12 entries
Paradoxes
Places where careful reasoning, one sensible step at a time, arrives somewhere impossible. Each with the solutions people have proposed, and why none quite closes the case.
- I.Zeno's paradoxesAchilles can never catch a tortoise with a head start, because each time he reaches where it was, it has moved on. Motion itself, Zeno argued, is impossible.Logic · Intermediate
- II.The sorites paradoxOne grain of sand is not a heap. Adding one grain never turns a non-heap into a heap. So, by that logic, a million grains are not a heap either.Logic · Intermediate
- III.The liar paradox'This sentence is false.' If it is true, it is false. If it is false, it is true. A single short sentence seems to break logic.Logic · Deep
- IV.Newcomb's problemA near-perfect predictor has filled two boxes. Take only the opaque one, or take both? Two airtight arguments give opposite answers.Decision · Deep
- V.The grandfather paradoxYou travel back in time and prevent your grandparents from ever meeting. Then you are never born, so you never travel back. So they do meet. So you are born...Time · Intermediate
- VI.The unexpected hangingA judge says a prisoner will be hanged next week on a day that will come as a surprise. The prisoner proves it cannot happen. Then it happens, and he is surprised.Knowledge · Intermediate
- VII.Russell's paradoxConsider the set of all sets that do not contain themselves. Does it contain itself? If it does, it doesn't. If it doesn't, it does. In 1901 this nearly broke mathematics.Logic · Deep
- VIII.The Fermi paradoxThe galaxy is vast and old, and life arose quickly on Earth. Even slow colonisers could have filled the Milky Way millions of years ago. So where is everybody?Reality · Introductory
- IX.Buridan's donkeyA hungry donkey stands exactly halfway between two identical bales of hay. With no reason to prefer either, a perfectly rational donkey would starve.Decision · Introductory
- X.The bootstrap paradoxA time traveller gives Shakespeare a copy of Hamlet, which Shakespeare copies and publishes. So who wrote Hamlet?Time · Intermediate
- XI.Pascal's muggingA stranger promises you an astronomically huge reward if you hand over your wallet. It is almost certainly a lie. But if the reward is big enough, the maths says pay.Decision · Intermediate
- XII.The St. Petersburg paradoxA coin-flipping game has an infinite expected payout. Yet almost no one would pay more than a few dollars to play it. Who is irrational: us, or the maths?Decision · Intermediate