The Barber Paradox
The Barber Paradox is a self-referential puzzle in set theory and logic. It describes a barber who shaves all those who do not shave themselves. The paradox arises when we ask whether the barber shaves himself. If he does, according to the definition, he must not shave himself. Conversely, if he does not shave himself, then he must shave himself. This creates a contradiction.
This paradox highlights issues in naive set theory, particularly concerning self-reference and definitions. It was introduced by the mathematician Bertrand Russell to illustrate problems in formal logic and the need for clearer definitions in mathematics.