Commentary Aristotle Physics
Lecture 6
Two ways in which motion is divided
Now, motion is divisible in two senses.
In the first place, it is divisible in virtue of the time that it occupies.
In the second place, it is divisible according to the motions of the several parts of that which is in motion:
for instance, if the whole AC is in motion, there will be a motion of AB and a motion of BC.
That being so, let DE be the motion of the part AB, and EZ the motion of the part BC. Then, the whole DZ must be the motion of AC, for DZ must constitute the motion of AC inasmuch as DE and EZ severally constitute the motions of each of its parts. But the motion of a thing can never be constituted by the motion of something else, and consequently, the whole motion is the motion of the whole magnitude.
Again, since every motion is a motion of something and the whole motion DZ is not the motion of either of the parts (for each of the parts, DE or EZ is the motion of one of the parts AB or BC) or of anything else
(for the whole motion is the motion of a whole, and the parts of the motion are the motions of the parts; and the parts of DZ are the motions of AB and BC and of nothing else, for a motion that is one cannot be the motion of more than one thing).
Since this is so, the whole motion will be the motion of the magnitude ABC.
Again, if there is a motion of the whole other than DZ, parts may be subtracted from it, and these motions will be equal to DE and EZ, respectively, since the motion of that which is one must be one.
So, if the whole motion OI may be divided into the motions of the parts, OI will be equal to DZ; if, on the other hand, there is any remainder, say KI, this will be a motion of nothing.
For it can be the motion neither of the whole nor of the parts (as the motion of that which is one must be one) nor of anything else, for a motion that is continuous must be the motion of things that are continuous.
And the same result follows if the division of OI reveals a surplus on the side of the motions of the parts.
Consequently, if this is impossible, the whole motion must be the same as and equal to DZ.
This, then, is what is meant by the division of motion according to the motions of the parts, and it must be applicable to everything that is divisible into parts.
Motion is also susceptible to another kind of division, that according to time. For since all motion is in time and all time is divisible, and in less time, the motion is less, it follows that every motion must be divisible according to time.
And, since everything that is in motion is in motion to something and for a certain time and has a motion belonging to it, it follows that the time, the motion, the act of being in motion, the thing that is in motion, and the sphere of the motion must all be susceptible to the same divisions (though spheres of motion are not all divisible in a like manner, and thus quantity is essentially divisible, but quality accidentally).
For suppose that A is the time occupied by the motion B. Then, if all the time has been occupied by the whole motion, it will take less of the motion to occupy half the time, and less again to occupy a further subdivision of the time, and so on to infinity.
Again, the time will be divisible similarly to the motion; for if the whole motion takes the whole time, then half the motion takes half the time; and, again, the lesser motion takes the lesser time.
In the same way, the being-in-motion will also be divisible. For let C be the whole being-in-motion.
Then the being-in-motion that corresponds to half the motion will be less than the whole being-in-motion, and that which corresponds to a quarter of the motion will be less again, and so on to infinity.
Moreover, by setting out successively the being-in-motion corresponding to each of the two motions DC (say) and CE, we may argue that the whole being-in-motion will correspond to the whole motion
(for if it were some other being-in-motion that corresponded to the whole motion, there would be more than one being-in-motion corresponding to the same motion), the argument being the same as that whereby we showed that the motion of a thing is divisible into the motions of the parts of the thing.
For if we take separately the being-in-motion corresponding to each of the two motions, we shall see that the whole being-in-motion is continuous.
The same reasoning will show the divisibility of the length, and in fact of everything that forms a sphere of change (though some of these are only accidentally divisible because that which changes is so), for the division of one term will involve the division of all.
So, too, in the matter of their being finite or infinite, they will all alike be either the one or the other.
And we now see that, in most cases, the fact that all the terms are divisible or infinite is a direct consequence of the fact that the thing that changes is divisible or infinite.
For the attributes “divisible” and “infinite” belong in the first instance to the thing that changes. That divisibility does so we have already shown; that infinity does so will be made clear in what follows.
806. Having established the facts needed for dividing motion, he now begins to treat of the division of motion.
And the treatment is divided into two parts.
In the first, he treats of the division of motion;
in the second, he uses his conclusions to refute errors about motion, at “Zeno’s reasoning” (239b5; [860]).
The first part is divided into two sections:
in the first, he discusses division of motion;
in the second, he discusses division of rest, at “since everything to which” (238b23; [851]).
The first section is divided into two parts:
in the first, he deals with division of motion;
in the second, he discusses finite and infinite with respect to motion (for both the divisible and the infinite seem to belong to the continuum), at “now, since the motion” (237b23; [841]).
The first is divided into two parts:
in the first, he shows how motion is divided;
in the second, he treats of the order of the parts of motion, at “since everything that changes” (235b6; [818]).
In regard to the first, he does two things:
first, he lists two ways by which motion is divided;
second, he mentions what else is divided when motion is divided, at “and, since everything” (235a13; [812]).
In regard to the first, he does two things:
first, he mentions the ways in which motion is divided;
second, he explains them, at “that being so” (234b24; [808]).
807. He says first (234b21) that motion is divided in two ways.
In one way, it is divided according to time, because it has been shown that motion occurs not in the now, but in time.
In a second way, it is divided according to the motions of the parts of the mobile. Let the mobile AC be divided, for any mobile can be divided, as we have shown. If, therefore, the entire mobile AC is being moved, then each of its parts, AB and BC, is in motion.
But notice that the dividing of motion according to the parts of the mobile can be understood in two ways.
In the first way, part would be being moved after part, which is not possible in that which is in motion per se in its entirety, for in the case of such a mobile, all the parts are moved together—not in isolation from the whole, but in the whole.
In the second way, the dividing of motion according to parts of the mobile can be taken in the same sense as the division of an accident whose subject is divisible depends on the division of that subject; for example, if a whole body is white, then, as the body is divided, the whiteness will be divided per accidens.
And it is in this sense that we are taking division of motion according to the parts of the mobile: just as both parts of the mobile are in motion at the same time as the whole is, so the motions of both parts occur at the same time. This shows that division of motion according to the parts of the mobile is different from the division according to time, in which two given parts of a motion do not occur at the same time.
But, if we were to compare the motion of one part to that of another part not absolutely but according to a fixed stage to be reached, then the motion of one part will precede in time the motion of another part. For if the mobile ABC is moved in the magnitude EFG such that EF is equal to length ABC of the mobile, it is clear that BC will reach F before AB does. According to this, the division of motion according to the parts of time and according to the parts of the mobile will be the same.
808. Then, at “that being so” (234b24), he explains these ways of dividing motion:
first, he shows that motion is divided according to the parts of the mobile;
second, he shows that it is divided according to the parts of time, at “motion is also susceptible” (235a10; [811]).
The first he shows by three arguments.