Commentary Aristotle Physics
Lecture 19. Clarification of certain things said about time
It is clear, then, that time is “the number of motion in respect of the before and after” and is continuous, since it is an attribute of what is continuous. The smallest number, in the strict sense of the word “number,” is two. But of one certain number, sometimes there is a minimum, sometimes not: for instance, of a line, the smallest in respect of multiplicity is two (or, if you like, one), but in respect of size, there is no minimum; for every line is divided to infinity. Hence, it is so with time. In respect of number, the minimum is one (or two); in point of extent, there is no minimum.
It is clear, too, that time is not described as fast or slow, but as many or few and as long or short.
For as continuous, it is long or short, and as a number, many or few, but it is not fast or slow—any more than any number with which we number is fast or slow.
Further, time is the same everywhere at once, but not the same time before and after, for while the present change is one, the change that has happened and that which will happen are different. Time is not number with which we count, but the number of things that are counted, and this is always different according as it occurs before or after, for the “nows” are different. And the number of a hundred horses and a hundred men is the same, but the things numbered are different—the horses from the men.
Further, as a motion can be one and the same again and again, so too can time—for instance, a year or a spring or an autumn.
Not only do we measure the motion by the time, but also the time by the motion, because they define each other. The time marks the motion, since it is its number, and the motion the time. We describe the time as much or little, measuring it by the motion, just as we know the number by what is numbered—for instance, the number of the horses by one horse as the unit. For we know how many horses there are by the use of the number; and again, by using the one horse as unit, we know the number of the horses itself. So it is with the time and the motion, for we measure the motion by the time and vice versa.
It is natural that this should happen, for the motion goes with the distance and the time with the motion, because they are quanta and continuous and divisible. The motion has these attributes because the distance is of this nature, and the time has them because of the motion.
And we measure both the distance by the motion and the motion by the distance, for we say that the road is long if the journey is long and that this is long if the road is long—the time, too, if the motion, and the motion, if the time.
593. Having defined time, the Philosopher now, in the light of that definition, gives an explanation of those things that are said about time.
About this, he does four things:
first, he shows in what sense a smallest part is to be found in time, and in what sense it is not;
second, he shows why time is said to be much and little, short and long, but not fast and slow, at “it is clear, too, that time” (220a32; [595]);
third, he shows in what sense time is the same, and in what sense it is not, at “further, there is the same” (220b3; [596]);
fourth, he shows how time is known through motion and vice-versa, at “not only do we” (220b14; [598]).
594. He says first (220a24) that the previously given definition of time makes clear that time is the number of motion according to before and after, as was expounded above, and that time is a type of continuum, as is likewise manifest from what has gone before. For although it does not have continuity insofar as it is a number, yet it has continuity by reason of that of which it is the number, for it is the number of a continuum, namely, of motion, as was said above. For time is not a number absolutely, but a number of something numbered. Among absolute numbers, there is unequivocally a minimum to be found, namely, two.
But, if we consider one certain number, namely, the number of something that is continuous, then there is in one sense a minimum and in one sense no minimum, because in the order of multitude there is a minimum, but not in the order of magnitude. For example, in a plurality of lines, there is a minimum according to plurality, namely, one line or two lines (one if you consider what is the minimum in number absolutely; two if you mean that which is least in the genus of number, having the account of number).
But, in respect of magnitude, there is no minimum in lines such that there would be some smallest lines, because it is always possible to divide any line whatsoever. A parallel situation is found in time, for there is a minimum according to multitude, namely, one or two—for example, one year or two years or two days or two hours. But, in the order of magnitude, there is no minimum, for of any given time, there are parts into which it may be divided.
595. Then, at “it is clear, too” (220a32), he gives a reason that time is not said to be slow or fast, but great and small or short and long. For it has already been shown that time is both a number and a continuum. Insofar, therefore, as it is the latter, time is said to be long and short; insofar as it is a number, it is said to be great and small. But to be fast and slow in no way belongs to number, neither to number absolutely (as is plain) nor to the number of some things. For to be fast or slow is said of something insofar as it is numbered: for a motion is called fast insofar as it is counted off in a short time, and slow conversely. Hence, it is clear that, in no sense can time be called fast or slow.
596. Then, at “further, there is the same” (220b3), he shows how time is the same and how not the same:
first, how it is the same or not the same absolutely;
second, how it is the same in a certain respect, at “further, as a motion” (220b12; [597]).
He therefore says first that the time existing at a given moment is the same everywhere; that is, it is the same in respect to everything that is being moved anywhere. For it is not diversified by reason of the diverse mobiles, but by reason of the diverse parts of the same motion. For this reason, a prior time and a later time are not the same. Why? Because the first and present motion, of which time is primarily and principally the number, is one; but one part of this motion has already taken place and is past, and another will be in the future. Hence, there is one time that is past and another time that is future.
This is so because time is not number absolutely, but the number of something numbered, namely, of the before and after in motion. And this number always varies and is before and after, because the nows, like before and after, are always other. But, if time were number absolutely, then the time corresponding to the change that is past and the time corresponding to the change that is to come would be the same, for number absolutely is one and the same of different things counted, such as in the case of one hundred horses and one hundred men. But number numbered varies with different things. For one hundred horses are not the same as one hundred men. Since time is the number of before and after in motion, and since the before and after of a past motion are not the same as those of that which follow, therefore the past time and the future time are different.
597. Then, at “further, as a motion” (220b12), he shows how the same time returns in a certain respect. And he says that, in the same way that one and the same motion may be repeated, so may one and the same time.
For one and the same motion can be duplicated specifically, but not numerically; for it is from the same sign of the ram that the sun first moves and later will move the following year. Therefore, just as there has been winter or spring or summer or fall, so also there will be not, indeed, the same one in number, but in species.
598. Then, at “not only do we” (220b14), he shows that, just as we know motion from time, so also time from motion:
first, by reason of number and the thing numbered;
second, from the likeness existing between magnitude and motion, at “it is natural that” (220b24; [599]).
Thus, he says first (220b14) that we not only measure time by motion, but motion by time, because each is defined in terms of the other. For one must take the quantity of the one according to the quantity of the other. Now, that time should determine motion comes about because it is the number of motion, but conversely, motion determines time as to us. For we sometimes perceive a quantity of time by means of motion, as when we declare a time to be long or short according to a measure of motion certain to us, since we sometimes know a number through the things that can be counted, and conversely. For we know by this number a multitude of horses, and likewise, by one horse, we know the number of horses. We would not know how many thousands there were unless we know what a thousand was. The same holds for time and motion: when a quantity of time is certain to us but the quantity of motion unknown, then we measure the motion by time, but we do the opposite when the motion is known and the time unknown.
599. Then, at “it is natural that” (220b24), he shows the same thing by comparing motion and magnitude. And he says that what has been just said of time and motion happens reasonably, for just as motion imitates magnitude in quantity and continuity and divisibility, so also does time imitate motion, since the latter are found in motion on account of their presence in magnitude, and they are found in time on account of their presence in motion. For we measure magnitude by means of motion, and motion by means of magnitude. We say that a road is long when we notice that our motion over it was long; and conversely, when we consider the magnitude of the road, we say that our motion was long. The same holds when relating time and motion, as we said above.