The Unexpected Hanging
W. V. O. Quine, popularising earlier folklore · 1953
The puzzle
A judge tells a prisoner: you will be hanged at noon on a weekday next week, and the day will surprise you.
Note
The prisoner reasons: it can’t be Friday, because by Thursday evening I would already know. So Friday is ruled out. Then it can’t be Thursday, since by Wednesday evening — Friday already eliminated — I would know. Working backward, no day is possible. The prisoner concludes the judge cannot fulfill the sentence. He is hanged on Wednesday and is genuinely surprised. The paradox is a knot of self-reference: the prediction you will be surprised interferes with the prisoner’s reasoning about it. Versions go back to the 1940s — Lennart Ekbom, the Swedish mathematician, may have circulated the puzzle first. Some treat it as a flaw in the prisoner’s induction; others as exposing a real limit on what self-aware predictions can claim. Either reading leaves something unaccounted for.