Various Works

  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

  contrary motions: for they are one and the same. (Yet their essence is

  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