Commentary Aristotle Physics
Lecture 20. Common and logical arguments that circular motion is continuous and first
Moreover, the result at which we have arrived—that circular motion is single and continuous, and rectilinear motion is not—is a reasonable one.
In rectilinear motion, we have a definite starting point, finishing point, and middle point, which all have their place in it in such a way that there is a point from which it can be said to start and at which it can be said to finish (for when anything is at the limits of its course, whether at the starting point or at the finishing point, it must be in a state of rest).
On the other hand, in circular motion, there are no such definite points. For why should any one point on the line be a limit rather than any other?
Any one point as much as any other is alike starting point, middle point, and finishing point, such that we can say of certain things both that they are always and that they never are at a starting point and at a finishing point.
(Hence, a revolving sphere, while it is in motion, is also in a sense at rest, for it continues to occupy the same place.)
The reason of this is that, in this case, all these characteristics belong to the center: the center is alike starting point, middle point, and finishing point of the space traversed.
Consequently, since this point is outside its circularity, there is no point at which what is in process of locomotion can be in a state of rest as having traversed its course, for in its locomotion, it is proceeding always about a central point, and not to an extreme point.
Therefore, it remains still, and the whole is, in a sense, always at rest as well as continuously in motion.
Our next point gives a convertible result. On the one hand, because rotation is the measure of motions, it must be the primary motion (for all things are measured by what is primary). On the other hand, because rotation is the primary motion, it is the measure of all other motions.
Again, circular motion is also the only motion that admits of being regular.
In rectilinear locomotion, the motion of things in leaving the starting point is not uniform with their motion in approaching the finishing point, since the velocity of a thing always increases proportionately as it removes itself farther from its position of rest.
On the other hand, circular motion is the only motion whose course is naturally such that it has no starting point or finishing point in itself, but is outside it.
As to locomotion being the primary motion, this is a truth that is attested by all who have ever made mention of motion in their theories: they all assign their first principles of motion to things that impart motion of this kind.
Thus “separation” and “combination” are motions in respect of place, and the motion imparted by “love” and “strife” takes these forms, the latter “separating” and the former “combining.”
Anaxagoras, too, says that “mind,” his first mover, “separates.” Similarly, those who assert no cause of this kind, but say that “void” accounts for motion, also hold that the motion of natural substance is motion in respect of place.
For their motion that is accounted for by “void” is locomotion, and its sphere of operation may be said to be place. Moreover, they are of the opinion that the primary substances are not subject to any of the other motions, though the things that are compounds of these substances are so subject.
The processes of increase and decrease and alteration, they say, are effects of the “combination” and “separation” of atoms. It is the same, too, with those who make out that the generation or corruption of a thing is accounted for by “density” or “rarity,” for it is by “combination” and “separation” that the place of these things in their systems is determined.
Moreover, to these we may add those who make soul the cause of motion, for they say that things that undergo motion have as their first principle “that which moves itself,” and when animals and all living things move themselves, the motion is autokinesis in respect of place.
Finally, it is to be noted that we say that a thing “is in motion” in the strict sense of the term only when its motion is motion in respect of place:
if a thing is in process of increase or decrease or is undergoing some alteration while remaining at rest in the same place, we say that it is in motion in some particular respect; we do not say that it “is in motion” without qualification.
We have argued, therefore, that there always was motion and always will be motion throughout all time, and we have explained what is the first principle of this eternal motion.
We have explained further which is the primary motion and which is the only motion that can be eternal, and we have pronounced the first mover to be unmoved.
1136. After proving with proper reasons that a circular motion is continuous and first, the Philosopher now proves the same with certain logical and common reasons.
And he gives three arguments.
With respect to the first (265a27), he says that it is reasonable that a circular motion be one and forever continuous, but not a straight one. For in a straight motion, a beginning, middle, and end are defined, and all three of these can be designated in a straight line. Therefore, in a straight line, there is a place from which the motion begins and one where it ends, since all motion rests at its termini, namely, the terminus from which or to which (he having distinguished these two states of rest in book 5). But, in a circular line, the termini are not distinct, for there is no reason that, in a circle, some designated point should be a terminus more than another, since each and every one alike is a beginning and an intermediate and an end. Consequently, the things that are moved circularly are in a sense always in the beginning and in the end—insofar as any point at all in a circle may be taken as a beginning or end—while in another sense, they are never in the beginning or end, inasmuch as no point in the circle is a beginning or end in act.
Hence it follows that a sphere is, in one sense, in motion and, in another sense, at rest, because, as was said in book 6, while the sphere is being moved, it always keeps the same place as to subject, and in this respect, it is at rest; but yet the place is always different in account, and in this respect, it is being moved.
Now, the reason that a beginning, middle, and end are not distinguished in a circular line is that these three belong to the center, from which, as from a beginning, lines proceed to the circumference and at which lines drawn from the circumference end. Moreover, it is the middle of the entire magnitude by virtue of its equidistance to all the points of the circumference.
And, therefore, since the beginning and end of a circular magnitude are outside its circularity—for they are in the center that is never reached by a thing moving circularly—no place can be assigned at which a thing in circular motion should be at rest, because anything in circular motion is always carried about the middle but not to what is ultimate, because it is not carried to the middle, which is the beginning and the ultimate.
On this account, a whole that is being moved in a spherical manner is, in one sense, always at rest and, in another sense, in continuous motion, as has been said.
From all this, the following argument may be extracted. Every motion that is never in its beginning and end is continuous. But a circular motion is of this kind. And, with this same middle term, it is proved that a straight motion cannot be continuous.
1137. Then, at “our next point” (265b8), he gives the second argument, saying that these two follow one another conversely, namely, that a circular motion is the measure of all motions and that it is the first of all motions. For all things are measured by what is first in their genus, as is proved in Metaphysics 10. Accordingly, this is a convertible proposition: “Whatever is a measure is the first in its genus; whatever is first is a measure.” But circular motion is the measure of all other motions, as is clear from what was said at the end of book 4. Therefore, circular motion is the first of motions. On the other hand, if one suppose that a circular motion is the first of motions on account of the arguments given above, it will be concluded that it is the measure of the other motions.
1138. The third argument he gives at “again, circular motion” (265b11), saying that only a circular motion can be regular, since things in motion in a straight line are being carried along in an irregular manner from beginning to end.
For as was said in book 5, a motion is irregular that is not equally swift throughout, and this must occur in every straight motion, for in natural motions, the further things in motion are from the first rest (from which the motion started), the swifter they are moved; and, in a forced motion, the farther they are from the ultimate rest (at which the motion terminates), the swifter they travel. For every natural motion is more intense near the end, but a forced motion at the beginning.
But this has no place in a circular motion in place, for in a circle, the beginning and end do not exist somewhere in the circling that occurs along the circumference, but outside it, that is, in the center, as was explained. Hence, there is no reason that a circular motion should be intensified or weakened on account of a nearness to its beginning or end, since it is always equally approaching the center, which is the beginning and end.
Now, it is plain from what was said in book 5 that a regular motion is more one motion than is an irregular one. Consequently, a circular motion is naturally prior to a straight motion. For the more a thing is one, the more it is by nature prior.
1139. Then, at “as to locomotion” (265b16), he shows through the opinions of the early philosophers that local motion is the first of motions. And he says that the statements of all the ancient philosophers who discussed motion attest to this truth, for they declare that the principles of things move with local motion.
He refers first to the opinion of Empedocles, who posited friendship and strife as the first moving principles, the former gathering and the latter separating—and gathering and separating are local motions.
Second, he shows the same thing through the opinion of Anaxagoras, who posited intellect as the first moving cause, whose work, according to him, is to separate what is commingled.
Third, he shows the same thing through the opinion of Democritus, who did not posit a moving cause, but said that all things are moved on account of the nature of the void. But a motion that is due to the void is a local motion or one similar to local motion, for void and place differ only in account, as was said in book 4. And so, by positing that things are first moved on account of the void, they posit local motion as naturally first rather than any of the other motions, but they believe that the other motions follow upon local motion. For those who follow Democritus declare that being increased and corrupted and altered occur by a certain assembling and separating of indivisible bodies.
Fourth, he shows the same thing through the opinions of the ancient philosophers of nature who posited only one cause, a material cause—namely, water, or air, or fire, or some intermediate. For from that one material cause, they explain the generation and ceasing to be of things through condensation and rarefaction, which are completed by a kind of assembling and separation.
Fifth, he shows the same through the opinion of Plato, who posited soul as the first cause of motion. For Plato posited that that which moves itself, which is the soul, is the principle of all things that are moved. But self-motion belongs to animals and all animate things, according to autokinesis with respect to place, that is, per se local change.
Sixth, he shows the same thing through what is commonly and popularly held. For we say “to be moved” in the proper sense only what is moved with respect to place. But, if something is at rest in place yet is moved with the motion of growth or decrease or alteration, it is said to be moved in a certain sense, but not absolutely.
1140. Then, at “we have argued” (266a5), he summarizes what he had said, namely, that motion always has been and always will be, and that there is some first principle of perpetual motions, and what the first motion is, and which motion happens to be perpetual, and that the first mover is immobile. For all these things have been set forth in what has preceded.