The paradox arises because:
* If the barber shaves himself, he violates the rule of only shaving those who don't shave themselves.
* If the barber doesn't shave himself, he fits the criteria of being someone who doesn't shave themselves, and therefore, according to the rule, he *must* shave himself.
There is no solution to this paradox. It demonstrates the potential for contradictions when defining sets based on self-reference.
This type of paradox is related to the famous Russell's Paradox, which deals with sets that contain themselves or don't contain themselves.