LECTURE 7 (235 b 6-236 b 19)

THE PART OF TIME IN WHICH A THING HAS FIRST BEEN MOVED IS INDIVISIBLE. HOW THERE CAN BE A FIRST MOTION

             818. After the Philosopher has shown how motion is divided, he here treats the order of the parts of motion.

             First he inquires whether there is a first in motion. Secondly, where he says, 'Now everything that changes . . .' (236 b 20), he explains how the things that are in motion precede each other.

             Concerning the first part he makes two points. First he shows that that in which something has first been changed is indivisible. Secondly, where he says, 'But there are two . . .' (236 a 7), he explains how there can be a first in motion and how not.

             Concerning the first part he makes two points. First he sets forth a certain thing which is necessary to prove his position. Secondly, where he says, 'We will now show . . .' (235 b 32), he establishes his position.

             Concerning the first part he makes two points. First he states his intention. Secondly, where he says, 'For that which changes . . .' (235 b 8), he proves his position.

             819. He says, therefore, first that, since whatever is changed is changed from one terminus to another, then whatever is changed, when it has already been changed, must be in the terminus to which.

             Next where he says, 'For that which changes . . .' (235 b 8), he proves this with two arguments. The first argument is particular, the second universal.

             The first argument is as follows. Whatever is changed must either leave the terminus from which it is changed (as is clear in local motion in which the place from which it is changed remains, and the mobile body is moved to some distance from it), or else the terminus from which must be removed (as in alteration, for when something becomes black from white, the whiteness leaves). To clarify this statement he adds that to be changed is either identical with 'leaving' or else is consequent upon 'leaving'. And thus to have been changed is consequent upon 'having left' the terminus from which. Moreover, it is clear that these are the same in subject but different in reason [ratio]. For 'to leave' refers to the terminus from which, but change is denominated by the terminus to which. And to clarify what he has said he adds, '. . . for there is a like relation between the two in each case' (235 b 12); that is, 'to have left' is related to 'to have been changed' in the same way that 'to leave' is related to 'to be changed'.

             From the foregoing he argues to prove his position in regard to one species of change. This is the change between contradictory opposites, that is, between being and non-being, as is clear in generation and corruption. It is clear from the foregoing that whatever is being changed leaves the terminus from which. It is also clear that whatever has been changed has already left the terminus from which. Hence, when something has been changed from non-being to being, it has already left non-being. But it can be truly said of anything that it is either being or non-being. Therefore, that which has been changed from non-being to being is in being when it has been changed. And likewise, that which has been changed from being to non-being must be in non-being. Hence it is clear that, in change in respect to contradictories, that which has been changed is in that to which it has been changed. And if this is true of this type of change, then it is also true for the same reason of the other types of change. And hence that which was first stated is clear.

             820. He gives the second, general argument where he says, 'Moreover if we take . . .' (235 b 18). He says that this same thing can be made clear by considering each type of change. In local change this point is manifest.

             For whatever has been changed must be somewhere, either in the terminus from which or somewhere else. But since that which has been changed has already left that from which it has been changed, it must be somewhere else. Therefore it must either be in the terminus to which, which we intend to show, or in some other place. If it is in the terminus to which the point is proven. But if it is somewhere else, we are saying that something is being moved to B, but when it has been changed, it is not in B but in C. Then it must be said that it is also changed from C to B, for C and B are not consecutively related. For all mutations of this kind are continuous. And in a continuum one sign is not consecutively related to another, for there must be between them something else of the same genus, as was proven above. Hence, if that which has been changed, when it has been changed, is in C, and if it is being changed from C to B, which is the terminus to which, then it follows that, when it has been changed, it is being changed to that to which it has been changed. This is impossible. For 'being changed' and 'having been changed' are not simultaneous, as was said above. It makes no difference whether these termini C and B are taken to refer to local motion or to any other kind of mutation. Hence it is universally and necessarily true that that which has been changed, when it has been changed, is in that to which it has been changed, that is, the terminus to which.

             And from this he concludes further that that which has been made, when it has been made, has being; and that which has been corrupted, when it has been corrupted, is non-being. For this was universally shown of all mutation. And this is especially clear in mutation in respect to contradictories, as is clear from what has been said.

             Thus it is clear that that which has been changed, when it has first been changed, is in that to which it has been changed.

             He adds the word 'first'. For after it has been changed to something, it can be changed again, and thus would not be there. But when it has first been changed, it must be there.

             821. Next where he says, 'We will now show . . .' (235 b 32), he shows that that which has been changed primarily and per se is in an indivisible. He says that the time in which that which has been changed was primarily changed must be indivisible.

             He explains why he adds the word 'primarily'. A thing is said to have been changed in something primarily when it has not been changed in that something by reason [ratio] of any of the parts of the latter:--as when a mobile body is said to be changed in a day because it was changed in some part of that day. It is not changed primarily in that day. He proves as follows that the time in which something is primarily changed is indivisible.

             Let A C be divisible and divided at B. Now it must be said that the mobile body either has been changed in each part, or is being changed in each part, or else is being changed in one part and has been changed in the other part. But if it has been changed in each part, then it was not primarily changed in the whole, but in the part. If it be granted that the body is being changed in each part, then it must be said that it is being changed in the whole. For a thing is said to be changed in a whole time when it is changed in each part of that time. But this is contrary to our supposition. For it was assumed that the body has been changed in the whole A C. Moreover, if it be granted that the body is being changed in one part and has been changed in the other part, the same inconsistency follows. For it would not then have been primarily changed in the whole, because, since the part is prior to the whole and since a body is being changed in a part of time prior to the whole, it would follow that there is something prior to what is primary. This is impossible. Hence it must be said that the time in which something has primarily been changed is indivisible.

             From this he concludes further that whatever has been corrupted and whatever has been made was corrupted and made in an indivisible time. For generation and corruption are the termini of alteration. Hence, if any motion is terminated in an instant (to have been changed primarily is the same thing as motion being terminated), it follows that generation and corruption occur in an instant.

             822. Next where he says, 'But there are two . . .' (236 a 7), he explains how there can be a first in motion.

             Concerning this he does two things. First he proposes the truth, and secondly he proves it, where he says, 'For suppose that A D . . .' (236 a 16).

             He says, therefore, first that the expression 'that in which something is primarily changed' can be taken in two ways. First, this may mean that in which the mutation is primarily perfected or terminated. For it can truly be said that something has been changed when the mutation has already been completed. Secondly, this expression may be understood to mean that in which something first begins to be changed. In this sense it is not primarily true to say that it has already been changed.

             Speaking of motion in the first sense which refers to the termination of the mutation, there is a 'that in which something is primarily changed'. For it sometimes happens that a mutation is primarily terminated, because there is a terminus for any mutation. It is in this sense that we meant that that which primarily has been changed is indivisible. And this is clear for this reason: there is an end or terminus of motion. And the terminus of every continuum is indivisible.

             But if we take this expression in the second sense which refers to the beginning of change, that is, the first part of motion, then there is no 'that in which something is primarily changed'. For there is no first part of mutation which is not preceded by some other part. And likewise there is no first part of time in which something is primarily being changed.

             823. Next where he says, 'For suppose that A D . . .' (236 a 16), he proves that, in regard to the beginning, there is no first in which something is changed.

             First he proves this with an argument taken from time. Secondly, where he says, 'So, too, of that which . . .' (236 a 28), he proves this with an argument taken from the mobile body. And thirdly, where he says, 'With regard, however . . .' (236 b 1), he proves this with an argument taken from that in which the motion occurs.

             The first argument is as follows. Let A D be a time in which something is primarily changed. This time is either divisible or indivisible. If it is indivisible, two inconsistencies follow. The first is that the 'nows' in time would be consecutive. This inconsistency follows because time is divided in the same way as motion, as was shown above. If some part of the motion were in A D, then it must be said that A D is a part of the time. And thus time would be composed of indivisibles. But the indivisible unit of time is the 'now'. Hence it would follow that the 'nows' are consecutive to each other in time.

             The second inconsistency is as follows. Let us grant that in the time C A, which precedes the time A D, the mobile body, which was given as being moved in A D, is totally at rest. If it is at rest in the whole of C A, it follows that it is at rest in A, which is a part of C A. Hence if A D is indivisible, as was granted, it would follow that the body is simultaneously at rest and in motion. For it was concluded that it is at rest in A, and it was granted that it is being moved in A D. And if A D is indivisible, then A and A D are the same. Hence it would follow that the body is at rest and in motion at the same time.

             But it must be noted that, if something is at rest in a whole time, it does not follow that it is at rest in the ultimate indivisible part of that time. For it was shown above that in the 'now' nothing is in motion or at rest. But Aristotle concludes here from the point which was granted by his adversary; namely, that the time in which something is primarily moved is indivisible. And if it could happen that something is moved in the indivisible 'now' of time, it could happen for the same reason that something is at rest in the indivisible 'now' of time.

             Having denied that A D, in which something is primarily moved, is indivisible, it necessarily follows that it is divisible. And from the fact that something is primarily being moved in A D, it follows that it is being moved in every part of A D. He proves this as follows. Let A D be divided into two parts. Then the mobile body is being changed either in neither part, or in both parts, or in only one part. If it is being changed in neither part, it follows that it is not being changed in the whole. If it is being changed in both parts, then it can be held that it is being changed in the whole. But if it is being moved in only one part, then it would follow that it is being moved in the whole, not primarily, but by reason of the part. Therefore, since it was granted that the body is being moved primarily in the whole, it must be granted that it is being moved in each part of A D. But time is divided to infinity, as is true of any continuum. And thus there is always a smaller part prior to a greater part, for example, the day is smaller than the month, and the hour is smaller than the day. Hence it is clear that there is no time in which something is primarily being moved, that is, there is no part of time in which something is primarily being moved. Thus it cannot be held that a day is that in which something is primarily moved. For it is being moved in the first hour of that day before it is moved in the whole day.

             824. Next where he says, 'So, too, of that which . . .' (236 a 28), he proves the same thing by considering the mobile body. He concludes from the foregoing that in that which is being changed there is nothing which is being changed first. If this be understood in respect to the motion of the whole or a part, some determinate sign is crossed. For it is clear that the first part of the mobile body crosses a determinate sign first, and secondly a second part, and so forth. Further, he is not speaking here of absolute motion. For it is clear that the whole and all of its parts are moved simultaneously. But the mobile body does not cross a determinate sign all at once. Rather this always occurs part by part. Hence, just as there is no first part of the mobile body before which there is no other smaller part, likewise there is no part of the mobile body which is moved first. Since time and the mobile body are divided in the same way, as was shown above, he concludes in regard to the mobile body the same thing that was properly demonstrated of time. He proves this as follows.

             Let D E be a mobile body. Now since every mobile body is divisible, as was proven above, let D F be the part which is moved first. And D F is moved by crossing some determinate sign in the time H I. Hence, if D F has been changed in this whole time, then it follows that that which was changed in half this time was moved less than and prior to D F. And for the same reason there will be something else prior to this part, and again another prior to that, and so on to infinity. For time is divided to infinity. Hence it is clear that in the mobile body there is nothing which was changed first.

             And thus it is clear that there cannot be a first in motion either in respect to the time or in respect to the mobile body.

             825. Next where he says, 'With regard, however . . .' (236 b 1), he proves the same thing in regard to that in which the motion occurs.

             He says that 'that which is changed', or better, 'that in respect to which something is changed', is different than the time and the mobile body. For in a mutation there are three things: the mobile body which is changed, for example, a man; that in which it is changed, the time; and that to which it is changed, for example, white. Two of these, the time and the mobile body, are infinitely divisible. But in regard to 'white' there is a different nature [ratio]. For 'white' is not divisible per se. Rather 'white' and all other such things are divisible per accidens, insofar as that of which 'white' or any other quality is an accident is divisible.

             The per accidens division of 'white' can occur in two ways. First, in respect to quantitative parts. For example, when a white surface is divided into two parts, the 'white' will be divided per accidens. Secondly, in respect to intention and remission. For the fact that one and the same part is more or less white is not due to the very nature [ratio] of whiteness. (If whiteness were separated, it would not be called more or less white, just as no substance is susceptible to more or less.) Rather this is due to the diverse modes of participating whiteness by a divisible subject. Hence, omitting that which is divided per accidens, if we take things in respect to which there is motion and which are divided per se and not per accidens, then also in these things there is no first.

             He makes this clear first in regard to the magnitude in which local motion occurs. Let there be a spatial magnitude which includes A B. And let this magnitude be divided at C. And let it be granted that something is moved first from B to C. Now B C is either divisible or indivisible. If it is indivisible, it follows that an indivisible will be joined to an indivisible, because for the same reason the second part of the motion will be in an indivisible. For, as was said above about time, it is necessary to divide magnitude and motion in the same way. But if B C is divisible, there will be some sign closer to B than C is. And thus the body will be changed to that sign before it is changed to C. And again there will be something prior to that sign, and so on to infinity. For the division of magnitude is endless. Therefore it is clear that there is no first to which the body has been changed by local motion.

             This is likewise clear in the mutation of quantity, which is increase and decrease. For this is also a mutation in respect to a continuum, that is, in respect to a quantity which is growing or decreasing. Since such a quantity is divisible to infinity, there is in it no first.

             And thus it is clear that only in qualitative mutation can there be something which is indivisible per se. Nevertheless, insofar as a quality is divisible per accidens, there is likewise no first in such a mutation. For there is either a succession of mutation insofar as a part is altered after another part (for it is clear that there is no first part of 'white' just as there is no first part of magnitude), or else there is a succession of alteration insofar as the same thing is either more white or less white. For a subject can variously be more white and less white in an infinity of ways. And thus alteration can be continuous and not have a first.