by Aristotle
And further, if there is always something of this nature, a mover that is itself unmoved and eternal, then that which is first moved by it must also be eternal. [260a1] Indeed this is clear also from the consideration that there would otherwise be no becoming and perishing and no change of any kind in other things, if there were nothing in motion to move them; for the motion imparted by the unmoved will always be imparted in the same way and be one and the same, since the unmoved [5] does not itself change in relation to that which is moved by it. But that which is moved by something that, though it is in motion, is moved directly by the unmoved stands in varying relations to the things that it moves, so that the motion that it causes will not be always the same: by reason of the fact that it occupies contrary positions or assumes contrary forms it will produce contrary motions in each several [10] thing that it moves and will cause it to be at one time at rest and at another time in motion.
The foregoing argument, then, has served to clear up the point about which we raised a difficulty at the outset—why is it that instead of all things being either in motion or at rest, or some things being always in motion and the remainder always at rest, there are things that are sometimes in motion and sometimes not? The cause [15] of this is now plain: it is because, while some things are moved by an eternal unmoved mover and are therefore always in motion, other things are moved by something that is in motion and changing, so that they too must change. But the unmoved mover, as has been said, since it remains simple and unvarying and in the same state, will cause motion that is one and simple.
[20] 7 · This matter will be made clearer, however, if we start afresh from another point. We must consider whether it is or is not possible that there should be a continuous motion, and, if it is possible, which this motion is, and which is the primary motion; for it is plain that if there must always be motion, and a particular motion is primary and continuous, then it is this motion that is imparted by the first [25] mover, and so it is necessarily one and the same and continuous and primary.
Now of the three kinds of motion that there are—motion in respect of magnitude, motion in respect of affection, and motion in respect of place—it is this last, which we call locomotion, that must be primary. For it is impossible that there should be increase without the previous occurrence of alteration; for that which is [30] increased, although in a sense it is increased by what is like itself, is in a sense increased by what is unlike itself: thus it is said that contrary is nourishment to contrary; but one thing gets attached to another by becoming like it. There must be alteration then, in that there is this change from contrary to contrary. But the fact that a thing is altered requires that there should be something that alters it, [260b1] something that makes the potentially hot actually hot: so it is plain that the mover does not maintain a uniform relation to it but is at one time nearer to and at another farther from that which is altered; and we cannot have this without locomotion. If, therefore, there must always be motion, there must also always be locomotion as the [5] primary motion, and, if there is a primary as distinguished from a secondary form of locomotion, it must be the primary form. Again, all affections have their origin in condensation and rarefaction: thus heavy and light, soft and hard, hot and cold, are considered to be forms of density and rarity. But condensation and rarefaction are [10] combination and separation, processes in virtue of which substances are said to become and perish; and in being combined and separated things must change in respect of place. And further, when a thing is increased or decreased its magnitude changes in respect of place.
Again, there is another point of view from which it will be clearly seen that [15] locomotion is primary. As in the case of other things so too in the case of motion the word ‘primary’ may be used in several ways. A thing is said to be prior to other things when, if it does not exist, the others will not exist, whereas it can exist without the others; and there is also priority in time and priority in being. Now there must be motion continuously, and it may exist continuously either by being continuous or by [20] being successive but rather by being continuous; and it is better that it should be continuous rather than successive motion, and we always assume the presence in nature of the better, if it be possible: since, then, continuous motion is possible (this will be proved later: for the present let us take it for granted), and no other motion can be continuous except locomotion, locomotion must be primary. For there is no [25] necessity for the subject of locomotion to be the subject either of increase or of alteration, nor need it become or perish; on the other hand there cannot be any one of these processes without the existence of the continuous motion imparted by the first mover.
Again, locomotion must be primary in time; for this is the only motion possible for eternal things. It is true indeed that, in the case of any individual thing that has a [30] becoming, locomotion must be the last of its motions; for after its becoming it first experiences alteration and increase, and locomotion is a motion that belongs to such things only when they are perfected. But there must previously be something else that is in process of locomotion to be the cause of the becoming of things that [261a1] become, without itself being in process of becoming, as e.g. the begotten is preceded by what begot it; otherwise becoming might be thought to be the primary motion on the ground that the thing must first become. But though this is so in the case of any [5] individual thing that becomes, nevertheless before anything becomes, something else must be in motion, not itself becoming but being, and before this there must again be something else. And since becoming cannot be primary—for, if it were, everything that is in motion would be perishable—it is plain that no one of the [10] motions next in order can be prior to locomotion. By the motions next in order I mean increase and then alteration, decrease, and perishing. All these are posterior to becoming; consequently, if not even becoming is prior to locomotion, then no one of the other processes of change is so either.
In general, that which is becoming appears as something imperfect and proceeding to a principle; and so what is posterior in the order of becoming is prior in the order of nature. Now all things that go through the process of becoming [15] acquire locomotion last. It is this that accounts for the fact that some living things, e.g. plants and many kinds of animals, owing to lack of the requisite organ,51 are entirely without motion, whereas others acquire it in the course of their being perfected. Therefore, if the degree in which things possess locomotion corresponds to the degree in which they have realized their natural development, then this motion must be prior to all others in respect of being; and not only for this reason [20] but also because a thing that is in motion loses its being less in the process of locomotion than in any other kind of motion: it is the only motion that does not involve a change of being in the sense in which there is a change in quality when a thing is altered and a change in quantity when a thing is increased or decreased. Above all it is plain that this motion, motion in respect of place, is what is in the strictest sense produced by that which moves itself; but it is the self-mover that we [25] declare to be the principle of things that are moved and impart motion and the primary source for things that are in motion.
It is clear, then, from the foregoing arguments that locomotion is the primary motion. We have now to show which kind of locomotion is primary. The same [30] process of reasoning will also make clear at the same time the truth of the assumption we have made both now and at a previous stage that it is possible that there should be a motion that is continuous and eternal. Now it is clear from the following considerations that no other motion can be continuous. Every other motion and change is from an opposite to an opposite: thus for the processes of [35] becoming and perishing the limits are what is and what is not, for alteration the contrary affections, and for increase and decrease either greatness and smallness or perfection and imperfection of magnitude; and changes to contraries are contrary changes. Now a thing that is undergoing any particular kind of motion, but though [261b1] previously existent has not alw
ays undergone it, must previously have been at rest. It is clear, then, that for the changing thing the contraries will be states of rest. And we have a similar result in the case of changes; for becoming and perishing, whether regarded without qualification or as affecting something in particular, are opposites: therefore provided it is impossible for a thing to undergo opposite changes [5] at the same time, the change will not be continuous, but a period of time will intervene between the opposite processes. The question whether these contradictory changes are contraries or not makes no difference, provided only it is impossible for them both to be present to the same thing at the same time: the point is of no importance to the argument. Nor does it matter if the thing need not rest in the [10] contradictory state, or if there is no change contrary to rest: it may be true that what is not is not at rest, and that perishing is a process to what is not. All that matters is the intervention of a time: it is this that prevents the change from being continuous; so, too, in our previous instances the important thing was not the relation of contrariety but the impossibility of the two processes being present at the same [15] time. And there is no need to be disturbed by the fact that there may be more than one contrary to the same thing, that motion will be contrary both to rest and to motion in the contrary direction. We have only to grasp the fact that motion is in a sense the opposite both of a state of rest and of the contrary motion, in the same way as the equal and the mean is the opposite both of that which surpasses it and of that [20] which it surpasses, and that it is impossible for the opposite motions or changes to be present to a thing at the same time. Furthermore, in the case of becoming and perishing it would seem to be an utterly absurd thing if as soon as anything has become it must necessarily perish and cannot continue to exist for any time; and this might generate a similar belief in the other cases, since it is natural that they should [25] all be uniform.
8 · Let us now proceed to maintain that it is possible that there should be an infinite motion that is single and continuous, and that this motion is rotatory motion. The motion of everything that is in process of locomotion is either rotatory or rectilinear or a compound of the two: consequently, if one of the former two is not [30] continuous, that which is composed of them both cannot be continuous either. Now it is plain that if the locomotion of a thing is rectilinear and finite it is not continuous locomotion; for the thing must turn back, and that which turns back in a straight line undergoes two contrary locomotions, since, so far as place is concerned, upward motion is the contrary of downward motion, forward motion of backward, and [35] motion to the left of motion to the right, these being the pairs of contraries in the sphere of place. But we have already defined single and continuous motion to be [262a1] motion of a single thing in a single period of time and operating within a sphere admitting of no further specific differentiation (for we have three things to consider, first that which is in motion, e.g. a man or a god, secondly the ‘when’, that is to say, the time, and thirdly the sphere within which it operates, which may be either place or affection or form or magnitude). Now contraries are specifically different and [5] not one; and within the sphere of place we have the above-mentioned distinctions. Moreover we have an indication that motion from A to B is the contrary of motion from B to A in the fact that, if they occur at the same time, they arrest and stop each other. And the same is true in the case of a circle: the motion from A towards B is the contrary of the motion from A towards C; for even if they are continuous and [10] there is no turning back they arrest each other, because contraries annihilate or obstruct one another. On the other hand lateral motion is not the contrary of upward motion. But what shows most clearly that rectilinear motion cannot be continuous is the fact that turning back necessarily implies coming to a stand, not only when it is a straight line that is traversed, but also in the case of locomotion in a [15] circle (which is not the same thing as rotatory locomotion; for a thing may either proceed on its course without a break or turn back again when it has reached the same point from which it started). We may assure ourselves of the necessity of this coming to a stand not only by perception but also by argument. We may start as follows: we have three points, beginning, middle, and end; and the middle is both [20] beginning and end relatively to each of the others, being one in number but two in definition. We have further the distinction between the potential and the actual. So in the straight line any one of the points lying between the two extremes is potentially a middle-point; but it is not actually so unless that which is in motion divides the line by coming to a stand at that point and beginning its motion again: [25] thus the middle-point becomes both a beginning and an end, a beginning of the latter part and an end of the first part. This is the case e.g. when A in the course of its locomotion comes to a stand at B and starts again towards C; but when its motion is continuous A cannot either have come to be or have ceased to be at the point B: it [30] can only have been there at a now, and not in any period of time except the whole52 of which the now is a dividing-point. To maintain that it has come to be and ceased to be there will involve the consequence that A in the course of its locomotion will [262b1] always be coming to a stand; for it is impossible that A should simultaneously have come to be at B and ceased to be there, so that the two things must have happened at different points of time, and therefore there will be the intervening period of time: consequently A will be in a state of rest at B, and similarly at all other points, since the same reasoning holds good in every case. When to A, that which is in the process [5] of locomotion, B, the middle-point, serves both as an end and as a beginning, A must come to a stand at B, because it makes it two just as one might do in thought. However, the point A is the beginning at which it has ceased to be, and it is at C that it has come to be when its course is finished and it comes to a stand. So this is how we must meet the difficulty that then arises, which is as follows. Suppose the line E [10] is equal to F, that A proceeds in continuous locomotion from the extreme point to C, and that, at the moment when A is at the point B, D is proceeding in uniform locomotion and with the same velocity as A from the extremity of F to G: then D will have reached G before A has reached C; for that which makes an earlier start [15] and departure must make an earlier arrival. For A has not simultaneously come to be and ceased to be at B, which is why it is late. For if it does both simultaneously, it will not be late—for this to happen it will be necessary that it should come to a stand there. Therefore we must not hold that when A came to be at B, D was at the same time in motion from the extremity of F; for the fact of A’s having come to be at B [20] will involve its ceasing to be there, and the two events will not be simultaneous, whereas the truth is that A is at B at a sectional point of time and does not occupy time there. In this case, therefore, where the motion of a thing is continuous, it is impossible to use this form of expression. On the other hand in the case of a thing that turns back in its course we must do so. For suppose G in the course of its locomotion proceeds to D and then turns back and proceeds downwards again: then the extreme point D has served as beginning and end for it, one point thus serving as two: therefore A must have come to a stand there; it cannot have [25] come to be at D and departed from D simultaneously, for in that case it would simultaneously be there and not be there at the same now. And here we cannot apply the same solution: we cannot argue that G is at D at a sectional point of time and has not come to be or ceased to be there. For here the goal that is reached is [30] necessarily one that is actual, not potential. Now the points in the middle are potential; but this one is actual, and regarded from below it is an end, while regarded from above it is a beginning, so that it stands in these same relations to the [263a1] motions. Therefore that which turns back in traversing a rectilinear course must come to a stand. Consequently there cannot be a continuous rectilinear motion that is eternal.