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  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

  change be qualified or unqualified, except that in the former case 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