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 a premise, follow it honestly, and land on something absurd. So to solve one of his paradoxes you do not argue with the ending; you find the premise that was false all along.
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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 false premise is that infinitely many steps must take forever. Each half also takes half the time, so the walk ends in a finite time. Newton and Leibniz's calculus gave that idea its tool, the limit, about two thousand years after Zeno.
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Across subjects
Theme connection
"Are We There Yet?"
Practice — a sample
SCIZeno's halves shrink as fast as they multiply; Eco's lists never shrink. The KEY DIFFERENCE shrinking makes is —
- A A full inventory
- B A finite total
- C A countable order
- D A mix of kinds
- E A steady rate
Sign in to answer and see why each option is right or wrong.
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