by Aristotle
Change within the same kind from a lesser to a greater or from a greater to a [226b1] 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 [5] 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 [10] 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 [15] contrary to motion, so that rest will be privation 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 say what it is to be together and apart, in contact, between, in succession, contiguous, and continuous, and to show in what circumstances [20] each of these terms is naturally applicable.
Things are said to be together in place when they are in one primary place and to be apart when they are in different places. Things are said to be in contact when their extremities are together.
Every change involves opposites, and opposites are either contraries or [227a7] contradictories; since a contradiction admits of nothing in the middle, it is evident that what is between must involve contraries. What is between involves three things at least; for the contrary is a last point in change, and that which a changing thing, changing continuously and naturally, naturally reaches before it reaches that to which it changes last, is between.36 A thing is moved continuously if it leaves no gap [10] or only the smallest possible gap in the material—not in the time (for a gap in the time does not prevent things moving continuously, while, on the other hand, there [226b25] 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 [30] local changes but in every other kind as well. 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 [227a1] 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 [5] one is not in succession to two, nor is the first day of the month to the second: in each case the latter is in succession to the former.
[10] 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 [15] 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 primary; for that which touches is necessarily in succession, but not everything that is in succession touches: [20] 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 necessarily being together. So natural union is last in coming to be; for the extremities must necessarily come into contact if they are to be naturally united; but things that are [25] in contact are not all naturally united, while where there is no contact clearly there is no natural union either. Hence, if as some say points and units have an independent existence of their own, it is impossible for the two to be identical; for [30] 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 be anything between units; for there is nothing between the numbers one and two.
[227b1] We have now said what it is to be together and apart, in 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 ways in which motion is said to be one; for we use the term ‘one’ in many ways.
Motion is one generically according to the different categories to which it may [5] 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 [10] blackening with every other blackening].37 But whiteness 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 [15] 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. [20]
Motion is one in an unqualified sense when it is one essentially or numerically; and the following distinctions will make clear what this is. There are three textures in connexion with which we speak of motion—what, where, when. I mean that there must be something that is in motion, e.g. a man or gold, and it must be in motion in [25] something, e.g. a place or an affection, and at some time (for all motion takes place in 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—for that in which the motion takes place (the species) must be one and incapable of subdivision, that during which it takes place [30] (the time) must be one and unintermittent, and that which is in motion must be one—not in an a
ccidental 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 the white may be one), nor if it is done in common (for there might be a case of two men [228a1] being restored to health at the same time in the same way, e.g. from inflammation of the eye, yet this motion is not 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 [5] 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 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 [10] 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, but with this difference: that if the states are two then it follows simply from this fact that the actuality must also in point of number be two (for only that which is numerically one can give rise to an actuality that is numerically one); but if the state is one, this is not in itself enough to make us regard the actuality also [15] 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 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.
[20] 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 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 [25] although we give them the same name: 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 [30] 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 [228b1] 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 [5] motion that includes intervals of 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 it is not intermittent) the time is one, the motion is specifically different; for motion that is one must be specifically one, though motion that is specifically one is [10] 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.
[15] 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 divisible. But the difference would seem to be one of degree. In every kind of motion we may have regularity or irregularity: thus there [20] 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 [25] any other magnitude that is not such that any part of it fits on to any other that may be chosen. Sometimes it is found neither in the subject 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 [30] 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 [229a1] 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 [5] 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 [10] 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 [15] 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 being is not the same, just as changing from health is different from changing to disease.) Nor are motions respectively from a contrary [20] 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 [25] 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 being may not be the same; ‘to health’ is distinct, I mean, from ‘from disease’, and ‘from health’ from ‘to disease’). [30]
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 [229b1] former, e.g. a motion from health to disease and a motion from disease to health. Moreover, the consideration of particular e
xamples will also show what kinds of processes are generally recognized as contrary: thus falling ill is regarded as contrary to recovering one’s health, and being taught as contrary to being led into [5] error by another; for their goals are contrary. (It is 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. becoming white, where [10] 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 admits of [15] 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 the place of white as goal; for the middle is opposed in a sense to either [20] of the extremes, as has been said above. Thus 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.