Commentary Aristotle Physics
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.
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. 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. 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.
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, 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.
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.