Lexicon of Arguments

 

Kursbuch 8; p. 15
Motion/change/Russell: old/Zenon: "state of change" - today/VsZenon: at one time in one place, at another time in another place - wrong, to say that it is in the next moment located in the "adjacent place" - wrong: jump within a moment (Zenon has correctly identified this)

Bertrand Russell Die Mathematik und die Metaphysiker 1901 in: Kursbuch 8 Mathematik 1967

15
Time: The banishment of the infinitely small quantity has peculiar consequences: e.g. there is no longer something like a next moment. (> Time/Russell). If there are to be no infinitely small quantities, no two moments follow one another directly, but there are always more moments inbetween.
Consequently, there must be an infinite number of additional moments between two arbitrary moments. If the number were finite, then one would be closer to the first of the two moments and it would be the next! This is precisely where the philosophy of the infinite begins.
Space: the same applies to the space. However small a space is, it can be further subdivided. In this way we never reach the infinitely small quantity. No finite number of divisions leads to a point.
Nevertheless, there are points, but they are not achieved by successive divisions. Points are not infinitely small distances.
Motion, change: strange results: earlier, it was thought that when something changes, it must be in a state of change when it moves, in a state of motion.
This is wrong from today's point of view: If a body moves, one can only say that it is at one time at the place and at another time at a different place.
We must not say that it will be at the next place in the next moment because there is no next moment.
>Zeno, >Change, >Beginning, >Time, >Space.