Commentary Aristotle Physics
Lecture 13
No change is infinite in its proper species; how motion can be infinite in time
Our next point is that no process of 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, as the case may be, is the limit—for instance, being is the limit of generation and non-being is the limit of ceasing to be.
And, in contrary changes, the particular contraries are the limits, since these are the extreme points of any such process of change, and consequently of every process of alteration, for alteration is always dependent upon some contraries.
Similarly, contraries are the extreme points of processes of increase and decrease: the limit of increase is to be found in the complete magnitude proper to the peculiar nature of the thing that is increasing, while the limit of decrease is the complete loss of such magnitude.
It is true that we cannot show locomotion to be finite in this way, since it is not always between contraries.
But, since it is impossible that that which cannot be cut—the term “impossible” being used in several senses—should be in process of being cut, and generally that that for which it is impossible to come to be should be in process of coming to be, it follows that it is impossible that that which cannot complete a change should be in process of changing to that to which it cannot complete a change.
If, then, it is to be assumed that that which is in locomotion is in process of changing, it must be capable of completing the change.
Consequently, its motion is not infinite, and it will not be in locomotion over an infinite distance, for it cannot traverse such a distance. It is evident, then, that a process of 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 process of change may be infinite in respect of the time that it occupies.
If it is not one process, it would seem that there is nothing to prevent its being infinite in this sense (for instance, if a process of locomotion be succeeded by a process of alteration, and that by a process of increase, and that again by a process of generation).
In this way, there may be motion forever 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 process, no motion can be infinite in respect of the time that it occupies, with the single exception of circular locomotion.
879. After showing that things that cannot be divided into parts are not moved, the Philosopher now intends to show that no change is infinite. This is against Heraclitus, who supposed that things are always in motion. About this, he does two things: first, he shows that no change is infinite according to its own species; second, how there can be infinites in time, at “but it remains” (241b12; [883]).
About the first he does two things: first, he shows for all changes except local motion that no change is infinite according to its species;
second, he shows the same thing for local motion, at “it is true that we cannot” (241b2; [881]).
880. The first reason is this. It was said above that every change is from something to something. Indeed, in some changes—namely, those that occur between contradictories, as do generation and ceasing to be, or between contraries, as do alteration and growing and decreasing—it is evident that they have predefined termini. Hence, in changes that occur between contradictory termini, the terminus is either affirmation or negation, as the terminus of generation is a being, and that of ceasing to be is non-being.
Likewise, in regard to changes that are between contraries, the contraries are termini at which, as at ultimate goals, changes of this kind are terminated. Hence, it follows that, since every alteration is from contrary to contrary, every alteration has some terminus.
The same must be said for growth and decrease, for the terminus of growth is perfect magnitude (and I say “perfect” in respect of the nature, for a different perfection of magnitude befits man from the one that befits a horse), and the terminus of decrease is the one that happens to be most removed from perfect magnitude with respect to a definite nature.
Consequently, it is evident that each of the above-mentioned changes has a goal at which it is terminated. But such a situation precludes the infinite. Therefore, none of these changes can be infinite.
881. Then, at “it is true that we cannot” (241b2), he proceeds to local motion.
And first he shows that the argument in regard to local motion is not the same as for the other changes. For it cannot be proved that local motion is finite (as we have proved other motions are finite), because it is terminated at something contrary or contradictory, for not every local motion is between strict contraries, where contraries refer to things most distant.
There is a maximum distance in the strict sense in the natural motions of heavy and light bodies, for the place of fire is at a maximum distance from the center of the earth, in accordance with the distance that nature determines for such bodies. Hence, such changes are between strict contraries, and thus it can be proved of such changes that they are not infinite any more than the others were.
But maximum distance in forced or voluntary motions does not depend strictly on certain definite termini, but on the intention or energy of the one causing the motion, who either does not desire to or cannot physically move something any farther. Hence, it is only in a qualified sense that there is maximum distance and a consequent contrariety. Hence, if you stick with the termini, it cannot be proved that no local motion is infinite.
882. Consequently, this must be proved by another argument, which is this. What is impossible to exist divided cannot be divided; and because things are said to be impossible in many senses—namely, what never can occur or what cannot occur except with great difficulty—he therefore explains his meaning of impossible here.
And he means it in the sense of that which cannot happen at all. For the same reason, what is impossible to have been made is impossible to make: for example, if it is impossible that contradictories be together, it is impossible that this be brought about. For the same reason, what is impossible to have been changed into something cannot be changed into it, because nothing tends toward the impossible. But everything that is being changed according to place is being changed into something. Therefore, it is possible through that motion to arrive at something. But the infinite cannot be gone through. Therefore, nothing is moved through the infinite. Thus, therefore, no local motion is infinite.
And so it is evident in all three kinds of change that no change can be infinite in such a way that it be not terminated by definite termini from which it derives its species.
883. Then, at “but it remains” (241b12), he shows how motion can be infinite in time. And he says that we must consider whether motion can be infinite in time in such a way that it remains numerically one and the same motion. For there is nothing to prevent motion from enduring through infinite time as long as it is not one and the same motion. But he leaves that matter in doubt when he adds perhaps, because he will settle the matter later.
And he gives an example: let us say that, after a local motion, there is an alteration, and after that a growing, and after that generation, and so on to infinity. In this way, motion could always endure throughout infinite time. And it would not be one and the same numerical motion, because a series of such motions as are given in the example do not form one numerical motion, as we have proved in book 5.
But that motion endure throughout infinite time in such a way that it remain one numerical motion can occur in only one species of motion, for a circular motion can endure as one and continuous throughout infinite time, as will be proved in book 8.