LECTURE 10 (238 b 23-239 b 4)

THE DIVISION OF REST AND OF COMING TO REST

             851. After the Philosopher has treated those things which pertain to the division of motion, he here treats those things which pertain to the division of rest. And since 'coming to rest' is the generation of rest, as was said in Book V, he first treats those things which pertain to 'coming to rest'. Secondly, where he says, 'Nor again can there . . .' (239 a 10), he treats those things which pertain to rest.

             Concerning the first part he makes three points. First he shows that whatever is 'coming to rest' is being moved. Secondly, where he says, 'From this it evidently . . .' (238 b 27), he shows that whatever is 'coming to rest' is 'coming to rest' in time. Thirdly, where he says, 'And that which is . . .' (238 b 31), he explains how there is a first in 'coming to rest'.

             852. He shows the first point as follows. Whatever is naturally subject to motion must be either in motion or at rest at the time and in the respect and in the manner in which it is naturally subject to motion. But that which is 'coming to rest', that is, that which tends toward rest, is not yet at rest. For otherwise a thing would simultaneously be tending toward rest and be at rest. Therefore, whatever is 'coming to rest', that is, whatever is tending toward rest, is being moved while it is 'coming to rest'.

             853. Next where he says, 'From this it evidently . . .' (238 b 27), he proves with two arguments that whatever is 'coming to rest' is 'coming to rest' in time. The first argument is as follows. Whatever is moved is moved in time, as was proven above. But whatever is 'coming to rest' is being moved, as we have just now proven. Therefore, whatever is 'coming to rest' is 'coming to rest' in time.

             The second argument is as follows. Fastness and slowness are determined according to time. But 'coming to rest', that is, tending toward rest, occurs faster and slower. Therefore whatever is 'coming to rest' is 'coming to rest' in time.

             854. Next where he says, 'And that which is . . .' (238 b 31), he explains how there is a first in 'coming to rest'.

             Concerning this he makes two points. First he explains how a thing is said to come to rest in a primary time, insofar as the primary is opposed to that which is called partial. Secondly, where he says, 'And just as there . . .' (238 b 38), he shows that there is no primary part in 'coming to rest'.

             He says, therefore, first that if in some time a thing is said to be 'coming to rest' primarily and per se, it must be 'coming to rest' in every part of that time. Let the time be divided into two parts. If it be said that it is not 'coming to rest' in either part, it follows that it is not 'coming to rest' in the whole time in which it was given as 'coming to rest'. Therefore, that which is 'coming to rest' is not 'coming to rest'.

             Nor can it be said that it is 'coming to rest' in only one part of the time. For then it would not be primarily 'coming to rest' in the whole time, but only by reason [ratio] of a part. Hence it follows that it is 'coming to rest' in both parts of the time. Thus it is said to be 'coming to rest' primarily in the whole time because it is 'coming to rest' in both parts of the time, as was said above of that which is being moved.

             855. Next where he says, 'And just as there . . .' (238 b 38), he shows that there is no first part in 'coming to rest'.

             He says that just as there is no primary part of time in which a mobile body is being moved, likewise there is no primary part in 'coming to rest'. For neither in 'being moved' nor in 'coming to rest' can there be a primary part.

             If this is not conceded, let A B be a primary part of time in which something is 'coming to rest'. A B cannot be indivisible. For it was shown above that there is no motion in an indivisible time, because that which is being moved has always already been moved through something, as was shown above. Further, it has just now been demonstrated that whatever is 'coming to rest' is being moved. Hence it follows that A B is divisible. Therefore the body is 'coming to rest' in every part of A B. For it was just shown that when in some time a thing is said to be 'coming to rest' primarily and per se, and not by reason [ratio] of a part, then it is 'coming to rest' in every part of that time. Therefore, since the part is prior to the whole, A B is not the first thing in which the body was 'coming to rest'. But everything in which something is 'coming to rest' is a time. And no time is indivisible, rather every time is infinitely divisible. Therefore, it follows that there will be no first in which a thing is 'coming to rest'.

             856. Next where he says, 'Nor again can there . . .' (239 a 10), he shows that the same is true of rest.

             Concerning this he makes two points. First he shows that there is no first in rest. Secondly, where he says, 'And since everything . . .' (239 a 23), he considers a point which distinguishes motion from rest.

             Since the same argument explains why there is no first in motion, 'coming to rest', and rest, therefore from the things which he has said above about motion and 'coming to rest' he concludes that the same is true of rest. He says that there is no first in which that which is at rest is at rest. To prove this he repeats a certain point which was proven above; namely, nothing is at rest in the indivisible of time. He also repeats two arguments by which this was proven above.

             The first is that there is no motion in the indivisible of time. But 'being moved' and 'being at rest' occur in the same thing. For we speak of 'being at rest' only when that which is naturally subject to motion is not being moved at the time and in the respect (for example, in respect to a quality or place or some such thing) in which it is naturally subject to motion. Therefore it follows that nothing is at rest in the indivisible of time.

             The second argument is as follows. We say that a thing is at rest when it is the same now as it was before. Thus we do not judge a state of rest by only one instance, but by a comparison of two instances to each other such that there is the same state in the two instances. But in the indivisible of time there is no now and before; there are not two instances. Therefore that part of time in which a thing is at rest is not indivisible.

             Having proven this he proceeds to the proof of his main point. If that in which a thing is at rest is divisible, having in itself a prior and a posterior, it follows that this is a time. For this is the nature [ratio] of time. And if this is a time, then the body must be at rest in every part of that time. He will demonstrate this in the same way that he argued above in regard to motion and 'coming to rest'. If the body is not at rest in every part, then it is at rest either in no part or in only one part. If it is at rest in no part, then it is not at rest in the whole. If it is at rest in only one part, then it is at rest primarily in that part and not in the whole. If the body is at rest in every part of the time, then there will be no first in rest, just as there is no first in motion.

             The reason for this is that everything is at rest or in motion in time. But in time there is no first, just as there is no first in magnitude or in any continuum. For every continuum is infinitely divisible, and thus before any part there is always a smaller part. And thus there is no first in motion or in 'coming to rest' or in rest.

             857. Next where he says, 'And since everything . . .' (239 a 23), he considers a certain point which distinguishes that which is being moved from that which is at rest.

             First he states his point, and secondly he proves it, where he says, 'For if a thing . . .' (239 a 27).

             In regard to the first part he sets forth two suppositions. The first is that whatever is moved is moved in time. The second is that whatever is changed is changed from one terminus to another. From these two propositions he intends to draw this conclusion: if a mobile body is moved primarily and per se, and not just by reason [ratio] of a part, it cannot exist in respect to some one and the same state of that in which the motion occurs (for example, in one and the same place or in one and the same disposition of whiteness) in some time (taking the time in itself and not in respect to some part of time).

             It is necessary to take 'mobile body' here as meaning 'that which is moved primarily'. For nothing prevents a body being moved in respect to a part while the body itself remains through the whole time in one and the same place. For example, a man who is sitting moves his foot.

             Further in respect to the time he says, '. . . when its motion is comprised within a particular period of time essentially--that is to say when it fills the whole and not merely a part of the time in question . . .' (239 a 24-25). For while a thing is being moved, it can be said to be in some one and the same place on a certain day. But this is said because it was in that place, not during the whole day, but in some 'now' of that day.

             858. Next where he says, 'For if a thing . . .' (239 a 27), he proves his position.

             He says that if that which is changed is through some whole time in some one and the same state, for example, in one place, it follows that it is at rest. For in a certain time both the body itself and each of its parts are in one and the same place. And it was said above that a body is at rest when it can be truly said that it and its parts are in one and the same state in different 'nows'. Hence, if this is the definition of 'being at rest', and if a body is not simultaneously in motion and at rest, then it follows that that which is being moved is not totally in something, for example, in one and the same place, in respect to some whole time, and not just some part of time.

             He explains why this follows. All time is divisible into diverse parts, one of which is prior to another. Hence, if through a whole time a body is in some one thing, it will be true to say that in the different parts of time the mobile body and its parts are in one and the same thing, for example, place. But this is 'being at rest'. For if it is said that in the diverse parts of time the body is not in one and the same state, but is in one and the same state only through one 'now', it does not follow that there is a time in which it is in one and the same thing. Rather it follows that it is in one and the same thing in respect to the 'now'.

             Moreover, although it follows that a thing is at rest if it is in one and the same state in time, nevertheless this does not follow if it is there in only one 'now'. For in each 'now' of a time in which there is motion that which is being moved remains or exists in respect to that in which the motion occurs, for example, in respect to place or quality or quantity. However, it is not at rest, for it has already been shown that there is no rest or motion in the 'now'. Rather it is true to say that nothing is being moved in the 'now'. And in this 'now' even that which is being moved is somewhere accidentally.

             But that which is being moved is not at rest accidentally in time. For otherwise, while a thing is being moved, it would be at rest. This is impossible. It follows, therefore, that that which is being moved, while it is being moved, is never in one and the same state through two 'nows', but only through one.

             859. This is clear in local motion. Let there be a magnitude A C which is divided in half at B. And let there be a body O which is equal to each of these, that is, A B and B C. And let O be moved from A B to B C. If these places are taken as totally distinct from each other, then there are only two places here. But it is clear that the mobile body leaves the first place and enters the second place successively and not all at once. Hence, insofar as place is divisible to infinity, the number of places is multiplied to infinity. For if A B is divided in half at D, and if B C is divided in half at E, it is clear that D E will be a place different from both A B and B C. And if this division is carried on infinitely in the same way, there will always be another place.

             The same thing is also clear in alteration. For that which changes from white to black crosses through infinite grades of whiteness, blackness, and intermediate colours.

             However, although there are an infinity of intermediaries, it does not follow that the body will not arrive at the extremity. For these middle places are not infinite in act, but only in potency, just as magnitude is not actually divided to infinity, but is divisible in potency.