Commentary Aristotle Physics
Lecture 16. Only circular motion can be continuous and eternal
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 circular motion.
The motion of everything that is in process of locomotion is either circular or rectilinear, or a compound of the two. Consequently, if one of the former two is not 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 2320undergoes two contrary locomotions.
For, so far as motion in respect of place is concerned, upward motion is the contrary of downward motion, forward motion of backward motion, and 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 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, such as a man or a god; second, the “when” of the motion, that is to say, the time; third, the sphere within which it operates, which may be either place or passion or essential form or magnitude.)
And contraries are specifically not one and the same, but distinct; 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 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 rest, not only when it is a straight line that is traversed but also in the case of locomotion in a circle.
(This is not the same thing as circular locomotion, for when a thing is carried along a circle, it may either proceed on its course without a break or be reflected when it has reached the same point from which it started).
We may assure ourselves of the necessity of this coming to rest not only on the strength of observation but also on theoretical grounds.
We may start as follows: we have three points—the starting point, middle point, and finishing point—of which the middle point, in its relations to the other two, is both a starting and a finishing point and, though numerically one, is theoretically two.
We have further the distinction between the potential and the actual. So, in the straight line in question, 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 rest at that point and beginning its motion again.
Thus, the middle point becomes both a starting point and a goal, the starting point of the latter part of the motion and the finishing point of the first part.
This is the case, for instance, when A, in the course of its locomotion, comes to rest at B and starts again toward C. But, when its motion is continuous, A cannot either have come to be or have ceased to be at the point B; it can only have been there at the moment of passing, its passage not being contained within any period of time except the whole of which the particular moment 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 always be coming to rest.
For it is impossible that A should simultaneously have come to be at B and ceased to be there, such 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 B (the middle point) serves to A (what is in process of locomotion) as both a finishing point and as a starting point for its motion, then A must come to rest at B, because it makes it two just as one might do in thought.
However, the point A is the real starting point at which the moving body has ceased to be, and it is at C that it has really come to be when its course is finished and it comes to rest.
1104. After showing that no change but local change can be continuous and perpetual, the Philosopher now shows that no local change can be continuous and perpetual unless it be a circular one.
About this, he does two things:
first, he proves his proposition by a demonstration;
second, he proves it dialectically, at “if we look” (264a8; [1123]).
About the first, he does two things:
first, he proves his proposition;
second, from the proven truth, he solves some doubts, at “so, this is how” (262b8; [1112]).
About the first, he does three things.
First, he mentions what he chiefly intends. For he intends to prove that it is possible that there be a motion that, being one, might be continued to infinity, and that such a motion can be none but a circular one. This is the first thing he proves.
1105. Second, at the motion of everything (261b28), he shows how to proceed. And he says that whatever is moved locally is moved either with a circular motion or in a straight one or in a motion that combines these two, like a motion through a chord and an arc. Hence, it is clear that, if either of the two simple motions (the circular or the rectilinear) cannot be infinitely continuous, much less can their combination. Therefore, one must omit the latter and attend to the simple ones.
1106. Third, at now, it is plain (261b31), he shows that a rectilinear motion upon a straight and finite magnitude cannot be infinitely continuous and that, consequently, no rectilinear motion can be infinitely continuous unless an actually infinite magnitude is assumed—and this was proved impossible in book 3 above.
He proves his point with two arguments, of which the following is the first. If anything be moved to infinity upon a finite magnitude, it has to be done by reflection. For it has been proved in book 6 that something will traverse a finite magnitude in finite time. When, therefore, the boundary of the finite magnitude is reached, the motion will cease, unless the mobile is returned by reflection to the beginning of the magnitude whence the motion began. But what is reflected in a rectilinear motion is being moved with contrary motions. And this he now proves.
Contrary motions are ones whose termini are contrary, as was proved in book 5. But the contrarieties of place are up and down, ahead and behind, and right and left. Now, whatever is reflected must be reflected according to one or the other of these contrarieties. Therefore, whatever is reflected is moved with contrary motions.
But it was shown in book 5 which motion is one and continuous: namely, the one that is of one subject, in one time, and in the same category that does not differ specifically.
For these three elements are considered in every motion:
first, there is the time;
second, there is the subject being moved, such as a man or a god, according to those who call the heavenly bodies “gods”;
third, there is that in which the motion occurs. In local motion, it is a place; in alteration, it is a passion, that is, a passible quality; in generation and ceasing to be, it is a form; in growth and decrease, it is a magnitude.
Now, it is clear that contraries differ with respect to species; hence, contrary motions cannot be one and continuous. But the six listed above are differences of place, and consequently, they must be contrary, because the differences of any genus are contrary. It remains, therefore, that it is impossible for that which moves by a reflected motion to be moved by one continuous motion.
1107. And because someone could doubt whether what is reflected is being moved with contrary motions on the ground that there does not appear a manifest and determinate contrariety in place, such as does appear in the other genera in which motion occurs (as was said in book 5), he therefore, in order to show the same point, adds a certain sign over and above the foregoing argument, which was based on the contrariety of termini.
And he says that the sign of this is that a motion from A to B is contrary to one from B to A, as happens in a reflected motion, because such motions, if they take place simultaneously, arrest and stop each other, that is, are such that one impedes the other and stops it.
And this happens not only in reflected straight motion, but in reflected circular motions. For let three points A, B, and C be designated on a circle. It is evident that, if something begins to be moved from A to B and later is moved from A to C, there was reflection, those two motions block one another, and one arrests the other, that is, causes the other to stop. But, if something is moved without interruption from A to B and again from B to C, there is no reflection. But the reason that reflected motions impede one another, both in straight and in circular motions, is that it is the nature of contraries to impede and destroy one another.
Motions that are diverse but not contrary, however, do not impede one another, for example, as an upward motion and a motion to the side (that is, to the right or left) do not obstruct one another; rather, something can at the same time be moved both upward and to the right.
1108. Then, at “but what shows” (262a12), he gives a second argument to show that reflected motions cannot be continuous to infinity, and it is an argument based on the pause that must intervene. He says, therefore, that it is above all the fact that what is reflected must rest between two motions that makes it clear that it is impossible for a rectilinear motion to be infinitely continuous. And this is true not only if something is moved through a straight line, but also if it is carried along according to a circle.
And, lest anyone suppose that being carried along in a circle is the same as circular locomotion, to exclude this, he adds that it is not the same to be carried along circularly according to the characteristics of a circle and to be carried along a circle, that is, to traverse a circle.
For it sometimes occurs that the motion of what is moved is according to a certain continuity, namely, as it traverses part after part according to the order of parts of the circle, and this is to be carried along a circle. But it sometimes occurs that what traverses a circle has not, when it returns to the point from which the motion began, traveled in an onward direction according to the order of the parts of the circle, but has returned backwards—and this is to be reflected. Therefore, whether the reflection occurs in a straight line or in a circular line, a pause must intervene.
1109. Belief in this can be based not only on sense (for it is sensibly evident), but also on an argument. The principle of this argument is that, since three things are involved in a magnitude that is traversed—namely, a beginning, a middle, and an end—the middle is both a beginning and an end when compared to both. For in respect to the end, the middle is a beginning, and in respect to the beginning, it is an end. Consequently, while it is one as to subject, it is two in account. Another principle to be taken is that what is in potency is other than what is in act.
Keeping these things in mind, it should be considered from what has been said that any one of the points—that is, each designated point between termini of a line over which something is being moved—is potentially a middle, but it is not one unless a division with respect to the motion takes place in such a way that, at a given point, the thing in motion stops and then resumes its motion at that point. Now, in this way, that middle will become an actual beginning and an actual end—that is, the beginning of the subsequent (inasmuch as the mobile resumes its motion from it) and an end of the first motion (inasmuch as the first motion was terminated there by reason of rest).
For let there be a line at whose beginning is A, at whose middle is B, and at whose end is C. Then let something be moved from A to B and stop there; then let it begin to be moved from B and be carried along to C.
In this example, it is plain that B is actually the end of the prior motion and the beginning of the subsequent one.
But, if something be moved continuously from A to C without any interval of rest, it is not possible to say that the mobile has come to be, that is, has arrived at, or has ceased to be, that is, has left, either the point A or the point B. It can be said only that it is in A or in B at a certain now. (But it cannot be said that it is so at a certain time, unless we should perchance say that a thing is somewhere in time because it is there in some now of time. And, so, what is being moved continuously from A to C in some time will be in B at an instant that is a divider of time. In this way, it will be said to be in B in that entire time, in the sense that we speak of something being moved in a day because it is in motion in a part of that day.)
And, because it seemed doubtful that what is in motion does not arrive at and leave each determinate point of a magnitude that is traversed by a continuous motion, he shows this. He says that, if someone grants that the mobile arrives at and then leaves some assigned point in the magnitude, it follows that it is at rest there. For it is impossible that a mobile arrive at and leave this point B in the same instant, because to arrive somewhere and to leave there are contraries, which cannot exist in the same instant.
Therefore, it must be at different nows that the mobile arrives at and leaves a given point of the magnitude. But there is an intermediate time between any two nows. Therefore, it will follow that the mobile A rests in B. For anything that is somewhere for a time is there before and after. And the same must be said for all the other signs or points, because the same reasoning applies to all.
Hence, it is plain that what is being carried along continuously over a magnitude is at no time arriving at or departing from any intermediate point. For when it is said that the mobile is at this point or comes to be in it or is approaching it, all these expressions imply that that point is a terminus of the motion. And when it is said that it leaves or departs, a beginning of motion is implied. But a designated point of a magnitude is not actually a middle or a beginning or an end, because the motion neither begins nor ends there; rather, it is these potentially only, since the motion could begin or end there. Hence, the mobile neither arrives at nor leaves an intermediate point, but it is said to be there absolutely in a now. For the existence of a mobile at some point of the magnitude is compared to the whole motion as the now is compared to time.
1110. But, when the mobile A uses B as an actual middle, beginning, and end, then it must stop there, for by moving and stopping, it makes that one point to be two, namely, a beginning and an end, as happens also in understanding. For we can simultaneously understand one point as it is one in subject, but if we consider it separately as a beginning and separately as an end, this will not take place simultaneously. So too, when that which is being moved uses a point as one, it will be there only in the one now. But, if it uses it as two—namely, as a beginning and end in act—it will be there for two nows, and thus for a middle time between them. And, so, it will be at rest. Therefore, it is plain that what is being moved continuously from A to C was neither present nor away from the intermediate B; that is, it neither arrived at it nor departed from it, but it was away from and left the first point A, as the actual beginning, and it was present in or arrived at the final point C, because there the motion is finished and the mobile rests.
It should be remarked that, in the foregoing, A was sometimes taken as the mobile and sometimes as the beginning of the magnitude.
1111. From all these things, it is clear that a reflected motion, whether it occurs along a circular magnitude or a straight one, cannot be continuous, but a rest intervenes, because the same point is actually the end of the first motion and the beginning of the reflected one. But, in a circular motion, the mobile does not use any point as an actual beginning and end, but each point is used as an intermediate. Therefore, a circular motion can be continuous, but a reflected one cannot.