LECTURE 19 (220 a 24-b 30)

CERTAIN THINGS WHICH ARE USUALLY SAID ABOUT TIME ARE CLARIFIED

             593. After the Philosopher has defined time, he here establishes from this definition the meaning [ratio] of things which are said about time.

             Concerning this he does four things. First he explains how a minimum is found in time and how not. Secondly, where he says, 'It is clear, too . . .' (220 a 34), he explains why time is called many and few, long and short, but not fast and slow. Thirdly, where he says, 'Further, there is the same . . .' (220 b 5), he explains how time is the same and how not. Fourthly, where he says, 'Not only do we . . .' (220 b 15), he explains how time is known by motion, and vice versa.

             594. He says, therefore, first that it is clear from the definition of motion given above that time is the number of motion in respect to before and after, as was explained above. Furthermore, it is clear from the foregoing that time is continuous. For, although it is not continuous from the fact that it is a number, nevertheless it is continuous because of that of which it is the number. For time is the number of a continuum, that is, motion, as was said above. Time is not a number simply, but a numbered number.

             In simple number there is found an altogether minimum number, that is, duality. But if we take the number of a continuous thing, in a way there is a minimum and in a way not. For in respect to multitude there is a minimum, but in respect to magnitude there is not. Thus, in many lines there is a minimum in respect to multitude, either one line or two: one, if that which is simply a minimum in number is taken; but two, if that which is a minimum in the genus of number, having the nature [ratio] of number, is taken. But in lines there is no minimum in respect to magnitude, so that there would be, for example, some smallest line. For any line can always be divided.

             Time must be described in like manner. In time there is a minimum in respect to multitude, that is, either one or two; for example, one year or two years, or two days or hours. But in time there is no minimum in respect to magnitude. For in any given time there are parts into which it is divided.

             595. Next where he says, 'It is clear, too . . .' (220 a 34), he explains the reason [ratio] why time is not called fast or slow, but is called many and few, long and short.

             It was already shown that time is a number and a continuum. Therefore, insofar as it is a continuum, time is called long and short, as also is a line. And insofar as time is a number, it is called many and few. But fast and slow in no way belong to number. Fast and slow do not belong simply to number, as is clear, nor can they belong to the number of some thing. For fast and slow is said of something insofar as it is numbered. A fast motion is said to be in that which is numbered by a short time, and a slow motion is the opposite. Hence it is clear that in no way can time be called fast or slow.

             596. Next where he says, 'Further, there is the same . . .' (220 b 5), he explains how time is the same and how not.

             First he explains how it is the same or not simply, and second, accidentally, where he says, 'Further, as a movement . . .' (220 b 12).

             He says, therefore, first that time, existing simultaneously, is the same everywhere, that is, in respect to everything which is moved anywhere. For time is not diversified by diverse mobile objects but by diverse parts of the same motion. Therefore, a prior time and later time are not the same. This is so because the present primary motion, whose number is time primarily and principally, is one. But that which is already done and past is a different part of this motion. And the future is another part. Hence, that which was is one time, and that which will be is still another time. This is so because time is not number simply, but the number of some numbered thing, that is, of the before and after in motion. This number is always different and before and after, because the 'nows' insofar as they are related to before and after are always different.

             But if time were number simply, then the time of a past motion and of a future motion would be the same. For simple number is one and the same for diverse numbered things, as a hundred horses and a hundred men. But numbered number is different for diverse things. A hundred horses are not a hundred men. And since time is the number of the before and after in motion, those things in motion which are related to the before and after as already past are different from those things which are related as future. And because of this past time is different from future time.

             597. Next where he says, 'Further, as a movement . . .' (220 b 12), he explains how the same time is repeated accidentally.

             He says that as one and the same motion can be repeated, likewise one and the same time can be repeated. For a motion which is one and the same in species, but not in number, is repeated. The sun will be moved at a later time from the same sign of the ram from which it was moved earlier. And the winter or spring or summer or fall was and will be. They are not one in number, but in species.

             598. Next where he says, 'Not only do we . . .' (220 b 15), he shows that, just as we know motion by time, we also know time by motion.

             He shows this first from the nature [ratio] of number and the numbered. Secondly, where he says, 'It is natural that . . .' (220 b 24), he shows this with a comparison of motion and magnitude.

             He says, therefore, first that not only do we measure motion by time, but we also measure time by motion, because they are defined by each other. For it is necessary to take the quantity of one according to the quantity of the other. Time determines motion because it is the number of motion. But conversely motion determines time in respect to us. For occasionally we perceive the quantity of time by motion, as when we say time is many or few according to a measure of motion known to us. Sometimes we know number by numerables, and sometimes vice versa. For we know a multitude of horses by number, and again we know the number of horses by one horse. We do not know how much a thousand is unless we know what a thousand is. It is the same with time and motion. For when the quantity of time is known to us and the quantity of motion is not, then we measure motion by time. And the opposite occurs when motion is known to us and time is unknown.

             599. Next where he says, 'It is natural that . . .' (220 b 24), he explains the same thing by comparing motion to magnitude. He says that what was said about time and motion is reasonable. As motion imitates magnitude in quantity, continuity, and divisibility, so also time imitates motion. For these things are found in motion because of magnitude, and in time because of motion. Moreover, we measure magnitude by motion and motion by magnitude. For we say that a road is long when we perceive that our motion was long; and conversely, when we consider the magnitude of the road, we say that our motion is long. And this is also true of time and motion, as was said above.