Commentary Aristotle Physics
Lecture 12
It is shown from speed and slowness that there is no separated void
Further, the truth of what we assert is plain from the following considerations. We see the same weight or body moving faster than another for two reasons, either because there is a difference in what it moves through, as between water, air, and earth, or because, other things being equal, the moving body differs from the other owing to excess of weight or of lightness.
Now, the medium causes a difference because it impedes the moving thing, most of all if it is moving in the opposite direction, but in a secondary degree even if it is at rest, and especially a medium that is not easily divided, that is, a medium that is somewhat dense. A, then, will move through B in time C, and through D, which is thinner, in time E (if the length of B is equal to D), in analogy to the density of the hindering body. For let B be water and D air; then, by so much as air is thinner and more incorporeal than water, A will move through D more quickly than through B. Let the speed have the same ratio to the speed, then, that air has to water. Then, if air is twice as thin, the body will traverse B in twice the time that it does D, and the time C will be twice the time E. And always, by so much as the medium is more incorporeal and less resistant and more easily divided, the faster will be the motion.
Now, there is no ratio in which the void is exceeded by body, as there is no ratio of zero to a number. For if four exceeds three by one and exceeds two by more than one, and exceeds one by still more than it exceeds two, still there is no ratio by which it exceeds zero; for that which exceeds must be divisible into the excess plus that which is exceeded, so that will be what it exceeds zero by plus-zero. For this reason, too, a line does not exceed a point unless it is composed of points. Similarly the void can bear no ratio to the full.
Therefore, neither can motion through the one [bear a ratio] to motion through the other.
But if a thing moves such and such a distance through the thickest medium in such and such a time, it moves through the void with a speed beyond any ratio.
For let Z be void, equal in magnitude to B and to D. Then, if A is to traverse and move through it in a certain time I—a time less than E, however—the void will bear this ratio to the full. But, in a time equal to I, A will traverse the part D itself of air. And it will surely also traverse in that time any substance Z that exceeds air in thinness in the ratio that the time E bears to the time I. For if the body Z be as much thinner than D as E exceeds I, then A, if it moves through Z, will traverse it in a time inverse to the speed of the motion, that is, in a time equal to I. If, then, there is no body in Z, A will traverse Z still more quickly. But we supposed that its traverse of Z when Z was void occupied the time I, such that it will traverse Z in an equal time whether Z be full or void. But this is impossible.
It is plain, then, that, if there is a time in which it will move through any part of the void, this impossible result will follow: it will be found to traverse a certain distance, whether this be full or void, in an equal time; for there will be some body that is in the same ratio to the other body as the time is to the time.
To sum the matter up, the cause of this result is obvious: between any two motions, there is a ratio (for they occupy time, and there is a ratio between any two times, so long as both are finite), but there is no ratio of void to full.
These are the consequences that result from a difference in the media.
The following depend upon an excess of one moving body over another. We see that bodies that have a greater impulse either of weight or of lightness, if they are alike in other respects, move faster over an equal space, and in the ratio that their magnitudes bear to each other. Therefore, they will also move through the void with this ratio of speed.
But that is impossible, for why should one move faster? (In moving through plena it must be so, for the greater divides them more quickly by its force. For a moving thing cleaves the medium either by its shape or by the impulse that the body that is carried along or is projected possesses.)
Therefore, all will possess equal velocity. But this is impossible.
It is evident from what has been said, then, that, if there is a void, a result follows that is the very opposite of the reason for which those who believe in a void set it up. They think that, if motion in respect of place is to exist, the void must exist, separated all by itself; but this is the same as to say that place is a separate cavity, which has already been stated to be impossible.
527. Here the Philosopher, arguing from the fast and slow in motion, shows that the void does not exist.
About this, he does two things:
first, he assigns the causes of fastness and slowness in motion;
second, he uses these causes to argue to his point, at “now, the medium causes” (215a29; [528]).
He therefore says first (215a24) that one and the same heavy body—or any other thing such as a stone or something of this sort—is carried more quickly for two reasons:
either on account of the medium in which it is being moved, such as air or earth or water;
or on account of differences in the object, such as being heavier or lighter, all other things being equal.
528. Then, at “now, the medium causes” (215a29), he argues to his point from the causes given.
First, from the differences of the medium;
second, from the differences in the mobile object, at “the following depend upon” (216a12; [539]).
As to the first, he does two things:
first, he gives an argument;
second, he recapitulates, at to sum the matter up (216a8; [533]).
Concerning the first, he does two things:
first, he gives his argument;
second, he shows that the conclusion follows from the premises, at “for let Z be void” (215b22; [532]).
529. Therefore, he first gives this argument. The ratio of motion to motion in regard to speed is equal to the ratio of medium to medium in respect of subtlety. But there is no ratio between empty space and full space. Therefore, motion in a void has no ratio to motion in the full.
First of all, he explains the first proposition of this argument. And he says that the medium through which a body is in motion is the cause of its fastness or slowness because it acts as an obstacle to the body in motion.
The greatest obstacle occurs when the medium is in a contrary motion, as is evident in the case of a ship whose motion is impeded by the wind.
The medium is an obstacle in a secondary way even if it is not in motion, for if it were in motion with the object, it would not be an obstacle but a help, as the water that carries a ship downstream.
But, among obstacles, a greater impediment is offered by things that are not easy to divide, such as the denser bodies.
He explains this by an example. Let the body in motion be A, and let the space through which it is being moved be B, and let the time in which A is being moved through B be C. Let us posit another space, D, of the same length as B, but let D be full of a subtler body than the one in B, such that a certain analogy, or ratio, exists between the bodies that impede the motion (for example, let B be full of water and D full of air). Now, to the extent that air is subtler than water and less condensed, to that extent will the mobile A be more quickly moved through D than through B. Therefore, the ratio of the velocities will equal the ratio of the subtlety of air to the subtlety of water. And, the greater the velocity, the less the time: because that motion is faster that covers the same interval in less time, as will be shown in book 6. Hence, if air is twice as subtle as water, the time it takes A to be moved through B, which is full of water, will be twice the time for A to pass through D, which is full of air. Consequently, the time C in which it travels the distance B will be twice the time it takes E to pass through D. Therefore, we can take it as a general rule that, in whatever ratio the medium (in which something is in motion) is subtler and less resistant and more easily divisible, in that ratio will the motion be faster.