Lecture 8 — The relation of “being moved” and “has been moved”

Now, everything that changes changes in time, and that in two senses: the time in which a thing is said to change may be the primary time, or on the other hand, it may be by reason of something else (such as when we say that a thing changes in a particular year because it changes in a particular day).

That being so, that which changes must be changing in any part of the primary time in which it changes.

This is clear from our definition of “first,” in which the word is said to express just this. It may also, however, be made evident by the following argument.

Let XR be the primary time in which that which is in motion is in motion, and (as all time is divisible) let it be divided at K. Now, in the time XK, it either is in motion or is not in motion, and the same is likewise true of the time KR.

Then, if it is in motion in neither of the two parts, it will be at rest in the whole, for it is impossible that it should be in motion in a time in no part of which it is in motion.

If, on the other hand, it is in motion in only one of the two parts of the time, XR cannot be the primary time in which it is in motion, for its motion will have reference to a time other than XR. It must, then, have been in motion in any part of XR.

And, now that this has been proved, it is evident that everything that is in motion must have been in motion before.

For if that which is in motion has traversed the distance KL in the primary time XR, then a thing that is in motion with equal velocity and began its motion at the same time will have traversed half the distance in half the time.

But, if this second thing whose velocity is equal has traversed a certain distance in a certain time, the original thing that is in motion must have traversed the same distance in the same time. Hence, that which is in motion must have been in motion before.

Again, if by taking the extreme moment of the time—for it is the moment that terminates the time, and time is that which is intermediate between moments—we are enabled to say that motion has taken place in the whole time XR (or, in fact, in any period of it), motion may likewise be said to have taken place in every other such period.

But half the time finds an extreme in the point of division. Therefore, motion will have taken place in half the time, and in fact in any part of it; for as soon as any division is made, there is always a time defined by moments.

If, then, all time is divisible, and that which is intermediate between moments is time, everything that is changing must have completed an infinite number of changes.

Again, since a thing that changes continuously and does not perish or cease to be moved must either be changing or have changed in any part of the time of its change, and since it cannot be changing in a moment, it follows that it must have changed at every moment in the time.

Consequently, since the moments are infinite in number, everything that is changing must have completed an infinite number of changes.

And not only must that which is changing have changed, but that which has changed must also previously have been changing,

since everything that has changed from something to something has changed in a period of time.

For suppose that a thing has changed from A to B in a moment.

Now, the moment in which it has changed cannot be the same as that in which it is at A (since, in that case, it would be in A and B at once), for we have shown above that what has changed, when it has changed, is not in that from which it has changed.

If, on the other hand, it is a different moment, there will be a period of time intermediate between the two, for as we saw, moments are not consecutive.

Since, then, it has changed in a period of time, and all time is divisible, in half the time, it will have completed another change, in a quarter another, and so on to infinity. Consequently, when it has changed, it must have previously been changing.

Moreover, the truth of what has been said is more evident in the case of magnitude, because the magnitude over which what is changing changes is continuous.

For suppose that a thing has changed from C to D. Then, if CD is indivisible, two things without parts will be consecutive. But, since this is impossible, that which is intermediate between them must be a magnitude and divisible into an infinite number of segments.

Consequently, before the change is completed, the thing changes to those segments. Everything that has changed, therefore, must previously have been changing.

For the same proof also holds good of change with respect to what is not continuous, namely, changes between contraries and between contradictories.

In such cases, we have only to take the time in which a thing has changed and again apply the same reasoning.

So, what has changed must have been changing and what is changing must have changed, and a process of change is preceded by a completion of change, and a completion by a process, and we can never take any stage and say that it is absolutely the first.

The reason for this is that no two things without parts can be contiguous, and therefore, in change, the process of division is infinite, just as lines may be infinitely divided such that one part is continually increasing and the other continually decreasing.

So it is evident also how what has become must previously have been in process of becoming, and that which is in process of becoming must previously have become—that is, everything that is divisible and continuous—

though it is not always the actual thing that is in process of becoming of which this is true; sometimes it is something else, that is to say, some part of the thing in question, such as the foundation stone of a house.

So, too, in the cases of that which is corruption and that which has perished, for that which becomes and that which perishes must contain an element of infiniteness as an immediate consequence of the fact that they are continuous things.

Thus, a thing cannot be in process of becoming without having become, or have become without having been in process of becoming. So, too, in the case of corruption and having perished: corruption must be preceded by having perished, and having perished must be preceded by corruption.

It is evident, then, that what has been made was previously being made, and what is being made must necessarily have been made, provided that divisible and continuous things are involved, for all magnitudes and all periods of time are infinitely divisible.

Consequently, no absolutely first stage of change can be represented by any particular part of space or time that the changing thing may occupy.

826. After explaining how a first is to be taken in motion and how not, the Philosopher now explains the order of precedence among the things present in motion.

First, he sets out things needed for explaining the proposition;

second, he explains the proposition, at and, now that this (236b32; [828]).

827. He therefore says first (236b19) that whatever is being changed is being changed in time, as we have explained. (Lect. 5, n. 794ff.)

But something is being changed in a time in two ways:

in one way, first and per se;

in another way, by reason of something else, that is, by reason of a part, as when something is said to be changed in a year because it is being changed in a day.

With this distinction in mind, he states what he intends to prove: if something is being first moved in a time, it is necessarily being moved in some part of that time.

This he proves in two ways.

First, he proves it from the definition of first, for here, something is said to be in a thing first if it belongs to it by reason of each and every part, as was said in the beginning of book 5. (Lect. 1, n. 639.)

Second, he proves the same thing with an argument. Let XR be the time in which something is being first moved, and since time is divisible, let XR be divided at K. Then, of necessity, in the part XK of the time, the object is either being moved or not, and likewise for the part KR. Now, if it be said that it is being moved in neither of those parts, it follows that it is not being moved in the whole time, but is at rest throughout that time, for it is impossible for a thing to be in motion in a time without being in motion in some part of it. But, if it be supposed that it is being moved in just one part of the time, it will follow that it is not being first moved in the time called XR, because that would require motion in respect to both parts and not in respect to just one. Therefore, of necessity, it must be in motion in each part of the time XR. And that is what we want to demonstrate: if something is being first moved in a time, it is being moved in every part of it.

828. Then, at and, now that this (236b32), he sets about proving the main proposition.

And about this, he does two things:

first, he introduces the proofs of the proposition;

second, he argues for the truth, at so, what has (237b3; [838]).

About the first, he does two things:

first, he shows that, before each state of being moved, there was a state of completed motion;

second, he shows that, conversely, there was a state of being moved before each state of completed motion, at and not only must (237a17; [832]).

829. He proves the first with three arguments.

The first is this. Let KL be the magnitude through which a mobile has been moved in the first time XR. It is clear that an equally fast mobile that began its motion with the first one will have covered half the magnitude in half the time. Since the first mobile (which we have said covers the entire magnitude) is as fast as the second, it follows that even it has, in half the time, already been moved through half the magnitude KL. It will follow, therefore, that what is being moved has been previously moved.

To get a better understanding of what we mean, it must be considered that, just as “point” is a name for the terminus of a line, so “completed motion” is a name for the terminus of a motion. Now, no matter what line or what part of a line you take, it is always true that, before the completion of the whole line, you can take a point according to which the line can be divided. Likewise, before any motion or part of a motion, you can take a state of completed motion, for while the mobile is being moved to its terminus, it has already passed a certain stage in respect to which the mobile is said to have been already changed. But, just as a point within a line is in potency before the line is actually divided (for a point is the very division of a line), so also the thing called “completed motion” (within a motion) is in potency as long as the motion does not stop there; but, if it does stop there, it will be actual. And since what is in act is better known than what is in potency, therefore Aristotle proves his proposition (that what is being continually moved has already been moved) by referring to an equally fast mobile whose motion has already been completed. This is like proving that, in a certain line, there is a point in potency by showing that a like line has been actually divided.

830. The second argument, which he gives at again, if by taking (237a3), is this. In the whole time XR or in any other, something is said to have been changed by the very fact that a final now of the time is taken—not that something is being moved in that now, but that the motion is terminated then. Hence, “having been moved” is taken here not for that which is at some time being moved, but for the fact that the motion is ended.

Now, the reason that the motion must be terminated in the final now of the time that measures the motion is that that now terminates the time, just as a point terminates a line. And all time is midway between two nows, just as a line is between two points. Therefore, since “being moved” occurs in time, it follows that “having been moved” occurs in the now that is the terminus of time. And, if that is the case with a motion in a whole period of time, the same must be true of the parts of motion that occur in the parts of time. Now, we have already shown that, if something is being first moved in the whole time, it is being moved in each part of the time. But, whichever part of time you take, it is terminated at some now. For the terminus of half of the time is the division, that is, the now that divided the time into two parts.

Therefore, it follows that what is being moved through the whole is previously moved at the middle of time, on account of the now that determines the middle. And the same reasoning applies to any part of time. For no matter how the time is divided, it will always be found that each part of the time is determined by two nows, and after the first now of the time measuring the motion, no matter which other now is taken, the object has already been moved in that part of the time, for that now—whichever it is—is the terminus of the time measuring the motion.

Now, because every period of time is divisible into times and each period exists between two nows, and because, in any now that happens to be the ending of a time measuring the motion, something has been moved, it follows that whatever is being changed has been changed an infinite number of times, because “having been changed” is the terminus of a motion, just as a point is of a line and a now is of a time.

Therefore, just as it is possible in any line to pick out to infinity a point ahead of a point, and a now before a now in any period of time (because both line and time are divisible to infinity), so in any “being moved,” it is possible to pick out infinitely many “having been moved”s, because motion, too, is divisible to infinity, just as the line and time, as was previously proved. (Lect. 6, n. 812ff.)

831. The third argument is at again, since a thing (237a11). In the case of anything that is being changed (if it is not ceasing to be and does not perish or cease to be moved, but is being continually changed), it is necessary that, in each now of the time in which it is being moved, it is being changed or has been changed.

But in the now nothing is being changed, as we have shown. (Lect. 5, n. 794.) Therefore, in each now of the time that measures continuous motion, the object has been changed. But, in any portion of time, there are an infinitude of nows, because the now divides time, and time is infinitely divisible.

Therefore, everything that is being changed has been changed an infinite number of times. And, so, it follows that before every state called “being moved” is a state called “having been moved,” which, however, does not exist outside the state of “being changed,” but is in it and terminates a part of it.

832. Then, at and not only must (237a17), he proves that, on the other hand, a state of being changed precedes each state of having been changed.

First, he proves it from the viewpoint of the time;

second, from the viewpoint of that in respect of which the motion occurs, at moreover, the truth (237a28; [836]).

About the first, he does three things:

first, he states the proposition;

second, he proves certain things needed for proving the proposition, at since everything that has changed (237a19; [833]);

third, he gives the proof of the main proposition, at since, then, it has changed (237a25; [835]).

He says first that, not only is it true that whatever is being changed had already been changed, but every state of having been changed must be preceded by a state of being changed, because the former is the terminus of the latter. Therefore, every having been changed must be preceded by a being changed.

833. Then, at since everything that has changed (237a19), he states something needed for his proof of the proposition, that whatever is being changed from something to something was changed in time. But note carefully that here the words has changed do not refer to the termination of motion, for it was explained above that the time in which a thing was changed is an indivisible. (Lect. 7, n. 821.) But here, has changed signifies that something was previously being moved, as though he said that whatever was being moved was being moved in time.

This he now proves. If our proposition is not true, then let there be something that was changed from A to B—that is, from one term to another—in a now. From this, it follows that when it is in A—in the terminus from which—in the same now, it was not yet changed, because it has already been proved that what was changed, when it was being changed, was not in the terminus from which, but more in the terminus to which. (Lect. 7, n. 819.) Otherwise, it would follow that it was at once in A and in B.

Therefore, it is necessary to say that, in one now, it is in A and in another, it was being changed. But between two nows there is a time, because two nows cannot be immediately connected, as we have shown. (Lect. 1, n. 754.) What remains, therefore, is that whatever is being changed is being changed in time.

834. But it seems that this conclusion has no application in generation and ceasing to be, between whose two termini there is nothing intermediate. For if a period of time occurs between the now in which something is at the terminus from which and the now in which it is at the terminus to which, it will follow that there is something between being and non-being, for in that intermediate time, the subject of change would be neither being nor non-being.

Nevertheless, because the argument that Aristotle gives here is demonstrative, it must be said that it applies somehow even to generation and ceasing to be, but in the sense that such changes are also instantaneous, since there can be no medium between the termini.

So, it must be said that whatever is being changed from non-being to being (or vice versa) is not in being and non-being at the same time. But, as will be said in book 8, (Lect. 17.) there is no final instant in which what is generated is a non-being, but there is a first instant in which it is a being, such that, in the entire time preceding that instant, it is non-being. However, between that now and the time preceding, there is nothing intermediate, such that there is no medium between being and non-being.

Now, since the time that precedes the instant in which something is generated first is the measure of some motion, it follows that, just as that instant in which something is first generated is the terminus of the preceding time that measures the motion, so the first instant of the being of the thing generated is the terminus of a preceding change.

If, therefore, generation is said to be the very beginning of being, it must be the terminus of a motion, and thus it takes place in an instant, because a motion’s being terminated—which is the same as having been changed—occurs in an indivisible of time, as we have shown. (Lect. 7, n. 821.)

However, if generation is taken as the very beginning of being plus the entire preceding motion of which it is the terminus, then it occurs not in an instant, but in time, such that what is being generated is a non-being during the entire preceding time and a being in the final instant. And the same applies to ceasing to be.

835. Then, at since, then, it has changed (237a25), he proves the main proposition with the following reason. Whatever has been changed was being changed in time, as we have proved. But time is divisible, and whatever is being changed in time is being changed in part of time. Therefore, it is necessary to say that what has been changed in some entire period of time was previously being changed during half of the time, and again during half of that half, and so on, because time is divisible infinitely. Therefore, it follows that what has been changed was previously being changed. Consequently, before every state of having been changed, there is a previous state of being changed.

836. Then, at moreover, the truth (237a28), he proves the same point with an argument based on that in respect of which a thing is changed:

first, as to motions in quantity;

second, as to other changes, at for the same proof (237a35; [837]).

He says first (237a28) that what was said to be common to every change from the viewpoint of time becomes clearer from the viewpoint of magnitude, for magnitude is better known than time, and magnitude is continuous, like a line, and in it, something is changed, namely, that which is according to place or according to increase and decrease. Therefore, consider something changed from C to D. Now, it cannot be said that the whole of CD is indivisible, because CD has to be part of a magnitude, just as the motion from C to D is part of a whole motion, for there is a correspondence between division of magnitude and division of motion, as we have shown. (Lect. 2.) But, if an indivisible is a part of a magnitude, it follows that two indivisibles are immediate neighbors—which is impossible, as we have shown. (Lect. 1, n. 753.) Therefore, the whole CD cannot be an indivisible, and consequently, that which is between C and D is a magnitude and can be infinitely divided. And something is always first changed in part of a magnitude before it has been changed throughout the entire magnitude. Therefore, anything that has been changed was previously being changed, just as, before any whole magnitude, there are its parts.

837. Then, at for the same proof (237a35), he shows that the same point is true in those changes that do not take place in terms of a continuum, such as alteration, which is between contrary qualities, and generation and ceasing to be, which are between contradictories. And although, in those changes, the demonstration is not derived from things in which the motion is, yet it is possible to take the time in which the changes occur, and then the demonstration will proceed the same way.

Thus, in the three changes, which are alteration, generation, and ceasing to be, only the first argument holds, while in the other three—growth, decrease, and local motion—both arguments hold.

838. Then, at so, what has changed (237b3), he argues for the main proposition:

first, in general;

second, with special application to generation and ceasing to be, at so it is evident (237b9; [839]).

Thus, he first (237b3) concludes from the foregoing that everything that has been changed was previously being changed, and that everything that is being changed has previously been changed. Consequently, it is true that a state of having been changed preceded a state of being changed, and vice versa. And, so, it is clear that a first something cannot be definitely pointed to.

The reason for this is that, in motion, an indivisible is not joined to an indivisible such as to make a motion be composed of indivisibles, because, if that were the case, we could discover a first. But it is not true, for motion is infinitely divisible, just as a line is, which can be infinitely decreased by division and increased by addition opposite to the decrease, in the sense that what is taken from one is being added to another, as was shown in book 3. (Lect. 10, n. 378.) For it is evident that, in a line, before each part of a line, one can take a point in its midst, and before that midpoint is a part of the line, and so on to infinity. However, the line is not infinite, because no part of the line is in front of the first point of the line.

Well, the same thing is true of motion. For since each part of motion is divisible, before each part of the motion, there is in the midst of that part an indivisible that is called “having been changed,” and before that indivisible, there is a part of the motion, and so on to infinity. Yet it does not follow that the motion is infinite, for in front of the first indivisible of motion, there was no part of motion. But note that the first indivisible is not one called “having been changed,” any more than the first point of a line is a dividing point.

839. Then, at so it is evident (237b9), he comes to the same conclusion with reference to generation and ceasing to be. And he makes a special point of these changes, because the relation of having been changed to being changed in generation and ceasing to be is not the same as it is in other changes.

For in the others, the state of having been changed and the state of being changed occur in respect to the same thing, such as to whiteness in the case of alteration. For to be being altered is to be being changed in respect to whiteness, and to have been altered is to have been changed in regard to whiteness; and the same is true in local motion, in growth, and in decrease.

But, in generation, having been changed refers to one thing and being changed to another. For the former is based on the form, but the latter, though not based on negation of a form (which is not of itself susceptible of more and less), is based on something joined to such a negation, something that is susceptible to more and less (namely, a quality).

Therefore, to have been generated is the terminus of being altered, and the same is true of having been corrupted. And because motions get their name from the terminus to which, as we have said in the beginning of book 5, (Lect. 1, n. 643.) being altered has two names, since it has two termini (substantial form and quality), for it can be called “to be altered” and “to come to be and cease to be.”

And this is the sense in which coming to be and ceasing to be are substituted for being altered, because the alteration terminates at being or non-being.

And consequently, Aristotle says that what has been made was previously being made, and what is being made must necessarily have been made, provided that divisible and continuous things are involved.

And Aristotle makes that addition (as the Commentator says) in order to exclude things that indivisibly come to be without continuous motion, such as understanding and sensing, which are motions only in an analogous sense, as will be shown in De anima 3.10. (Cf. St. Thomas, Commentary on De anima, bk. 3, lect. 9.) But it could be that Aristotle made this addition in order to show that generation should include the entire continuous motion that precedes it.

840. But the statement what is being made has been previously made applies in different ways to different things. For some things, such as air and water, are simple and have simple generation, and in these cases, part is not generated after part, but the whole and the parts are altered and generated at once.

And it is in such that what has been made was previously being made and what is being made has been previously made, on account of the preceding alteration being continuous.

But other things are composites of unlike parts. In these cases, part is generated after part, as in an animal the heart is first generated, and in a house the foundation. In such things, what is being made was not itself previously made, but a part was.

And this is what he adds: it is not always such that what is being made has been itself previously made, but something pertaining to it has been made, as the foundation of a house.

But, since we must come to a part that is entirely being made at once, then in some part, that which is being made has been made in relation to a terminus taken in the preceding alteration;

for example, in the generation of an animal, the heart has already been made, and while the heart is being generated, something else has already been made—not indeed that there has been made some part of the heart, but some alteration ordained to the generation of the heart.

And what has been said of generation is to be understood with regard to ceasing to be. For there is something infinite immediately present in what is produced in being and is corrupted, since it is continuous.

For the very coming to be and the ceasing to be are continuous. Therefore, there is no being produced in being, unless something has been previously made, and nothing has been made unless it was previously being produced in being. And the same is true of ceasing to be and having ceased to be. For a having ceased to be is always prior to a ceasing to be and a ceasing to be prior to a having ceased to be.

From this it is evident that whatever has been made was previously being made, and that all that is being made has in some way previously been made. And the reason is that every magnitude and every period of time are infinitely divisible. Consequently, in whatever period of time something comes to be, it is not coming to be in that time as in a first time, because it always possible to find a period previous. And what we have said of generation and ceasing to be is true also of illumination, which is the termination of the local motion of the illuminating body, just as generation or ceasing to be is the terminus of an alteration.