Commentary Aristotle Physics
The first is this. Let KL be the magnitude through which a mobile has been moved in the first time XR. It is clear that an equally fast mobile that began its motion with the first one will have covered half the magnitude in half the time. Since the first mobile (which we have said covers the entire magnitude) is as fast as the second, it follows that even it has, in half the time, already been moved through half the magnitude KL. It will follow, therefore, that what is being moved has been previously moved.
To get a better understanding of what we mean, it must be considered that, just as “point” is a name for the terminus of a line, so “completed motion” is a name for the terminus of a motion. Now, no matter what line or what part of a line you take, it is always true that, before the completion of the whole line, you can take a point according to which the line can be divided. Likewise, before any motion or part of a motion, you can take a state of completed motion, for while the mobile is being moved to its terminus, it has already passed a certain stage in respect to which the mobile is said to have been already changed. But, just as a point within a line is in potency before the line is actually divided (for a point is the very division of a line), so also the thing called “completed motion” (within a motion) is in potency as long as the motion does not stop there; but, if it does stop there, it will be actual. And since what is in act is better known than what is in potency, therefore Aristotle proves his proposition (that what is being continually moved has already been moved) by referring to an equally fast mobile whose motion has already been completed. This is like proving that, in a certain line, there is a point in potency by showing that a like line has been actually divided.
830. The second argument, which he gives at “again, if by taking” (237a3), is this. In the whole time XR or in any other, something is said to have been changed by the very fact that a final now of the time is taken—not that something is being moved in that now, but that the motion is terminated then. Hence, “having been moved” is taken here not for that which is at some time being moved, but for the fact that the motion is ended.
Now, the reason that the motion must be terminated in the final now of the time that measures the motion is that that now terminates the time, just as a point terminates a line. And all time is midway between two nows, just as a line is between two points. Therefore, since “being moved” occurs in time, it follows that “having been moved” occurs in the now that is the terminus of time. And, if that is the case with a motion in a whole period of time, the same must be true of the parts of motion that occur in the parts of time. Now, we have already shown that, if something is being first moved in the whole time, it is being moved in each part of the time. But, whichever part of time you take, it is terminated at some now. For the terminus of half of the time is the division, that is, the now that divided the time into two parts.
Therefore, it follows that what is being moved through the whole is previously moved at the middle of time, on account of the now that determines the middle. And the same reasoning applies to any part of time. For no matter how the time is divided, it will always be found that each part of the time is determined by two nows, and after the first now of the time measuring the motion, no matter which other now is taken, the object has already been moved in that part of the time, for that now—whichever it is—is the terminus of the time measuring the motion.
Now, because every period of time is divisible into times and each period exists between two nows, and because, in any now that happens to be the ending of a time measuring the motion, something has been moved, it follows that whatever is being changed has been changed an infinite number of times, because “having been changed” is the terminus of a motion, just as a point is of a line and a now is of a time.
Therefore, just as it is possible in any line to pick out to infinity a point ahead of a point, and a now before a now in any period of time (because both line and time are divisible to infinity), so in any “being moved,” it is possible to pick out infinitely many “having been moved”s, because motion, too, is divisible to infinity, just as the line and time, as was previously proved.
831. The third argument is at “again, since a thing” (237a11). In the case of anything that is being changed (if it is not ceasing to be and does not perish or cease to be moved, but is being continually changed), it is necessary that, in each now of the time in which it is being moved, it is being changed or has been changed.
But in the now nothing is being changed, as we have shown. Therefore, in each now of the time that measures continuous motion, the object has been changed. But, in any portion of time, there are an infinitude of nows, because the now divides time, and time is infinitely divisible.
Therefore, everything that is being changed has been changed an infinite number of times. And, so, it follows that before every state called “being moved” is a state called “having been moved,” which, however, does not exist outside the state of “being changed,” but is in it and terminates a part of it.
832. Then, at “and not only must” (237a17), he proves that, on the other hand, a state of being changed precedes each state of having been changed.
First, he proves it from the viewpoint of the time;
second, from the viewpoint of that in respect of which the motion occurs, at “moreover, the truth” (237a28; [836]).
About the first, he does three things:
first, he states the proposition;
second, he proves certain things needed for proving the proposition, at “since everything that has changed” (237a19; [833]);
third, he gives the proof of the main proposition, at “since, then, it has changed” (237a25; [835]).
He says first that, not only is it true that whatever is being changed had already been changed, but every state of having been changed must be preceded by a state of being changed, because the former is the terminus of the latter. Therefore, every having been changed must be preceded by a being changed.
833. Then, at “since everything that has changed” (237a19), he states something needed for his proof of the proposition, that whatever is being changed from something to something was changed in time. But note carefully that here the words has changed do not refer to the termination of motion, for it was explained above that the time in which a thing was changed is an indivisible. But here, has changed signifies that something was previously being moved, as though he said that whatever was being moved was being moved in time.
This he now proves. If our proposition is not true, then let there be something that was changed from A to B—that is, from one term to another—in a now. From this, it follows that when it is in A—in the terminus from which—in the same now, it was not yet changed, because it has already been proved that what was changed, when it was being changed, was not in the terminus from which, but more in the terminus to which. Otherwise, it would follow that it was at once in A and in B.
Therefore, it is necessary to say that, in one now, it is in A and in another, it was being changed. But between two nows there is a time, because two nows cannot be immediately connected, as we have shown. What remains, therefore, is that whatever is being changed is being changed in time.
834. But it seems that this conclusion has no application in generation and ceasing to be, between whose two termini there is nothing intermediate. For if a period of time occurs between the now in which something is at the terminus from which and the now in which it is at the terminus to which, it will follow that there is something between being and non-being, for in that intermediate time, the subject of change would be neither being nor non-being.
Nevertheless, because the argument that Aristotle gives here is demonstrative, it must be said that it applies somehow even to generation and ceasing to be, but in the sense that such changes are also instantaneous, since there can be no medium between the termini.
So, it must be said that whatever is being changed from non-being to being (or vice versa) is not in being and non-being at the same time. But, as will be said in book 8, there is no final instant in which what is generated is a non-being, but there is a first instant in which it is a being, such that, in the entire time preceding that instant, it is non-being. However, between that now and the time preceding, there is nothing intermediate, such that there is no medium between being and non-being.
Now, since the time that precedes the instant in which something is generated first is the measure of some motion, it follows that, just as that instant in which something is first generated is the terminus of the preceding time that measures the motion, so the first instant of the being of the thing generated is the terminus of a preceding change.
If, therefore, generation is said to be the very beginning of being, it must be the terminus of a motion, and thus it takes place in an instant, because a motion’s being terminated—which is the same as having been changed—occurs in an indivisible of time, as we have shown.
However, if generation is taken as the very beginning of being plus the entire preceding motion of which it is the terminus, then it occurs not in an instant, but in time, such that what is being generated is a non-being during the entire preceding time and a being in the final instant. And the same applies to ceasing to be.