Lexicon of Arguments

 

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

13
RussellVsZenon: Zenon only made the mistake of drawing the conclusion (if he drew any conclusions at all) that because there is no state of change, the world would be in the same state at any given time.
But this conclusion cannot be drawn according to Weierstrass.
15
Time: The banishment of the infinitely small quantities has peculiar consequences: e.g. there is no longer anything 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 other 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 so would be the next! This is precisely where the philosophy of the infinite begins.
19
Zenon/Russell: Everyone who attacked Zenon was not right about it, because they allowed his premisses. Zenon probably invoked the assumption that the whole has more elements than a part.
20
Then Achilles must have been in more places than the turtle. And it followed that he could never catch up with them.
If we allow the axiom that the whole thing has more elements than a part, Zeno's conclusion fits perfectly.
The retention of the axiom leads to other paradoxes of which I call one: the paradox of Tristram Shandy. It is the reversal of the Zenonian paradox and says that the turtle can get everywhere if you give it only enough time. Tristram Shandy needed two years to list the course of the first two days of his life and complained that the material accumulated faster than he could capture it.
Russell: I assert now that if he had lived his life that way further on, he would not have missed any part of his biography. For the hundredth part is written in the thousandth year, and so on.
>Zeno, >Commentaries on Zeno.