Lecture 7 — How there can be a first motion

Since everything that changes changes from something to something, that which has changed must, at the moment when it has first changed, be in that to which it has changed.

For what changes retires from or leaves that from which it changes, and leaving, if not identical with changing, is at any rate a consequence of it. And, if leaving is a consequence of changing, having left is a consequence of having changed, since both are related to both in a similar way. Since one kind of change is change in a relation of contradiction, a thing that has changed from non-being to being has left non-being. Therefore, it will be in being, for everything must either be or not be.

Thus, it is evident that, in contradictory change, what has changed must be in that to which it has changed.

And, if this is true in this kind of change, it will be true in all other kinds as well, for in this matter, what holds good in the case of one will hold good likewise in the case of the rest.

Moreover, if we take each kind of change separately, the truth of our conclusion will be equally evident, on the ground that what has changed must be somewhere or in something.

For since it has left that from which it has changed and must be somewhere, it must be either in that to which it has changed or in something else.

If, then, that which has changed to B is in something other than B, say C, it must again be changing from C to B, for it cannot be assumed that there is no interval between C and B, since change is continuous.

Thus we have the result that the thing that has changed, at the moment when it has changed, is changing to that to which it has changed, which is impossible, and thus that which has changed must be in that to which it has changed. So it is evident likewise that what has come to be, at the moment when it has come to be, will be, and what has ceased to be will not be.

For what we have said applies universally to every kind of change, and its truth is most obvious in the case of contradictory change. It is clear, then, that that which has changed, as soon as it is changed, is in that to which it has changed.

The “primary when” in which that which has changed effected the completion of its change must be atomic, and by “primary,” I mean having the characteristics in question not because of something else belonging to it, but because of itself.

For let AC be divisible, and let it be divided at B. If, then, the completion of change has been effected in AB or again in BC, AC cannot be the primary thing in which the completion of change has been effected.

If, on the other hand, it has been changing in both AB and BC (for it must either have changed or be changing in each of them), it must have been changing in the whole AC; but our assumption was that AC contains only the completion of the change.

It is equally impossible to suppose that one part of AC contains the process of the change and the other its the completion, for then we shall have something prior to what is primary.

So, that in which the completion of change has been effected must be indivisible. It is also evident, therefore, that that in which what has ceased to be has so ceased is atomic, as is that in which what has come to be has come to be.

But there are two senses of the expression “in which something has been first changed.”

On the one hand, it may mean the first time containing the completion of the process of change—the moment when it is correct to say “it has changed.”

On the other hand, it may mean the first time containing the beginning of the process of change.

Now, the first time that has reference to the completion is something really existent, since a change may really be completed, and there is such a thing as the end of change, which we have in fact shown to be indivisible because it is a limit.

But that which has reference to the beginning is not existent at all, for there is no such thing as the beginning of a change, and the time occupied by the change does not contain any first time in which the change began.

For suppose that AD is such a first time. Then, it cannot be indivisible; for if it were, the moment immediately preceding the change and the moment in which the change begins would be consecutive (and moments cannot be consecutive).

Again, if the changing thing is at rest in the whole preceding time CA (for we may suppose that it is at rest), it is at rest in A also, and so if AD is without parts, it will simultaneously be at rest and have changed (for it is at rest in A and has changed in D).

Since, then, AD is not without parts, it must be divisible, and the changing thing must have changed in every part of it.

For if it has changed in neither of the two parts into which AD is divided, it has not changed in the whole either; but if it is in process of change in both parts, it is likewise in process of change in the whole;

and if, again, it has changed in one of the two parts, the whole is not the first time in which it has changed, and it must therefore have changed in every part.

It is evident, then, that, with reference to the beginning of change, there is no first time in which change has been effected, since the divisions are infinite.

So, too, of that which has changed, there is no primary part that has changed. For suppose that, of DE, the primary part that has changed is DZ (everything that changes having been shown to be divisible), and let OI be the time in which DZ has changed.

If DZ has changed in the whole time, then there will be a part that has changed in half the time, a part less than, and therefore prior to, DZ.

And, again, there will be another part prior to this, and yet another, and so on to infinity. Thus, of that which changes, there cannot be any primary part that has changed.

It is evident, then, from what has been said, that neither of that which changes nor of the time in which it changes is there any primary part.

However, with regard to the actual subject of change—that is to say, that in respect of which a thing changes—there is a difference to be observed. For in a process of change, we may distinguish three terms: that which changes, that in which it changes, and the actual subject of change (for instance, the man, the time, and the fair complexion).

Of these, the man and the time are divisible, but with the fair complexion, it is otherwise (though they are all divisible accidentally, for that in which the fair complexion or any other quality is an accident is divisible).

For of actual subjects of change, it will be seen that those that are classed as essentially divisible, not accidentally, have no primary part. Take the case of magnitudes:

let AB be a magnitude, and suppose that it has moved from B to a primary “where” C. Then, if BC is taken to be indivisible, two things without parts will have to be contiguous (which is impossible):

if, on the other hand, it is taken to be divisible, there will be something prior to C to which the magnitude has changed, and something else again prior to that, and so on to infinity, because the process of division may be continued without end.

Thus, there can be no primary where to which a thing has changed. And, if we take the case of quantitative change, we shall get a like result, for here too, the change is in something continuous. It is evident, then, that only in qualitative motion can there be anything essentially indivisible.

818. After explaining how motion is divided, the Philosopher now discusses the order of the parts of motion.

First, he asks whether there is a first in motion;

second, he shows how the factors involved in motion precede one another, at now, everything that changes (236b19; [826]).

About the first, he does two things:

first, he shows that that into which something is first changed is indivisible;

second, he shows how a first can and cannot be found in motion, at but there are two (236a7; [822]).

About the first, he does two things:

first, he mentions things necessary for explaining the proposition;

second, he proves the proposition, at the “primary when” (235b32; [821]).

About the first, he does two things:

first, he mentions his proposition;

second, he proves it, at for what changes (235b8; [819]).

819. He says first (235b6) that, because whatever is being changed is being changed from one terminus to the other, when the subject of change has now been changed, it has to be in the terminus to which.

Then, at for what changes (235b8), he proves this proposition with two arguments, the first of which is particular, and the second universal.

The first argument is this: either everything being changed must be distant from the terminus at which the change starts (as is evident in local motion, in which the place from which the motion starts remains and the mobile gets to be distant from it) or the terminus from which must cease to be, as in the motion called alteration, for when something white becomes black, the whiteness ceases to be.

In order to explain this proposition, he adds that either the process of being changed is the same as departing or the latter is a consequence of change and, therefore, having left (from the terminus from which) is a consequence of having been changed. But it is evident that they are the same in reality but different in account. For departing is spoken of in relation to the terminus from which, whereas change gets its name from the terminus to which. And in explanation of this, Aristotle adds that both are related to both in a similar way: as departing is related to being changed, so having departed is related to having been changed.

From these premises, he argues to the conclusion, using as his example the species of change that involves terms contradictorily opposed, where the transition is between being and non-being, as in generation and ceasing to be.

For it is evident from the foregoing that whatever is being changed departs from the terminus from which and that whatever has been changed has already departed. When, therefore, something has been changed from non-being to being, it has already departed from non-being. But, of anything at all, it is true to say that it either is or is not.

Therefore, what has been changed from non-being to being is in being when the change is over. Likewise, what has been changed from being to non-being must be in non-being. Therefore, it is evident that in the change that involves contradictories, the thing that has been changed exists in that into which it has been changed. And, if it is true in that type of change, then for an equal reason, it is true in other changes. From this, the first proposition is clear.

820. Then, at moreover, if we take (235b18), the second argument, a general one, is given. And he says that the same conclusion can be proved by considering any change at all; he makes this clear through local motion. Whatever has been changed must be somewhere, that is, either in the terminus from which or in some other. But, since what has been changed has already departed from that from which it has been changed, it must be elsewhere. Therefore, it must be either in that in which we are trying to prove it is—that is, in the terminus to which—or elsewhere. If it is in the former, our point is proved; if not, then let us suppose that something is being moved into B and, when the change is finished, the thing is not in B, but in C. Then we must say that, from C, it is also changed into B, because there is no interval between C and B. For a change of the type under discussion is continuous, and in continua, one part is not consecutive to another, for between two parts, there occurs a part that is similar to those two, as was proved above. (Lect. 1, n. 754.)

Hence, it will follow that, if what has been changed is in C when it has been changed and, from C, it is being changed to B (which is the terminus to which), then when it has been changed, it is also being changed into what it has already become—which is impossible. For being changed and having been changed are never simultaneous, as we have shown above. (Lect. 2, n. 761.) Now, it makes no difference whether the termini C and B are applied to local motion or to any other change. Consequently, it is universally true that what has been changed is (when it has been changed) in that into which it has been changed, that is, in the terminus to which.

From this, he further concludes that what has been made, when it has been made, has being, and that what is corrupted, when it is corrupted, is not being. For this has been shown universally of every change, and this is most manifest in changes that are according to contradiction, as is clear from what has been said.

Thus, it is manifest that what has been changed, as soon as it has been changed, is that into which it has been changed. He added as soon as because, after it has been changed into something, it could depart from it and not be there; but, as soon as it has been changed, it must be there.

821. Then, at we will now show (235b30), he shows that to have been changed is first and per se in an indivisible, and he says that that time in which what has been changed was first changed must be atomic, that is, indivisible. He explains why he adds first by saying that A is said to have been first changed as soon as it is not said to have been changed merely by reason of any of its parts. For example, if we say that a mobile has been changed in a day because it was changed in some part of the day, then it was not first changed in the day.

But that the time in which something has been first changed is indivisible he now proves. If the said time were divisible, let it be AC, and let it be divided at B. Now, three things are possible: either the change is over in each part of the time, or it is going on in each part, or in one part it is going on and in the other it is over.

Now, if it is over in each part, then it was first completely changed not in the whole, but in the part; but if it is being changed in each part, then it is also being changed in the whole (for the reason that something is said to be changing in a whole period of time is that the change was going on during each part of the whole time). But this is against our assumption that, in the whole of AC, it had been changed.

On the other hand, if it be supposed that, in one part of the time, it is being changed and, in the other part, it has been changed, the same difficulty ensues:

it was not first changed in the whole time, for since the part is prior to the whole and something is in motion in a part of time before it is moved in the entire time, it follows that there was something prior to the first, which is impossible. Consequently, it must be admitted that the time in which the thing was first completely changed is indivisible.

From this, he further concludes that everything that has ceased to be and everything that has been completely made were made and ceased to be in an indivisible of time, because generation and ceasing to be are the termini of alteration. Consequently, if a motion is terminated in an instant (for these two things are the same—that is, the termination of a motion and to have been first changed), it follows that generation and ceasing to be occur in an instant.

822. Then, at but there are two (236a7), he shows how to find the first thing in a motion.

About this, he does two things:

first, he proposes the truth;

second, he proves it, at for suppose that AD (236a17; [823]).

He says first (236a7) that the expression in which something has been first changed has two interpretations:

first, it can mean that in which the change is first complete or terminated—in which case, it is true to say that something has been changed when the change is now over;

second, it can mean that in which it first began to be changed, and not that in which it was first true to say that it has been changed.

Taken in the first sense—according to the termination of the change—it is applied to instances of motion in which there exists a first in which something has been changed. For a change can be first terminated at some time, because every change has a termination. It was in this sense that we understood that that in which something was first changed is an indivisible, which was proved on the ground that it is the end—that is, the terminus, of the motion—and we know that every terminus of a continuum is an indivisible.

But if it is taken in the second sense—according to the beginning of the change (that is, according to the first part of the motion)—then there is no first in which something has been changed. For no beginning of a change can be definitely pointed out—that is, no part that is not preceded by some other part. In like manner, it is not possible to isolate a first time in which something is first being moved.

823. Then, at for suppose that AD (236a17), he proves that, if one looks at the beginning of a motion, it is not possible to assign a first in which something has been changed.

He proves this first with an argument from time;

second, with an argument from the mobile, at so, too, of that which (236a27; [824]);

third, with an argument from that in which the motion occurs, at however, with regard (236a35; [825]).

As to the first, he gives this reason. Let AD be an element of time in which something has been first changed. Now, AD must be either divisible or indivisible. If it is the latter, two difficulties ensue.

The first is that the nows in time are consecutive. This difficulty follows from the fact that time is divided just like motion, as was shown above. (Lect. 6, n. 813.) But, if any part of the motion was present in AD, then AD must have been a part of time and, consequently, time will be composed of indivisibles. However, the indivisibles of time are the nows. It will follow, therefore, that the nows are consecutive in time.

And there is a second difficulty. Let us suppose that, in the time CA, which preceded AD, the same mobile that was being moved in time AD was entirely at rest. If, therefore, it was at rest in the entire time CA, it was at rest in A, which is an element of the time CA. If, therefore, AD is indivisible, as we supposed, it will follow that a thing is at rest and in motion at the same time; for we have already concluded that it was at rest in A and assumed that it was in motion in AD. But, if AD is indivisible, then A is the same as AD. It will follow, therefore, that a thing is at rest and in motion in the same time.

It should be noted, however, that, if a thing was at rest throughout an entire time, it does not follow that it was at rest in the last indivisible of that time; for we have already shown that, in the now, things are neither at rest nor in motion. (Lect. 5, n. 794.) But Aristotle concludes this here by arguing from what his adversary has proposed: that the element of time in which the object was first being moved is an indivisible. And if it can be in motion in an indivisible of time, there is no reason why it could not also be at rest.

Therefore, having rejected the indivisibility of time AD, we are left with the fact that it is divisible. And, since it is in AD that the object is said to be first moved, then it is being moved in any part of AD.

This he now proves. Let AD be divided into two parts; then the object is being moved either in neither part or in both parts or in one part only. If in neither part, then it is not being moved in the whole time. If in both parts, then it could be granted that it is being moved in the whole time. But, if in one part only, it will follow that it is being moved in the whole time but not first, but by reason of the part. Therefore, since it is agreed to be moving in the whole time, it has been in motion in each part of the whole time. But time is divided infinitely, just like any continuum; consequently, it is possible always to consider a part smaller than a previous one (such as a day before a month and an hour before a day). Therefore, it is evident that it is impossible to find a time in which it is first being moved such that a previous could not be found. For if you were to assume that it is in a day that the object is first moved, that assumption would not be true, because it would have been first moved in the first part of the day before it was moved in the whole day.

824. Then, at so, too, of that which (236a27), he establishes the same point by considering the mobile, and he concludes from the foregoing that in that which is being changed it is not possible to take something that is first changed. Now, this is to be understood in the sense that some definite point is to be crossed through the motion of the whole or of the part: it is evident that the first part of the mobile will first pass a given point, and a second part will pass it after that, and so on.

Otherwise, if it were understood in the sense of the absolute nature of motion, what we have to say would not be to the point, for it is clear that the whole is being moved at the same time as all the parts, but the whole does not pass a certain point all at once, but part before part continuously. Hence, just as it is impossible to find a first part of the mobile than which there is not a previous smaller part, so also is it impossible to isolate a part of the mobile that would be first moved.

And because time and mobile are correspondingly divided, as we have shown above, (Lect. 6, n. 813.) he now concludes about the mobile what was concluded about time. Here is his proof. Let DE be a mobile, and (because every mobile can be divided, as was proved above (Lect. 5, n. 796.)) let DZ be the part that is first being moved. And let DZ be moved such that it passes a definite point in the time TI. If, therefore, DZ has been changed in this whole time, it follows that what has been changed in half the time is both less than DZ and moved prior to DZ. And, for the same reason, there will be something prior to that, and so on forever, because time can be divided infinitely, It is evident, therefore, that one cannot find something in the mobile that has been first changed. Hence, it is clear that a first cannot be found in motion, whether we consider the time or the mobile.

825. Then, at however, with regard (236a35), he proves the same thing by considering that in which the motion occurs.

But first he mentions that the situation with respect to that in respect of which a thing changes is not exactly the same as it was with respect to time and the mobile. For since there are three things to be considered in change—the mobile that is being changed (e.g., a man), that in which it is being changed (the time), and that into which it is being changed (e.g., white)—two of these, the time and the mobile, are always divisible. But with white it is another story, because a white thing is not divisible per se, but it and things like it are divisible per accidens, inasmuch as the subject of whiteness or of any other quality is divisible.

Now, the per accidens division of white can take place in two ways.

In one way, the white can be divided per accidens according to the quantitative parts, as when a white surface is split into two parts.

In another way, it can be according to greater or less intensity, for the fact that one and the same part is whiter or less white is not due to the account of whiteness (because, if it existed in isolation, whiteness would be constant and never subject to more and less, any more than a substance is susceptible to more and less), but to the varying degrees in which a divisible subject participates in whiteness.

Therefore, neglecting what is divided per accidens in motion and considering only what is divided per se, it is impossible to find a first.

And he proves this first of all in magnitudes in which there is local motion. Let the magnitude AC be divided at B, and suppose that C is that into which something is first moved from B. Now, BC is either divisible or indivisible. If it is the latter, it follows that an indivisible will be touching an indivisible, for there is no reason that the second part of the motion will not be into an indivisible, since we can divide a magnitude just as the motion was divided, and as time was.

But, if BC is divisible, it is possible to take a stage prior to B than to C, and so the thing will be changed from B into that stage before it is changed into C, and into a stage prior to that one, and so on, because there is no limit to the division of a magnitude. It is therefore evident that it is impossible to find a first stage into which a thing has been changed in local motion.

The same is true in change of quantity, that is, growing and decreasing. For even these changes are in terms of a continuum—that is, in terms of added quantity or subtracted quantity—in which no first is to be found, since there can be division to infinity.

And so it is clear that it is only in qualitative change that something is per se indivisible. But, inasmuch as divisibility is found in this per accidens, likewise no first is discernible in such change. This is true whether the succession consists in part being altered after part (for it is evident that no first part of white can be found any more than a first part of magnitude can) or the succession is based on one and the same thing becoming more and more white or less and less white, for a subject can be modified in an infinite number of ways with regard to degrees of whiteness. Thus, the motion involved in alteration can be continuous and not possess a first.