* The Rule: The barber shaves all those in the village who do not shave themselves.
* The Problem: Let's consider the barber himself. Does he shave himself?
* If he shaves himself: He violates the rule, as the rule states he only shaves those who *don't* shave themselves.
* If he doesn't shave himself: He must be shaved by the barber (according to the rule), meaning he *does* shave himself.
The Paradox: There's no way to satisfy the rule without creating a contradiction. This means the initial statement about the barber is logically impossible.
The Importance: This paradox demonstrates the dangers of self-referential statements and the need for careful consideration of logical definitions. It's a foundational concept in set theory and logic.