Russell's Barber Paradox: the barber who can't shave himself
In a certain village there is exactly one barber. He shaves all — and only — the men who do not shave themselves. Every man in the village is shaved either by himself or by the barber, never both. So: who shaves the barber?
Reveal the answer
Either answer collapses into contradiction. If the barber shaves himself, he breaks his own rule, since he only shaves men who don't shave themselves. If he doesn't shave himself, the rule says he must. No such barber can consistently exist. Bertrand Russell used this vignette in his 1918 lectures 'The Philosophy of Logical Atomism' to illustrate Russell's Paradox (1901), the contradiction at the heart of naive set theory, where the 'set of all sets that do not contain themselves' can neither contain nor exclude itself. Russell credited an unnamed acquaintance with suggesting the barber version, but it's carried his name ever since. Distinct from Lewis Carroll's 'Barbershop Paradox' (three barbers, a chain of conditionals) — same trade, unrelated puzzle.