for a certain length of time or temporarily." Nevertheless, although we may look all around the moving thing and the motion itself as change of place, we shall never find time if we hold to what Aristotle says.
We must ourselves retort, naturally we shall not find it. Aristotle does not just remark indefinitely that time is something connected with motion; instead, he says more precisely: ἀριθμὸς κινήσεως—a number connected with motion or, as he formulates it in one place, οὐκ ἄρα κίνησις ὁ χρόνος ἀλλ᾿ ᾗ ἀριθμὸν ἔχει ἡ κίνησις;16 time is not itself motion but exists so far as motion has a number. Time is a number. This again is astonishing, for numbers are just exactly that of which we say that they are timeless, extratemporal. How then is time supposed to be a number? But here, as Aristotle expressly stresses, the expression "number" (ἀριθμὸς) must be understood in the sense of ἀριθμούμενον. Time is number not in the sense of the number that numbers as such but of the number that is numbered, counted. Time as number of motion is what is counted in connection with motion. Let us try an experiment. What can I count about the motion of the rod? Obviously, since the motion is a change of place, I can count the individual locations occupied by the rod in transition from one to the other. But, if I add up these locations, the sum of them to all eternity will never give me time but only the whole stretch run through, a piece of space but not time. Now we are able to count and to determine by counting the speed of the rod in its transition from one place to the other. What is speed? If we take the physical concept of speed, s = d/t, then speed is the path traversed divided by the elapsed time. From this formula it can be seen externally that time is involved in speed, because motion requires time. But this does not yet explain what time itself is. We have not come a single step closer to time. What does it mean, then, to say that the rod has a certain speed? Patently, among other things, it means that the rod is moving in time. Its motion runs its course in time. How puzzling it is that all motions take—use up—time and yet time doesn't diminish at all. Let us think of 1000 particular motions in the time between ten and eleven o'clock. Think also, as a second instance, of 100,000 motions in the same time. All of them take this same time. In the second instance, when many more of them are taking this time, does the time itself diminish or does it remain quantitatively equal to itself? Is the time that is taken by the motions thereby all used up? If not, then it manifestly does not depend on the motions. Nevertheless, it is supposed to be what is counted in connection with motion. It seems to be pure assertion on Aristotle's part that time is what is counted in connection with motion. Even if we go so far as to mark the rod's change of place by numbers, so that we provide each place with a number
14. Aristotle, Physica, 219b 3f.