12 234b 10–20.
13 Chapter 7.
14 sc. BC will have more right than AC to be regarded as that in which the change has been completed.
15 234b 10 sqq.
16 235b 33. The ‘primary time’ is the irreducible minimum: thus the very terms of the definition make it clear that a thing must be changing in the whole of the ‘primary time’ in which it changes.
17 235b 6 sqq.
18 231b 6 sqq.
19 i. e. you may begin by cutting off half the line, then half of what remains, and so on, the part cut off thus continuously increasing and the part remaining continually decreasing.
20 Ch. 6.
21 238b 31 sqq.
22 226b 12 sqq.
23 sc. time.
24 i. e. a space only just large enough to contain it, not a larger space of which only part is occupied.
25 233a 13 sqq.
26 viz. the first argument given above, ll. 11–14.
27 234b 10 sqq.
28 239a 27.
29 231b 18 sqq.
30 232b 23 sqq.
BOOK VII
1 Everything that is in motion must be moved by something. (25) For if it has not the source of its motion in itself it is evident that it is moved by something other than itself, for there must be something else that moves it. If on the other hand it has the source of its motion in itself, let AB be taken to represent that which is in motion essentially of itself and not in virtue of the fact that something belonging to it is in motion. Now in the first place to assume that AB, (30) because it is in motion as a whole and is not moved by anything external to itself, is therefore moved by itself—this is just as if, supposing that JK is moving KL and is also itself in motion, we were to deny that JL is moved by anything on the ground that it is not evident which is the part that is moving it and which the part that is moved. In the second place that which is in motion without being moved by anything does not necessarily cease from its motion because something else is at rest, but a thing must be moved by something if the fact of something else having ceased from its motion causes it to be at rest. [242a] Thus, if this is accepted, everything that is in motion must be moved by something. (5) For AB, which has been taken to represent that which is in motion, must be divisible, since everything that is in motion is divisible. Let it be divided, then, at C. Now if CB is not in motion, then AB will not be in motion: for if it is, it is clear that AC would be in motion while BC is at rest, (10) and thus AB cannot be in motion essentially and primarily. But ex hypothesi AB is in motion essentially and primarily. Therefore if CB is not in motion AB will be at rest. But we have agreed that that which is at rest if something else is not in motion must be moved by something. Consequently, everything that is in motion must be moved by something: for that which is in motion will always be divisible, (15) and if a part of it is not in motion the whole must be at rest.
Since everything that is in motion must be moved by something, let us take the case in which a thing is in locomotion and is moved by something that is itself in motion, and that again is moved by something else that is in motion, and that by something else, (20) and so on continually: then the series cannot go on to infinity, but there must be some first movent. For let us suppose that this is not so and take the series to be infinite. Let A then be moved by B, B by C, C by D, and so on, each member of the series being moved by that which comes next to it. Then since ex hypothesi the movent while causing motion is also itself in motion, and the motion of the moved and the motion of the movent must proceed simultaneously (for the movent is causing motion and the moved is being moved simultaneously) it is evident that the respective motions of A, (25) B, C, and each of the other moved movents are simultaneous. Let us take the motion of each separately and let E be the motion of A, F of B, and G and H respectively the motions of C and D: for though they are all moved severally one by another, yet we may still take the motion of each as numerically one, since every motion is from something to something and is not infinite in respect of its extreme points. (30) By a motion that is numerically one I mean a motion that proceeds from something numerically one and the same to something numerically one and the same in a period of time numerically one and the same: for a motion may be the same generically, specifically, (35) or numerically: it is generically the same if it belongs to the same category, e. g. substance or quality: it is specifically the same if it proceeds from something specifically the same to something specifically the same, e. g. from white to black or from good to bad, which is not of a kind specifically distinct: it is numerically the same if it proceeds from something numerically one to something numerically one in the same period of time, e. g. from a particular white to a particular black, or from a particular place to a particular place, in a particular period of time: for if the period of time were not one and the same, the motion would no longer be numerically one though it would still be specifically one. [242b] We have dealt with this question above.1 (4) Now let us further take the time in which A has completed its motion, (8) and let it be represented by J. Then since the motion of A is finite the time will also be finite. But since the movents and the things moved are infinite, the motion EFGH, i. e. the motion that is composed of all the individual motions, (15) must be infinite. For the motions of A, B, and the others may be equal, or the motions of the others may be greater: but assuming what is conceivable, we find that whether they are equal or some are greater, in both cases the whole motion is infinite. And since the motion of A and that of each of the others are simultaneous, the whole motion must occupy the same time as the motion of A: but the time occupied by the motion of A is finite: consequently the motion will be infinite in a finite time, which is impossible.
It might be thought that what we set out to prove has thus been shown, (20) but our argument so far does not prove it, because it does not yet prove that anything impossible results from the contrary supposition: for in a finite time there may be an infinite motion, though not of one thing, but of many: and in the case that we are considering this is so: for each thing accomplishes its own motion, and there is no impossibility in many things being in motion simultaneously. But if (as we see to be universally the case) that which primarily is moved locally and corporeally must be either in contact with or continuous with that which moves it, (25) the things moved and the movents must be continuous or in contact with one another, so that together they all form a single unity: whether this unity is finite or infinite makes no difference to our present argument; for in any case since the things in motion are infinite in number the whole motion will be infinite, if, as is theoretically possible, each motion is either equal to or greater than that which follows it in the series: for we shall take as actual that which is theoretically possible. If, (30) then, A, B, C, D form an infinite magnitude that passes through the motion EFGH in the finite time J, this involves the conclusion that an infinite motion is passed through in a finite time: and whether the magnitude in question is finite or infinite this is in either case impossible. Therefore the series must come to an end, and there must be a first movent and a first moved: for the fact that this impossibility results only from the assumption of a particular case is immaterial, since the case assumed is theoretically possible, and the assumption of a theoretically possible case ought not to give rise to any impossible result. [243a]
2 That which is the first movent of a thing—in the sense that it supplies not ‘that for the sake of which’ but the source of the motion—is always together with that which is moved by it (by ‘together’ I mean that there is nothing intermediate between them). (5) This is universally true wherever one thing is moved by another. And since there are three kinds of motion, local, qualitative, and quantitative, there must also be three kinds of movent, that which causes locomotion, that which causes alteration, and that which causes increase or decrease.
Let us begin with locomotion, (10) for this is the primary motion. Everything that is in locomotion is moved either by itself or by someth
ing else. In the case of things that are moved by themselves it is evident that the moved and the movent are together: for they contain within themselves their first movent, so that there is nothing in between. The motion of things that are moved by something else must proceed in one of four ways: for there are four kinds of locomotion caused by something other than that which is in motion, (15) viz. pulling, pushing, carrying, and twirling. All forms of locomotion are reducible to these. Thus pushing on is a form of pushing in which that which is causing motion away from itself follows up that which it pushes and continues to push it: pushing off occurs when the movent does not follow up the thing that it has moved: throwing when the movent causes a motion away from itself more violent than the natural locomotion of the thing moved, (20) which continues its course so long as it is controlled by the motion imparted to it. [243b] Again, pushing apart and pushing together are forms respectively of pushing off and pulling: pushing apart is pushing off, which may be a motion either away from the pusher or away from something else, while pushing together is pulling, which may be a motion towards something else as well as towards the puller. (5) We may similarly classify all the varieties of these last two, e. g. packing and combing: the former is a form of pushing together, the latter a form of pushing apart. The same is true of the other processes of combination and separation (they will all be found to be forms of pushing apart or of pushing together), except such as are involved in the processes of becoming and perishing. (At the same time it is evident that there is no other kind of motion but combination and separation: for they may all be apportioned to one or other of those already mentioned. (10)) Again, inhaling is a form of pulling, exhaling a form of pushing: and the same is true of spitting and of all other motions that proceed through the body, whether secretive or assimilative, the assimilative being forms of pulling, the secretive of pushing off. (15) All other kinds of locomotion must be similarly reduced, for they all fall under one or other of our four heads. And again, of these four, carrying and twirling are reducible to pulling and pushing. For carrying always follows one of the other three methods, for that which is carried is in motion accidentally, because it is in or upon something that is in motion, and that which carries it is in doing so being either pulled or pushed or twirled; (20) thus carrying belongs to all the other three kinds of motion in common. [244a] And twirling is a compound of pulling and pushing, for that which is twirling a thing must be pulling one part of the thing and pushing another part, since it impels one part away from itself and another part towards itself. If, therefore, it can be shown that that which is pushing and that which is pulling are adjacent respectively to that which is being pushed and that which is being pulled, it will be evident that in all locomotion there is nothing intermediate between moved and movent. (5) But the former fact is clear even from the definitions of pushing and pulling, for pushing is motion to something else from oneself or from something else, and pulling is motion from something else to oneself or to something else, when the motion of that which is pulling is quicker than the motion that would separate from one another the two things that are continuous:2 for it is this that causes one thing to be pulled on along with the other. (10) (It might indeed be thought that there is a form of pulling that arises in another way: that wood, e. g. pulls fire in a manner different from that described above. But it makes no difference whether that which pulls is in motion or is stationary when it is pulling: in the latter case it pulls to the place where it is, while in the former it pulls to the place where it was.) Now it is impossible to move anything either from oneself to something else or from something else to oneself without being in contact with it: it is evident, (15) therefore, that in all locomotion there is nothing intermediate between moved and movent. [244b]
Nor again is there anything intermediate between that which undergoes and that which causes alteration: this can be proved by induction: for in every case we find that the respective extremities of that which causes and that which undergoes alteration are adjacent. For our assumption is that things that are undergoing alteration are altered in virtue of their being affected in respect of their so-called affective qualities, since that which is of a certain quality is altered in so far as it is sensible, and the characteristics in which bodies differ from one another are sensible characteristics: for every body differs from another in possessing a greater or lesser number of sensible characteristics or in possessing the same sensible characteristics in a greater or lesser degree. But the alteration of that which undergoes alteration is also caused by the above-mentioned characteristics, (5) which are affections of some particular underlying quality. Thus we say that a thing is altered by becoming hot or sweet or thick or dry or white: and we make these assertions alike of what is inanimate and of what is animate, and further, where animate things are in question, we make them both of the parts that have no power of sense-perception and of the senses themselves. (10) For in a way even the senses undergo alteration, since the active sense is a motion through the body in the course of which the sense is affected in a certain way. We see, then, that the animate is capable of every kind of alteration of which the inanimate is capable: but the inanimate is not capable of every kind of alteration of which the animate is capable, since it is not capable of alteration in respect of the senses: moreover the inanimate is unconscious of being affected by alteration, (15) whereas the animate is conscious of it, though there is nothing to prevent the animate also being unconscious of it when the process of the alteration does not concern the senses. [245a] Since, then, the alteration of that which undergoes alteration is caused by sensible things, in every case of such alteration it is evident that the respective extremities of that which causes and that which undergoes alteration are adjacent. Thus the air is continuous with that which causes the alteration, (5) and the body that undergoes alteration is continuous with the air. Again, the colour is continuous with the light and the light with the sight. And the same is true of hearing and smelling: for the primary movent in respect to the moved is the air. Similarly, in the case of tasting, the flavour is adjacent to the sense of taste. And it is just the same in the case of things that are inanimate and incapable of sense-perception. (10) Thus there can be nothing intermediate between that which undergoes and that which causes alteration.
Nor, again, can there be anything intermediate between that which suffers and that which causes increase: for the part of the latter that starts the increase does so by becoming attached in such a way to the former that the whole becomes one. Again, the decrease of that which suffers decrease is caused by a part of the thing becoming detached. So that which causes increase and that which causes decrease must be continuous with that which suffers increase and that which suffers decrease respectively: and if two things are continuous with one another there can be nothing intermediate between them. (15)
It is evident, therefore, that between the extremities of the moved and the movent that are respectively first and last in reference to the moved there is nothing intermediate. [245b]
3 Everything, we say, that undergoes alteration is altered by sensible causes, and there is alteration only in things that are said to be essentially affected by sensible things. The truth of this is to be seen from the following considerations. Of all other things it would be most natural to suppose that there is alteration in figures and shapes, (5) and in acquired states and in the processes of acquiring and losing these: but as a matter of fact in neither of these two classes of things is there alteration.
In the first place, when a particular formation of a thing is completed, (10) we do not call it by the name of its material: e. g. we do not call the statue ‘bronze’ or the pyramid3 ‘wax’ or the bed ‘wood’, but we use a derived expression and call them ‘of bronze’, ‘waxen’, and ‘wooden’ respectively. But when a thing has been affected and altered in any way we still call it by the original name: thus we speak of the bronze or the wax being dry or fluid or hard or hot. (15) And not only so: we also speak of the particul
ar fluid or hot substance as being bronze, giving the material the same name as that which we use to describe the affection.
[246a] Since, therefore, having regard to the figure or shape of a thing we no longer call that which has become of a certain figure by the name of the material that exhibits the figure, whereas having regard to a thing’s affections or alterations we still call it by the name of its material, it is evident that becomings of the former kind cannot be alterations.
Moreover it would seem absurd even to speak in this way, to speak, (5) that is to say, of a man or house or anything else that has come into existence as having been altered. Though it may be true that every such becoming is necessarily the result of something’s being altered, the result, e. g. of the material’s being condensed or rarefied or heated or cooled, nevertheless it is not the things that are coming into existence that are altered, and their becoming is not an alteration.
Again, (10) acquired states, whether of the body or of the soul, are not alterations. For some are excellences and others are defects, and neither excellence nor defect is an alteration: excellence is a perfection (for when anything acquires its proper excellence we call it perfect, (15) since it is then if ever that we have a thing in its natural state: e. g. we have a perfect circle when we have one as good as possible), while defect is a perishing of or departure from this condition. So just as when speaking of a house we do not call its arrival at perfection an alteration (for it would be absurd to suppose that the coping or the tiling is an alteration or that in receiving its coping or its tiling a house is altered and not perfected), (20) the same also holds good in the case of excellences and defects and of the persons or things that possess or acquire them: for excellences are perfections of a thing’s nature and defects are departures from it: consequently they are not alterations. [246b]
The Basic Works of Aristotle (Modern Library Classics) Page 49