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Full Idea
The arrow paradox starts with the assumption that space and time are atomic; the tortoise starts with the opposite assumption that space and time are infinitely divisible.
Gist of Idea
Space and time are atomic in the arrow, and divisible in the tortoise
Source
Keith Devlin (Goodbye Descartes [1997], Ch. 2)
Book Ref
Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.24
A Reaction
Aquinas similarly covers all options (the cosmos has a beginning, or no beginning). The nature of movement in a space which involves quantum leaps remains metaphysically puzzling. Where is a particle at half of the Planck time?
| 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] |