The Barber Paradox

The Barber Paradox is a self-referential puzzle related to set theory and logic. It describes a barber who shaves all those men who do not shave themselves. The paradox arises when you ask, "Does the barber shave himself?" If he does, then according to the rule, he must not shave himself. But if he doesn't shave himself, then he must shave himself since he only shaves those who don’t. This creates a logical contradiction, illustrating the complexities and limits in formal systems of reasoning and the challenges in defining sets and categories.