LECTURE 8 (236 b 20-237 b 23)

BEFORE EVERY 'BEING MOVED' THERE IS A 'HAS BEEN MOVED'. AND BEFORE EVERY 'HAS BEEN MOVED' THERE IS A 'BEING MOVED'

             826. After the Philosopher has shown in what sense there is a first in motion and in what sense not, he here explains the mutual order of things found in motion.

             First he sets forth a certain point which is necessary for the proof of his position. Secondly, where he says, 'And now that this . . .' (236 b 34),

he proves his position.

             827. He says, therefore, first that whatever is changed is changed in time, as was shown above. But a thing is said to be changed in time in two ways: first, primarily and per se; and secondly, in respect to another, that is, by reason of a part, as when a thing is said to be changed in a year because it was changed in a day.

             Having made this distinction, he states what he intends to prove; namely, if a thing is changed primarily in some time, it must be changed in every part of that time. He proves this in two ways.

             He proves this first from the definition of 'primary'. For something is said to happen to a thing primarily when it happens to it in respect to each of its parts, as was said at the beginning of Book V.

             Secondly he proves this same thing with the following argument. Let V Q be a time in which something is primarily moved. And since every time is divisible, let V Q be divided at J. It must be said that in that part of the time which is V J the body is either moved or not moved. The same is true of the part J Q. If it be granted that the body is moved in neither of these parts, it follows that it is not moved in the whole V Q, but is at rest in V Q. For it is impossible for a thing to be moved in a time in no part of which it is moved. Moreover, if it be granted that the body is moved in one part of the time, but not in the other, then it would follow that it is not moved primarily in the time V Q. For the body must be moved in respect to each part, and not in respect to just one part. Therefore, it must be said that it is moved in every part of the time V Q. And this is what we wished to demonstrate; namely, when a thing is moved primarily in some time, it is moved in every part of that time.

             828. Next where he says, 'And now that this . . .' (236 b 34), he proceeds to the proof of his main point. Concerning this he does two things. First he brings in demonstrations to prove his position. Secondly, where he says, 'So that which has . . .' (237 b 3), he concludes to the truth which has been determined.

             Concerning the first part he makes two points. First he shows that, before every 'being moved', there is a 'has been moved'. Secondly, where he says, 'And not only must . . .' (237 a 17), he shows conversely that before any 'has been moved', there is a 'being moved'.

             829. He proves the first point with three arguments. The first is as follows. Let it be granted that a mobile body is moved through the magnitude J K in the primary time V Q. Now it is clear that another mobile body, which is of equal velocity and which began to be moved simultaneously with the first body, will be moved through half this magnitude in half the time. And since the first mobile body, which was given as being moved through the whole magnitude, has the same velocity, it follows that in half the time V Q it also was moved through the same magnitude, that is, through part of the whole magnitude J K. Hence it follows that that which is being moved previously was moved.

             In order that that which is said here be understood more clearly, it should be realized that 'having been moved' is said to be the terminus of a motion in the same way that a point is said to be the terminus of a line. For whatever line or part of a line you might take, it can always be said that, before the whole line ends, there is some point in respect to which the line is divided. And likewise before any motion, or any part of a motion, there is something which has been changed. For while the mobile body is in the state of being moved to some terminus, it has already crossed some sign in respect to which it is said to be already changed. Further, a point within a line is in potency before the line is divided, but it is in act when the line has been divided. For a point is the division of the line. Likewise, that which I call a 'has been changed' within a motion is in potency when the motion is not terminated there. But it is in act if the motion is terminated there. And since that which is in act is better known than that which is in potency, Aristotle proved that that which is continuously being moved has already been moved by means of another mobile body of equal velocity whose motion was already terminated. It would be the same situation if one were to prove that in some line there is a point in potency by means of another line of the same nature [ratio] which is actually divided.

             830. He gives the second argument where he says, 'Again, if by taking . . .' (237 a 4). The argument is as follows.

             In the total time V Q, or in any other time, a thing is said to have been moved because there is an ultimate 'now' of that time. This does not mean that the body is moved in that 'now', but that the motion is terminated in that 'now'. Hence, by 'having been moved' he here means the termination of the motion and not the state of 'being moved at some time'. Therefore, the motion must be terminated in the ultimate 'now' of the time which measures the motion. For this 'now' determines the time; that is, it is the terminus of the time, just as a point is the terminus of a line. And every time must be an intermediate between two 'nows', just as a line is an intermediate between two points. Hence, since 'being moved' is in time, it follows that 'having been moved' is in the 'now', which is the terminus of the time. And if this is true of the motion which occurs in the total time, it must likewise be true of the parts of the motion which occur in part of the time. For it was already shown that that which is moved primarily in a total time is moved in each part of that time. Further, any given part of time is terminated at some 'now'. For the extremity of half of a time must be a division, that is, a 'now', which divides the two parts of the time. For this reason it follows that that which is moved through a whole was previously moved in the middle, because the 'now' determines the middle. And the same argument applies to any other part of the time. For no matter how time is divided, it is always found that every part of time is determined by two 'nows'. And no matter what 'now' is taken after the first 'now' of the time which measures the motion, the body has already been moved in that 'now'. For any 'now' that is taken is the terminus of the time which measures the motion.

             Every time is divisible into other times. Every time is an intermediate between two 'nows'. And, as has been proven, the body has been changed in every 'now' which is an extremity of the time which measures the motion. Because of this it follows that whatever is being changed has been changed an infinite number of times. For 'having been changed' is the terminus of a motion, just as a point is the terminus of a line, and as a 'now' is the terminus of a time.

             In any line an infinite number of points can be designated before the last point. And in any time an infinite number of 'nows' can be designated before the last 'now'. For both of these are divisible to infinity. In the same way in any 'being moved' an infinite number of 'having been moved' can be designated. For a motion is divisible to infinity, just as is a line or a time, as was proven above.

             831. He gives the third argument where he says, 'Again, since a thing . . .' (237 a 12). The argument is as follows.

             Whatever is being changed continuously, as long as it is not corrupted or does not cease to be moved, must either be 'being moved' or 'having been moved' in every 'now' of the time in which it is moved. But it is not being moved in the 'now', as was shown above. Therefore it is necessary that it has been moved in every 'now' of the time which measures this continuous motion. But in any time there is an infinity of 'nows'. For the 'now' is the division of time, and time is infinitely divisible. Therefore, whatever is being changed has been changed an infinite number of times. And thus it follows that before every 'being moved' there is a 'has been moved', not as if it existed outside of the 'being moved', but in it as terminating one of its parts.

             832. Next where he says, 'And not only must . . .' (237 a 17), he proves conversely that before every 'has been moved' there is a 'being moved'.

             He proves this first in respect to the time, and secondly in respect to the thing according to which the motion occurs, where he says, 'Moreover, the truth . . .' (237 a 28).

             Concerning the first part he makes three points. First he states his position. Secondly, where he says, '. . . since everything that has changed . . .' (237 a 19), he demonstrates a certain thing which is necessary to prove his position. Thirdly, where he says, 'Since, then, it has changed . . .' (237 a 25), he brings forth the proof of his main position.

             He says, therefore, first that not only is it necessary that whatever is being changed already has been changed, but it is also necessary that whatever has been changed was previously being changed. For 'having been changed' is the terminus of 'being moved'. Hence, before a thing has been changed, there must be a preceding 'being moved'.

             833. Next where he says, '. . . since everything that has changed . . .' (237 a 19), he gives a certain point which is necessary for the proof of his position. This point is that whatever is changed from something to something has been changed in time.

             It must be noted that 'having been changed' does not here mean the same thing as 'motion being terminated'. For it was shown above that that part of time in which a thing is said primarily to have been changed is indivisible. Rather, 'having been changed' here means that the thing was previously being moved: as if one were to say that whatever was being moved was being moved in time.

             He proves this as follows. If this were not true, then the thing would have been changed in a 'now' from A to B, that is, from one terminus to another. Granting this, it follows that when it is in A, the terminus from which, it has not yet been changed in that 'now'. For it was shown above that that which is changed, when it has been changed, is not in the terminus from which but in the terminus to which. Hence it would follow that the mobile body would be in A and in B simultaneously. Hence it must be said it is in A in one 'now' and has been changed in another 'now'. But between any two 'nows' there is an intermediate time. For two 'nows' cannot be immediately joined to each other, as was shown above. Thus it follows that whatever is changed is changed in time.

             834. However it seems that this conclusion indicates that generation and corruption occur in an instant and that there is no intermediary between the termini of generation and corruption. For if between the 'now' when the body is in the terminus from which and the 'now' when the body is in the terminus to which there is an intermediate time, it would then follow that there is an intermediary between being and non-being. For in that intermediate time that which is changed is neither being nor non-being.

             But since the argument given here is demonstrative, it must be said that in a way it applies even to generation and corruption. For even these mutations in a way occur in a short period of time [momentaneae], although there cannot be any intermediary between their extremes.

             Therefore it must be said that that which is changed from non-being to being, or vice versa, is not simultaneously in both non-being and being. But, as will be said in Book VIII, this does not mean that there is an ultimate instant in which that which is being generated is non-being. Rather this means that there is a first instant in which it is being, such that in the whole time which precedes that instant it is non-being. And between the time and the instant that terminates the motion there is no intermediary. Thus it is not necessary that there be an intermediary between being and non-being. Rather, since the time which precedes the instant in which the body was first generated measures some motion, it follows that just as that instant in which the body was first generated is the terminus of the preceding time which measures the motion, likewise 'to begin to be' is the terminus of the preceding motion.

             Therefore, if this beginning of being be called generation, it is the terminus of a motion, and it occurs in an instant. For the termination of motion, which is the state of 'having been changed', occurs in an indivisible part of time, as was shown above.

             But if generation be taken to mean this beginning of being together with the whole preceding motion of which it is the terminus, then it does not occur in an instant, but in time. In the whole preceding time that which is generated is non-being, and in the ultimate instant it is being. And the same must be said of corruption.

             835. Next where he says, 'Since, then, it has changed . . .' (237 a 25), he proves his main point with the following argument.

             Whatever has been changed was changed in time, as has been proven. But all time is divisible. And that which is changed in some time is changed in every part of that time. Hence it must be said that that which has been changed in some whole time was previously being changed in half the time, and again in half of that half, and so on to infinity, for time is infinitely divisible. Hence it follows that whatever has been changed was previously being changed; and thus before every 'having been changed' there is a preceding 'being changed'.

             836. Next where he says, 'Moreover, the truth . . .' (237 a 28), he proves the same thing by means of an argument dealing with that in respect to which the change occurs.

             He does this first in respect to motions in quantity, and secondly in respect to the other mutations, where he says, '. . . for the same proof . . .' (237 a 35).

             He says, therefore, first that that which was said in common about all mutations from the point of view of time, can be more clearly understood from the point of view of magnitude. For magnitude is more evident than time. And magnitude is continuous, just as time is. And there is change in magnitude, both in respect to place and in respect to increase and decrease.

             Hence, let there be something which has changed from C to D. It cannot be said that the whole of C D is indivisible. For C D must be a part of some magnitude, just as the motion from C to D is a part of a whole motion. For magnitude and motion are divided in the same way, as was shown above. But if something which is indivisible is a part of a magnitude, it follows that two indivisibles would be immediately joined. This is impossible, as was shown above. Hence it cannot be said that the whole of C D is indivisible. Thus it must be that there is a certain magnitude between C and D, which consequently can be divided to infinity. But 'being changed' in part of a magnitude is always prior to 'having been changed' through the whole magnitude. Hence it must be that whatever has been changed previously was being changed, just as before any whole magnitude there must be a part of that magnitude.

             837. Next where he says, '. . . for the same proof . . .' (237 a 35), he shows that the same thing must be true of the other mutations. These latter do not occur in respect to something continuous. He is speaking of alteration, which occurs between contrary qualities, and of generation and corruption, which occur between contradictory opposites. For although in these cases his point cannot be demonstrated from the point of view of the thing in respect to which the motion occurs, nevertheless one can consider the time in which such mutations occur, and proceed in the same way.

             Hence in these three mutations, that is, alteration, corruption, and generation, only the first argument has value. But in the other three mutations, that is increase, decrease, and local motion, both arguments have value.

             838. Next where he says, 'So that which has . . .' (237 b 3), he concludes to his main point. He does this first in general, and secondly in a special way in respect to generation and corruption, where he says, 'So it is evident . . .' (237 b 10).

             He concludes, therefore, from the foregoing that whatever has been changed must previously have been 'being changed', and whatever is being changed must previously have been changed. And thus it is true to say that in the state of 'being changed' there is a previous 'having been changed', and in the state of 'having been changed' there is a previous 'being changed'. And hence it becomes clear that in no way is there a first.

             The reason for this is that in motion an indivisible is not joined to an indivisible such that the whole motion is composed of indivisibles. For if this were the case, there would be a first. But this is not true, because motion is divisible to infinity, just as a line is. Lines are infinitely diminished by division, and infinitely increased by the addition which is opposed to diminishing; that is, that which is subtracted from one line is added to another, as was shown in Book III. For in a line it is clear that before any part of that line there is a point in the middle of that part. And before that middle point there is another part of the line, and so on to infinity. Nevertheless the line is not infinite, because before the first point of the line there is no part of the line.

             Motion must be understood in the same way. For since any part of motion is divisible, then before any part of motion there is an indivisible in the middle of that part. This indivisible is a 'has been changed'. And before that indivisible there is a part of the motion, and so on to infinity. Nevertheless it does not follow that motion is infinite. For before the first indivisible of motion there is no part of the motion. However, that first indivisible is not called a 'having been changed', just as the first point of a line is not called a division.

             839. Next where he says, 'So it is evident . . .' (237 b 10), he concludes the same thing in a special way in regard to generation and corruption.

             He does this because in generation and corruption 'having been changed' is related to 'being changed' differently than in the other kinds of mutation.

             For in the other cases 'having been changed' and 'being changed' occur in respect to the same thing. Thus 'having been altered' and 'being altered' both occur in respect to white. For 'being altered' is 'being changed' in respect to whiteness. And 'having been altered' is 'having been changed' in respect to whiteness. And the same must be said of local motion and of increase and decrease.

             But in generation 'having been changed' occurs in respect to one thing, and 'being changed' occurs in respect to something else. For 'having been changed' occurs in respect to the form. But 'being changed' does not occur in respect to the negation of the form, which in itself is not susceptible to more and less. Rather 'being changed' occurs in respect to something joined to the negation which is susceptible of more and less. This is a quality. Therefore 'having been generated', and also 'having been corrupted', is the terminus of 'being altered'. And since a motion is named by the terminus to which, as was said at the beginning of Book V, this 'being altered', which has two termini--a substantial form and a quality--is named in two ways. For it can be called a 'being altered', and a 'becoming' and 'being corrupted'.

             And by 'becoming' and 'being corrupted' he here means that 'being altered' which is terminated at being or non-being. Hence he says, '. . . that which has become must previously have been in process of becoming, and that which is in process of becoming must previously have become, everything (that is) that is divisible and continuous' (237 b 10-12). This is added, as the Commentator says, to exclude certain things, that is, understanding and sensation, which occur indivisibly without a continuous motion. These things are called motions only equivocally, as is said in De Anima, III. Or else it can be said that the Philosopher adds this in order that generation be understood to include the whole preceding continuous motion.

             840. But that which becomes, having previously been made, is found in different things in different ways.

             For simple things, like air or fire, have a simple generation. In such things part is not generated before part. Rather the whole and the parts are generated and altered simultaneously. And in such things that which has been made was previously becoming itself and that which becomes previously has been made itself because of the continuity of the preceding alteration.

             However, certain things are composed of dissimilar parts, one part of which is generated after another. For example, in an animal the heart is generated first, and in a house the foundation is generated first. In such things that which becomes was previously made, not itself, but something else. He adds that that which becomes has not always been previously made itself. Rather sometimes part of it has been made, for example, the foundation of the house. But since it is necessary to arrive at some part which becomes a whole at once, it must be that in some part that which becomes has been made in respect to some terminus taken in the preceding alteration. For example, while the animal is being generated, the heart has already been made. And while the heart is being generated, something else has already been made. This latter is not a part of the heart. Rather some alteration, ordained to the generation of the heart, has been completed.

             And what is said of generation must also be said of corruption. For in that which becomes and is corrupted there is immediately present a certain infinity, because it is continuous. Becoming and being corrupted are themselves continua. And hence there is no becoming unless something has previously been made. And a thing has not been made unless it was previously becoming. And the same thing must be said of 'being corrupted' and 'having been corrupted'. For 'having been corrupted' is always prior to 'being corrupted'. And 'being corrupted' is prior to 'having been corrupted'.

             Hence it is clear that whatever has been made must previously have been becoming. And whatever becomes must previously have been made in some way. This is so because every magnitude and every time is divisible to infinity. And therefore in whatever time something becomes, this will not be the first time because there is a prior part. And that which was said of generation and corruption must also be understood to be true of illumination. For illumination is the terminus of the local motion of an illuminating body, just as generation and corruption are the termini of alterations.