The Complete Works of Aristotle

by Barnes, Jonathan, Aristotle

  Nor in reference to contradictory change shall we find anything impossible—e.g. if it is argued that if a thing is changing from not-white to white, and is in [20] neither condition, then it will be neither white nor not-white; for the fact that it is not wholly in either condition will not preclude us from calling it white or not-white. We call a thing white or not-white not because it is wholly either one or the other, but because most of its parts or the most essential parts of it are so: not being in a certain condition is different from not being wholly in that condition. So, too, in the [25] case of being and not-being and all other conditions which stand in a contradictory relation: while the changing thing must of necessity be in one of the two opposites, it is never wholly in either.

  Again, in the case of circles and spheres and everything that moves within its [30] own dimensions, it is argued that they will be at rest, on the ground that such things, themselves and their parts, will occupy the same position for a period of time, and that therefore they will be at once at rest and in motion. For, first, the parts do not occupy the same place for any period of time; and secondly, the whole also is always [240b1] changing to a different position; for the circumference from A is not the same as that from B or C or any other point except accidentally, as a musical man is the [5] same as a man. Thus one is always changing into another, and the thing will never be at rest. And it is the same with the sphere and everything else which moves within its own dimensions.

  10 · That having been demonstrated, we next assert that that which is without parts cannot be in motion except accidentally, i.e. in so far as the body or [10] the magnitude to which it belongs is in motion, just as that which is in a boat may be in motion in consequence of the locomotion of the boat, or a part may be in motion in virtue of the motion of the whole. (By ‘that which is without parts’ I mean that which is quantitatively indivisible.) For parts have different motions—those in virtue of themselves, and those in virtue of the motion of the whole. The distinction [15] may be seen most clearly in the case of a sphere, in which the velocities of the parts near the centre and of those on the surface are different from one another and from that of the whole; this implies that there is not one motion. As we have said, then, that which is without parts can be in motion in the sense in which a man sitting in a boat is in motion when the boat is travelling, but it cannot be in motion of itself. For [20] suppose that it is changing from AB to BC—either from one magnitude to another, or from one form to another, or from some state to its contradictory—and let D be the primary time in which it undergoes the change. Then in the time in which it is changing it must be either in AB or in BC or partly in one and partly in the other; [25] for this, as we saw, is true of everything that is changing. Now it cannot be partly in each of the two; for then it would be divisible into parts. Nor again can it be in BC; for then it will have changed, whereas the assumption is that it is changing. It remains, then, that in the time in which it is changing, it is in AB. That being so, it [30] will be at rest; for, as we saw, to be in the same condition for a period of time is to be at rest. So it is not possible for that which has no parts to be in motion or to change in any way; for only one condition could have made it possible for it to have motion, viz. that time should be composed of nows, in which case at any now it would have [241a1] moved or changed, so that it would never be in motion, but would always have been moving. But this we have already shown to be impossible: time is not composed of nows, just as a line is not composed of points, and motion is not composed of movings; for this theory simply makes motion consist of indivisibles in exactly the [5] same way as time is made to consist of nows or a length of points.

  Again, it may be shown in the following way that there can be no motion of a point or of any other indivisible. That which is in motion can never traverse a space greater than itself without first traversing a space equal to or less than itself. That being so, it is evident that the point also must first traverse a space equal to or less [10] than itself. But since it is indivisible, it is impossible for it to traverse a lesser space first: so it will have to traverse a distance equal to itself. Thus the line will be composed of points; for the point, as it continually traverses a distance equal to itself, will be a measure of the whole line. But since this is impossible, it is likewise impossible for the indivisible to be in motion.

  [15] Again, since motion is always in time and never in a now, and all time is divisible, for everything that is in motion there must be a time less than that in which it traverses a distance as great as itself. For that in which it is in motion will be a time, because all motion is in time; and all time has been shown above to be divisible. Therefore, if a point is in motion, there must be a time less than that in which it has itself traversed its own length. But this is impossible; for in less time it [20] must traverse less distance, and thus the indivisible will be divisible into something less, just as the time is so divisible; for that which is without parts and indivisible could be in motion only if it were possible to move in an indivisible now; for in the two questions—that of motion in a now and that of motion of something indivisible—the same principle is involved [25].

  No change is infinite; for every change, whether between contradictories or between contraries, is a change from something to something. Thus in contradictory changes the positive or the negative is the limit, e.g. being is the limit of coming to be and not-being is the limit of ceasing to be; and in contrary changes the particular [30] contraries are the limits, since these are the extreme points of the change, and consequently of every alteration; for alteration is always dependent upon some contraries. Similarly for increase and decrease: the limit of increase is to be found in the complete magnitude proper to the peculiar nature of the thing, while the limit of [241b1] decrease is the loss of such magnitude. Locomotion, it is true, we cannot show to be finite in this way, since it is not always between contraries. But since that which cannot be cut (in the sense that it is not possible that it should be cut, the term ‘cannot’ being used in several ways)—since it is not possible that that which in this [5] sense cannot be cut should be being cut, and generally that that which cannot come to be should be coming to be, it follows that it is not possible that that which cannot have changed should be changing to that to which it cannot have changed. If, then, that which is in locomotion is to be changing to something, it must be capable of having changed. Consequently its motion is not infinite, and it will not be in [10] locomotion over an infinite distance; for it cannot have traversed such a distance.

  It is evident, then, that a change cannot be infinite in the sense that it is not defined by limits. But it remains to be considered whether it is possible in the sense that one and the same change may be infinite in respect of the time which it occupies. If it is not one change, it would seem that there is nothing to prevent its being infinite; e.g. if a locomotion be succeeded by an alteration and that by an [15] increase and that again by a coming to be: in this way there may be motion for ever so far as the time is concerned; but it will not be one motion, because all these motions do not compose one. If it is to be one, no motion can be infinite in respect of the time that it occupies, with the single exception of rotatory locomotion [20].

  BOOK VII

  1 · Everything that is in motion must be moved by something. For if it has not the source of its motion in itself it is evident that it is moved by something other [35] 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 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, because it is in motion as a whole and is not [40] moved by anything external to itself, is therefore moved by itself—this is just as if, supposing that KL is moving LM and is also itself in motion, we were to deny that KM 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 mo
ved. In the second place that which is in [242a35] 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. If this is accepted, everything that is in motion must be moved by something. For if AB is [40] assumed to be in motion, it 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, and thus AB cannot be in motion in its own right and primarily. But ex hypothesi [45] AB is in motion in its own right 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 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, and if a part of it is not in motion the whole must be at rest.

  [50] 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, and so on continually: then the series cannot go on to infinity, but there must be some first mover. For let us suppose that this is not so and take the [55] 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 mover while causing motion is also itself in motion, the motion of the moved and the motion of the mover must proceed simultaneously (for the mover is [60] causing motion and the moved is being moved simultaneously); so it is evident that the motions of A, B, C, and each of the other moved movers 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 [65] 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. 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 [242b35] same generically, specifically, or numerically: it is generically the same if it is of 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 time, e.g. from a particular white to a particular black, or from a particular place to a particular place, in a particular time; for if the time [40] were not one and the same, the motion would no longer be numerically one though it would still be specifically one. We have dealt with this question above.45 Now let us further take the time in which A has completed its motion, and let it be represented by K. Then since the motion of A is finite the time will also be finite. But since the movers and the things moved are infinite, the motion EFGH, i.e. the motion that is [45] composed of all the individual motions, 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 possible, 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 [50] 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, but our argument so far does not prove it, because it does not yet prove that anything [55] impossible results; 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 moves locally and corporeally must be either in contact with or continuous with that which is moved, the things moved and the movers must be [60] continuous or in contact with one another, so that together they all form a 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 motion will be [65] infinite, if it is possible for the motions to be either equal to or greater than one another; for we shall take as actual that which is possible. If, then, A, B, C, D form, either finite or infinite magnitude that passes through the motion EFGH in the finite time K, it follows that an infinite motion is passed through in a finite time: and [70] 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 mover and a first moved; for the fact that this impossibility rests on an assumption is immaterial, since the case assumed is possible, and the assumption of a possible case [243a30] ought not to give rise to any impossible result.

  2 · That which is the first mover 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 between them). This is universally true wherever one thing is moved by another. And since there are [35] three kinds of motion, local, qualitative, and quantitative, there must also be three kinds of mover, that which causes locomotion, that which causes alteration, and that which causes increase or decrease.

  Let us begin with locomotion, for this is the primary motion. Everything that is [10] in locomotion is moved either by itself or by something else. In the case of things that are moved by themselves it is evident that the moved and the mover are together; for they contain within themselves their first mover, so that there is [15] 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, 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 mover does not follow up the thing that it has moved; throwing when the mover causes a motion [243b1] away from itself more violent than the natural locomotion of the thing moved, which continues its course so long as it is controlled by the motion imparted to it. 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 [5] 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. 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 [10] processes of becoming and perishing. (At the same time it is evident that combination and separation are not a different kind of motion; for they may all be apportioned to one or other of those already mentioned.) 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 excretive or assimilative, the [15] assimilative being forms of pulling, the excretive of pushing off. 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 [244a1] twirled; thus carrying belongs to all the other three kinds of motion in common. 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 together with that which is [5] being pushed and that which is being pulled, it will be evident that in all locomotion there is nothing between moved and mover.

  But the former fact is clear even from the definitions; 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 [10] pulling is quicker than the motion that would separate from one another the two things that are continuous; for it is this that causes one thing to be pulled on along with the other. (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 the 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 [15] without being in contact with it: it is evident, therefore, that in all locomotion there [244b1] is nothing between moved and mover.