Commentary Aristotle Physics
Lecture 17. The definition of time
We must take this as our starting point and try to discover what exactly it has to do with motion, since we wish to know what time is. Now, we perceive motion and time together, for even when it is dark and we are not being affected through the body, if any motion takes place in the mind, we at once suppose that some time also has elapsed.
And, further, when some time is thought to have passed, some motion also along with it seems to have taken place. Hence time is either motion or something of motion. Since, then, it is not motion, it must be the other.
But what is moved is moved from something to something, and all magnitude is continuous. Therefore, the motion goes with the magnitude. Because the magnitude is continuous, the motion too must be continuous, and if the motion, then the time. For the time that has passed is always thought to be in proportion to the motion.
The distinction of “before” and “after” holds primarily, then, in place—and there in virtue of relative position. Since, then, “before” and “after” hold in magnitude, they must hold also in motion, these corresponding to the things which are there. But the distinction of “before” and “after” must hold also in time, for time and motion always correspond with each other.
The “before” and “after” of these is identical in substratum with motion yet differs from it in definition and is not identical with motion.
But we apprehend time only when we have marked motion, marking it by “before” and “after”; and it is only when we have perceived “before” and “after” in motion that we say that time has elapsed.
Now, we mark them by judging that A and B are different and that some third thing is intermediate to them. When we think of the extremes as different from the middle and the mind pronounces that the “nows” are two, one before and one after, it is then that we say that there is time, and this that we say is time.
For what is bounded by the “now” is thought to be time—we may assume this. When, therefore, we perceive one “now,” and neither as before and after in a motion nor as an identity but in relation to a before and an after, no time is thought to have elapsed, because there has been no motion either. On the other hand, when we do perceive a “before” and an “after,” then we say that there is time. For time is just this—the number of motion according to “before” and “after.” Hence, time is not motion, but only motion insofar as it admits of enumeration.
A proof of this is that we discriminate the more or the less by number, but more or less motion by time. Time, then, is a kind of number.
Number, we must note, is used in two senses—both of what is numbered or the numerable and also of that by which we count. Time obviously is what is numbered, not that by which we count: these are different kinds of thing.
571. After treating of time dialectically, the Philosopher here begins to determine the truth.
First, he determines the truth concerning time;
second, he brings up and solves some objections about the truth already determined, at “it is also worth considering” (223a16; [625]).
In regard to the first, he does two things:
first, he comes to a conclusion about time absolutely;
second, in relation to things measured by time, at “time is a measure” (220b32; [600]).
As to the first, he does three things:
first, he makes clear what time is;
second, what the now of time is, at “just as motion is” (219b8; [582]);
third, from the definition he gives of time, he explains the things said about time, at “it is clear, then” (220a24; [593]).
About the first, he does two things:
first, he gives the definition of time;
second, he explains it, at “a proof of this” (219b3; [581]).
The first point is divided into three parts according to the three parts that he investigates of the definition;
the second part begins at “but what is moved” (219a10; [575]);
the third part at “now, we mark them” (219a25; [580]).
572. First (219a1), therefore, he investigates this part: that time is something of motion. He says that, since we are investigating what time is, we must begin by understanding what aspect of motion time is. That time is something of motion is manifested by the very fact that we sense motion and time together. For it happens that we perceive the flow of time even though we are not sensing any particular sensible motion, such as if we are in the dark and do not see any external object moving. And if, while we are in this situation, we are not undergoing any bodily changes brought about by an external agent, then we are not sensing any motion of a sensible body. Yet, if there is a motion within our soul, such as a succession of thoughts and imaginings, suddenly it appears to us that some time is elapsing. Thus, by perceiving any sort of motion, we perceive time, and vice versa: when we perceive time, we are simultaneously perceiving a motion. Hence, although time is not a motion, as we have already shown, yet it is somehow connected with motion.
573. What has just been said about the perceiving of time and of motion raises a difficulty. For if time follows upon some sensible motion outside the mind, it follows that whoever does not sense that motion does not sense time; but the opposite of that is said here. And, if time depends upon some motion of the mind, it follows that things are not connected to time except through the medium of the mind, and thus time will not be a thing of nature, but a notion in the mind like the notion of genus and species. But, if time follows upon any and every motion, then there are as many times as there are motions—which is impossible, for there cannot be two times together, as we said above.
574. In order to clear up this difficulty, it must be remembered that there is one first motion that is the cause of every other motion. Hence, whatever is in a changeable state of being possesses that state on account of the first motion, which is the motion of the first mobile being. Whoever, therefore, perceives any motion, whether it exists in sensible things or in the mind, is perceiving changeable being, and consequently is perceiving the first motion, which time follows. Thus, anyone who perceives any motion whatsoever is perceiving time, although time follows upon just the one first motion by which all other motions are caused and measured. Consequently, there remains only one time.
575. Then, at “but what is moved” (219a10), he investigates the second part of the definition of time. For supposing that time is something of motion—namely, that it follows upon motion—there still remains the task of investigating according to what does time follow upon motion. The answer is that it follows upon motion according to “before” and “after.”
As to this, then, he does three things:
first, he shows how before and after are found in motion;
second, how they are related to motion, at “the ‘before’ and ‘after’” (219a19; [578]);
third, he shows that time follows motion according to before and after, at “but we apprehend time” (219a22; [579]).
About the first, he does two things:
first, he shows that the continuity of time is due to the continuity of motion and magnitude;
second, that the same is true of the before and after of time, at “the distinction of” (219a14; [577]).
576. He first says, therefore, that everything that is being moved is being moved from something to something. But, of motions, the first is local motion, which is from place to place along a magnitude. But it is the first motion that time follows upon, and therefore, in order to investigate time, one must first consider local motion. Since, then, motion according to place is motion according to a magnitude from one place to another, and since every magnitude is continuous, motion must follow magnitude in regard to its continuity, such that, just as magnitude is continuous, so also is motion. Consequently, time also is continuous, for the quantity of the first motion and the quantity of time correspond. For time is not measured according to the quantity of just any motion, since something is slowly moved over a small distance in a large amount of time (and the opposite for a fast object). Time, however, corresponds only to the quantity of the first motion.
577. Then, at “the distinction of” (219a14; [577]), he shows that the same order prevails in respect to before and after, saying that before and after are first of all in a place or in a magnitude. This is so because a magnitude is a quantity having position; position, however, implies before and after. Hence, from its position, place has before and after. And, because there is before and after in magnitude, it follows that there is a before and after in motion corresponding to the things which are there, namely, in magnitude and place. Consequently, there is a prior and subsequent also in time, since motion and time are so related that the one always follows the other.
578. Then, at “the ‘before’ and ‘after’” (219a19), he shows how before and after are related to motion. And he says that the before and after of these—namely, of time and of motion—is motion according to its being, yet in account, it is distinct from motion and not motion. For it is the account of motion that it be the act of a being in potency, but that there be a before and after in motion occurs in it by reason of the order of the parts of the magnitude. Accordingly, regarding subject, before and after are the same as motion, but they differ from it as to account. Hence, the task remains to inquire, since time follows motion, whether it follows upon it inasmuch as it is motion, or inasmuch as it has a before and after.
579. Then, at “but we apprehend time” (219a22), he shows that time follows upon motion by reason of before and after. For it has been shown that the reason that time follows motion is that we recognize both simultaneously. Therefore, time follows motion according to that which, when it is perceived in motion, time is perceived. But we perceive time when we distinguish a before and after in motion; and we say time is passing when we have a sense of the before and after in motion. Consequently, time follows motion according to before and after.
580. Then, at “now, we mark them” (219a25), he shows what aspect of motion time is, saying that it is the number of motion. He explains this by using the same means as before, namely, our knowledge of time and motion.
For it is clear that, when we take two parts of motion with some medium between them, we determine that time exists. For when we perceive the differing boundaries of something and the mind calls them two nows, one being before and the other after—as though the mind were counting the befores and afters in a motion—that is what we call time. For time seems to be determined by the now. (This statement is taken for granted at present, but later it will be explained.)
When, therefore, we sense one now but do not discern a before and after of motion, or when, in discerning a before and after, we take the same now as the end of the prior and the beginning of the subsequent, no time seems to exist because no motion seemed to exist.
But when we discern a before and after and count them, then we say that time is produced. This is so because time is nothing less than the numbering of motion according to before and after, for we perceive time, as was said, when we count the before and after of motion. It is clear, therefore, that time is not motion, but accompanies motions inasmuch as it is counted. Hence, time is the number of motion.
But, if someone objects to this definition and says that before and after are determined by time, and consequently that the definition is circular, he should remember that before and after are placed in the definition of time inasmuch as they are caused in motion by magnitude, and not inasmuch as they are measured out of time.
That is why Aristotle had previously shown that before and after are present in magnitude before they are so in motion and that they are in motion before they are in time, to exclude this objection.
581. Then, at “a proof of this” (219b3), he clarifies the given definition in two ways.
The first way is by a sign. Now, that which is a standard of judging something to be more and less is a number of it. But the standard for judging whether a motion is greater or smaller is time. Therefore, time is a number.
Second, at “number, we must note” (219b5), he makes clearer what has been stated by distinguishing number, saying there are two.
First, there is that which is actually numbered, or which can be, as when we say ten men or a hundred horses, and this is called number numbered, because it is a number applied to the things that are numbered.
Then there is the number by which we count, that is, number considered absolutely, such as two, three, four.
Now, time is not a counting number, for otherwise, the number of anything would be time. Rather, it is a number numbered, because it is the number of before and after in motion that we call time, or else the things that are counted before and after. Therefore, although number is discrete quantity, time is nevertheless a continuous quantity on account of the thing counted, just as ten measures of cloth is a continuous quantity, even though ten is a discrete quantity.