alteration: what corresponds in the category of quality to equality in
the category of quantity is 'likeness'. However, let us say that there
is equal velocity where the same change is accomplished in an equal
time. Are we, then, to find the commensurability in the subject of the
affection or in the affection itself? In the case that we have just
been considering it is the fact that health is one and the same that
enables us to arrive at the conclusion that the one alteration is
neither more nor less than the other, but that both are alike. If on
the other hand the affection is different in the two cases, e.g.
when the alterations take the form of becoming white and becoming
healthy respectively, here there is no sameness or equality or
likeness inasmuch as the difference in the affections at once makes
the alterations specifically different, and there is no unity of
alteration any more than there would be unity of locomotion under like
conditions. So we must find out how many species there are of
alteration and of locomotion respectively. Now if the things that
are in motion-that is to say, the things to which the motions belong
essentially and not accidentally-differ specifically, then their
respective motions will also differ specifically: if on the other hand
they differ generically or numerically, the motions also will differ
generically or numerically as the case may be. But there still remains
the question whether, supposing that two alterations are of equal
velocity, we ought to look for this equality in the sameness (or
likeness) of the affections, or in the things altered, to see e.g.
whether a certain quantity of each has become white. Or ought we not
rather to look for it in both? That is to say, the alterations are the
same or different according as the affections are the same or
different, while they are equal or unequal according as the things
altered are equal or unequal.
And now we must consider the same question in the case of becoming
and perishing: how is one becoming of equal velocity with another?
They are of equal velocity if in an equal time there are produced
two things that are the same and specifically inseparable, e.g. two
men (not merely generically inseparable as e.g. two animals).
Similarly one is quicker than the other if in an equal time the
product is different in the two cases. I state it thus because we have
no pair of terms that will convey this 'difference' in the way in
which unlikeness is conveyed. If we adopt the theory that it is number
that constitutes being, we may indeed speak of a 'greater number'
and a 'lesser number' within the same species, but there is no
common term that will include both relations, nor are there terms to
express each of them separately in the same way as we indicate a
higher degree or preponderance of an affection by 'more', of a
quantity by 'greater.'
5
Now since wherever there is a movent, its motion always acts upon
something, is always in something, and always extends to something (by
'is always in something' I mean that it occupies a time: and by
'extends to something' I mean that it involves the traversing of a
certain amount of distance: for at any moment when a thing is
causing motion, it also has caused motion, so that there must always
be a certain amount of distance that has been traversed and a
certain amount of time that has been occupied). then, A the movement
have moved B a distance G in a time D, then in the same time the
same force A will move 1/2B twice the distance G, and in 1/2D it
will move 1/2B the whole distance for G: thus the rules of
proportion will be observed. Again if a given force move a given
weight a certain distance in a certain time and half the distance in
half the time, half the motive power will move half the weight the
same distance in the same time. Let E represent half the motive
power A and Z half the weight B: then the ratio between the motive
power and the weight in the one case is similar and proportionate to
the ratio in the other, so that each force will cause the same
distance to be traversed in the same time. But if E move Z a
distance G in a time D, it does not necessarily follow that E can move
twice Z half the distance G in the same time. If, then, A move B a
distance G in a time D, it does not follow that E, being half of A,
will in the time D or in any fraction of it cause B to traverse a part
of G the ratio between which and the whole of G is proportionate to
that between A and E (whatever fraction of AE may be): in fact it
might well be that it will cause no motion at all; for it does not
follow that, if a given motive power causes a certain amount of
motion, half that power will cause motion either of any particular
amount or in any length of time: otherwise one man might move a
ship, since both the motive power of the ship-haulers and the distance
that they all cause the ship to traverse are divisible into as many
parts as there are men. Hence Zeno's reasoning is false when he argues
that there is no part of the millet that does not make a sound: for
there is no reason why any such part should not in any length of
time fail to move the air that the whole bushel moves in falling. In
fact it does not of itself move even such a quantity of the air as
it would move if this part were by itself: for no part even exists
otherwise than potentially.
If on the other hand we have two forces each of which separately
moves one of two weights a given distance in a given time, then the
forces in combination will move the combined weights an equal distance
in an equal time: for in this case the rules of proportion apply.
Then does this hold good of alteration and of increase also?
Surely it does, for in any given case we have a definite thing that
cause increase and a definite thing that suffers increase, and the one
causes and the other suffers a certain amount of increase in a certain
amount of time. Similarly we have a definite thing that causes
alteration and a definite thing that undergoes alteration, and a
certain amount, or rather degree, of alteration is completed in a
certain amount of time: thus in twice as much time twice as much
alteration will be completed and conversely twice as much alteration
will occupy twice as much time: and the alteration of half of its
object will occupy half as much time and in half as much time half
of the object will be altered: or again, in the same amount of time it
will be altered twice as much.
On the other hand if that which causes alteration or increase causes
a certain amount of increase or alteration respectively in a certain
amount of time, it does not necessarily follow that half the force
will occupy twice the time in altering or increasing the object, or
that in twice the time the alteration or increase will be completed by
it: it may happen that there will be no alteration or increase at all,
the case being the same as with the weight.
Book VIII
/> 1
IT remains to consider the following question. Was there ever a
becoming of motion before which it had no being, and is it perishing
again so as to leave nothing in motion? Or are we to say that it never
had any becoming and is not perishing, but always was and always
will be? Is it in fact an immortal never-failing property of things
that are, a sort of life as it were to all naturally constituted
things?
Now the existence of motion is asserted by all who have anything
to say about nature, because they all concern themselves with the
construction of the world and study the question of becoming and
perishing, which processes could not come about without the
existence of motion. But those who say that there is an infinite
number of worlds, some of which are in process of becoming while
others are in process of perishing, assert that there is always motion
(for these processes of becoming and perishing of the worlds
necessarily involve motion), whereas those who hold that there is only
one world, whether everlasting or not, make corresponding
assumptions in regard to motion. If then it is possible that at any
time nothing should be in motion, this must come about in one of two
ways: either in the manner described by Anaxagoras, who says that
all things were together and at rest for an infinite period of time,
and that then Mind introduced motion and separated them; or in the
manner described by Empedocles, according to whom the universe is
alternately in motion and at rest-in motion, when Love is making the
one out of many, or Strife is making many out of one, and at rest in
the intermediate periods of time-his account being as follows:
'Since One hath learned to spring from Manifold,
And One disjoined makes manifold arise,
Thus they Become, nor stable is their life:
But since their motion must alternate be,
Thus have they ever Rest upon their round':
for we must suppose that he means by this that they alternate from the
one motion to the other. We must consider, then, how this matter
stands, for the discovery of the truth about it is of importance,
not only for the study of nature, but also for the investigation of
the First Principle.
Let us take our start from what we have already laid down in our
course on Physics. Motion, we say, is the fulfilment of the movable in
so far as it is movable. Each kind of motion, therefore, necessarily
involves the presence of the things that are capable of that motion.
In fact, even apart from the definition of motion, every one would
admit that in each kind of motion it is that which is capable of
that motion that is in motion: thus it is that which is capable of
alteration that is altered, and that which is capable of local
change that is in locomotion: and so there must be something capable
of being burned before there can be a process of being burned, and
something capable of burning before there can be a process of burning.
Moreover, these things also must either have a beginning before
which they had no being, or they must be eternal. Now if there was a
becoming of every movable thing, it follows that before the motion
in question another change or motion must have taken place in which
that which was capable of being moved or of causing motion had its
becoming. To suppose, on the other hand, that these things were in
being throughout all previous time without there being any motion
appears unreasonable on a moment's thought, and still more
unreasonable, we shall find, on further consideration. For if we are
to say that, while there are on the one hand things that are
movable, and on the other hand things that are motive, there is a time
when there is a first movent and a first moved, and another time
when there is no such thing but only something that is at rest, then
this thing that is at rest must previously have been in process of
change: for there must have been some cause of its rest, rest being
the privation of motion. Therefore, before this first change there
will be a previous change. For some things cause motion in only one
way, while others can produce either of two contrary motions: thus
fire causes heating but not cooling, whereas it would seem that
knowledge may be directed to two contrary ends while remaining one and
the same. Even in the former class, however, there seems to be
something similar, for a cold thing in a sense causes heating by
turning away and retiring, just as one possessed of knowledge
voluntarily makes an error when he uses his knowledge in the reverse
way. But at any rate all things that are capable respectively of
affecting and being affected, or of causing motion and being moved,
are capable of it not under all conditions, but only when they are
in a particular condition and approach one another: so it is on the
approach of one thing to another that the one causes motion and the
other is moved, and when they are present under such conditions as
rendered the one motive and the other movable. So if the motion was
not always in process, it is clear that they must have been in a
condition not such as to render them capable respectively of being
moved and of causing motion, and one or other of them must have been
in process of change: for in what is relative this is a necessary
consequence: e.g. if one thing is double another when before it was
not so, one or other of them, if not both, must have been in process
of change. It follows then, that there will be a process of change
previous to the first.
(Further, how can there be any 'before' and 'after' without the
existence of time? Or how can there be any time without the
existence of motion? If, then, time is the number of motion or
itself a kind of motion, it follows that, if there is always time,
motion must also be eternal. But so far as time is concerned we see
that all with one exception are in agreement in saying that it is
uncreated: in fact, it is just this that enables Democritus to show
that all things cannot have had a becoming: for time, he says, is
uncreated. Plato alone asserts the creation of time, saying that it
had a becoming together with the universe, the universe according to
him having had a becoming. Now since time cannot exist and is
unthinkable apart from the moment, and the moment a kind of
middle-point, uniting as it does in itself both a beginning and an
end, a beginning of future time and an end of past time, it follows
that there must always be time: for the extremity of the last period
of time that we take must be found in some moment, since time contains
no point of contact for us except the moment. Therefore, since the
moment is both a beginning and an end, there must always be time on
both sides of it. But if this is true of time, it is evident that it
must also be true of motion, time being a kind of affection of
motion.)
The same reasoning will also serve to show the imperishability of
motion: just as a becoming of motion would in
volve, as we saw, the
existence of a process of change previous to the first, in the same
way a perishing of motion would involve the existence of a process
of change subsequent to the last: for when a thing ceases to be moved,
it does not therefore at the same time cease to be movable-e.g. the
cessation of the process of being burned does not involve the
cessation of the capacity of being burned, since a thing may be
capable of being burned without being in process of being
burned-nor, when a thing ceases to be movent, does it therefore at the
same time cease to a be motive. Again, the destructive agent will have
to be destroyed, after what it destroys has been destroyed, and then
that which has the capacity of destroying it will have to be destroyed
afterwards, (so that there will be a process of change subsequent to
the last,) for being destroyed also is a kind of change. If, then,
view which we are criticizing involves these impossible
consequences, it is clear that motion is eternal and cannot have
existed at one time and not at another: in fact such a view can hardly
be described as anythling else than fantastic.
And much the same may be said of the view that such is the ordinance
of nature and that this must be regarded as a principle, as would seem
to be the view of Empedocles when he says that the constitution of the
world is of necessity such that Love and Strife alternately
predominate and cause motion, while in the intermediate period of time
there is a state of rest. Probably also those who like like
Anaxagoras, assert a single principle (of motion) would hold this
view. But that which is produced or directed by nature can never be
anything disorderly: for nature is everywhere the cause of order.
Moreover, there is no ratio in the relation of the infinite to the
infinite, whereas order always means ratio. But if we say that there
is first a state of rest for an infinite time, and then motion is
started at some moment, and that the fact that it is this rather
than a previous moment is of no importance, and involves no order,