Commentary Aristotle Physics
Lecture 12
That which is without quantitative parts can be moved only accidentally
Our next point is that what is without parts cannot be in motion except accidentally; that is, it can be in motion only insofar as the body or the magnitude is in motion and the partless is in motion by inclusion therein;
just as that which is in a boat may be in motion in consequence of the locomotion of the boat, or a part may be in motion in virtue of the motion of the whole.
It must be remembered, however, that, by “what is incapable of being divided into parts,” I mean what is indivisible in respect of quantity.
(The case of the motion of a part is not exactly parallel, for parts have motions belonging essentially and severally to themselves distinct from the motion of the whole.
The distinction may be seen most clearly in the case of a revolving sphere, in which the velocities of the parts near the center and of those on the outside are different from one another and from that of the whole; this implies that there is not one motion, but many.)
As we have said, then, what is without parts can be in motion in the sense in which a man sitting in a boat is in motion when the boat is travelling, but it cannot be in motion of itself.
For suppose that it is changing from AB to BC—either from one magnitude to another, or from one form to another, or from some state to its contradictory—and let D be the first time in which it undergoes the change. Then, in the time in which it is changing, it must be either in AB or in BC or partly in one and partly in the other—for this, as we saw, is true of everything that is changing.
Now, it cannot be partly in each of the two, for then it would be divisible into parts. Nor, again, can it be in BC, for then it will have completed the change, whereas the assumption is that the change is in process. It remains, then, that, in the time in which it is changing, it is in AB. That being so, it will be at rest, for as we saw, to be in the same condition for a period of time is to be at rest.
So, it is not possible for that which has no parts to be in motion or to change in any way, for only one condition could have made it possible for it to have motion: that time should be composed of moments, in which case, at any moment, it would have completed a motion or a change, such that it would never be in motion, but would always have been in motion.
But this we have already shown above to be impossible: time is not composed of moments, just as a line is not composed of points, and motion is not composed of instants. For this theory simply makes motion consist of indivisibles in exactly the same way as time is made to consist of moments or a length of points.
Again, it may be shown in the following way that there can be no motion of a point or of any other indivisible. That which is in motion can never traverse a space greater than itself without first traversing a space equal to or less than itself.
That being so, it is evident that the point also must first traverse a space equal to or less than itself. But, since it is indivisible, there can be no space less than itself for it to traverse first, so it will have to traverse a distance equal to itself.
Thus, the line will be composed of points, for the point, as it continually traverses a distance equal to itself, will be a measure of the whole line. But, since this is impossible, it is likewise impossible for the indivisible to be in motion.
Again, since motion is always in a period of time and never in a moment, and all time is divisible, there must be for everything that is in motion a time less than that in which it traverses a distance as great as itself.
For that in which it is in motion will be a time, because all motion is in a period of time; and all time has been shown above to be divisible.
Therefore, if a point is in motion, there must be a time less than that in which it has itself traversed any distance. But this is impossible, for in less time, it must traverse less distance, and thus the indivisible will be divisible into something less than itself, just as the time is so divisible.
The only condition under which that which is without parts and indivisible could be in motion would have been the possibility of the infinitely small being in motion in a moment; for in the two questions—that of motion in a moment and that of motion of something indivisible—the same principle is involved.
872. After answering the arguments of Zeno, who tried to disprove motion, the Philosopher now intends to show that a thing incapable of being divided into parts cannot be moved. This will answer the opinion of Democritus, who posited atoms that are per se mobile.
About this, he does two things:
first, he proposes his intention;
second, he proves his proposition, at “for suppose that” (240b20; [876]).
He says first (240b8) that, assuming what we have proved above, it must be said that a thing incapable of being divided into parts cannot be moved, except perhaps per accidens, as a point is moved in a whole body in which there is a point (for example, in a line or a surface).
873. To be in motion as a result of something else being in motion can occur in two ways.
In one way, what is moved as the result of something else being moved is not part of the latter, as what is on a ship is being moved when the ship is being moved, and as whiteness is moved with the motion of body, since it is not of the body.
In a second way, it can be in motion as a part is moved when the whole is moved.
And, because “what is incapable of being divided into parts” has many senses, just as “what is capable of being divided into parts” has, he shows how he uses the phrase here and says, I mean what is indivisible in respect of quantity.
For some things are indivisible according to species, as when we say that fire and air are indivisible, because they cannot be further resolved into several bodies that differ in species.
But, in regard to such an indivisible, there is nothing to prevent it from being moved. Consequently, Aristotle intends to exclude motion from what is indivisible according to quantity.
874. Because he had said that the part is being moved when the whole is, and someone might say that the part is not moved at all, he adds that there are some motions of parts precisely as parts that are diverse from the motion of the whole, insofar as there is a motion of the whole.
This difference is particularly clear in the motion of a sphere, because the speed of the parts near the center is not the same as that of those outside, that is, on the exterior surface of the sphere, the speed of whose parts is considered to be the speed of the whole. It is as if there is not just one motion, but the motions of many parts involved. For it is evident that whatever traverses a larger magnitude in an equal time is faster. Now, while the sphere is rotating, it is clear that an external part describes a larger circle than an interior part; hence the velocity of the external part is greater than that of an interior part. Yet the velocity of the whole sphere is the same as the velocity of the interior and exterior part.
But this diversity of motions is to be understood in the sense in which motion is ascribed to parts of a continuum, that is, in a potential sense.
Hence, there is actually one motion of the whole and of the parts, but potentially there are diverse motions, those of the parts being different from one another and from the motion of the whole.
And so, when it is said that a part is being moved per accidens with the motion of the whole, it is a per accidens that is in potency per se—which is something not true of motion per accidens, when it is taken in the sense that accidents or forms are said to be moved per accidens.
875. Having made a distinction among things that are moved, he explains his intention. He says that what is indivisible in respect of quantity can indeed be moved per accidens when something else is moved, but it is not moved as a part, for no magnitude is made up of indivisibles, as we have proved. Now, something not a part of another is moved along with the other in the same way that one sitting in a ship is moved along with the motion of a ship. But, per se, the indivisible cannot be moved.
He had proved this point previously, not as a main proposition, but incidentally. Hence, in addition to the reason cited earlier, he now gives a further explanation of the truth and adds reasons that are strong enough to prove the proposition.
876. Then, at “for suppose that” (240b20), he proves his point with three arguments.
The first of these is this. If it is insisted that an indivisible can be moved, let it be moved from AB into BC. (In this argument, it makes no difference whether AB and BC are two magnitudes or two places, as in local motion and growth and decrease, or whether they are two forms, that is, qualities, as in the motion of alteration, or two things that are contradictorily opposed, as in generation and ceasing to be.) Let ED be the time in which something is changed from one terminus to the other first, that is, not by reason of a part. In this time, then, it is necessary that what is being moved be either in AB (the terminus from which) or in BC (the terminus to which), or else a part is in one terminus and a part in the other. For anything being moved must be moved in one of these three ways, as was said above.
Now, the third situation is impossible, namely, that it be in each term according to its various parts, for then the mobile would be divided into parts, and we have assumed that it is an indivisible mobile.
Likewise, it cannot be the second alternative, namely, that it be in BC (the terminus to which). For when it is in the terminus to which, it has been already changed (as is clear from what we have said above), but we are assuming that it is being changed. What remains, therefore, is that, in the entire time that the indivisible is being changed, it remains at AB, the terminus from which. From which it follows that it is at rest, for resting is nothing more than to be in one and the same state throughout a definite period of time. For since there is a prior and a subsequent in time, if time is divisible, whatever for a period of time is in one and the same state keeps itself the same as it was previously—which is to rest. But it is impossible that a thing is at rest while it is being changed. Therefore, it cannot be that an indivisible is moved or changed in any way whatsoever.
The only way in which there could be motion of an indivisible thing is to have the time composed of nows, for in the now, there is always a condition called “having been moved” or “having been changed.”
And, because what has been moved precisely as such is not now being moved, it follows that, in the now, nothing is being moved, but has been moved. But, if time were made up of nows, there would be a way in which motion could be posited in an indivisible, because it could be granted that, in each of those nows of which time is composed, it would be in one; and in the whole time—that is, in all the nows—it would be in many. And thus it would be in motion throughout the entire time, but not in one now.
But it has been proved above that it is impossible for time to be made up of nows. Indeed, we have proved that neither is time composed of nows, nor a line of points, nor a motion of instants (where “instants” refers to states called “having been changed”). For anyone who says that an indivisible is being moved or that motion is composed of indivisibles is making time be composed of nows or a magnitude of points—which is impossible. Therefore, it is also impossible that a thing incapable of being divided into parts be moved.
877. The second argument is given at “again, it may be shown” (241a6). He says that, if we look at the consequences, it is clear that neither a point nor any indivisible can be moved. And this special argument applies to local motion. For whatever is being moved according to place cannot traverse a distance greater than the mobile itself before traversing one that is equal to or less than it; rather, a mobile always traverses a magnitude equal to itself or less than itself before one greater than itself. If this is so, then it is clear that a point, if it is being moved, will first traverse a length less than or equal to itself, before it traverses one greater than itself. But it is impossible for it to traverse something less than itself, since it is indivisible. So it has to traverse a length equal to itself. Consequently, it must number all the points in the line, for the point, since it is being moved through a motion equal to a line, is by that very fact being moved through the whole line, and thus is always measuring the whole line—and this it does by counting all the points. Therefore, it follows that a line arises from points. Therefore, if this is impossible, it is impossible for an indivisible to be moved.
878. The third argument is at “again, since motion” (241a15). Since motion is always in a period of time and never in a now, and since all time is divisible, as was shown above, then in every time in which something is moved, there must be a lesser time in which a lesser mobile is moved. For supposing the same speed, it is plain that the lesser mobile crosses a given mark in a lesser time than does a greater mobile, such as the part crossing in a lesser time than the whole, as is evident from what is above. If, therefore, a point is in motion, there must be a time less than that in which it is moved. But this is impossible, for it would follow that, in that lesser time, something less than a point would be moved, and thus the indivisible would be divisible into something less, just as time is divisible. This would be the only condition under which the indivisible could be in motion, namely, if it were possible for something to be moved in an indivisible now, for just as there is nothing smaller than the now in time, so one cannot take a smaller mobile.
And, so, it is evident that, in the two questions—that of motion in a now and that of an indivisible being moved—the same principle is involved. But it is impossible for motion to occur in a now. Therefore, it is impossible for an indivisible to be moved.