considerations:
(1) From the nature of time-for it is infinite.
(2) From the division of magnitudes-for the mathematicians also use the notion of the
(3) If coming to be and passing away do not give out, it is only because that from
which things come to be is infinite.
(4) Because the limited always finds its limit in something, so that there must be no
limit, if everything is always limited by something different from itself.
(5) Most of all, a reason which is peculiarly appropriate and presents the difficulty
that is felt by everybody-not only number but also mathematical magnitudes and
what is outside the heaven are supposed to be infinite because they never give out in
Explain the five reason for the existence of the infinite.
The last fact (that what is outside is infinite) leads people to suppose that body also is
infinite, and that there is an infinite number of worlds. Why should there be body in
one part of the void rather than in another? Grant only that mass is anywhere and it
follows that it must be everywhere. Also, if void and place are infinite, there must be
infinite body too, for in the case of eternal things what may be must be. But the
problem of the infinite is difficult: many contradictions result whether we suppose it to
exist or not to exist. If it exists, we have still to ask how it exists; as a substance or as
the essential attribute of some entity? Or in neither way, yet none the less is there
something which is infinite or some things which are infinitely many?
The problem, however, which specially belongs to the physicist is to investigate
whether there is a sensible magnitude which is infinite.
We must begin by distinguishing the various senses in which the term 'infinite' is used.
(1) What is incapable of being gone through, because it is not in its nature to be gone
through (the sense in which the voice is 'invisible').
(2) What admits of being gone through, the process however having no termination,
or what scarcely admits of being gone through.
(3) What naturally admits of being gone through, but is not actually gone through or
does not actually reach an end.
Further, everything that is infinite may be so in respect of addition or division or both.
Book III - Part 5
Now it is impossible that the infinite should be a thing which is itself infinite, separable
from sensible objects. If the infinite is neither a magnitude nor an aggregate, but is
itself a substance and not an attribute, it will be indivisible; for the divisible must be
either a magnitude or an aggregate. But if indivisible, then not infinite, except in the
sense (1) in which the voice is 'invisible'. But this is not the sense in which it is used
by those who say that the infinite exists, nor that in which we are investigating it,
namely as (2) 'that which cannot be gone through'. But if the infinite exists as an
attribute, it would not be, qua infinite an element in substances, any more than the
invisible would be an element of speech, though the voice is invisible.
Explain the phrase, "it is impossible that the infinite should be a thing which is
itself infinite, separable from sensible objects"
Further, how can the infinite be itself any thing, unless both number and magnitude, of
which it is an essential attribute, exist in that way? If they are not substances, a
fortiori the infinite is not.
It is plain, too, that the infinite cannot be an actual thing and a substance and
principle. For any part of it that is taken will be infinite, if it has parts: for 'to be
infinite' and 'the infinite' are the same, if it is a substance and not predicated of a
subject. Hence it will be either indivisible or divisible into infinites. But the same thing
cannot be many infinites. (Yet just as part of air is air, so a part of the infinite would
be infinite, if it is supposed to be a substance and principle.) Therefore the infinite
must be without parts and indivisible. But this cannot be true of what is infinite in full
completion: for it must be a definite quantity.
Suppose then that infinity belongs to substance as an attribute. But, if so, it cannot, as
we have said, be described as a principle, but rather that of which it is an
attribute-the air or the even number.
Thus the view of those who speak after the manner of the Pythagoreans is absurd.
With the same breath they treat the infinite as substance, and divide it into parts.
This discussion, however, involves the more general question whether the infinite can
be present in mathematical objects and things which are intelligible and do not have
extension, as well as among sensible objects. Our inquiry (as physicists) is limited to
its special subject-matter, the objects of sense, and we have to ask whether there is
or is not among them a body which is infinite in the direction of increase.
We may begin with a dialectical argument and show as follows that there is no such
thing. If 'bounded by a surface' is the definition of body there cannot be an infinite
body either intelligible or sensible. Nor can number taken in abstraction be infinite,
for number or that which has number is numerable. If then the numerable can be
numbered, it would also be possible to go through the infinite.
If, on the other hand, we investigate the question more in accordance with principles
appropriate to physics, we are led as follows to the same result.
The infinite body must be either (1) compound, or (2) simple; yet neither alternative
Why cannot the infinite be either compound or simple?
(1) Compound the infinite body will not be, if the elements are finite in number. For
they must be more than one, and the contraries must always balance, and no one of
them can be infinite. If one of the bodies falls in any degree short of the other in
potency-suppose fire is finite in amount while air is infinite and a given quantity of fire
exceeds in power the same amount of air in any ratio provided it is numerically
definite-the infinite body will obviously prevail over and annihilate the finite body. On
the other hand, it is impossible that each should be infinite. 'Body' is what has
extension in all directions and the infinite is what is boundlessly extended, so that the
infinite body would be extended in all directions ad infinitum.
Nor (2) can the infinite body be one and simple, whether it is, as some hold, a thing
over and above the elements (from which they generate the elements) or is not thus
(a) We must consider the former alternative; for there are some people who make
this the infinite, and not air or water, in order that the other elements may not be
annihilated by the element which is infinite. They have contrariety with each other-air
is cold, water moist, fire hot; if one were infinite, the others by now would have
ceased to be. As it is, they say, the infinite is different from them and is their source.
It is impossible, however, that there should be such a body; not because it is infinite
on that point a general proof can be given which applies equally to all, air, water, or
anything else-but simply because there is, as a matter of fact, no such sensible body,
alongside the so-called elements. Everything can be resolved into the elements of
which it is composed. Hence the body in question would have been present in our
world here, alongside air and fire and earth and water: but nothing of the kind is
(b) Nor can fire or any other of the elements be infinite. For generally, and apart
from the question of how any of them could be infinite, the All, even if it were limited,
cannot either be or become one of them, as Heraclitus says that at some time all
things become fire. (The same argument applies also to the one which the physicists
suppose to exist alongside the elements: for everything changes from contrary to
contrary, e.g. from hot to cold).
The preceding consideration of the various cases serves to show us whether it is or is
not possible that there should be an infinite sensible body. The following arguments
give a general demonstration that it is not possible.
It is the nature of every kind of sensible body to be somewhere, and there is a place
appropriate to each, the same for the part and for the whole, e.g. for the whole earth
and for a single clod, and for fire and for a spark.
Suppose (a) that the infinite sensible body is homogeneous. Then each part will be
either immovable or always being carried along. Yet neither is possible. For why
downwards rather than upwards or in any other direction? I mean, e.g, if you take a
clod, where will it be moved or where will it be at rest? For ex hypothesi the place of
the body akin to it is infinite. Will it occupy the whole place, then? And how? What
then will be the nature of its rest and of its movement, or where will they be? It will
either be at home everywhere-then it will not be moved; or it will be moved
everywhere-then it will not come to rest.
But if (b) the All has dissimilar parts, the proper places of the parts will be dissimilar
also, and the body of the All will have no unity except that of contact. Then, further,
the parts will be either finite or infinite in variety of kind. (i) Finite they cannot be, for
if the All is to be infinite, some of them would have to be infinite, while the others
were not, e.g. fire or water will be infinite. But, as we have seen before, such an
element would destroy what is contrary to it. (This indeed is the reason why none of
the physicists made fire or earth the one infinite body, but either water or air or what
is intermediate between them, because the abode of each of the two was plainly
determinate, while the others have an ambiguous place between up and down.)
But (ii) if the parts are infinite in number and simple, their proper places too will be
infinite in number, and the same will be true of the elements themselves. If that is
impossible, and the places are finite, the whole too must be finite; for the place and
the body cannot but fit each other. Neither is the whole place larger than what can
be filled by the body (and then the body would no longer be infinite), nor is the body
larger than the place; for either there would be an empty space or a body whose
nature it is to be nowhere.
Anaxagoras gives an absurd account of why the infinite is at rest. He says that the
infinite itself is the cause of its being fixed. This because it is in itself, since nothing
else contains it-on the assumption that wherever anything is, it is there by its own
nature. But this is not true: a thing could be somewhere by compulsion, and not
where it is its nature to be.
Even if it is true as true can be that the whole is not moved (for what is fixed by itself
and is in itself must be immovable), yet we must explain why it is not its nature to be
moved. It is not enough just to make this statement and then decamp. Anything else
might be in a state of rest, but there is no reason why it should not be its nature to be
moved. The earth is not carried along, and would not be carried along if it were
infinite, provided it is held together by the centre. But it would not be because there
was no other region in which it could be carried along that it would remain at the
centre, but because this is its nature. Yet in this case also we may say that it fixes
itself. If then in the case of the earth, supposed to be infinite, it is at rest, not because
it is infinite, but because it has weight and what is heavy rests at the centre and the
earth is at the centre, similarly the infinite also would rest in itself, not because it is
infinite and fixes itself, but owing to some other cause.
Another difficulty emerges at the same time. Any part of the infinite body ought to
remain at rest. Just as the infinite remains at rest in itself because it fixes itself, so too
any part of it you may take will remain in itself. The appropriate places of the whole
and of the part are alike, e.g. of the whole earth and of a clod the appropriate place
is the lower region; of fire as a whole and of a spark, the upper region. If, therefore,
to be in itself is the place of the infinite, that also will be appropriate to the part.
Therefore it will remain in itself.
In general, the view that there is an infinite body is plainly incompatible with the
doctrine that there is necessarily a proper place for each kind of body, if every
sensible body has either weight or lightness, and if a body has a natural locomotion
towards the centre if it is heavy, and upwards if it is light. This would need to be true
of the infinite also. But neither character can belong to it: it cannot be either as a
whole, nor can it be half the one and half the other. For how should you divide it? or
how can the infinite have the one part up and the other down, or an extremity and a
Further, every sensible body is in place, and the kinds or differences of place are
up-down, before-behind, right-left; and these distinctions hold not only in relation to
us and by arbitrary agreement, but also in the whole itself. But in the infinite body
they cannot exist. In general, if it is impossible that there should be an infinite place,
and if every body is in place, there cannot be an infinite body.
Surely what is in a special place is in place, and what is in place is in a special place.
Just, then, as the infinite cannot be quantity-that would imply that it has a particular
quantity, e,g, two or three cubits; quantity just means these-so a thing's being in place
means that it is somewhere, and that is either up or down or in some other of the six
differences of position: but each of these is a limit.
It is plain from these arguments that there is no body which is actually infinite.
Book III - Part 6
But on the other hand to suppose that the infinite does not exist in any way leads
obviously to many impossible consequences: there will be a beginning and an end of
time, a magnitude will not be divisible into magnitudes, number will not be infinite. If,
then, in view of the above considerations, neither alternative seems possible, an
arbiter must be called in; and clearly there is a sense in which the infinite exists and
another in which it does not.
We must keep in mind that the word 'is' means either what potentially is or what fully
is. Further, a thing is infinite either by addition or by division.
Now, as we have seen, magnitude is not actually infinite. But by division it is infinite.
(There is no difficulty in refuting the theory of indivisible lines.) The alternative then
remains that the infinite has a potential existence.
But the phrase 'potential existence' is ambiguous. When we speak of the potential
existence of a statue we mean that there will be an actual statue. It is not so with the
infinite. There will not be an actual infinite. The word 'is' has many senses, and we
say that the infinite 'is' in the sense in which we say 'it is day' or 'it is the games',
because one thing after another is always coming into existence. For of these things
too the distinction between potential and actual existence holds. We say that there
are Olympic games, both in the sense that they may occur and that they are actually
The infinite exhibits itself in different ways-in time, in the generations of man, and in
the division of magnitudes. For generally the infinite has this mode of existence: one
thing is always being taken after another, and each thing that is taken is always finite,
but always different. Again, 'being' has more than one sense, so that we must not
regard the infinite as a 'this', such as a man or a horse, but must suppose it to exist in
the sense in which we speak of the day or the games as existing things whose being
has not come to them like that of a substance, but consists in a process of coming to
be or passing away; definite if you like at each stage, yet always different.
In what sense does the infinite exist?
But when this takes place in spatial magnitudes, what is taken perists, while in the
succession of time and of men it takes place by the passing away of these in such a
way that the source of supply never gives out.
Explain infinite by division and infinite by addition.
In a way the infinite by addition is the same thing as the infinite by division. In a finite
magnitude, the infinite by addition comes about in a way inverse to that of the other.
For in proportion as we see division going on, in the same proportion we see
addition being made to what is already marked off. For if we take a determinate part
of a finite magnitude and add another part determined by the same ratio (not taking
in the same amount of the original whole), and so on, we shall not traverse the given
magnitude. But if we increase the ratio of the part, so as always to take in the same
amount, we shall traverse the magnitude, for every finite magnitude is exhausted by
means of any determinate quantity however small.
The infinite, then, exists in no other way, but in this way it does exist, potentially and
by reduction. It exists fully in the sense in which we say 'it is day' or 'it is the games';
and potentially as matter exists, not independently as what is finite does.
Explain the preceding paragraph.
By addition then, also, there is potentially an infinite, namely, what we have
described as being in a sense the same as the infinite in respect of division. For it will
always be possible to take something ah extra. Yet the sum of the parts taken will
not exceed every determinate magnitude, just as in the direction of division every
determinate magnitude is surpassed in smallness and there will be a smaller part.
But in respect of addition there cannot be an infinite which even potentially exceeds
every assignable magnitude, unless it has the attribute of being actually infinite, as the
physicists hold to be true of the body which is outside the world, whose essential
nature is air or something of the kind. But if there cannot be in this way a sensible
body which is infinite in the full sense, evidently there can no more be a body which
is potentially infinite in respect of addition, except as the inverse of the infinite by
division, as we have said. It is for this reason that Plato also made the infinites two in
number, because it is supposed to be possible to exceed all limits and to proceed ad
infinitum in the direction both of increase and of reduction. Yet though he makes the
infinites two, he does not use them. For in the numbers the infinite in the direction of
reduction is not present, as the monad is the smallest; nor is the infinite in the
direction of increase, for the parts number only up to the decad.
The infinite turns out to be the contrary of what it is said to be. It is not what has
nothing outside it that is infinite, but what always has something outside it. This is
indicated by the fact that rings also that have no bezel are described as 'endless',
because it is always possible to take a part which is outside a given part. The
description depends on a certain similarity, but it is not true in the full sense of the
word. This condition alone is not sufficient: it is necessary also that the next part
which is taken should never be the same. In the circle, the latter condition is not
satisfied: it is only the adjacent part from which the new part is different.
Our definition then is as follows:
A quantity is infinite if it is such that we can always take a part outside what has been
already taken. On the other hand, what has nothing outside it is complete and whole.
For thus we define the whole-that from which nothing is wanting, as a whole man or
a whole box. What is true of each particular is true of the whole as such-the whole is
that of which nothing is outside. On the other hand that from which something is
absent and outside, however small that may be, is not 'all'. 'Whole' and 'complete'
are either quite identical or closely akin. Nothing is complete (teleion) which has no
end (telos); and the end is a limit.
Hence Parmenides must be thought to have spoken better than Melissus. The latter
says that the whole is infinite, but the former describes it as limited, 'equally balanced
from the middle'. For to connect the infinite with the all and the whole is not like
joining two pieces of string; for it is from this they get the dignity they ascribe to the
infinite-its containing all things and holding the all in itself-from its having a certain
similarity to the whole. It is in fact the matter of the completeness which belongs to
size, and what is potentially a whole, though not in the full sense. It is divisible both in
the direction of reduction and of the inverse addition. It is a whole and limited; not,
however, in virtue of its own nature, but in virtue of what is other than it. It does not
contain, but, in so far as it is infinite, is contained. Consequently, also, it is
unknowable, qua infinite; for the matter has no form. (Hence it is plain that the infinite
stands in the relation of part rather than of whole. For the matter is part of the whole,
as the bronze is of the bronze statue.) If it contains in the case of sensible things, in
the case of intelligible things the great and the small ought to contain them. But it is
absurd and impossible to suppose that the unknowable and indeterminate should
contain and determine.
End of first reading.
Book VIII - 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:
Explain Anaxagoras' and Empedocles' views regarding motion and the universe.
'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.)
Why must motion exist in order for there to be time?
Why must time be eternal?
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
Why must motion be eternal?
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
Why are Love and Strife insufficient principles to account for motion?
Book VIII - 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.
Why must there be a first movent that moves itself? Note- some translations use the
word "mover" rather than "movent." Both terms mean, "that which imparts motion."
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 way we shall get this same result as
follows. If everything that is in motion is moved by something that is in motion, either
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.
Why is mind the "unmoved movent?"
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.
How might an object move itself?
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.
Book VIII - 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.
How many unmoved movers are there?
When was the initial movement enacted?
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.
Book VIII - 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
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
Why must locomotion be the primary type of motion?
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.
Book VIII - 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
Why is rotation the primary locomotion?
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
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.
Book VIII - 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
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 corresponding amount from it, because it is infinite. Consequently the
duration of the part of G which is occupied by all A in moving the whole of B, will be
finite. Therefore a finite thing cannot impart to anything an infinite motion. It is clear,
then, that it is impossible for the finite to cause motion during an infinite time.
Why cannot the finite be the cause of a motion during an infinite time?
It has now to be shown that in no case is it possible for an infinite force to reside in a
finite magnitude. This can be shown as follows: we take it for granted that the greater
force is always that which in less time than another does an equal amount of work
when engaged in any activity-in heating, for example, or sweetening or throwing; in
fact, in causing any kind of motion. Then that on which the forces act must be
affected to some extent by our supposed finite magnitude possessing an infinite force
as well as by anything else, in fact to a greater extent than by anything else, since the
infinite force is greater than any other. But then there cannot be any time in which its
action could take place. Suppose that A is the time occupied by the infinite power in
the performance of an act of heating or pushing, and that AB is the time occupied by
a finite power in the performance of the same act: then by adding to the latter another
finite power and continually increasing the magnitude of the power so added I shall at
some time or other reach a point at which the finite power has completed the motive
act in the time A: for by continual addition to a finite magnitude I must arrive at a
magnitude that exceeds any assigned limit, and in the same way by continual
subtraction I must arrive at one that falls short of any assigned limit. So we get the
result that the finite force will occupy the same amount of time in performing the
motive act as the infinite force. But this is impossible. Therefore nothing finite can
possess an infinite force. So it is also impossible for a finite force to reside in an
infinite magnitude. It is true that a greater force can reside in a lesser magnitude: but
the superiority of any such greater force can be still greater if the magnitude in which
it resides is greater. Now let AB be an infinite magnitude. Then BG possesses a
certain force that occupies a certain time, let us say the time Z in moving D. Now if I
take a magnitude twice as great at BG, the time occupied by this magnitude in
moving D will be half of EZ (assuming this to be the proportion): so we may call this
time ZH. That being so, by continually taking a greater magnitude in this way I shall
never arrive at the full AB, whereas I shall always be getting a lesser fraction of the
time given. Therefore the force must be infinite, since it exceeds any finite force.
Moreover the time occupied by the action of any finite force must also be finite: for if
a given force moves something in a certain time, a greater force will do so in a lesser
time, but still a definite time, in inverse proportion. But a force must always be
infinite-just as a number or a magnitude is-if it exceeds all definite limits. This point
may also be proved in another way-by taking a finite magnitude in which there
resides a force the same in kind as that which resides in the infinite magnitude, so that
this force will be a measure of the finite force residing in the infinite magnitude.
Why cannot an infinite force reside in a finite magnitude?
It is plain, then, from the foregoing arguments that it is impossible for an infinite force
to reside in a finite magnitude or for a finite force to reside in an infinite magnitude.
But before proceeding to our conclusion it will be well to discuss a difficulty that
arises in connexion with locomotion. If everything that is in motion with the exception
of things that move themselves is moved by something else, how is it that some
things, e.g. things thrown, continue to be in motion when their movent is no longer in
contact with them? If we say that the movent in such cases moves something else at
the same time, that the thrower e.g. also moves the air, and that this in being moved
is also a movent, then it would be no more possible for this second thing than for the
original thing to be in motion when the original movent is not in contact with it or
moving it: all the things moved would have to be in motion simultaneously and also to
have ceased simultaneously to be in motion when the original movent ceases to move
them, even if, like the magnet, it makes that which it has moved capable of being a
movent. Therefore, while we must accept this explanation to the extent of saying that
the original movent gives the power of being a movent either to air or to water or to
something else of the kind, naturally adapted for imparting and undergoing motion,
we must say further that this thing does not cease simultaneously to impart motion
and to undergo motion: it ceases to be in motion at the moment when its movent
ceases to move it, but it still remains a movent, and so it causes something else
consecutive with it to be in motion, and of this again the same may be said. The
motion begins to cease when the motive force produced in one member of the
consecutive series is at each stage less than that possessed by the preceding
member, and it finally ceases when one member no longer causes the next member
to be a movent but only causes it to be in motion. The motion of these last two-of the
one as movent and of the other as moved-must cease simultaneously, and with this
the whole motion ceases. Now the things in which this motion is produced are things
that admit of being sometimes in motion and sometimes at rest, and the motion is not
continuous but only appears so: for it is motion of things that are either successive or
in contact, there being not one movent but a number of movents consecutive with
one another: and so motion of this kind takes place in air and water. Some say that it
is 'mutual replacement': but we must recognize that the difficulty raised cannot be
solved otherwise than in the way we have described. So far as they are affected by
'mutual replacement', all the members of the series are moved and impart motion
simultaneously, so that their motions also cease simultaneously: but our present
problem concerns the appearance of continuous motion in a single thing, and
therefore, since it cannot be moved throughout its motion by the same movent, the
question is, what moves it?
Resuming our main argument, we proceed from the positions that there must be
continuous motion in the world of things, that this is a single motion, that a single
motion must be a motion of a magnitude (for that which is without magnitude cannot
be in motion), and that the magnitude must be a single magnitude moved by a single
movent (for otherwise there will not be continuous motion but a consecutive series of
separate motions), and that if the movement is a single thing, it is either itself in
motion or itself unmoved: if, then, it is in motion, it will have to be subject to the same
conditions as that which it moves, that is to say it will itself be in process of change
and in being so will also have to be moved by something: so we have a series that
must come to an end, and a point will be reached at which motion is imparted by
something that is unmoved. Thus we have a movent that has no need to change along
with that which it moves but will be able to cause motion always (for the causing of
motion under these conditions involves no effort): and this motion alone is regular, or
at least it is so in a higher degree than any other, since the movent is never subject to
any change. So, too, in order that the motion may continue to be of the same
character, the moved must not be subject to change in respect of its relation to the
movent. Moreover the movent must occupy either the centre or the circumference,
since these are the first principles from which a sphere is derived. But the things
nearest the movent are those whose motion is quickest, and in this case it is the
motion of the circumference that is the quickest: therefore the movent occupies the
Why must the movent occupy the circumference of the rotational motion and be itself motionless?
There is a further difficulty in supposing it to be possible for anything that is in motion
to cause motion continuously and not merely in the way in which it is caused by
something repeatedly pushing (in which case the continuity amounts to no more than
successiveness). Such a movent must either itself continue to push or pull or perform
both these actions, or else the action must be taken up by something else and be
passed on from one movent to another (the process that we described before as
occurring in the case of things thrown, since the air or the water, being divisible, is a
movent only in virtue of the fact that different parts of the air are moved one after
another): and in either case the motion cannot be a single motion, but only a
consecutive series of motions. The only continuous motion, then, is that which is
caused by the unmoved movent: and this motion is continuous because the movent
remains always invariable, so that its relation to that which it moves remains also
invariable and continuous.
Now that these points are settled, it is clear that the first unmoved movent cannot
have any magnitude. For if it has magnitude, this must be either a finite or an infinite
magnitude. Now we have already'proved in our course on Physics that there cannot
be an infinite magnitude: and we have now proved that it is impossible for a finite
magnitude to have an infinite force, and also that it is impossible for a thing to be
moved by a finite magnitude during an infinite time. But the first movent causes a
motion that is eternal and does cause it during an infinite time. It is clear, therefore,
that the first movent is indivisible and is without parts and without magnitude.
Why cannot the unmoved mover (movent) not have magnitude?
Has Aristotle proven the existence of God?