more from this thinker | more from this text
Full Idea
Zeno's so-called 'Achilles' claims that the slowest runner will never be caught by the fastest runner, because the one behind has first to reach the point from which the one in front started, and so the slower one is bound always to be in front.
Clarification
'Achilles' was famous for his speed
Gist of Idea
The fast runner must always reach the point from which the slower runner started
Source
report of Zeno (Elea) (fragments/reports [c.450 BCE]) by Aristotle - Physics 239b14
Book Ref
Aristotle: 'Physics', ed/tr. Waterfield,Robin [OUP 1996], p.161
A Reaction
The point is that the slower runner will always have moved on when the faster runner catches up with the starting point. We must understand how humble the early Greeks felt when they confronted arguments like this. It was like a divine revelation.
| 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] |