In the second place, if there is to be change of change and becoming of becoming, we shall have an infinite regress. [226a] Thus if one of a series of changes is to be a change of change, (35) 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. (5) 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. (10) 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, (15) 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, (20) 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 ago3 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. (25) 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, (30) 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, (35) and to things that do not move themselves locally.
[226b] 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. (5) 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, (10) 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, (15) 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’, (20) 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, (25) 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. (30) This is manifestly true not only in local changes but in every other kind as well.
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, (35) 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). [227a] 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 the second: in each case the latter is ‘in succession’ to the former. (5)
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, (10) 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, (15) 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. (20) And if there is continuity there is ne
cessarily 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, (25) while where 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. (30) 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. [227b]
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, (5) 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. (10) 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 the same thing changes from the same to the same, (15) 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, (20) 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 be something that is in motion, e. g. a man or gold, and it must be in motion in something, (25) 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, (30) 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). [228a]
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. (5) 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, (10) 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 that is numerically one), but if the state is one, (15) 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, (20) 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’: (25) 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. (30) 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. [228b] 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 rest will be not one but many, (5) 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, (10) 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, (15) 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 b
e 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, (20) 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, (25) 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: (30) 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. [229a] 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)
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, (10) 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, (15) as there is no other way in which they can be opposed.
The Basic Works of Aristotle (Modern Library Classics) Page 44
