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Full Idea
The Achilles argument is that (if the front runner keeps running) each time the pursuer reaches a spot where the pursuer has been, the pursued has moved a bit beyond.
Gist of Idea
Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on
Source
Willard Quine (The Ways of Paradox [1961], p.03)
Book Ref
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.3
A Reaction
Quine is always wonderfully lucid, and this is the clearest simple statement of the paradox.
| 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] |