Commentary Aristotle Physics
Lecture 19. Proofs that circular motion can be continuous and is the first motion
On the other hand, in motion on a circular line, we shall find singleness and continuity, for here we are met by no impossible consequence.
That which is in motion from A will according to the same position be simultaneously in motion to A (since it is in motion to the point at which it will finally arrive), and yet it will not be undergoing two contrary or opposite motions.
For a motion to a point and a motion from that point are not always contraries or opposites: they are contraries only if they are on the same straight line (for then, they are contrary to one another in respect of place, as, for instance, the two motions along the diameter of the circle, since the ends of this are at the greatest possible distance from one another), and they are opposites only if they are along the same line.
Therefore, in the case we are now considering, there is nothing to prevent the motion being continuous and free from all intermission, for circular motion is motion of a thing from its place to its place, whereas rectilinear motion is motion from its place to another place.
Moreover, the progress of circular motion is never localized within certain fixed limits, whereas that of rectilinear motion repeatedly is so.
Now, a motion that is always shifting its ground from moment to moment can be continuous, but a motion that is repeatedly localized within certain fixed limits cannot be so, since the same thing would then have to undergo simultaneously two opposite motions.
So, too, there cannot be continuous motion in a semicircle or in any other arc of a circle, since here also the same ground must be traversed repeatedly and two contrary processes of change must occur.
The reason is that, in these motions, the starting point and the termination do not coincide, whereas in motion over a circle, they do coincide, and so this is the only perfect motion.
This differentiation also provides another means of showing that the other kinds of motion cannot be continuous either, for in all of them, we find that there is the same ground to be traversed repeatedly.
Thus, in alteration, there are the intermediate stages of the process, and in quantitative change, there are the intervening degrees of magnitude, and in generation and corruption, the same thing is true.
It makes no difference whether we take the intermediate stages of the process to be few or many, or whether we add or subtract one, for in either case, we find that there is still the same ground to be traversed repeatedly.
Moreover, it is plain from what has been said that those physicists who assert that all sensible things are always in motion are wrong, for their motion must be one or another of the motions just mentioned. In fact, they mostly conceive it as alteration (things are always in flux and decay, they say), and they go so far as to speak even of generation and corruption as a process of alteration.
On the other hand, our argument has enabled us to assert the fact, applying universally to all motions, that no motion admits of continuity except circular motion. Consequently, neither alteration nor increase admits of continuity. We need now say no more in support of the position that there is no process of change that admits of infinity or continuity except circular locomotion.
It can now be shown plainly that rotation is the primary locomotion.
Every locomotion, as we said before, is either circular or rectilinear or a compound of the two; the two former must be prior to the last, since they are the elements of which the latter consists.
Moreover, circular locomotion is prior to rectilinear locomotion, because it is more simple and complete, which may be shown as follows.
The straight line traversed in rectilinear motion cannot be infinite, for there is no such thing as an infinite straight line; and, even if there were, it would not be traversed by anything in motion, for the impossible does not happen, and it is impossible to traverse an infinite distance.
On the other hand, rectilinear motion on a finite straight line is, in fact, two motions, if it turns back a composite motion; but, if it does not turn back, it is incomplete and perishable.
And in the order of nature, of definition, and of time alike, the complete is prior to the incomplete and the imperishable to the perishable.
Again, a motion that admits of being eternal is prior to one that does not. Now, circular motion can be eternal, but no other motion, whether locomotion or motion of any other kind, can be so, for in all of them, rest must occur, and with the occurrence of rest, the motion has perished.
1129. After showing that no local motion but a circular one can be continuous, the Philosopher now shows that a circular motion can be continuous and first.
First of all, he shows this with proper arguments;
second, with logical and common arguments, at “moreover, the result” (265a27; [1136]).
About the first, he does two things:
first, he shows that a circular motion is continuous;
second, he shows that it is the first, at “it can now be shown” (265a13; [1134]).
About the first, he does two things:
first, he gives two arguments to prove that circular motion can be continuous;
second, from the same arguments, he concludes that no other motion can be continuous, at “this differentiation” (264b28; [1132]).
1130. That a circular motion can be one continuous motion he proves (264b9) with this first argument. That from which nothing impossible follows is said to be possible. But nothing impossible follows from the statement that a circular motion is forever continuous.
This is plain from the fact that, in a circular motion, that which is being moved from somewhere—for instance, from A—is at the same time being moved to the same point according to the same position, that is, according to the same progress of the mobile, the same order of parts having been maintained.
This, however, does not happen in a reflected motion, for when something turns back, it is disposed according to a contrary order of parts in its motion. For either that part of the mobile to the front in the first motion must be at the rear in the reflection or that part that was facing one difference of place (for example, the right or above) must face a contrary direction in reflection. But, in a circular motion, the same position is maintained while a thing is being moved toward the point from which it departed. Consequently, it could be said that, even from the very beginning of its motion, while it was departing from A, it was being moved toward that which it would finally reach, namely, the very same A.
Nor does this lead to the impossibility of being moved with contrary or opposite motions at one and the same time, as followed in rectilinear motion. For not every motion to some terminus is contrary or opposite to one from the same terminus, but such contrariety is present in the straight line, according to which contrariety in place is gauged. For contrariety between two termini is not according to a circular line, whatever part of the circumference be taken, but according to the diameter. Contraries, indeed, are things most far apart; but the greatest distance between two termini is not measured according to a circular line, but according to a straight line. For between two points, an infinite number of curves can be drawn, but only one straight line. But the measure in any genus is that which is one.
Consequently, it is plain that, if one takes a circle and divides it half, and AB is its diameter, a motion through the diameter from A to B is contrary to a motion over the same diameter from B to A. But a motion over the semicircle from A to B is not contrary to a motion from B to A over the other semicircle. But it was contrariety that prevented a reflected motion from being continuous, as appears from the reasons given above. Therefore, once contrariety has been removed, nothing prevents a circular motion from being continuous and also not failing at any time.
And the reason for this is that a circular motion is completed by the fact that it is from the same to the same, and thus its continuity is not impaired by this. But a rectilinear motion is completed by its being from one thing to another; hence, if it returns from that other to the same from which it began, it will be not one continuous motion, but two.
1131. Then, at “moreover, the progress” (264b18), he gives the second argument, saying that a circular motion does not exist in identical things, but a rectilinear motion is very often in identical things.
Now, what this means is that, if something is moved from A to B across a diameter, and again from B to A across the same diameter, it has to return across the same middles through which it previously travelled.
Consequently, it is being carried over the same middle a number of times. But, if something is moved through a semicircle from A to B, and again from B to A through the other semicircle—and this is motion in the circular manner—it is clear that it does not return to the same point over the same middles.
Now, it is in the definition of opposites that they be considered with relation to the same thing. Thus, it is clear that to be moved from the same to the same with a circular motion is without opposition, but to be moved from the same to the same with a reflected motion is with opposition.
In this way, it is plain that a circular motion that does not return to the same over the same middles, but always passes through one and another, can be one and continuous, because it does not have opposition.
But that motion that returns to the same terminus by traversing the same middles more than once—namely, reflected motion—cannot be forever continuous, because that would require something being moved with contrary motions at one and the same time, as was proved above.
And, from the same argument, it can be concluded that a motion confined to a semicircle, or to any portion of a circle, cannot be continuous in perpetuity, because such motions require repeated traversing of the same middles and involve being moved with contrary motions, as though a return to the beginning should be made. The reason is that the end is not joined to the beginning when you are dealing with a straight line, or a semicircle, or an arc of a circle; rather, the beginning and end are apart. It is only in a circle that the end is joined to the beginning.
And, for this reason, only a circular motion is a perfect motion, since a thing is perfect from attaining its principle.
1132. Then, at “this differentiation” (264b28), he proves from the same argument that in no other genus of motion can there be continuous motion.
First, he proves the proposition;
second, he draws a corollary from what was said, at “moreover, it is plain” (265a2; [1133]).
He says first (264b28) that, also from this distinction between circular motion and other local motions, it is plain that in the other genera of motion there can also not be any infinitely continuous motions, for in all the other genera of motion, if anything is to be moved from a thing to itself, it follows that the same thing will be repeatedly traversed. For example, in alteration, the intermediate qualities must be passed through, for the passage from hot to cold is through tepid, and if a return is to be made from cold to hot, tepid must be traversed again. The same is apparent in a motion according to quantity, for if what is moved from large to small should return again to large, the intermediate quantity must be traversed twice. Generation and corruption present a similar situation: if air comes to be from fire, and then again fire from air, the intermediate dispositions must be traversed twice (for a middle may be placed in generation and ceasing to be, insofar as one considers the dispositional changes).
And, because the intermediates are traversed in different ways in changes that are diverse, he adds that it makes no difference whether many or few intermediates are introduced through which something is moved from one extreme to the other, or whether the intermediate is taken in a positive sense (as pallid between white and black) or in a remotive sense (as, between good and evil, that which is neither good nor evil)—for be they what they may, it always happens that the same are traversed a number of times.
1133. Then, at “moreover, it is plain” (265a2), he concludes from the foregoing that the early natural philosophers did not phrase the matter well when they said that all sensible things are forever in motion, because that would necessitate their being moved with respect to one of the previously given motions, which we have shown cannot be forever continuous—and especially because they said that the ever-continuous motion is alteration.
For they assert that all things are always being corrupted and ceasing to be, and yet they say that generation and ceasing to be are nothing more than alteration, and so, in saying that all things are forever ceasing to be, they are saying that all things are forever being altered.
But it was proved in the argument given above that nothing can be moved forever except by a circular motion. Thus, it remains that according to neither alteration nor growth can all things be forever in motion, as they said.
Finally, he concludes by way of summary to the chief proposition: no change can be infinite and continuous except a circular one.
1134. Then, at “it can now be shown” (265a13), he proves with two arguments that circular motion is the first of motions.
The first argument is this. Every local motion, as stated above, is either circular or straight, or a combination of the two. But circular and straight are prior to the combination, which is composed of them. But between these two, the circular is prior to the straight, for the circular is simpler and more perfect than the straight. And this he proves as follows. Straight motion cannot go on infinitely, for this would occur in two ways.
First, in such a way that the magnitude traversed by the straight motion would be infinite, which is impossible. But even if there were some infinite magnitude, nothing would be moved to infinity. For what is impossible to be, never comes to be nor is generated; but it is impossible to traverse the infinite; therefore, nothing is moved toward the end of traversing the infinite. Therefore, there cannot be an infinite straight motion over an infinite magnitude.
In a second way, an infinite straight motion can be understood as being a reflected motion over a finite magnitude. But a reflected motion is not one, as was proved above, but is a composition of two motions.
But, if a reflection does not occur upon a finite straight line, the motion will be imperfect and destroyed: imperfect, because further addition can be made to it; destroyed, because, when the terminus of the magnitude is reached, the motion will cease.
From all this, it is clear that a circular motion, which is not composed of two, and which is not destroyed when it comes to a terminus (for its beginning and end are identical), is simpler and more perfect than a straight motion. Now, the perfect is prior to the imperfect, and likewise, the imperishable is prior to the perishable in nature, account, and time, as was shown above when it was proved that local change is prior to other motions. Therefore, it is necessary that circular motion be prior to straight.
1135. Then, at “again, a motion” (265a24), he gives the second argument, which is this. A motion that can be perpetual is prior to one that cannot be perpetual, because the perpetual is prior to the non-perpetual, both in time and in nature. But a circular motion and no other can be perpetual, for the others must be followed by rest, and where rest intervenes, motion is destroyed. What is left, therefore, is that circular motion is prior to all the other motions. (The premises of this argument are plain from what has been said previously.)