more from Bertrand Russell

Single Idea 7557

[catalogued under 5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox]

Full Idea

Presumably Zeno appealed to the axiom that the whole has more terms than the parts; so if Achilles were to overtake the tortoise, he would have been in more places than the tortoise, which he can't be; but the conclusion is absurd, so reject the axiom.

Gist of Idea

To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts

Source

Bertrand Russell (Mathematics and the Metaphysicians [1901], p.89)

Book Reference

Russell,Bertrand: 'Mysticism and Logic' [Unwin 1989], p.89


A Reaction

The point is that the axiom is normally acceptable (a statue contains more particles than the arm of the statue), but it breaks down when discussing infinity (Idea 7556). Modern theories of infinity are needed to solve Zeno's Paradoxes.

Related Idea

Idea 7556 A collection is infinite if you can remove some terms without diminishing its number [Russell]