Commentary Aristotle Physics
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. 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. 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 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. 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, 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.