Zeno Says You Never Arrive
What if it takes us forever to get there? Consider the “dichotomy paradox” posed by the Greek philosopher Zeno. He observed that to walk across a thing—for instance, Greenland (which belongs to Denmark)—first you need to walk across half of it. Then you need to walk across half of what’s left, then half of what’s left after that, and so forth. Since there is always another half to go, you’ll never reach the other end. How would you solve this and his other paradoxes of motion?
Key concepts
- Reductio Ad Absurdum
- Zeno's method: grant your opponent's premise, follow it honestly, and show where it lands. He was not arguing that nothing moves for the fun of it — he was defending his teacher Parmenides by making the alternative look worse.
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Every work — at a glance
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Zeno's Dichotomy Paradox — Zeno of Elea, c. 450 BC (paradox)
To cross anything you must first cross half of it, then half of the rest, forever — so motion needs infinitely many steps and is therefore impossible.
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What to know
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01
The halving paradoxes fall to one fix. The steps shrink as fast as they multiply, so infinitely many of them still sum to a finite distance crossed in a finite time. Newton and Leibniz gave that intuition a rigorous name — the limit — about two thousand years after Zeno posed the paradoxes of motion.
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Across subjects
Theme connection
"Are We There Yet?"
Practice — a sample
SPCIf you were advising Priya how to prove a runner can finish, which would you tell her to use?
- A Reductio reasoning
- B Moral hazard
- C Semantic drift
- D Rosy memory
- E Program music
Sign in to answer and see why each option is right or wrong.
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