Lecture 5 — The “now” of time and the solution of various difficulties

The present also is necessarily indivisible—“the present” not in the sense in which the word is applied to one thing in virtue of another, but in its proper and primary sense, in which sense it is inherent in all time.

For the present is something that is an extremity of that which was done (no part of the future being on this side of it) and also of the future (no part of the past being on the other side of it): it is a limit of both, as we have said. And, if it is once shown that it is essentially of this character and one and the same, it will at once be evident also that it is indivisible.

Now the present that is the extremity of both times must be one and the same.

For if each extremity were different, the one could not be consecutive to the other, because nothing continuous can be composed of things having no parts.

And, if the one is apart from the other, there will be time between them, because everything continuous is such that there is something univocal between its limits and described by the same name as itself.

But, if the intermediate thing is time, it will be divisible, for all time has been shown to be divisible. Thus, on this assumption, the present is divisible.

But, if the present is divisible, there will be part of the past in the future and part of the future in the past, for past time will be marked off from future time at the actual point of division.

Also, the present will be a present not in the proper sense, but in virtue of something else, for the division that yields it will not be a division proper.

Furthermore, there will be a part of the present that is past and a part that is future, and it will not always be the same part that is past or future.

In fact, one and the same present will not be simultaneous, for the time may be divided at many points. If, therefore, the present cannot possibly have these characteristics, it follows that it must be the same present that belongs to each of the two times.

But, if this is so, it is evident that the present is also indivisible, for if it is divisible, it will be involved in the same implications as before. From what has been said, then, it is clear that time contains something indivisible, and this is what we call a present.

We will now show that nothing can be in motion in a present. For if this is possible, there can be both quicker and slower motion in the present. Suppose that, in the present N, the quicker has traversed the distance AB. That being so, the slower will in the same present traverse a distance less than AB, say AG.

But, since the slower will have occupied the whole present in traversing AG, the quicker will occupy less than this in traversing it.

Thus, we shall have a division of the present, even though we found it to be indivisible. It is impossible, therefore, for anything to be in motion in a present.

Nor can anything be at rest in a present, for as we were saying, only that can be at rest that is naturally designed to be in motion but is not in motion when, where, or as it would naturally be so. Thus, since nothing is naturally designed to be in motion in a present, it is clear that nothing can be at rest in a present either.

Moreover, inasmuch as it is the same present that belongs to both the times, since it is possible for a thing to be in motion throughout one time and to be at rest throughout the other, and since that which is in motion or at rest for the whole of a time will be in motion or at rest, as the case may be, in any part of it in which it is naturally apt to be in motion or at rest—

this being so, the assumption that there can be motion or rest in a present implies that the same thing can at the same time be at rest and in motion, for both the times have the same extremity, namely, the present.

Again, when we say that a thing is at rest, we imply that its condition in whole and in part is, at the time of speaking, uniform with what it was previously; but the present contains no “previously”; consequently, there can be no rest in it.

It follows, then, that the motion of that which is in motion and the rest of that which is at rest must occupy time.

Further, what is being changed must be divisible. For since every change is from something to something, and a thing is no longer changing when it is at the goal of its change, and when both it itself and all its parts are at the starting point of its change, it is not changing (for that which is in whole and in part in an unvarying condition is not in a state of change), it follows, therefore, that part of that which is being changed must be at the starting point, and part at the goal, for as a whole, it cannot be in both or in neither.

(Here, by “goal of change,” I mean that into which it is first changed during the process of change: for instance, in a process of change from white, the goal in question will be grey, not black, for it is not necessary that what is changing should be at either of the extremes.)

It is evident, therefore, that everything that changes must be divisible.

787. After showing that no continuum is composed of indivisibles and that no continuum is indivisible, thus making it clear that motion is divisible, the Philosopher now determines about the division of motion.

First, he states certain facts necessary for the division of motion;

second, he treats of the division of motion, at now, motion is divisible (234b21; [806]).

About the first, he does two things:

first, he shows that, in an indivisible point of time, there is neither motion nor rest;

second, that an indivisible cannot be moved, at further, what is being changed (234b10; [796]).

About the first, he does two things:

first, he shows that the indivisible point of time is the now;

second, that, nothing is being moved or is at rest in the now, at we will now show (234a24; [794]).

About the first, he does three things:

first, he states his intention;

second, he states facts from which his proposition can be reached, at for the present (233b35; [789]);

third, he shows what follows from his proposition, at now the present (234a5; [790]).

788. About the first (233b33), we must take into account that something is called “now” in relation to something else and not in relation to itself; for example, we say that what is being done in the course of a whole day is being done now, yet the whole day is not said to be present according to its entirety, but according to some part of itself.

For it is evident that part of a whole day has passed and part is still to come, and neither of them is now. Thus, it is evident that the entire present day is not a now primarily and per se, but only through something belonging to it—and what is true of the day is true of an hour or any other period of time.

He therefore says that what is now primarily and per se and not according to something else is necessarily indivisible and present in every time.

789. Then, at for the present (233b35), he proves his proposition. For it is evident that it is possible in regard to any finite continuum to take an extremity outside of which there is existing nothing of that of which it is the extremity, just as nothing of a line is outside the point that terminates the line. But past time is a continuum that is terminated at the present. Therefore, it is possible to take something as the extremity of that which was done—that is, the past—such that there is nothing of the past beyond it, and nothing of the future previous to it. In like manner, it is possible to take an extremity of the future beyond which there is nothing of the past. Now, that extremity will be the limit of both, of the past and of the future; for since the totality of time is a continuum, the past and the future must be joined at one term. And, if the now fits the description just given, it is clear that it is indivisible.

790. Then he shows what follows from these premises, at now the present (234a5).

About this, he does two things:

first, he shows that, on the supposition that the now is indivisible, the limit of the past and the limit of the future must be one and the same now;

second, he shows that, on the other hand, if each is the now, then the now must be indivisible, at but, if this is so (234a20; [793]).

About the first, he does two things:

First (234a5), he concludes from the foregoing that it must be the same now that is the limit of the past and of the future.

791. Second, at for if each extremity (234a6), he proves this statement with the following argument. If the now that is the beginning of the future is other than the now that is the end of the past, then either these two nows are consecutive and immediately follow one upon the other or one is apart from and distinct from the other. But it cannot be that they are immediately consecutive, because it will then follow that time is composed of an aggregate of nows—which cannot be, because no continuum is composed of indivisible parts, as was said above. (Lect. 1ff.) Neither can it be that one now is apart from the other and distant from it, because there would then have to be a time between those two nows. For it is the very nature of a continuum that there is something continuous between any two given indivisibles, just as there is line between any two given points of a line.

But he proves that this is impossible in two ways.

First of all, if there were a period of time between the two nows in question, it would follow that something univocal—that is, of the same kind—would exist between the two, which is impossible, for it is not possible that there be a line between the extremities of two lines that touch or are consecutive. For that is contrary to the account of consecutive things, which were defined as things between which nothing like them occurs. (Bk. 5, lect. 5, n. 689.) And so, since future time is consecutive to past time, it is impossible that, between the end of the past and the beginning of the future, there be an intervening time.

He proves the same point in another way. Whatever is intermediate between the past and the future is called “now.” If, therefore, there is any time between the limits of the past and future, it will follow that that will also be called a now. But all time is divisible, as has been proved. (Lect. 3.) Consequently, it would follow that the now is divisible.

792. Although above he has given the principles from which it could be proved that the now is indivisible, yet because he had not derived the conclusion from these principles, he now shows that the now is indivisible, at but, if the present (234a11).

And he does this with three arguments.

The first of these is that, if the now were divisible, it will follow that something of the past would be in the future and something of the future would be in the past. For since the now is the extremity of the past and the extremity of the future, and every extremity is in that of which it is the extremity, as a point in a line, then necessarily the entire now would be both in the past as its end and in the future as its beginning. But, if the now were divided, that division must determine the past and the future. For any division made in time distinguishes past and future, for among any parts of time taken at random, one is related to the other as past to future. It will follow, therefore, that part of the now would be past and part would be future. And so, since the now would be in the past and in the future, it will follow that something of the future would be in the past and something of the past would be in the future.

The second argument he gives at also, the present (234a13). If the now be divisible, it will be such not according to itself, but according to something else. For no divisible is the very division by which it is divided. But the division of time is the now. For that by which a continuum is divided is nothing but a term common to two parts. But that is what we understand by the now: a term common to the past and future. Thus, therefore, it is clear that what is divisible cannot be the now according to itself.

The third argument is given at furthermore, there will be (234a14). Whenever time is divided, one part is always past and the other future. If, therefore, the now is divided, necessarily part of it will be past and part future. But past and future are not the same. It will follow, therefore, that the now is not the same as itself, that is, something existing as a whole all at once (which is against the definition of the now, for when we speak of the now, we consider it as existing completely in the present); rather, there will be much diversity and even succession in the now, just as there is in time, which can be divided any number of times.

793. Therefore, having thus shown that the now is divisible (as a consequence of supposing that the now that is the extremity of the past and of the future is not identical), and having rejected this consequent, he rejects the antecedent. And that is what he says: if it is impossible for the now to be divisible, then it must be admitted that the now that is the extremity both of the past and of the future is one and the same.

Then, at but, if this is so (234a20), he shows that conversely, if the now of the past and of the future is the same, then it must be indivisible, for if it were divisible, all the aforementioned inconsistencies would follow.

And so, from the fact that the now cannot be admitted to be divisible (as though the now of the past were something distinct from the now of the future)—and is indeed not divisible, if the now of the present is the same as the now of the future—he concludes that it is clear that, in time, there must be something indivisible that is called the now.

794. Then, at we will now show (234a24), he shows that, in the now, there can be neither motion nor rest:

first, he shows it for motion;

second, for rest, at nor can anything (234a31; [795]).

He first says, therefore (234a24), that it is clear from what follows that, in the now, nothing can be in motion, for if anything were in motion in the now, two things could then be in motion, one of which is faster than the other. So, let N be the now, and let there be a faster body being moved in N through the magnitude AB. In an equal time, a slower body is moved a smaller distance. Therefore, in this instant, it traverses the smaller magnitude AG. But the faster will cover the same distance in less time than the slower. Therefore, because the slower body traversed the magnitude AG in the very now, the faster traversed the same magnitude in less than the now. Hence, the now is divided. But it was already proved that the now cannot be divided. Therefore, nothing can be moved in a now.

795. Then, at nor can anything (234a31), he proves the same thing for rest, giving three arguments.

The first is this. It was said in book 5 (Lect. 4, n. 683.) that an object at rest is one that is naturally capable of being in motion but is not in motion when it is capable of being in motion or in respect to the part by which it is capable of being in motion or in the manner in which it is apt to be in motion.

For if a thing lacks what it is not naturally capable of having (as a stone lacks sight) or lacks it when it is not naturally due to have it (as a dog lacks sight before the ninth day), or in the part in which it is not naturally capable of having it (as sight in the foot or in the hand), or in the way in which it is not apt to have it (as for a man to have sight as keen as an eaglets), none of these reasons is sufficient for saying that a thing is deprived of sight.

Now, rest is privation of motion. Hence, nothing is at rest except what is apt to be moved, and when and as it is apt. But it has been shown that nothing is naturally capable of being moved in the very now. Therefore, it is clear that nothing is at rest in the now.

The second argument is given at moreover, inasmuch as (234a34). That which is being moved in an entire period of time is being moved in each part of that time in which it is apt to be moved; likewise, what is at rest in a given period of time is at rest in each period of that time in which it is apt to be at rest.

But the same now is in two periods of time, in one of which the mobile is totally at rest and in the other of which it is totally in motion (as appears in that which is in motion after rest or at rest after motion). Therefore, if something is apt to rest and be in motion in the now, it will follow that something is at once in motion and at rest, which is impossible.

The third argument is given at again, when we say (234b5). Rest is said of things that maintain themselves now just as they were previously, both in their entirety and in respect of all their parts. For it is on this account that a thing is said to be in motion: that now it is different from what it was previously in respect to place or quantity or quality. But, in the now itself, there is nothing previous; otherwise, the now would be divisible, because the word “previous” refers to the past. Therefore, it is impossible to rest in the now.

From this, he further concludes that necessarily anything that is being moved and anything that is at rest is being moved and is at rest in time.

796. Then, at further, what is being changed (234b10), he shows that, whatever is in motion is divisible. For every change is from this to that. But, when something is at the goal, it is no longer being changed, but has been changed, for nothing can be at the same time in the state of being changed and in that of having been changed, as was said above. (Lect. 2, n. 761.) But, when something is at the starting point of change both in its entirety and in regard to all its parts, then it is not being changed; for it was said above that whatever maintains itself constant in its entirety and in regard to all its parts is not being changed, but is at rest.

He adds, and all its parts, because, when a thing is beginning to be changed, it does not emerge in its entirety from the place it previously occupied, but part emerges after part.

Moreover, it cannot be said that it is in both terms in its entirety and in regard to its parts while it is being moved; for then something would be in two places at one time.

Nor, again, can it be said that it is in neither of the termini, for we are now speaking of the nearest end into which a thing is being changed and not of the remotest; for example, if something is being changed from white to black, black is the remote end, but grey is the nearer one. In like manner, if a line ABCD is divided into three equal parts, it is clear that a mobile that, in the beginning of the motion, was in AB as in a place equal to itself can be neither in AB nor in CD during the motion; for at some time, it is in its entirety in BC.

Therefore, when it is said that what is being moved cannot happen to be in either extremity while it is being moved, this must be understood as referring not to the remotest extremity, but to a nearer one.

What is left, therefore, is that whatever is being changed is partly in one and partly in the other while it is being changed; for example, when something is being changed from AB to BC, during the motion, the part leaving the place AB is entering the place BC; likewise, when something is being moved from white to black, the part that ceases to be white becomes grey or light grey.

Consequently, it is clear that anything that is being moved, since it is partly in one and partly in the other, is divisible.

797. But it should be mentioned that the Commentator here raises the problem that, if Aristotle does not intend in this place to demonstrate that every mobile is divisible, but only what is mobile in regard to motion (which he said is present in only three genera: quantity, quality and place (Bk. 5, lect. 4, n. 678.)), then his demonstration will not be universal but particular, because even the subject of substantial change is found to be divisible. Hence, he seems to be speaking of what is subject to any and every type of change, including even generation and ceasing to be in the genus of substance. And this is evident from his very words: he does not say what is being moved, but what is being changed.

But, in that case, his demonstration has no value, because some changes are indivisible, such as generation and ceasing to be of substance, which do not consume time. In such changes, it is not true that what is being changed is partly in one extremity and partly in the other, for when fire is generated, it is not partly fire and partly non-fire.

798. In the face of this problem, he proposes a number of solutions, one of which is Alexander’s, who says that no change is indivisible or in non-time. But this must be rejected because it conflicts with an opinion that is held as probable and famous with Aristotle and all Peripatetics: certain changes are in non-time, such as illumination and the like.

The Commentator mentions also the solution of Themistius, who says that, even if there be changes in non-time, they are hidden, whereas Aristotle appeals to what is evident, namely, that change occurs in time. But this he also rejects, because change and the changeable are divided in the same way, and the divisibility of a mobile is more hidden than the divisibility of change. Hence Aristotle’s demonstration would not be valid, because someone could say that, although things that change by changes evidently divisible are themselves divisible, yet there are some hidden changeable beings that are indivisible.

He mentions, too, the solution of Avempace, who says that the problem here is not about the quantitative division of the things capable of change, but of that division whereby the subject is divided by contrary accidents, one of which is changed into the other.

799. Then the Commentator adds his own solution: those changes that are said to occur in non-time are the extremities of certain divisible motions. It happens, therefore, that something should be changed in non-time, insofar as every motion is terminated in an instant. And, because what is accidental is ignored when it comes to demonstrating, Aristotle proceeds in this demonstration as though every change were divisible and in time.

800. But, if you consider the matter correctly, you will see that this objection is not to the point. For in his demonstration, Aristotle does not use as his principle the statement that every change is divisible (since he proceeds rather from the divisibility of the mobile to the division of change, as will be clear later; (Lect. 6, n. 808ff.) for as he says later, divisibility is first in the mobile before it is in motion or change (Lect. 6, n. 817.)).

Rather, he uses principles that are evident and must be conceded in any and every case of change: what is being changed in regard to a certain matter is not being changed in regard to that matter as long as it is totally and according to all its parts still in the starting point; and, when it is in the goal, it is not being changed, but has been changed; and it cannot be entirely in both terms or entirely in either of them, as was explained. Hence, it necessarily follows that, in any change whatsoever, what is being changed is, during the change, partly in one extremity and partly in the other.

But this occurs in various ways in various changes. For in changes between whose extremities there is something intermediate, it can happen that the mobile is, during the change, partly in one extreme and partly in the other extreme precisely as extremes. But, in those between whose extremes there is nothing intermediate, that which is being changed does not have different parts in different extremities precisely as extremities, but by reason of something connected with the extremities.

For example, when matter is being changed from privation of fire to the form of fire, then while it is in the state of being changed, it is indeed under privation as to itself, but it is yet partly under the form of fire, not inasmuch as it is fire, but according to something connected with it—that is, according to the particular disposition for fire, which disposition it partly receives before it has the form of fire. That is why Aristotle will later prove that even generation and ceasing-to-be are divisible, because what is generated was previously being generated and what ceases to be was previously ceasing to be. (Lect. 8.)

Perhaps this was the sense in which Alexander understood the statement that every change is divisible: either according to itself or according to a motion connected with it. So also Themistius understood by the statement that Aristotle took what was evident and abstracted from what was hidden that the proper place for treating of the divisibility or indivisibility of changes would not be reached until later. (Lect. 6.)

Nevertheless, in all divisibles and indivisibles, what Aristotle says here is true, for even changes that are called indivisible are in a sense divisible, not by reason of their extremities, but by reason of something connected to them. And this is what Averroes wanted to say when he said that it is per accidens that some changes occur in non-time.

801. However, there is here another difficulty. For when it comes to alteration, it does not seem to be true that what is being altered is partly in one terminus and partly in the other during the alteration. For the motion of alteration does not take place in such a way that first one part and then another is altered; rather, the entire thing that was less hot becomes hotter.

For which reason, Aristotle even says in De sensu et sensato that alterations are not like local motions. For in the latter, the subject reaches the intermediate before the goal, but such is not the case with things that are altered; for some things are altered all at once and not part by part, for it is the entire water that all at once freezes. (Aristotle, De sensu et sensato, c. 6, 446b28; cf. St. Thomas, Commentary on De sensu, tr. 1, c. 15.)

802. But to this it must be replied that, in this book, Aristotle is treating of motion as continuous. And continuity is primarily and per se and strictly found only in local motion, which alone can be continuous and regular, as will be shown in book 8. (Lect. 15.) Therefore, the demonstrations given in book 6 pertain completely to local motion but incompletely to other motions, that is, only to the extent that they are continuous and regular.

Consequently, it must be said that what is mobile in respect of place always enters a new place part by part before it is there in its entirety; but, in alteration, that is only partially true. For it is clear that every alteration depends on the power of the agent that causes the alteration: as its power is stronger, it is able to alter a greater body.

Therefore, since the cause of the alteration has finite power, a body capable of being altered is subject to its power up to a certain limit of quantity, which receives the impression of the agent all at once; hence, the whole is altered all at once, and not part after part. Yet that which is altered can in turn alter something else conjoined to it, although its power in acting will be less forceful, and so on, until the power involved in the series of alterations is depleted. An example of this is fire that all at once heats one section of air that in turn heats another, and thus part after part is altered.

Hence, in De sensu et sensato, after the passage referenced above, Aristotle goes on to say: yet, if the object heated or frozen is large, part after part will be affected. But the first part had to be altered all at once and suddenly by the agent. (Aristotle, De sensu et sensato, c. 6, 447a3; cf. St. Thomas, Commentary on De sensu, tr. 1, c. 15.)

Yet, even in things that are altered all at once, it is possible to discover some kind of succession, because, since alteration depends on contact with the cause that alters, the parts closer to the body that causes the alteration will more completely receive at the very beginning an impression from the agent; thus, the state of perfect alteration is reached successively according to an order of parts. This is especially true when the body to be altered has something that resists the power of the altering cause.

Consequently, the conclusion—namely, that what is being changed is, while it is being changed, partly in the terminus from which and partly in the terminus to which (in the sense that one part reaches the terminus to which before another does)—is unqualifiedly and absolutely true in local motion. But, in alteration, it is qualifiedly true, as we have said.

803. Some, on the other hand, have held that the present doctrine is truer when applied to alteration than when applied to local motion, For they hold that the statement “what is being changed is partly in the terminus from which and partly in the terminus to which” is not to be interpreted as meaning that one part of the thing in motion is in one terminus and another in the other, but that reference is being made to the parts of the termini; that is, that what is being moved has part of the terminus from which and part of the terminus to which, as something in motion from white to black is at the very beginning neither perfectly white nor perfectly black, but imperfectly partakes of both. But, in local motion, this does not seem to be true except in the sense that the thing in motion, while it is between the two extremities, somehow partakes of both extremities. For example, if earth were to be moved to the place normal to fire, then, while it was in the region proper to air, it would have a part of each extremity (that is, earth and fire), in the sense that the place of air is above that of earth and below that of fire.

804. But this is a forced explanation and against Aristotle’s opinion. For in the first place, we need only look at the very words of Aristotle. For he says as a conclusion that it follows, therefore, that part of that which is being changed must be at the starting point, and part at the goal. He is speaking therefore about the parts of the mobile, and not about the parts of the termini.

In the second place, it is against Aristotle’s intention. For Aristotle brings to light facts that will prove that what is being changed is divisible—a statement that could not be proved if you held to the interpretation given.

Hence, Avempace said that Aristotle does not intend here to prove that a mobile can be divided into quantitative parts, but according to forms, in the sense that what is being moved from contrary to contrary has, while it is being moved, something from each contrary. But the intention of Aristotle is expressly to show that a mobile can be divided into its quantitative parts, just as any continuum, for he makes use of that fact in the demonstrations that will follow. (Lect. 6ff.)

Nor can we heed the opinion that such an interpretation will help to prove that a mobile can be divided on the basis of continuity. For the very fact that a mobile, while it is being moved, partakes of each terminus, not perfectly possessing the terminus to which all at once, reveals that change is divisible on the basis of continuity. And thus, since a divisible cannot exist in an indivisible, it follows that the mobile also can be divided as a continuum. For in the matters to follow, Aristotle will clearly prove that motion is divisible, because the mobile is divisible. (Lect. 6.) Hence, if he intended to conclude that a mobile is divisible because motion is divisible, he would be arguing in a circle.

Third, such an interpretation appears to conflict with Aristotle’s own interpretation at here, by “goal of change,” I mean that into which it is first changed during the process of change (234b17).

This shows that he does not intend to say that it is partly in the terminus from which and partly in the terminus to which just because it is midway and, as it were, sharing in both extremities, but because, in regard to one part of itself, it is in one extreme, and according to another part, in what is midway.

805. But, with respect to this explanation of Aristotle, one might wonder why he says that into which it is first changed, for it seems impossible to discover that into which it is first changed, since a magnitude can be divided to infinity.

Therefore, it must be said that that into which it is first changed in local motion is the place next to but not part of the place from which the local motion starts. For if we took it to mean a place that included part of the original place, we would not be assigning the first place into which it is being moved.

The following example will illustrate this. Let AB be the place from which a mobile is being moved, and let BC be the adjacent place equal to AB. Now, since AB can be divided, let it be divided at D, and take a point G near C such that the place GC is equal to BD. It is clear that the mobile will arrive at DG before it reaches BC. Moreover, since AD can be divided, a place prior to DG can be taken, and so on to infinity.

Similarly, in regard to alteration, the first into which something is changed must be considered to be an intermediate; for example, when something is changed from white to black, the first into which the subject is changed is into grey, not into less white.