The Barber Paradox is a self-referential paradox related to set theory and logic, often attributed to the mathematician and philosopher Bertrand Russell. It presents a scenario involving a barber who shaves all and only those men who do not shave themselves. The paradox arises when we ask the question: "Does the barber shave himself?" If the barber shaves himself, according to the definition, he should not be shaving himself (because he only shaves those who do not shave themselves).
Articles by others on the same topic
For a binary relation , no object can satisfy for every . Putting would give for . The forward direction derives by a negation introduction subproof assuming ; the reverse direction then gives , a contradiction. Thus this argument even avoids needing the law of excluded middle. The familiar interpretation reads as “ shaves ”; the logical obstruction is self-application rather than a physical peculiarity of shaving.