of becoming, we shall have an infinite regress. Thus if one of a
series of changes is to be a change of change, the preceding change
must also be so: e.g. if simple becoming was ever in process of
becoming, then that which was becoming simple becoming was also in
process of becoming, so that we should not yet have arrived at what
was in process of simple becoming but only at what was already in
process of becoming in process of becoming. And this again was
sometime in process of becoming, so that even then we should not
have arrived at what was in process of simple becoming. And since in
an infinite series there is no first term, here there will be no first
stage and therefore no following stage either. On this hypothesis,
then, nothing can become or be moved or change.
Thirdly, if a thing is capable of any particular motion, it is
also capable of the corresponding contrary motion or the corresponding
coming to rest, and a thing that is capable of becoming is also
capable of perishing: consequently, if there be becoming of
becoming, that which is in process of becoming is in process of
perishing at the very moment when it has reached the stage of
becoming: since it cannot be in process of perishing when it is just
beginning to become or after it has ceased to become: for that which
is in process of perishing must be in existence.
Fourthly, there must be a substrate underlying all processes of
becoming and changing. What can this be in the present case? It is
either the body or the soul that undergoes alteration: what is it that
correspondingly becomes motion or becoming? And again what is the goal
of their motion? It must be the motion or becoming of something from
something to something else. But in what sense can this be so? For the
becoming of learning cannot be learning: so neither can the becoming
of becoming be becoming, nor can the becoming of any process be that
process.
Finally, since there are three kinds of motion, the substratum and
the goal of motion must be one or other of these, e.g. locomotion will
have to be altered or to be locally moved.
To sum up, then, since everything that is moved is moved in one of
three ways, either accidentally, or partially, or essentially,
change can change only accidentally, as e.g. when a man who is being
restored to health runs or learns: and accidental change we have
long ago decided to leave out of account.
Since, then, motion can belong neither to Being nor to Relation
nor to Agent and Patient, it remains that there can be motion only
in respect of Quality, Quantity, and Place: for with each of these
we have a pair of contraries. Motion in respect of Quality let us call
alteration, a general designation that is used to include both
contraries: and by Quality I do not here mean a property of
substance (in that sense that which constitutes a specific distinction
is a quality) but a passive quality in virtue of which a thing is said
to be acted on or to be incapable of being acted on. Motion in respect
of Quantity has no name that includes both contraries, but it is
called increase or decrease according as one or the other is
designated: that is to say motion in the direction of complete
magnitude is increase, motion in the contrary direction is decrease.
Motion in respect of Place has no name either general or particular:
but we may designate it by the general name of locomotion, though
strictly the term 'locomotion' is applicable to things that change
their place only when they have not the power to come to a stand,
and to things that do not move themselves locally.
Change within the same kind from a lesser to a greater or from a
greater to a lesser degree is alteration: for it is motion either from
a contrary or to a contrary, whether in an unqualified or in a
qualified sense: for change to a lesser degree of a quality will be
called change to the contrary of that quality, and change to a greater
degree of a quality will be regarded as change from the contrary of
that quality to the quality itself. It makes no difference whether the
contraries will have to be contrary to one another only in a qualified
sense: and a thing's possessing a quality in a greater or in a
lesser degree means the presence or absence in it of more or less of
the opposite quality. It is now clear, then, that there are only these
three kinds of motion.
The term 'immovable' we apply in the first place to that which is
absolutely incapable of being moved (just as we correspondingly
apply the term invisible to sound); in the second place to that
which is moved with difficulty after a long time or whose movement
is slow at the start-in fact, what we describe as hard to move; and in
the third place to that which is naturally designed for and capable of
motion, but is not in motion when, where, and as it naturally would be
so. This last is the only kind of immovable thing of which I use the
term 'being at rest': for rest is contrary to motion, so that rest
will be negation of motion in that which is capable of admitting
motion.
The foregoing remarks are sufficient to explain the essential nature
of motion and rest, the number of kinds of change, and the different
varieties of motion.
3
Let us now proceed to define the terms 'together' and 'apart', 'in
contact', 'between', 'in succession', 'contiguous', and
'continuous', and to show in what circumstances each of these terms is
naturally applicable.
Things are said to be together in place when they are in one place
(in the strictest sense of the word 'place') and to be apart when they
are in different places.
Things are said to be in contact when their extremities are
together.
That which a changing thing, if it changes continuously in a natural
manner, naturally reaches before it reaches that to which it changes
last, is between. Thus 'between' implies the presence of at least
three things: for in a process of change it is the contrary that is
'last': and a thing is moved continuously if it leaves no gap or
only the smallest possible gap in the material-not in the time (for
a gap in the time does not prevent things having a 'between', while,
on the other hand, there is nothing to prevent the highest note
sounding immediately after the lowest) but in the material in which
the motion takes place. This is manifestly true not only in local
changes but in every other kind as well. (Now every change implies a
pair of opposites, and opposites may be either contraries or
contradictories; since then contradiction admits of no mean term, it
is obvious that 'between' must imply a pair of contraries) That is
locally contrary which is most distant in a straight line: for the
shortest line is definitely limited, and that which is definitely
limited constitutes a measure.
A thing is 'in succession' when it is after the beginning in
position or in form or in some other respect in which it is definitely
so regarded, and when further there is nothing of the same kind as
itself between it and that to which it is in succession, e.g. a line
or lines if it is a line, a unit or units if it is a unit, a house
if it is a house (there is nothing to prevent something of a different
kind being between). For that which is in succession is in
succession to a particular thing, and is something posterior: for
one is not 'in succession' to two, nor is the first day of the month
to be second: in each case the latter is 'in succession' to the
former.
A thing that is in succession and touches is 'contiguous'. The
'continuous' is a subdivision of the contiguous: things are called
continuous when the touching limits of each become one and the same
and are, as the word implies, contained in each other: continuity is
impossible if these extremities are two. This definition makes it
plain that continuity belongs to things that naturally in virtue of
their mutual contact form a unity. And in whatever way that which
holds them together is one, so too will the whole be one, e.g. by a
rivet or glue or contact or organic union.
It is obvious that of these terms 'in succession' is first in
order of analysis: for that which touches is necessarily in
succession, but not everything that is in succession touches: and so
succession is a property of things prior in definition, e.g.
numbers, while contact is not. And if there is continuity there is
necessarily contact, but if there is contact, that alone does not
imply continuity: for the extremities of things may be 'together'
without necessarily being one: but they cannot be one without being
necessarily together. So natural junction is last in coming to be: for
the extremities must necessarily come into contact if they are to be
naturally joined: but things that are in contact are not all naturally
joined, while there is no contact clearly there is no natural junction
either. Hence, if as some say 'point' and 'unit' have an independent
existence of their own, it is impossible for the two to be
identical: for points can touch while units can only be in succession.
Moreover, there can always be something between points (for all
lines are intermediate between points), whereas it is not necessary
that there should possibly be anything between units: for there can be
nothing between the numbers one and two.
We have now defined what is meant by 'together' and 'apart',
'contact', 'between' and 'in succession', 'contiguous' and
'continuous': and we have shown in what circumstances each of these
terms is applicable.
4
There are many senses in which motion is said to be 'one': for we
use the term 'one' in many senses.
Motion is one generically according to the different categories to
which it may be assigned: thus any locomotion is one generically
with any other locomotion, whereas alteration is different generically
from locomotion.
Motion is one specifically when besides being one generically it
also takes place in a species incapable of subdivision: e.g. colour
has specific differences: therefore blackening and whitening differ
specifically; but at all events every whitening will be specifically
the same with every other whitening and every blackening with every
other blackening. But white is not further subdivided by specific
differences: hence any whitening is specifically one with any other
whitening. Where it happens that the genus is at the same time a
species, it is clear that the motion will then in a sense be one
specifically though not in an unqualified sense: learning is an
example of this, knowledge being on the one hand a species of
apprehension and on the other hand a genus including the various
knowledges. A difficulty, however, may be raised as to whether a
motion is specifically one when the same thing changes from the same
to the same, e.g. when one point changes again and again from a
particular place to a particular place: if this motion is specifically
one, circular motion will be the same as rectilinear motion, and
rolling the same as walking. But is not this difficulty removed by the
principle already laid down that if that in which the motion takes
place is specifically different (as in the present instance the
circular path is specifically different from the straight) the
motion itself is also different? We have explained, then, what is
meant by saying that motion is one generically or one specifically.
Motion is one in an unqualified sense when it is one essentially
or numerically: and the following distinctions will make clear what
this kind of motion is. There are three classes of things in connexion
with which we speak of motion, the 'that which', the 'that in
which', and the 'that during which'. I mean that there must he
something that is in motion, e.g. a man or gold, and it must be in
motion in something, e.g. a place or an affection, and during
something, for all motion takes place during a time. Of these three it
is the thing in which the motion takes place that makes it one
generically or specifically, it is the thing moved that makes the
motion one in subject, and it is the time that makes it consecutive:
but it is the three together that make it one without qualification:
to effect this, that in which the motion takes place (the species)
must be one and incapable of subdivision, that during which it takes
place (the time) must be one and unintermittent, and that which is
in motion must be one-not in an accidental sense (i.e. it must be
one as the white that blackens is one or Coriscus who walks is one,
not in the accidental sense in which Coriscus and white may be one),
nor merely in virtue of community of nature (for there might be a case
of two men being restored to health at the same time in the same
way, e.g. from inflammation of the eye, yet this motion is not
really one, but only specifically one).
Suppose, however, that Socrates undergoes an alteration specifically
the same but at one time and again at another: in this case if it is
possible for that which ceased to be again to come into being and
remain numerically the same, then this motion too will be one:
otherwise it will be the same but not one. And akin to this difficulty
there is another; viz. is health one? and generally are the states and
affections in bodies severally one in essence although (as is clear)
the things that contain them are obviously in motion and in flux? Thus
if a person's health at daybreak and at the present moment is one
and the same, why should not this health be numerically one with
that which he recovers after an interval? The same argument applies in
each case. There is, however, we may answer, this difference: that
if the states are two then it follows simply from this fact that the
activities must also in point of number be two (for only that which is
numerically one can give rise to an activity th
at is numerically one),
but if the state is one, this is not in itself enough to make us
regard the activity also as one: for when a man ceases walking, the
walking no longer is, but it will again be if he begins to walk again.
But, be this as it may, if in the above instance the health is one and
the same, then it must be possible for that which is one and the
same to come to be and to cease to be many times. However, these
difficulties lie outside our present inquiry.
Since every motion is continuous, a motion that is one in an
unqualified sense must (since every motion is divisible) be
continuous, and a continuous motion must be one. There will not be
continuity between any motion and any other indiscriminately any
more than there is between any two things chosen at random in any
other sphere: there can be continuity only when the extremities of the
two things are one. Now some things have no extremities at all: and
the extremities of others differ specifically although we give them
the same name of 'end': how should e.g. the 'end' of a line and the
'end' of walking touch or come to be one? Motions that are not the
same either specifically or generically may, it is true, be
consecutive (e.g. a man may run and then at once fall ill of a fever),
and again, in the torch-race we have consecutive but not continuous
locomotion: for according to our definition there can be continuity
only when the ends of the two things are one. Hence motions may be
consecutive or successive in virtue of the time being continuous,
but there can be continuity only in virtue of the motions themselves
being continuous, that is when the end of each is one with the end
of the other. Motion, therefore, that is in an unqualified sense
continuous and one must be specifically the same, of one thing, and in
one time. Unity is required in respect of time in order that there may
be no interval of immobility, for where there is intermission of
motion there must be rest, and a motion that includes intervals of