- If the barber does not shave himself, he must bide by the rule and shave himself.
- If he does shave himself, according to the rule he will not shave himself.

This paradox is attributed to the British logician Bertrand Russell, who in 1901 constructed Russell's paradox to demonstrate the self-contradictory nature of Cantor's elementary set theory by formalizing the Barber paradox. The paradox also underlies the proof of Gödel's incompleteness theorem as well as Alan Turing's proof of the undecidability of the halting problem.