Commentary Aristotle Physics
Lecture 20. How motion and other things are in time
Time is a measure of motion and of being moved, and it measures the motion by determining a motion that will measure exactly the whole motion, as the cubit does the length by determining an amount that will measure out the whole. Further, “to be in time” means for motion that both it and its essence are measured by time: it simultaneously measures both the motion and its essence, and this is what being in time means for it, that its essence should be measured.
Clearly, then, “to be in time” has the same meaning for other things also, namely, that their being should be measured by time. “To be in time” is one of two things: either to exist when time exists, or as we say of some things that they are “in number.” The latter means either what is a part or mode of number—in general, something that belongs to number—or that things have a number. Now, since time is number, the “now” and the “before” and the like are in time, just as “unit” and “odd” and “even” are in number, namely, in the sense that the one set belongs to number, the other to time. But things are in time as they are in number. If this is so, they are contained by time as things in place are contained by place. Plainly, too, to be in time does not mean to co-exist with time, any more than to be in motion or in place means to co-exist with motion or place. For if “to be in something” is to mean this, then all things will be in anything, and the heaven will be in a grain because, when the grain is, then also is the heaven. But this is a merely accidental conjunction, but the other is necessarily involved: what is in time necessarily involves that there is time when it is, and what is in motion, that there is motion when it is.
Since what is in time is so in the same sense as what is in number is so, a time greater than everything in time can be found. So, it is necessary that all the things in time should be contained by time, just like other things also that are in anything, such as the things in place by place.
A thing, then, will be affected by time, just as we are accustomed to say that time wastes things away, that all things grow old through time, and that there is oblivion owing to the lapse of time, but we do not say the same of getting to know or of becoming young or good. For time is by its nature the cause rather of decay, since it is the number of change, and change removes what is.
Hence, plainly, things that are always are not, as such, in time, for they are not contained in time, nor is their being measured by time.
A proof of this is that none of them is affected by time, which indicates that they are not in time.
Since time is the measure of motion, it will be the measure of rest too, indirectly, since all rest is in time.
For it does not follow that what is in time is moved, though what is in motion is necessarily moved. Time is not motion, but the number of motion, and what is at rest can also be in the number of motion.
Not every immobile thing can be said to be at rest, but only that which can be moved, though it actually is not moved, as was said above. “To be in number” means that there is a number of the thing and that its being is measured by the number in which it is. Hence, if a thing is “in time,” it will be measured by time.
But time will measure what is moved and what is at rest, the one qua moved and the other qua at rest; it will measure their motion and rest respectively.
Hence, what is moved will not be measurable by the time simply insofar as it has quantity, but insofar as its motion has quantity.
Thus, none of the things that are neither moved nor at rest are in time, for to be in time is to be measured by time, while time is the measure of motion and rest.
Plainly, then, neither will everything that does not exist be in time, namely, those non-existent things that cannot exist, as the diagonal cannot be commensurate with the side.
Generally, if time is directly the measure of motion and indirectly of other things, it is clear that a thing whose existence is measured by it will have its existence in motion and rest.
Those things, therefore, that are subject to corruption and generation—generally, those that at one time exist but at another do not—are necessarily in time, for there is a greater time that will extend both beyond their existence and beyond the time that measures their existence.
Of things that do not exist but are contained by time, some were, as Homer once was, and some will be, such as a future event, and this depends on the direction in which time contains them.
If on both, they have both modes of existence. As to such things as it does not contain in any way, they neither were nor are nor will be.
These are those non-existents whose opposites always are, as the incommensurability of the diagonal always is—and this will not be in time. Nor will the commensurability, therefore.
Hence, this eternally is not, because it is contrary to what eternally is. A thing whose contrary is not eternal can be and not be, and it is of such things that there is generation and passing away.
600. After settling the question of time in itself, the Philosopher now discusses it in relation to things that are in time.
As to this, he does two things:
first, he compares time with things that exist in time;
second, with things that exist in the now, at “the ‘now’ is the link” (222a10; [612]).
Concerning the first, he does two things:
first, he compares time to motion;
second, to other things that are in time, at “clearly, then, ‘to be in time’” (221a7; [602]).
601. In regard to the first, note that motion is related to time in a way different from the way other things are related to it. Motion is measured by time both as to what it is and as to its duration, that is, its existence. But other things, such as a man or a stone, are measured by time as to their existence or their duration insofar as they have a changeable existence; but, as to what they are in themselves, they are not measured by time. Rather, it is the now of time that corresponds to what they are in themselves, as was said above.
He says therefore (220b32) that time is the measure of motion itself, and of being moved, by which he means the duration of motion. Now, time measures motion because a certain part of the motion is determined by time, which part then measures the whole motion. And this is necessary, because each thing is measured by something of the same genus, as is said in Metaphysics 10.
This is evident in the measures of lengths, since a cubit can measure the entire length of a piece of cloth or of a road, because the cubit determines some part of the length, which part then measures the whole. Likewise, by means of a part of motion, time measures an entire motion, for by means of the motion of one hour, the motion of a whole day is measured, and by means of the daily motion, the yearly motion is measured. Therefore, since motion is measured by times, for motion to be in time is nothing more than for it to be measured by time, both as to what it is and as to its duration, for according to both aspects, it is measured by time, as was said.
602. Then, at “clearly, then, ‘to be in time’” (221a7), he shows how it is related to other things:
first, how other things are in time;
second, what things belong in time, at “since what is in time” (221a26; [603]).
He first says (221a7) that, since for motion to be in time is for it to be measured by time, both as to itself and as to its existence, it is clear that it is likewise the same for other things to exist in time and to be measured by time, not as to what they are, but as to their existence, since motion is essentially measured by time, but other things only insofar as they have motion.
He proves that, for a thing to exist in time is to have its existence measured by time in the following way. To be in time can mean two things:
first, as something is said to exist in time, because it co-exists with time;
second, as something is said to exist in time in the way that things are said to exist in number.
And this latter also has two meanings:
For something is present as a part in a number, as two is in four, and as its proper passion, such as even and odd, or whatever else that belongs to number;
or it can be there not because it is anything pertaining to number, but because number belongs to it as numbered, as men may be said to be in such and such a number.
But, because time is a number, something can be in time in both ways. For the now, and before and after, and things of this sort exist in time as unity exists in number, of which it is a part, and as do even and odd, which are passions of number, and as do the superfluous and the perfect. (A number is called “perfect” if the sum of the parts measuring it equals the number; for example, six is measured by one, two, and three, which, added together, equal six. A number is called “superfluous” if its divisors total up to a number that exceeds it: for example, twelve is measured by one, two, three, four, and six, which equal sixteen when added together.) And that is the way in which some things exist in time, as being something of time. But things that are not something of time are said to be in time as things numbered exist in number. Consequently, these latter things that are in time must be contained under time as under a number, just as things in place are contained under place as under a measure.
Then he explains the very first way of something’s existing in time. And he says it is clear that it is not the same thing to exist in time and to exist when time exists, just as it is not the same to be in motion and in place and to be in existence when place and motion exist. Otherwise, it would follow that all things would be in anything; for example, the heavens would be in a grain of millet, because when the millet exists, the heavens exist.
There are two differences between these situations. When something is said to be when something else exists, it is accidental to the one that it exists at the same time as the other; but that in which something exists as in a measure follows necessarily, as time necessarily follows upon that which is in time, and motion upon that which is in motion, so that they are together.
603. Then, at “since what is in time” (221a26), he shows to what things it belongs to be in time.
First, he shows that not all beings exist in time;
second, that not all non-beings do, at “hence, plainly” (221b3; [611]).
As to the first, he does two things:
first, he shows that things that are always do not exist in time;
second, that nevertheless things that are at rest are in time as such, at “since time is the measure” (221b7; [606]).
As to the first, he does two things:
first, he mentions the facts from which he proceeds to the manifestation of his proposition;
second, he argues for the proposition, at “hence, plainly” (221b3; [605]).
Now, he mentions two things.
The first of these (221a26) is that, when something is in time as the numbered is in a number, then necessarily there is some time that can be taken larger than everything that exists in that time, just as it is possible to take a number larger than everything that is numbered. Consequently, all things that exist in time are of necessity contained under time and comprehended under it, just as things in place are comprehended under place.
604. The second thing is then mentioned, at “a thing, then, will be” (221a30), and it is that whatever exists in time suffers something under time, in the sense of suffering that pertains to defect.
And he proves this from the way people ordinarily speak: we are accustomed to say that length of time wastes things away—that is, decays and corrupts them—and again that, on account of time, all things that exist in time grow old, and that on account of time forgetting occurs, for things we have recently learned remain in the memory but, with length of time, they slip away.
And, lest anyone should say that perfections are attributed to time as well as defects, he subsequently forestalls this, giving, in effect, three reasons over and above the three already given.
Complementing his statement that forgetting occurs on account of time, he adds that no one learns on account of time, for if a person should neglect study for a long time, he does not on that account learn, while he does forget on account of time.
In keeping with his statement that all things grow old in time, he adds that nothing becomes new on account of time. A thing is not renewed on account of a long existence; rather, it becomes antiquated.
To match his statement that time wastes things away, he adds that time does not make a thing good (that is, whole and perfect), but rather wasted and decayed. The reason for this is that time corrupts things even when there is no other manifest corrupting agent. All this is due to the very account of time, for time is the number of motion, and it is in the account of motion to put a distance between what now is and the condition it was in previously. Consequently, since time is the number of the first motion, which causes mutability in all things, it follows that length of time causes all things that exist in time to be removed from their former condition.
605. Then, at “hence, plainly” (221b3), he argues for his proposition from the foregoing premises.
He does so first of all from the first premise. It has been shown that whatever exists in time is contained under time, while whatever things are always are not contained under time as exceeding time. Neither is the being—that is, the duration—of such things measured under time, since they endure to infinity, and the infinite cannot be measured. Therefore, those things that exist forever are not in time. But this is true insofar as they exist always. For the heavenly bodies exist forever according to the being of their substance, but not in regard to where they are; consequently, their duration is not measured by time, yet their local motion is.
Second, at “a proof of this” (221b5), he proves the same point from the second of the points laid down before. And he says that a sign that those things that exist forever do not exist in time is that they do not suffer from time, as though not existing in time. They neither waste away nor grow old, as was said of things that exist in time.
606. Then, at “since time is the measure” (221b7), because he had shown that those things that exist forever do not exist in time, while those things that are at rest also remain the same way, someone might think that things at rest are, as such, not measured by time. Therefore, to obviate this, he shows that time is also the measure of rest.
And, in regard to this, he does five things.
First, he proposes what he intends and says that, because time is the measure of motion per se, it will also be per accidens the measure of rest, since all rest is in time just as all motion is.
607. Second, at “for it does not follow” (221b9), he excludes something that might lead one to think that rest is not measured by time. For since time is the measure of motion, someone might suppose that a thing at rest, because it is not in motion, is not in time. Consequently, to exclude this, he says that not everything in time need be in motion in the same way that everything in motion has necessarily to be moved. For time is not a motion, but the number of motion. Now, it occurs that not only what is being moved may be in the number of motion but also what is at rest.
608. Third, at “not every immobile thing” (221b12), he proves the proposition that a thing at rest is in the number of motion, as to be measured by time. To do this, he adduces that not every immobile thing (not everything that is not in motion) is at rest. Rather, a thing at rest is something that is by nature disposed to be moved but is deprived of motion, as it was said above in book 3 that that is moved whose immobility is rest, since rest is not the negation of motion, but its privation.
Consequently, it is evident that the being of a thing at rest is the being of a mobile being. Hence, since the being of a mobile being is in time and is measured by time, the being of a thing at rest is measured by time. Now, we are saying here that a thing is in time as in a number, because there is some number for that thing, and because its existence is measured by the number of time. Thus, it is clear that a thing at rest exists in time and is measured by time not insofar as it is rest, but insofar as it is a mobile being. That is why he said in the beginning that time is per se a measure of motion but per accidens a measure of rest.
609. Fourth, at “but time will measure” (221b16), he shows in what sense a mobile thing and a thing at rest are measured by time. And he says that time measures what is moved or at rest not insofar as it is a stone or a man, but insofar as it is in motion or at rest. For measuring is properly due to quantity, and so time is properly the measure of that whose quantity is measured by time. Now, both the quantity of motion and the quantity of rest are known from the measuring done by time, but not the quantity of the thing in motion. Hence, the thing in motion is not measured by time according to its own proper quantity, but according to the quantity of its motion. From this it is clear that time properly is the measure of motion and of rest: of motion per se, but of rest per accidens.
610. Fifth, at “thus, none of the things” (221b20), he adduces a certain corollary from the foregoing. For if nothing is measured by time except insofar as it is in motion or at rest, it follows that whatsoever things are neither in motion nor at rest, such as the separated substances, are not in time, for being in motion or at rest is to be in time, to be measured by time. Time is the measure of motion and of rest, as is clear from the foregoing.
611. Then, at “plainly, then” (221b23), he shows that not all non-beings are in time. He says it is clear from the foregoing that not every non-being is in time, as in the case of things that cannot be otherwise, such as that a diagonal be commensurate with the side of a square. For this is impossible, because it can never be true. Now, such things are not measured by time.
And he proves it in this way: time is primarily and per se the measure of motion, and anything else is measured by time only per accidens. Consequently, whatever is measured by time must be capable of motion and rest. Hence, things generable and corruptible, and all things that sometimes exist and sometimes not, exist in time, since they are in motion and rest, for some time can be found that is greater than they are and that exceeds their duration, and which for that reason measures their substances not in regard to the nature of the substances, but in regard to their existence or duration.
But, among things that do not exist but are nevertheless contained by time: some things existed at one time, as Homer; others will exist, as some future event; or, if they are contained both by past and present time, they both will be and were. But things that are in no way contained by time neither are, nor were, nor will be. Such are things that forever are not and whose opposites forever are—for example, that a diagonal be not commensurable to the side forever is, and hence it is not measured by time. And, for this reason, neither is its contrary measured by time, namely, that the diagonal is symmetrical, that is, commensurable. The reason that it forever is not is that it is the contrary of what forever is.
But, of whatever things the contrary does not always exist, such things can exist and not exist, and are subject to generation and corruption; such things are measured by time.