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Full Idea
The idea that an infinite number of instants make up an infinitely long time is not true, and therefore the conclusion that Achilles will never overtake the tortoise does not follow.
Gist of Idea
The tortoise won't win, because infinite instants don't compose an infinitely long time
Source
Bertrand Russell (Our Knowledge of the External World [1914], 6)
Book Ref
Russell,Bertrand: 'Our Knowledge of the External World' [Routledge 1993], p.178
A Reaction
Aristotle spotted this, but didn't express it as clearly as Russell.
| 5109 | The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle] |
| 1507 | We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea] |
| 21585 | The tortoise won't win, because infinite instants don't compose an infinitely long time [Russell] |
| 7557 | To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell] |
| 14149 | The Achilles Paradox concerns the one-one correlation of infinite classes [Russell] |
| 21690 | Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine] |
| 8075 | Space and time are atomic in the arrow, and divisible in the tortoise [Devlin] |
| 4229 | An infinite series of tasks can't be completed because it has no last member [Lowe] |
| 20457 | Zeno assumes collecting an infinity of things makes an infinite thing [Rovelli] |