rest will be not one but many, so that a motion that is interrupted by
stationariness is not one or continuous, and it is so interrupted if
there is an interval of time. And though of a motion that is not
specifically one (even if the time is unintermittent) the time is one,
the motion is specifically different, and so cannot really be one, for
motion that is one must be specifically one, though motion that is
specifically one is not necessarily one in an unqualified sense. We
have now explained what we mean when we call a motion one without
qualification.
Further, a motion is also said to be one generically,
specifically, or essentially when it is complete, just as in other
cases completeness and wholeness are characteristics of what is one:
and sometimes a motion even if incomplete is said to be one,
provided only that it is continuous.
And besides the cases already mentioned there is another in which
a motion is said to be one, viz. when it is regular: for in a sense
a motion that is irregular is not regarded as one, that title
belonging rather to that which is regular, as a straight line is
regular, the irregular being as such divisible. But the difference
would seem to be one of degree. In every kind of motion we may have
regularity or irregularity: thus there may be regular alteration,
and locomotion in a regular path, e.g. in a circle or on a straight
line, and it is the same with regard to increase and decrease. The
difference that makes a motion irregular is sometimes to be found in
its path: thus a motion cannot be regular if its path is an
irregular magnitude, e.g. a broken line, a spiral, or any other
magnitude that is not such that any part of it taken at random fits on
to any other that may be chosen. Sometimes it is found neither in
the place nor in the time nor in the goal but in the manner of the
motion: for in some cases the motion is differentiated by quickness
and slowness: thus if its velocity is uniform a motion is regular,
if not it is irregular. So quickness and slowness are not species of
motion nor do they constitute specific differences of motion,
because this distinction occurs in connexion with all the distinct
species of motion. The same is true of heaviness and lightness when
they refer to the same thing: e.g. they do not specifically
distinguish earth from itself or fire from itself. Irregular motion,
therefore, while in virtue of being continuous it is one, is so in a
lesser degree, as is the case with locomotion in a broken line: and
a lesser degree of something always means an admixture of its
contrary. And since every motion that is one can be both regular and
irregular, motions that are consecutive but not specifically the
same cannot be one and continuous: for how should a motion composed of
alteration and locomotion be regular? If a motion is to be regular its
parts ought to fit one another.
5
We have further to determine what motions are contrary to each
other, and to determine similarly how it is with rest. And we have
first to decide whether contrary motions are motions respectively from
and to the same thing, e.g. a motion from health and a motion to
health (where the opposition, it would seem, is of the same kind as
that between coming to be and ceasing to be); or motions
respectively from contraries, e.g. a motion from health and a motion
from disease; or motions respectively to contraries, e.g. a motion
to health and a motion to disease; or motions respectively from a
contrary and to the opposite contrary, e.g. a motion from health and a
motion to disease; or motions respectively from a contrary to the
opposite contrary and from the latter to the former, e.g. a motion
from health to disease and a motion from disease to health: for
motions must be contrary to one another in one or more of these
ways, as there is no other way in which they can be opposed.
Now motions respectively from a contrary and to the opposite
contrary, e.g. a motion from health and a motion to disease, are not
not the same, just as changing from health is different from
changing to disease.) Nor are motion respectively from a contrary
and from the opposite contrary contrary motions, for a motion from a
contrary is at the same time a motion to a contrary or to an
intermediate (of this, however, we shall speak later), but changing to
a contrary rather than changing from a contrary would seem to be the
cause of the contrariety of motions, the latter being the loss, the
former the gain, of contrariness. Moreover, each several motion
takes its name rather from the goal than from the starting-point of
change, e.g. motion to health we call convalescence, motion to disease
sickening. Thus we are left with motions respectively to contraries,
and motions respectively to contraries from the opposite contraries.
Now it would seem that motions to contraries are at the same time
motions from contraries (though their essence may not be the same; 'to
health' is distinct, I mean, from 'from disease', and 'from health'
from 'to disease').
Since then change differs from motion (motion being change from a
particular subject to a particular subject), it follows that
contrary motions are motions respectively from a contrary to the
opposite contrary and from the latter to the former, e.g. a motion
from health to disease and a motion from disease to health.
Moreover, the consideration of particular examples will also show what
kinds of processes are generally recognized as contrary: thus
falling ill is regarded as contrary to recovering one's health,
these processes having contrary goals, and being taught as contrary to
being led into error by another, it being possible to acquire error,
like knowledge, either by one's own agency or by that of another.
Similarly we have upward locomotion and downward locomotion, which are
contrary lengthwise, locomotion to the right and locomotion to the
left, which are contrary breadthwise, and forward locomotion and
backward locomotion, which too are contraries. On the other hand, a
process simply to a contrary, e.g. that denoted by the expression
'becoming white', where no starting-point is specified, is a change
but not a motion. And in all cases of a thing that has no contrary
we have as contraries change from and change to the same thing. Thus
coming to be is contrary to ceasing to be, and losing to gaining.
But these are changes and not motions. And wherever a pair of
contraries admit of an intermediate, motions to that intermediate must
be held to be in a sense motions to one or other of the contraries:
for the intermediate serves as a contrary for the purposes of the
motion, in whichever direction the change may be, e.g. grey in a
motion from grey to white takes the place of black as
starting-point, in a motion from white to grey it takes the place of
black as goal, and in a motion from black to grey it takes th
e place
of white as goal: for the middle is opposed in a sense to either of
the extremes, as has been said above. Thus we see that two motions are
contrary to each other only when one is a motion from a contrary to
the opposite contrary and the other is a motion from the latter to the
former.
6
But since a motion appears to have contrary to it not only another
motion but also a state of rest, we must determine how this is so. A
motion has for its contrary in the strict sense of the term another
motion, but it also has for an opposite a state of rest (for rest is
the privation of motion and the privation of anything may be called
its contrary), and motion of one kind has for its opposite rest of
that kind, e.g. local motion has local rest. This statement,
however, needs further qualification: there remains the question, is
the opposite of remaining at a particular place motion from or
motion to that place? It is surely clear that since there are two
subjects between which motion takes place, motion from one of these
(A) to its contrary (B) has for its opposite remaining in A while
the reverse motion has for its opposite remaining in B. At the same
time these two are also contrary to each other: for it would be absurd
to suppose that there are contrary motions and not opposite states
of rest. States of rest in contraries are opposed. To take an example,
a state of rest in health is (1) contrary to a state of rest in
disease, and (2) the motion to which it is contrary is that from
health to disease. For (2) it would be absurd that its contrary motion
should be that from disease to health, since motion to that in which a
thing is at rest is rather a coming to rest, the coming to rest
being found to come into being simultaneously with the motion; and one
of these two motions it must be. And (1) rest in whiteness is of
course not contrary to rest in health.
Of all things that have no contraries there are opposite changes
(viz. change from the thing and change to the thing, e.g. change
from being and change to being), but no motion. So, too, of such
things there is no remaining though there is absence of change. Should
there be a particular subject, absence of change in its being will
be contrary to absence of change in its not-being. And here a
difficulty may be raised: if not-being is not a particular
something, what is it, it may be asked, that is contrary to absence of
change in a thing's being? and is this absence of change a state of
rest? If it is, then either it is not true that every state of rest is
contrary to a motion or else coming to be and ceasing to be are
motion. It is clear then that, since we exclude these from among
motions, we must not say that this absence of change is a state of
rest: we must say that it is similar to a state of rest and call it
absence of change. And it will have for its contrary either nothing or
absence of change in the thing's not-being, or the ceasing to be of
the thing: for such ceasing to be is change from it and the thing's
coming to be is change to it.
Again, a further difficulty may be raised. How is it, it may be
asked, that whereas in local change both remaining and moving may be
natural or unnatural, in the other changes this is not so? e.g.
alteration is not now natural and now unnatural, for convalescence
is no more natural or unnatural than falling ill, whitening no more
natural or unnatural than blackening; so, too, with increase and
decrease: these are not contrary to each other in the sense that
either of them is natural while the other is unnatural, nor is one
increase contrary to another in this sense; and the same account may
be given of becoming and perishing: it is not true that becoming is
natural and perishing unnatural (for growing old is natural), nor do
we observe one becoming to be natural and another unnatural. We answer
that if what happens under violence is unnatural, then violent
perishing is unnatural and as such contrary to natural perishing.
Are there then also some becomings that are violent and not the result
of natural necessity, and are therefore contrary to natural becomings,
and violent increases and decreases, e.g. the rapid growth to maturity
of profligates and the rapid ripening of seeds even when not packed
close in the earth? And how is it with alterations? Surely just the
same: we may say that some alterations are violent while others are
natural, e.g. patients alter naturally or unnaturally according as
they throw off fevers on the critical days or not. But, it may be
objected, then we shall have perishings contrary to one another, not
to becoming. Certainly: and why should not this in a sense be so? Thus
it is so if one perishing is pleasant and another painful: and so
one perishing will be contrary to another not in an unqualified sense,
but in so far as one has this quality and the other that.
Now motions and states of rest universally exhibit contrariety in
the manner described above, e.g. upward motion and rest above are
respectively contrary to downward motion and rest below, these being
instances of local contrariety; and upward locomotion belongs
naturally to fire and downward to earth, i.e. the locomotions of the
two are contrary to each other. And again, fire moves up naturally and
down unnaturally: and its natural motion is certainly contrary to
its unnatural motion. Similarly with remaining: remaining above is
contrary to motion from above downwards, and to earth this remaining
comes unnaturally, this motion naturally. So the unnatural remaining
of a thing is contrary to its natural motion, just as we find a
similar contrariety in the motion of the same thing: one of its
motions, the upward or the downward, will be natural, the other
unnatural.
Here, however, the question arises, has every state of rest that
is not permanent a becoming, and is this becoming a coming to a
standstill? If so, there must be a becoming of that which is at rest
unnaturally, e.g. of earth at rest above: and therefore this earth
during the time that it was being carried violently upward was
coming to a standstill. But whereas the velocity of that which comes
to a standstill seems always to increase, the velocity of that which
is carried violently seems always to decrease: so it will he in a
state of rest without having become so. Moreover 'coming to a
standstill' is generally recognized to be identical or at least
concomitant with the locomotion of a thing to its proper place.
There is also another difficulty involved in the view that remaining
in a particular place is contrary to motion from that place. For
when a thing is moving from or discarding something, it still
appears to have that which is being discarded, so that if a state of
rest is itself contrary to the motion from the state of rest to its
contrary, the contraries rest and motion will be simultaneously
predicable of the same thing. May we not say, however, that in so
far as the thing
is still stationary it is in a state of rest in a
qualified sense? For, in fact, whenever a thing is in motion, part
of it is at the starting-point while part is at the goal to which it
is changing: and consequently a motion finds its true contrary
rather in another motion than in a state of rest.
With regard to motion and rest, then, we have now explained in
what sense each of them is one and under what conditions they
exhibit contrariety.
[With regard to coming to a standstill the question may be raised
whether there is an opposite state of rest to unnatural as well as
to natural motions. It would be absurd if this were not the case:
for a thing may remain still merely under violence: thus we shall have
a thing being in a non-permanent state of rest without having become
so. But it is clear that it must be the case: for just as there is
unnatural motion, so, too, a thing may be in an unnatural state of
rest. Further, some things have a natural and an unnatural motion,
e.g. fire has a natural upward motion and an unnatural downward
motion: is it, then, this unnatural downward motion or is it the
natural downward motion of earth that is contrary to the natural
upward motion? Surely it is clear that both are contrary to it
though not in the same sense: the natural motion of earth is
contrary inasmuch as the motion of fire is also natural, whereas the
upward motion of fire as being natural is contrary to the downward
motion of fire as being unnatural. The same is true of the
corresponding cases of remaining. But there would seem to be a sense
in which a state of rest and a motion are opposites.]
Book VI
1
Now if the terms 'continuous', 'in contact', and 'in succession' are
understood as defined above things being 'continuous' if their
extremities are one, 'in contact' if their extremities are together,
and 'in succession' if there is nothing of their own kind intermediate
between them-nothing that is continuous can be composed 'of
indivisibles': e.g. a line cannot be composed of points, the line
being continuous and the point indivisible. For the extremities of two