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Physics
By Aristotle
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Physics.
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Physics
By Aristotle
Written 350 B.C.E
Translated by R. P. Hardie and R. K. Gaye
Part 1
Everything that is in motion must be moved by something. For if it has
not the source of its motion in itself it is evident that it is moved by
something other than itself, for there must be something else that moves
it. If on the other hand it has the source of its motion in itself, let
AB be taken to represent that which is in motion essentially of itself
and not in virtue of the fact that something belonging to it is in motion.
Now in the first place to assume that Ab, because it is in motion as a
whole and is not moved by anything external to itself, is therefore moved
by itself-this is just as if, supposing that KL is moving LM and is also
itself in motion, we were to deny that KM is moved by anything on the ground
that it is not evident which is the part that is moving it and which the
part that is moved. In the second place that which is in motion without
being moved by anything does not necessarily cease from its motion because
something else is at rest, but a thing must be moved by something if the
fact of something else having ceased from its motion causes it to be at
rest. Thus, if this is accepted, everything that is in motion must be moved
by something. For AB, which has been taken to represent that which is in
motion, must be divisible since everything that is in motion is divisible.
Let it be divided, then, at G. Now if GB is not in motion, then AB will
not be in motion: for if it is, it is clear that AG would be in motion
while BG is at rest, and thus AB cannot be in motion essentially and primarily.
But ex hypothesi AB is in motion essentially and primarily. Therefore if
GB is not in motion AB will be at rest. But we have agreed that that which
is at rest if something else is not in motion must be moved by something.
Consequently, everything that is in motion must be moved by something:
for that which is in motion will always be divisible, and if a part of
it is not in motion the whole must be at rest.
Since everything that is in motion must be moved by something,
let us take the case in which a thing is in locomotion and is moved by
something that is itself in motion, and that again is moved by something
else that is in motion, and that by something else, and so on continually:
then the series cannot go on to infinity, but there must be some first
movent. For let us suppose that this is not so and take the series to be
infinite. Let A then be moved by B, B by G, G by D, and so on, each member
of the series being moved by that which comes next to it. Then since ex
hypothesi the movent while causing motion is also itself in motion, and
the motion of the moved and the motion of the movent must proceed simultaneously
(for the movent is causing motion and the moved is being moved simultaneously)
it is evident that the respective motions of A, B, G, and each of the other
moved movents are simultaneous. Let us take the motion of each separately
and let E be the motion of A, Z of B, and H and O respectively the motions
of G and D: for though they are all moved severally one by another, yet
we may still take the motion of each as numerically one, since every motion
is from something to something and is not infinite in respect of its extreme
points. By a motion that is numerically one I mean a motion that proceeds
from something numerically one and the same to something numerically one
and the same in a period of time numerically one and the same: for a motion
may be the same generically, specifically, or numerically: it is generically
the same if it belongs to the same category, e.g. substance or quality:
it is specifically the same if it proceeds from something specifically
the same to something specifically the same, e.g. from white to black or
from good to bad, which is not of a kind specifically distinct: it is numerically
the same if it proceeds from something numerically one to something numerically
one in the same period of time, e.g. from a particular white to a particular
black, or from a particular place to a particular place, in a particular
period of time: for if the period of time were not one and the same, the
motion would no longer be numerically one though it would still be specifically
one.
We have dealt with this question above. Now let us further take
the time in which A has completed its motion, and let it be represented
by K. Then since the motion of A is finite the time will also be finite.
But since the movents and the things moved are infinite, the motion EZHO,
i.e. the motion that is composed of all the individual motions, must be
infinite. For the motions of A, B, and the others may be equal, or the
motions of the others may be greater: but assuming what is conceivable,
we find that whether they are equal or some are greater, in both cases
the whole motion is infinite. And since the motion of A and that of each
of the others are simultaneous, the whole motion must occupy the same time
as the motion of A: but the time occupied by the motion of A is finite:
consequently the motion will be infinite in a finite time, which is
impossible.
It might be thought that what we set out to prove has thus been
shown, but our argument so far does not prove it, because it does not yet
prove that anything impossible results from the contrary supposition: for
in a finite time there may be an infinite motion, though not of one thing,
but of many: and in the case that we are considering this is so: for each
thing accomplishes its own motion, and there is no impossibility in many
things being in motion simultaneously. But if (as we see to be universally
the case) that which primarily is moved locally and corporeally must be
either in contact with or continuous with that which moves it, the things
moved and the movents must be continuous or in contact with one another,
so that together they all form a single unity: whether this unity is finite
or infinite makes no difference to our present argument; for in any case
since the things in motion are infinite in number the whole motion will
be infinite, if, as is theoretically possible, each motion is either equal
to or greater than that which follows it in the series: for we shall take
as actual that which is theoretically possible. If, then, A, B, G, D form
an infinite magnitude that passes through the motion EZHO in the finite
time K, this involves the conclusion that an infinite motion is passed
through in a finite time: and whether the magnitude in question is finite
or infinite this is in either case impossible. Therefore the series must
come to an end, and there must be a first movent and a first moved: for
the fact that this impossibility results only from the assumption of a
particular case is immaterial, since the case assumed is theoretically
possible, and the assumption of a theoretically possible case ought not
to give rise to any impossible result.
Part 2
That which is the first movement of a thing-in the sense that it
supplies not 'that for the sake of which' but the source of the motion-is
always together with that which is moved by it by 'together' I mean that
there is nothing intermediate between them). This is universally true wherever
one thing is moved by another. And since there are three kinds of motion,
local, qualitative, and quantitative, there must also be three kinds of
movent, that which causes locomotion, that which causes alteration, and
that which causes increase or decrease.
Let us begin with locomotion, for this is the primary motion. Everything
that is in locomotion is moved either by itself or by something else. In
the case of things that are moved by themselves it is evident that the
moved and the movent are together: for they contain within themselves their
first movent, so that there is nothing in between. The motion of things
that are moved by something else must proceed in one of four ways: for
there are four kinds of locomotion caused by something other than that
which is in motion, viz. pulling, pushing, carrying, and twirling. All
forms of locomotion are reducible to these. Thus pushing on is a form of
pushing in which that which is causing motion away from itself follows
up that which it pushes and continues to push it: pushing off occurs when
the movent does not follow up the thing that it has moved: throwing when
the movent causes a motion away from itself more violent than the natural
locomotion of the thing moved, which continues its course so long as it
is controlled by the motion imparted to it. Again, pushing apart and pushing
together are forms respectively of pushing off and pulling: pushing apart
is pushing off, which may be a motion either away from the pusher or away
from something else, while pushing together is pulling, which may be a
motion towards something else as well as the puller. We may similarly classify
all the varieties of these last two, e.g. packing and combing: the former
is a form of pushing together, the latter a form of pushing apart. The
same is true of the other processes of combination and separation (they
will all be found to be forms of pushing apart or of pushing together),
except such as are involved in the processes of becoming and perishing.
(At same time it is evident that there is no other kind of motion but combination
and separation: for they may all be apportioned to one or other of those
already mentioned.) Again, inhaling is a form of pulling, exhaling a form
of pushing: and the same is true of spitting and of all other motions that
proceed through the body, whether secretive or assimilative, the assimilative
being forms of pulling, the secretive of pushing off. All other kinds of
locomotion must be similarly reduced, for they all fall under one or other
of our four heads. And again, of these four, carrying and twirling are
to pulling and pushing. For carrying always follows one of the other three
methods, for that which is carried is in motion accidentally, because it
is in or upon something that is in motion, and that which carries it is
in doing so being either pulled or pushed or twirled; thus carrying belongs
to all the other three kinds of motion in common. And twirling is a compound
of pulling and pushing, for that which is twirling a thing must be pulling
one part of the thing and pushing another part, since it impels one part
away from itself and another part towards itself. If, therefore, it can
be shown that that which is pushing and that which is pushing and pulling
are adjacent respectively to that which is being pushed and that which
is being pulled, it will be evident that in all locomotion there is nothing
intermediate between moved and movent. But the former fact is clear even
from the definitions of pushing and pulling, for pushing is motion to something
else from oneself or from something else, and pulling is motion from something
else to oneself or to something else, when the motion of that which is
pulling is quicker than the motion that would separate from one another
the two things that are continuous: for it is this that causes one thing
to be pulled on along with the other. (It might indeed be thought that
there is a form of pulling that arises in another way: that wood, e.g.
pulls fire in a manner different from that described above. But it makes
no difference whether that which pulls is in motion or is stationary when
it is pulling: in the latter case it pulls to the place where it is, while
in the former it pulls to the place where it was.) Now it is impossible
to move anything either from oneself to something else or something else
to oneself without being in contact with it: it is evident, therefore,
that in all locomotion there is nothing intermediate between moved and
movent.
Nor again is there anything intermediate between that which undergoes
and that which causes alteration: this can be proved by induction: for
in every case we find that the respective extremities of that which causes
and that which undergoes alteration are adjacent. For our assumption is
that things that are undergoing alteration are altered in virtue of their
being affected in respect of their so-called affective qualities, since
that which is of a certain quality is altered in so far as it is sensible,
and the characteristics in which bodies differ from one another are sensible
characteristics: for every body differs from another in possessing a greater
or lesser number of sensible characteristics or in possessing the same
sensible characteristics in a greater or lesser degree. But the alteration
of that which undergoes alteration is also caused by the above-mentioned
characteristics, which are affections of some particular underlying quality.
Thus we say that a thing is altered by becoming hot or sweet or thick or
dry or white: and we make these assertions alike of what is inanimate and
of what is animate, and further, where animate things are in question,
we make them both of the parts that have no power of sense-perception and
of the senses themselves. For in a way even the senses undergo alteration,
since the active sense is a motion through the body in the course of which
the sense is affected in a certain way. We see, then, that the animate
is capable of every kind of alteration of which the inanimate is capable:
but the inanimate is not capable of every kind of alteration of which the
animate is capable, since it is not capable of alteration in respect of
the senses: moreover the inanimate is unconscious of being affected by
alteration, whereas the animate is conscious of it, though there is nothing
to prevent the animate also being unconscious of it when the process of
the alteration does not concern the senses. Since, then, the alteration
of that which undergoes alteration is caused by sensible things, in every
case of such alteration it is evident that the respective extremities of
that which causes and that which undergoes alteration are adjacent. Thus
the air is continuous with that which causes the alteration, and the body
that undergoes alteration is continuous with the air. Again, the colour
is continuous with the light and the light with the sight. And the same
is true of hearing and smelling: for the primary movent in respect to the
moved is the air. Similarly, in the case of tasting, the flavour is adjacent
to the sense of taste. And it is just the same in the case of things that
are inanimate and incapable of sense-perception. Thus there can be nothing
intermediate between that which undergoes and that which causes
alteration.
Nor, again, can there be anything intermediate between that which
suffers and that which causes increase: for the part of the latter that
starts the increase does so by becoming attached in such a way to the former
that the whole becomes one. Again, the decrease of that which suffers decrease
is caused by a part of the thing becoming detached. So that which causes
increase and that which causes decrease must be continuous with that which
suffers increase and that which suffers decrease respectively: and if two
things are continuous with one another there can be nothing intermediate
between them.
It is evident, therefore, that between the extremities of the moved
and the movent that are respectively first and last in reference to the
moved there is nothing intermediate.
Part 3
Everything, we say, that undergoes alteration is altered by sensible
causes, and there is alteration only in things that are said to be essentially
affected by sensible things. The truth of this is to be seen from the following
considerations. Of all other things it would be most natural to suppose
that there is alteration in figures and shapes, and in acquired states
and in the processes of acquiring and losing these: but as a matter of
fact in neither of these two classes of things is there
alteration.
In the first place, when a particular formation of a thing is completed,
we do not call it by the name of its material: e.g. we do not call the
statue 'bronze' or the pyramid 'wax' or the bed 'wood', but we use a derived
expression and call them 'of bronze', 'waxen', and 'wooden' respectively.
But when a thing has been affected and altered in any way we still call
it by the original name: thus we speak of the bronze or the wax being dry
or fluid or hard or hot.
And not only so: we also speak of the particular fluid or hot substance
as being bronze, giving the material the same name as that which we use
to describe the affection.
Since, therefore, having regard to the figure or shape of a thing
we no longer call that which has become of a certain figure by the name
of the material that exhibits the figure, whereas having regard to a thing's
affections or alterations we still call it by the name of its material,
it is evident that becomings of the former kind cannot be
alterations.
Moreover it would seem absurd even to speak in this way, to speak,
that is to say, of a man or house or anything else that has come into existence
as having been altered. Though it may be true that every such becoming
is necessarily the result of something's being altered, the result, e.g.
of the material's being condensed or rarefied or heated or cooled, nevertheless
it is not the things that are coming into existence that are altered, and
their becoming is not an alteration.
Again, acquired states, whether of the body or of the soul, are
not alterations. For some are excellences and others are defects, and neither
excellence nor defect is an alteration: excellence is a perfection (for
when anything acquires its proper excellence we call it perfect, since
it is then if ever that we have a thing in its natural state: e.g. we have
a perfect circle when we have one as good as possible), while defect is
a perishing of or departure from this condition. So as when speaking of
a house we do not call its arrival at perfection an alteration (for it
would be absurd to suppose that the coping or the tiling is an alteration
or that in receiving its coping or its tiling a house is altered and not
perfected), the same also holds good in the case of excellences and defects
and of the persons or things that possess or acquire them: for excellences
are perfections of a thing's nature and defects are departures from it:
consequently they are not alterations.
Further, we say that all excellences depend upon particular relations.
Thus bodily excellences such as health and a good state of body we regard
as consisting in a blending of hot and cold elements within the body in
due proportion, in relation either to one another or to the surrounding
atmosphere: and in like manner we regard beauty, strength, and all the
other bodily excellences and defects. Each of them exists in virtue of
a particular relation and puts that which possesses it in a good or bad
condition with regard to its proper affections, where by 'proper' affections
I mean those influences that from the natural constitution of a thing tend
to promote or destroy its existence. Since then, relatives are neither
themselves alterations nor the subjects of alteration or of becoming or
in fact of any change whatever, it is evident that neither states nor the
processes of losing and acquiring states are alterations, though it may
be true that their becoming or perishing is necessarily, like the becoming
or perishing of a specific character or form, the result of the alteration
of certain other things, e.g. hot and cold or dry and wet elements or the
elements, whatever they may be, on which the states primarily depend. For
each several bodily defect or excellence involves a relation with those
things from which the possessor of the defect or excellence is naturally
subject to alteration: thus excellence disposes its possessor to be unaffected
by these influences or to be affected by those of them that ought to be
admitted, while defect disposes its possessor to be affected by them or
to be unaffected by those of them that ought to be admitted.
And the case is similar in regard to the states of the soul, all
of which (like those of body) exist in virtue of particular relations,
the excellences being perfections of nature and the defects departures
from it: moreover, excellence puts its possessor in good condition, while
defect puts its possessor in a bad condition, to meet his proper affections.
Consequently these cannot any more than the bodily states be alterations,
nor can the processes of losing and acquiring them be so, though their
becoming is necessarily the result of an alteration of the sensitive part
of the soul, and this is altered by sensible objects: for all moral excellence
is concerned with bodily pleasures and pains, which again depend either
upon acting or upon remembering or upon anticipating. Now those that depend
upon action are determined by sense-perception, i.e. they are stimulated
by something sensible: and those that depend upon memory or anticipation
are likewise to be traced to sense-perception, for in these cases pleasure
is felt either in remembering what one has experienced or in anticipating
what one is going to experience. Thus all pleasure of this kind must be
produced by sensible things: and since the presence in any one of moral
defect or excellence involves the presence in him of pleasure or pain (with
which moral excellence and defect are always concerned), and these pleasures
and pains are alterations of the sensitive part, it is evident that the
loss and acquisition of these states no less than the loss and acquisition
of the states of the body must be the result of the alteration of something
else. Consequently, though their becoming is accompanied by an alteration,
they are not themselves alterations.
Again, the states of the intellectual part of the soul are not
alterations, nor is there any becoming of them. In the first place it is
much more true of the possession of knowledge that it depends upon a particular
relation. And further, it is evident that there is no becoming of these
states. For that which is potentially possessed of knowledge becomes actually
possessed of it not by being set in motion at all itself but by reason
of the presence of something else: i.e. it is when it meets with the particular
object that it knows in a manner the particular through its knowledge of
the universal. (Again, there is no becoming of the actual use and activity
of these states, unless it is thought that there is a becoming of vision
and touching and that the activity in question is similar to these.) And
the original acquisition of knowledge is not a becoming or an alteration:
for the terms 'knowing' and 'understanding' imply that the intellect has
reached a state of rest and come to a standstill, and there is no becoming
that leads to a state of rest, since, as we have said above, change at
all can have a becoming. Moreover, just as to say, when any one has passed
from a state of intoxication or sleep or disease to the contrary state,
that he has become possessed of knowledge again is incorrect in spite of
the fact that he was previously incapable of using his knowledge, so, too,
when any one originally acquires the state, it is incorrect to say that
he becomes possessed of knowledge: for the possession of understanding
and knowledge is produced by the soul's settling down out of the restlessness
natural to it. Hence, too, in learning and in forming judgements on matters
relating to their sense-perceptions children are inferior to adults owing
to the great amount of restlessness and motion in their souls. Nature itself
causes the soul to settle down and come to a state of rest for the performance
of some of its functions, while for the performance of others other things
do so: but in either case the result is brought about through the alteration
of something in the body, as we see in the case of the use and activity
of the intellect arising from a man's becoming sober or being awakened.
It is evident, then, from the preceding argument that alteration and being
altered occur in sensible things and in the sensitive part of the soul,
and, except accidentally, in nothing else.
Part 4
A difficulty may be raised as to whether every motion is commensurable
with every other or not. Now if they are all commensurable and if two things
to have the same velocity must accomplish an equal motion in an equal time,
then we may have a circumference equal to a straight line, or, of course,
the one may be greater or less than the other. Further, if one thing alters
and another accomplishes a locomotion in an equal time, we may have an
alteration and a locomotion equal to one another: thus an affection will
be equal to a length, which is impossible. But is it not only when an equal
motion is accomplished by two things in an equal time that the velocities
of the two are equal? Now an affection cannot be equal to a length. Therefore
there cannot be an alteration equal to or less than a locomotion: and consequently
it is not the case that every motion is commensurable with every
other.
But how will our conclusion work out in the case of the circle
and the straight line? It would be absurd to suppose that the motion of
one in a circle and of another in a straight line cannot be similar, but
that the one must inevitably move more quickly or more slowly than the
other, just as if the course of one were downhill and of the other uphill.
Moreover it does not as a matter of fact make any difference to the argument
to say that the one motion must inevitably be quicker or slower than the
other: for then the circumference can be greater or less than the straight
line; and if so it is possible for the two to be equal. For if in the time
A the quicker (B) passes over the distance B' and the slower (G) passes
over the distance G', B' will be greater than G': for this is what we took
'quicker' to mean: and so quicker motion also implies that one thing traverses
an equal distance in less time than another: consequently there will be
a part of A in which B will pass over a part of the circle equal to G',
while G will occupy the whole of A in passing over G'. None the less, if
the two motions are commensurable, we are confronted with the consequence
stated above, viz. that there may be a straight line equal to a circle.
But these are not commensurable: and so the corresponding motions are not
commensurable either.
But may we say that things are always commensurable if the same
terms are applied to them without equivocation? e.g. a pen, a wine, and
the highest note in a scale are not commensurable: we cannot say whether
any one of them is sharper than any other: and why is this? they are incommensurable
because it is only equivocally that the same term 'sharp' is applied to
them: whereas the highest note in a scale is commensurable with the leading-note,
because the term 'sharp' has the same meaning as applied to both. Can it
be, then, that the term 'quick' has not the same meaning as applied to
straight motion and to circular motion respectively? If so, far less will
it have the same meaning as applied to alteration and to
locomotion.
Or shall we in the first place deny that things are always commensurable
if the same terms are applied to them without equivocation? For the term
'much' has the same meaning whether applied to water or to air, yet water
and air are not commensurable in respect of it: or, if this illustration
is not considered satisfactory, 'double' at any rate would seem to have
the same meaning as applied to each (denoting in each case the proportion
of two to one), yet water and air are not commensurable in respect of it.
But here again may we not take up the same position and say that the term
'much' is equivocal? In fact there are some terms of which even the definitions
are equivocal; e.g. if 'much' were defined as 'so much and more','so much'
would mean something different in different cases: 'equal' is similarly
equivocal; and 'one' again is perhaps inevitably an equivocal term; and
if 'one' is equivocal, so is 'two'. Otherwise why is it that some things
are commensurable while others are not, if the nature of the attribute
in the two cases is really one and the same?
Can it be that the incommensurability of two things in respect
of any attribute is due to a difference in that which is primarily capable
of carrying the attribute? Thus horse and dog are so commensurable that
we may say which is the whiter, since that which primarily contains the
whiteness is the same in both, viz. the surface: and similarly they are
commensurable in respect of size. But water and speech are not commensurable
in respect of clearness, since that which primarily contains the attribute
is different in the two cases. It would seem, however that we must reject
this solution, since clearly we could thus make all equivocal attributes
univocal and say merely that that contains each of them is different in
different cases: thus 'equality', 'sweetness', and 'whiteness' will severally
always be the same, though that which contains them is different in different
cases. Moreover, it is not any casual thing that is capable of carrying
any attribute: each single attribute can be carried primarily only by one
single thing.
Must we then say that, if two things are to be commensurable in
respect of any attribute, not only must the attribute in question be applicable
to both without equivocation, but there must also be no specific differences
either in the attribute itself or in that which contains the attribute-that
these, I mean, must not be divisible in the way in which colour is divided
into kinds? Thus in this respect one thing will not be commensurable with
another, i.e. we cannot say that one is more coloured than the other where
only colour in general and not any particular colour is meant; but they
are commensurable in respect of whiteness.
Similarly in the case of motion: two things are of the same velocity
if they occupy an equal time in accomplishing a certain equal amount of
motion. Suppose, then, that in a certain time an alteration is undergone
by one half of a body's length and a locomotion is accomplished the other
half: can be say that in this case the alteration is equal to the locomotion
and of the same velocity? That would be absurd, and the reason is that
there are different species of motion. And if in consequence of this we
must say that two things are of equal velocity if they accomplish locomotion
over an equal distance in an equal time, we have to admit the equality
of a straight line and a circumference. What, then, is the reason of this?
Is it that locomotion is a genus or that line is a genus? (We may leave
the time out of account, since that is one and the same.) If the lines
are specifically different, the locomotions also differ specifically from
one another: for locomotion is specifically differentiated according to
the specific differentiation of that over which it takes place. (It is
also similarly differentiated, it would seem, accordingly as the instrument
of the locomotion is different: thus if feet are the instrument, it is
walking, if wings it is flying; but perhaps we should rather say that this
is not so, and that in this case the differences in the locomotion are
merely differences of posture in that which is in motion.) We may say,
therefore, that things are of equal velocity in an equal time they traverse
the same magnitude: and when I call it 'the same' I mean that it contains
no specific difference and therefore no difference in the motion that takes
place over it. So we have now to consider how motion is differentiated:
and this discussion serves to show that the genus is not a unity but contains
a plurality latent in it and distinct from it, and that in the case of
equivocal terms sometimes the different senses in which they are used are
far removed from one another, while sometimes there is a certain likeness
between them, and sometimes again they are nearly related either generically
or analogically, with the result that they seem not to be equivocal though
they really are.
When, then, is there a difference of species? Is an attribute specifically
different if the subject is different while the attribute is the same,
or must the attribute itself be different as well? And how are we to define
the limits of a species? What will enable us to decide that particular
instances of whiteness or sweetness are the same or different? Is it enough
that it appears different in one subject from what appears in another?
Or must there be no sameness at all? And further, where alteration is in
question, how is one alteration to be of equal velocity with another? One
person may be cured quickly and another slowly, and cures may also be simultaneous:
so that, recovery of health being an alteration, we have here alterations
of equal velocity, since each alteration occupies an equal time. But what
alteration? We cannot here speak of an 'equal' 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.'
Part 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.