Lecture 23 — Solution of difficulties about the existence and unity of time

It is also worth considering how time can be related to the soul and why time is thought to be in everything, both in earth and in sea and in heaven.

Is it because it is an attribute, or state, or motion (since it is the number of motion) and all these things are movable (for they are all in place), and time and motion are together, both in respect of potentiality and in respect of act?

Whether or not time would exist if soul did not exist is a question that may fairly be asked.

For if there cannot be someone to count, there cannot be anything that can be counted, such that there evidently cannot be number; for number is either what has been or can be counted. But if nothing but soul, or reason in soul, is qualified to count, there would not be time unless there were soul,

but only that of which time is a being of a sort, that is, if motion can exist without soul, and the before and after are attributes of motion, and time is these qua numerable.

One might also raise the question what sort of motion time is the number of.

Must we not say “of any kind”? For things both come into being in time and pass away, and grow, and are altered in time, and are moved locally; thus, it is of each motion qua motion that time is the number. And so it is simply the number of continuous motion, not of any particular kind of it.

But other things as well may have been moved now, and there would be a number of each of the two motions. Is there another time, then, and will there be two equal times at once?

Surely not. A time that is both similar and simultaneous is one and the same time, and even those that are not simultaneous are one in kind, for if there were dogs and horses, and seven of each, it would be the same number.

So, too, motions that have simultaneous limits have the same time, yet the one may in fact be fast and the other not, and one may be locomotion and the other alteration; still the time of the two changes is the same if their number also is equal and simultaneous. For this reason, while the motions are different and separate, the time is everywhere the same, because the number of equal and simultaneous motions is everywhere one and the same.

Now, there is such a thing as locomotion, and in locomotion, there is included circular motion, and everything is measured by some one thing near it, units by a unit, horses by a horse, and similarly times by some definite time, and as we said, time is measured by motion as well as motion by time (this being so because, by a motion definite in time, the quantity both of the motion and of the time is measured).

If, then, what is first is the measure of all things that are near it, regular circular motion is above all else the measure, because the number of this is the best known. Now, neither alteration nor increase nor coming into being can be regular, but locomotion can be.

This is also why time is thought to be the motion of the sphere, because the other motions are measured by this, and time by this motion.

This also explains the common saying that human affairs form a circle, and that there is a circle in all other things that have a natural motion and coming into being and passing away. This is because all other things are discriminated by time and end and begin as though conforming to a cycle, for even time itself is thought to be a circle. And this opinion again is held because time is the measure of this kind of locomotion and is itself measured by such. To say that the things that come into being form a circle is to say that there is a circle of time, and this is to say that it is measured by the circular motion, for apart from the measure nothing else to be measured is observed; the whole is just a plurality of measures.

It is said rightly, too, that the number of the sheep and of the dogs is the same number if the two numbers are equal, but not the same ten or the same ten things, just as the equilateral and the scalene are not the same triangle, yet they are the same figure, because they are both triangles.

For things are called the same so-and-so if they do not differ by a difference that divides that thing, but not if they do; for instance, triangle differs from triangle by a difference that divides triangle, and therefore they are different triangles;

yet they do not differ by a difference that divides figure, but are in one and the same division of it.

For a figure of the one kind is a circle and a figure of another kind a triangle, and a triangle of one kind is equilateral and a triangle of another kind scalene. They are the same figure, then—triangle—but not the same triangle.

Therefore, the number of two groups also is the same number (for their number does not differ by a differentia of number), but it is not the same ten, for the things of which it is asserted differ: one group are dogs, and the other horses. We have now discussed time—both time itself and the matters appropriate to the consideration of it.

625. After determining the truth about time, the Philosopher now settles certain doubts about time:

first, in regard to the existence of time;

second, in regard to the unity of time, at one might also raise (223a29; [630]).

As to the first, he does two things:

first, he raises the doubts;

second, he solves them, at is it because it is an attribute (223a18; [626]).

He says first (223a16) that certain problems require diligent consideration, such as that of how time is related to the soul and that of how time seems to be everywhere, namely, on earth, on the sea, and in the air.

626. Then, at is it because it is an attribute (223a18), he answers these questions:

first, he answers the second question, because it is easier;

second, he answers the first one, at whether or not time (223a21; [627]).

He says, therefore (223a18), that time is a certain accident of motion, because it is its number (an accident is often called a “possession” and “passion”). Hence, wherever there is motion, there must be time. Now, all bodies are mobile—if not with other motions, at least with respect to local motion, because all things are in place. And, because someone could say that, although they are mobile, they are not all being moved, but some are at rest, and thus time does not seem to be in all, to counter this, he adds that time accompanies motion, whether motion be actual or potential. For things that are capable of motion and are not actually being moved are at rest. But time measures not only motion, but rest as well, as was said above. (Lect. 20, n. 566ff.) Hence, wherever there is motion either actually or potentially, there time is.

627. Then, at whether or not time (223a21), he answers the first question.

As to this, he does three things:

first, he raises the question;

second, he gives an objection to the question, at for if there cannot be (223a22; [628]);

third, he resolves the question, at but only that of which (223b1; [629]).

The question, therefore, is this: would time exist if no soul existed?

628. Second, at for if there cannot be (223a22), he objects, saying it would not. For if it were impossible for something able to count to exist, it would be impossible for some thing countable to exist, namely, be able to be counted. But, if there is nothing countable, then there is no number, because number does not exist except in what is being actually counted or what is potentially countable. Consequently, if there is no one able to count, there is no number. But only the soul is disposed by nature for counting, and among the parts of the soul, only the intellect, since counting consists in comparing the things counted with one primary measure, and comparing is a function of reason. Consequently, if there is no intellective soul, there is no number. But time is a number, as was said. (Lect. 17, n. 580.) If, therefore, there is no intellective soul, there is no time.

629. Then, at but only that of which (223a26), he answers the question. He says that it is necessary either to say either that time is not, if the soul is not, or to say what is truer, that time is still some sort of being even without the soul’s existing, similar to motion’s existing without the soul’s existing. For as motion is posited, so is it also necessary to posit time, because before and after exist in motion, and it is these things (the before and after in motion), insofar as they are numerable, that are time.

To make this solution more evident, it must be considered that, once a series of numbered things is posited, it is necessary to posit number. Hence just as counted things depend on someone’s counting, so also does their number.

However, the existence of counted things does not depend on an intellect—unless it be an intellect that is the cause of things, as is the divine intellect; it does not depend on the intellect of the soul.

Hence, neither does the number of things depend on the intellect in the human soul; only the counting of them, which counting is an act of the soul, depends on the intellect in the soul.

Consequently, just as there can be things perceptible to sense even though no sense exists, and intelligible even though no intelligence exists, so there can exist both countable things and number even though no counter exist.

But perhaps the conditional he first mentioned is true, that if no counter could exist, nothing countable could exist, just as the proposition is true that, if there could be no one to sense, there could be nothing sensible. For if there is something sensible, it can be sensed, and if it can be sensed, there can be something to sense it—although it does not follow that, if there is something sensible, there is something sensing. In like manner, it follows that, if there is something countable, there can be someone to count. Consequently, if no one to count could exist, nothing countable could exist. However, it does not follow that, if there is no one counting, there is nothing countable, which is the objection raised by the Philosopher.

Therefore, if motion had a fixed existence in reality, as a stone or a horse has, one could say unqualifiedly that, just as, with no soul existing, there exists a number of stones, so also, with no soul existing, there would exist a number of motion, which is time.

However, motion does not have a fixed existence in reality, nor is anything actual of motion found in things, but a certain indivisible of motion that divides motion; indeed, the totality of motion comes to be on account of the mind considering and comparing a previous state of the mobile to a subsequent state.

According to this, then, time also has no existence outside the soul except according to its indivisible; but the totality of time is had by an ordering process of the mind enumerating the prior and subsequent in motion, as was said above. (Lect. 17, n. 572ff.) And therefore the Philosopher said significantly that, with no soul existing, time is a being of a sort, that is, imperfectly. This is similar to the statement that motion exists imperfectly without a soul existing.

So, this answers the arguments mentioned earlier, (Lect. 15, n. 559.) to show that time does not exist on the ground that it is composed of parts that do not exist. For it is clear from the foregoing that, like motion, it does not have perfect existence outside the soul.

630. Then, at one might also raise (223a29), he raises a question about the oneness of time, or about the relation of time to motion.

As to this, he does three things:

first, he raises the question;

second, he answers it, at must we not say (223a30);

third, he explains something he took as a presupposition, at it is said rightly (224a2; [637]).

So he says first (223a29) that, since time is the number of motion, there is question of whose, or of what sort, motion it is the number.

Then, at must we not say (223a30), he answers the question.

First, he rejects a false solution;

second, he gives the true one, at now, there is such (223b12; [634]).

In regard to the first, he does three things:

first, he gives the false answer;

second, he disproves it by leading to a discrepancy, at but other things as well (223b1; [632]);

third, he shows that this discrepancy is really an impossibility, at surely not (223b3; [633]).

631. The first solution, therefore, is that time is the number of any motion whatsoever. To prove this, he brings up that every motion exists in time—namely, generation, and increase, and alteration, and local motion. Now, what is found in every motion belongs to motion as such. But to exist in time is to be numbered by time. Consequently, it seems that every motion as such has a number; hence, since time is the number of motion, it seems to follow that time is the number of each and every continuous motion and not of some definite motion.

632. Then, at but other things as well (223b1), he disproves this solution. Let us assume two things that are moving together: if, therefore, time is the number of any motion at all, it will follow that, of two simultaneous motions, each will have its own time, and so it will further follow that two equal times exist at once—for instance, two days or two hours. Now, it is not strange for two unequal times to exist at once, such as a day and an hour.

633. Then, at surely not (223b3), he shows that it is impossible for two equal times to exist at once. For every time that is simultaneous and similar—that is, equal—is one; but time that is not simultaneous is not numerically one, although it is one in species, as day with day and year with year. And he explains this by a similarity in other things that are numbered.

For if there are seven horses and seven dogs, there is no difference so far as the number is concerned, but the difference is due to the species of the things counted.

In like manner, for all motions that have simultaneous terms, both as to their beginning and as to their end, there is the same time; yet the motions differ according to their proper accounts, insofar as one, perhaps, is fast and the other slow, or one is local motion and the other alteration.

But the time is the same if the number of the alteration and of the local motion is the same, supposing, of course, that they are simultaneous.

Consequently, motions must be distinct from one another, but the time in all of them is the same—because there is one and the same number for all those that are equal and simultaneous, no matter where they occur.

634. Then, at now, there is such (223b12), he gives the true solution.

Concerning this, he does three things:

first, he sets out certain facts required for the solution;

second, from these, he arrives at the solution, at if, then, what is first (223b18; [635]);

third, he makes the solution clear by appealing to the statements of others, at this is also why (223b21; [636]).

In regard to the first, he mentions three preliminary facts.

The first of these is that, among motions, the first and more simple and regular is local motion, and among these, circular motion, as will be proved in book 8. (Lect. 14ff.)

The second is that each thing is numbered by something near it, that is, by something of the same genus, as units by a unit and horses by a horse, as is clear in Metaphysics 10. (Aristotle, Metaphysics I.1; cf. St. Thomas, Commentary on Metaphysics, bk. 10, lect. 2.) Hence, time must be measured by some definite time, as we see that all times are measured by the day.

The third presupposition is that time is measured by motion, and motion by time, as was said above. (Lect. 19, n. 598.) This is so because it is in terms of some definite motion and some definite time that the quantity of any motion and time is measured.

635. Then, at if, then, what is first (223b18), he concludes from the foregoing that, if something that is first is the measure of all things that are near it—that is, of all the things in its genus—it is necessary that circular motion, which is regular above all, be the measure of all motions. Now, a motion is called regular if it is one and uniform. But such regularity cannot be found in alteration and growth, because they are not incessantly continuous or of constant speed. But regularity can be found in change of place, because there can be a local motion that is continuous and uniform, and the only such motion is circular motion, as will be proved in book 8. (Lect. 19–20.)

Now, among circular motions, the most uniform and regular is the first motion, which turns the whole firmament in a daily cycle; hence, that revolution, as being the first and simplest and most regular, is the measure of all motions. But a regular motion must be the measure and number of the others, because every measure ought to be most certain—and those that are uniform are such.

We can gather from this that, if the first circular motion measures every motion and motions are measured by time insofar as they are measured by some motion, it has to be said that time is the number of the first circular motion, according to which time is measured, and in relation to which are measured all other motions that are timed.

636. Then, at this also is why (223b21), he corroborates his solution by appealing to the opinions of others.

He does so, first of all, by the opinion of those who were led to assert that the motion of the heavenly sphere is time, (Cf. lect. 16, n. 565ff.) for the reason that all other motions, and time itself, are measured by that motion, for it is evident that we speak of a complete day or year by reckoning from the motion of the heavens;

second, from a common saying, at this also explains (223b23). And he says that, because of this—namely, that time is the number of the first circular motion—it comes about that people are accustomed to say that there is a cycle in human affairs and in other things that move naturally and come into being and pass away. This is so because all such things are measured by time and have a beginning and an end in time, as if time moved in a circle, because time itself seems to be a certain circle. And this again seems to be so because time is a measure of circular motion and is also measured by such a circular motion. And therefore, to say that, of things that take place in time, there is a certain circle is nothing other than to say that time is a certain circle, which occurs because time is measured by a circular motion. For what is measured does not seem to be different from its measure, but rather, many measures are seen to make one whole, as many units make one number, and many measures of cloth one quantity of cloth. And this is true when a homogeneous measure is taken.

From all this, it is clear that time first measures and numbers the first circular motion and, through it, measures all other motions. Consequently, there is but one time, due to the oneness of the first motion; and yet whoever perceives any motion whatever perceives time, because mutability in all mobile things is caused from first motion, as was said above. (Lect. 17, n. 574.)

637. Then, at it is said rightly (224a2), he explains how something he mentioned above is to be understood. He said that the number of seven dogs and seven horses is the same number. How this is true he now explains. And he says that it is correct to say, if the number of certain different things is equal (for example, of sheep and dogs), that the number is the same—for example, if the sheep and the dogs are both ten. But it cannot be said that to be ten is the same for the dogs and sheep, for ten dogs are not the same ten as ten sheep. The reason for this is that a genus can be predicated, with the addition of unity or identity, of several individuals of the same species. In like manner, the remote genus can be predicated of several species existing under one proximate genus; but neither can the species be predicated of individuals, nor the proximate genus of diverse species, with the addition of unity or identity.

And he then gives an example of what he means. There are two species of triangle, the equilateral having three equal sides and scalene having three unequal sides. Now, figure is the genus for triangle. We therefore cannot say that equilateral and scalene are the same triangle, but we can say that they are the same figure, because both are contained under triangle, which is one species of figure. He gives the reason for this, which is that, since identical and diverse (or different) are opposed, we can speak of identity whenever no difference is found, but we cannot speak of identity where there is a difference. But it is clear that equilateral and scalene differ mutually by reason of a difference that divides triangle, because they are diverse species of triangle. But equilateral and scalene do not differ in respect of the difference figure; rather, they are contained under one and the same difference that divides figure.

And this is clear thus. If we divide figure into its species that are brought about by differences, it will be found that one species is a circle, another a triangle, and so on for the other species of figure. But, if we divide triangle, we will find that one species is equilateral, another scalene. It is clear, therefore, that equilateral and scalene are one figure, because they are contained under the one species of figure, the species triangle, but they are not one triangle, because they are diverse species of triangle.

The same thing applies to our proposition. Number is divided into diverse species, one of which is ten. Therefore, all things that are ten are said to have one number, because they do not differ from the other in regard to the species of their number, since they are contained under one and the same species of number. But we cannot say that they are the same ten, because the things being called “ten” are different, since some are dogs and some horses.

Aristotle seems to have brought up this point so that no one, in trying to uphold the unity of time, would be content with saying that there is one number for things that are equal in number, even though the things be diverse; for although one might have the same ten or three on account of a unity of species, yet it is not the same ten or three on account of the diversity in number as based on matter. Hence, according to this reasoning, it would follow that time would be specifically one, but not numerically. Therefore, to get at the true unity of time, we must have recourse to the unity of the first motion, which is the first thing measured by time, and by which time itself is measured.

Finally, in summary, he concludes that we have finished with our consideration of time, and of the things that are proper to a consideration of time.