Commentary Aristotle Physics
Lecture 10. The division of rest and of coming to rest
Since everything to which motion or rest is natural is in motion or at rest in the natural time, place, and manner, what is coming to rest, when it is coming to rest, must be in motion.
For if it is not in motion it must be at rest; but that which is at rest cannot be coming to rest.
From this, it evidently follows that coming to rest must occupy a period of time.
For the motion of that which is in motion occupies a period of time, and that which is coming to rest has been shown to be in motion; consequently, coming to rest must occupy a period of time.
Again, since the terms “quicker” and “slower” are used only of that which occupies a period of time, and something may come to rest either more swiftly or more slowly, the same conclusion follows.
And that which is coming to rest must be coming to rest in any part of the first time in which it is coming to rest.
For if it is coming to rest in neither of two parts into which the time may be divided, it cannot be coming to rest in the whole time, with the result that what is coming to rest will not be coming to rest.
If, on the other hand, it is coming to rest in only one of the two parts of the time, the whole cannot be the first time in which it is coming to rest.
For it is coming to rest in the whole time not first, but in virtue of something distinct from itself, the argument being the same as that we used above about things in motion.
And, just as there is no first time in which that which is in motion is in motion, so too there is no first time in which that which is coming to rest is coming to rest, there being no first stage either of being in motion or of coming to rest.
For let AB be the first time in which a thing is coming to rest.
Now, AB cannot be without parts, for there cannot be motion in that which is without parts, because the moving thing would necessarily have been already moved for part of the time of its motion, and that which is coming to rest has been shown to be in motion.
But, since AB is therefore divisible, the thing is coming to rest in every one of the parts of AB, for we have shown above that it is coming to rest in every one of the parts in which it is primarily coming to rest.
Since, then, that in which primarily a thing is coming to rest must be a period of time and not something indivisible, and since all time is infinitely divisible, there cannot be anything in which primarily it is coming to rest.
Nor, again, can there be a first time at which the being at rest of that which is at rest occurred.
For it cannot have occurred in that which has no parts, because there cannot be motion in that which is indivisible, and that in which rest takes place is the same as that in which motion takes place.
For we defined a state of rest to be the state of a thing to which motion is natural but that is not in motion when (that is to say in that in which) motion would be natural to it.
Again, our use of the phrase “being at rest” also implies that the previous state of a thing is still unaltered, not one point only but two at least being thus needed to determine its presence.
Consequently, that in which a thing is at rest cannot be without parts. Since, then, it is divisible, it must be a period of time, and the thing must be at rest in every one of its parts, as may be shown by the same method as that used above in similar demonstrations.
So, there can be no first part of the time; the reason is that rest and motion are always in a period of time, and a period of time has no first part any more than a magnitude or, in fact, anything continuous, for everything continuous is divisible into an infinite number of parts.
And, since everything that is in motion is in motion in a period of time and changes from something to something, when its motion is in a time throughout which something is being moved per se and not by reason of some element of time, then it is impossible that, in that time, that which is in motion should be over against some mobile that is being moved first.
For if a thing—itself and each of its parts—occupies the same space for a definite period of time, it is at rest, for it is in just these circumstances that we use the term “to be at rest,” when, at one moment after another, it can be said with truth that a thing, itself and its parts, occupies the same space.
So, if this is being at rest, it is impossible for that which is changing to be as a whole, during the first time, in one state (for the whole period of time is divisible), such that, in one part of it after another, it will be true to say that the thing, itself and its parts, occupies the same space.
If this is not so, and the given proposition is true only at a single moment, then the thing will be in one state not for any period of time, but only at a moment that limits the time. It is true that, at any moment, it is always over against something stable, but it is not at rest, for at a moment, it is not possible for anything to be either in motion or at rest.
So, while it is true to say that that which is in motion is at a moment not in motion and is according to something, it cannot in a period of time be over against that which is at rest, for that would involve the conclusion that that which is in locomotion is at rest.
851. After finishing the things that pertain to the division of motion, the Philosopher now determines about things that pertain to the division of rest. And, because coming to rest is generation of rest, as we have said in book 5, first, he determines the things that pertain to coming to rest;
second, he determines the things that pertain to rest, at “nor, again, can there” (239a10; [856]).
About the first, he does three things:
first, he shows that whatever is coming to rest is being moved;
second, he shows that whatever is coming to rest does so in time, at “from this, it evidently” (238b26; [853]);
third, he shows how a first is spoken of in coming to rest, at “and that which is” (238b31; [854]).
852. He shows the first (238b23) thus. Everything apt to be moved must be either in motion or at rest at the time when it is apt to be moved and in the place in which it is apt to be moved and in the way in which it is apt to be moved. But what is coming to rest is not yet at rest—otherwise, it would happen that a thing would be at the same time coming to rest and at rest. Therefore, whatever is coming to rest is in motion while it is coming to rest.
853. Then, at “from this, it evidently” (238b26), he proves by two arguments that whatever is coming to rest is doing so in time.
This is the first. Whatever is being moved is being moved in time, as has been proved. But whatever is coming to rest is being moved, as we have just proved. Therefore, whatever is coming to rest is coming to rest in time.
The second argument is that swiftness and slowness are determined according to time. But it can happen that something may come to rest either more swiftly or more slowly. Therefore, whatever is coming to rest does so in time.
854. Then, at “and that which is” (238b31), he shows how first is spoken of in coming to rest.
About this, he does two things:
first, he shows how something is said to be first coming to rest in a given time, where “first” is opposed to what is spoken of in reference to a part;
second, he shows that, in coming to rest, it is not possible to discern a first part, at “and, just as there” (238b36; [855]).
He says first (238b31) that, if at a certain time something is said to be coming to rest first and per se and not by reason of a part, then it must be coming to rest in each part of that time.
For time can be divided into two parts, and if it is said that it is coming to rest in neither, it will follow that it is not coming to rest in the whole time, in which it was assumed to be coming to rest.
Therefore, something coming to rest is not coming to rest. Nor can it be said that it is coming to rest in only one of the parts, for then it would not be coming to rest first, but only by reason of a part.
Hence, it will remain that it is coming to rest in both. For it is said to be coming to rest in the whole time only because it is coming to rest in each part, as was said above about things in motion.
855. Then, at “and, just as there” (238b36), he shows that there is no first part in coming to rest. And he says that, just as it is not possible to find in time a first part in which a mobile is being moved, so also in regard to coming to rest, for in neither case can there be a first part.
If this is denied, then let AB be the first part of time in which something is coming to rest. This part cannot be indivisible, because it has been shown above that motion does not occur in an indivisible of time (for it is always true that whatever is being moved has already been moved, as we have shown above), and moreover, whatever is coming to rest is being moved, as we have just now proved.
Hence, AB must be divisible. Therefore, there is a coming to rest in each part of it, for we have just shown that, when, in a given time, something is coming to rest first and per se, and not by reason of a part, it is coming to rest in each part of that given time.
Therefore, since the part is prior to the whole, AB was not the first in which there was a coming to rest. And, because that in which something is coming to rest is a time and all time is divisible to infinity, it follows that it is impossible to find a first in which something is coming to rest.
856. Then, at “nor, again, can there” (239a10), he shows that the same thing is true for rest.
About this, he does two things:
first, he shows that there is no first in rest;
second, he gives a method to distinguish motion from rest, at “and, since everything” (239a23; [857]).
And, because it is for the same reason that no first is found in motion and in coming to rest and in rest, therefore he concludes the same thing for rest as he concluded for motion and coming to rest. And he says that there is no first in which a thing at rest has been at rest. To prove this, he repeats something previously proved: nothing is at rest in an indivisible of time.
Likewise, he repeats the two reasons he used when he proved this.
The first of these is that there is no motion in an indivisible of time. But to rest and to be in motion are in the same, because we do not say that something is resting unless what is capable of being moved is not being moved when it is apt to be moved and in that in which it is apt to be moved (for example, quality or place or something of this sort). Hence, it remains that nothing is at rest in an indivisible of time.
The second reason is that we say something is at rest when it maintains itself as it was previously—as if to say that we do not judge rest by reason of one thing only, but by comparing two things to one another and seeing that there is a similar situation in both. But it is impossible to find a now and something previous in something indivisible, or to find any two things. Therefore, that element of time in which something is at rest is not indivisible.
Having established this, he proceeds further to prove the main proposition. For if that in which something is at rest is divisible into parts that possess a prior and a subsequent, it follows that it is a time; for this is the very account of time. And, if it is time, then it must be resting in each part of it. And this will be demonstrated in the same way that it was demonstrated in motion and in coming to rest: if it is not at rest in each part, it will be at rest in no part or in one only. If it is in no part, then not in the whole; if in one only, then in that part first and not in the whole first. But, if it is at rest in each part of the time, it will not be possible to discover a first in rest any more than in motion.
The reason for this is that things are at rest and in motion in time. But, in time, there is no first any more than in a magnitude or in any continuum, for every continuum is divisible to infinity, and consequently, it is always possible to find a part smaller than another. And that is why there is no first in motion or in coming to rest or in rest.
857. Then, at “and, since everything” (239a23), he gives a way through which what is in motion is distinguished from what is at rest.
First, he mentions it;
second, he proves it, at “for if a thing” (239a26; [858]).
In regard to the first, he gives two suppositions, the first of which is that whatever is being moved is being moved in time.
The second is that whatever is being changed is being changed from one terminus to another.
From these two things, he intends to conclude a third: if you take a mobile that is being moved first and per se and not by reason of its part only, it cannot remain one and the same with respect to that in which the motion is—for example, it cannot remain in one and the same place, or retain one and the same degree of whiteness—during a given period of time, provided that you take it as being in time according to itself and not according to something that is in time.
The reason why you must take a mobile that is being moved first and per se is that there is nothing to prevent a thing from being moved according to a part even though it remains in one and the same place throughout the entire time, as when a man sitting down moves his foot.
And the reason that he speaks of a time throughout which something is being moved per se and not by reason of some element of time is that, while a thing is being moved, it can be said that, on such and such a day, it is in one and the same place; but this would be said because it was in that place not throughout the day, but in some now of that day.
858. Then, at “for if a thing” (239a26), he proves the proposition. And he says that, if what is being changed is, throughout a definite period of time, in one and the same state—for example, in one place—it follows that it is at rest, due to the fact that, in that time, there is present in one and the same place the entire mobile and each part of it; for we have already said that this is to be at rest: when it is true to say of something that it and its parts are in one and the same state in different nows. If, therefore, this is the definition of being at rest, and if nothing can be at rest and in motion at the same time, it follows that the whole that is being moved cannot be totally in one state—for instance, in one and the same place—during the first time (that is, the whole time), not only in some part of it.
Why this follows he now explains. Every period of time is divisible into diverse parts, of which one is prior to another. Hence, if something is in one state throughout the entire period, it will be true to say that, in one and in another part of the time, the whole mobile and its parts are in one and the same state, such as place—and this is to be at rest. For if it is said to be in one and the same state not in different parts of time, but throughout one now, it does not follow that there is a time in which it is in one and the same state, but only at a moment in which it is in one and the same state.
For although the conclusion can be drawn that something is at rest from the fact that it remains in one and the same state during a period of time, that conclusion cannot be drawn if it remains in one and the same state in just one now.
For whatever is being moved is always stable—that is, existing—according to something of that in which it is being moved in each now of the time in which it is being moved (for example, place or quality or quantity). Yet it is not for that reason at rest, because it has already been proved that neither rest nor motion can occur in a now. But it is true to say that, in the very now, something is not being moved and that, in the now, even what is being moved is somewhere or according to something. But what is being moved in time cannot be under any aspect at rest, for then it would happen that something is at rest while it is in motion—which is impossible. What remains, therefore, is that whatever is being moved is never, as long as it is being moved, in one and the same state for two nows, but for only one.
859. And this point is clear in local motion. For let AC be a magnitude divided in half at B, and let O be a body equal to each half (to AB and to BC), and let that body be moved from AB to BC. If no part of one of these two places can be a part of the other, there will be only two places for that body on AC. But it is evident that O does not relinquish its first place and enter the second all at once, but successively. Hence, because place is divisible to infinity, the places also are multiplied to infinity. For if the half part AB is again halved at D, and the other half part BC at E, it is evident that DE will be a place distinct from both AB and BC. By continuing such divisions, different places will be found.
The same point is clear in alteration. For what passes from white to black passes through an infinitude of shades of whiteness and blackness and intermediate colors.
However, it does not follow that, since there are an infinitude of intermediates, the ultimate cannot be reached, because these intermediate places are infinite not in act, but only in potency, just as a magnitude is not actually divided infinitely, but is potentially divisible.