Barber Paradox - The Paradox

The Paradox

Suppose there is a town with just one barber, who is male. In this town, every man keeps himself clean-shaven, and he does so by doing exactly one of two things:

1. Shaving himself, or
2. going to the barber.

Another way to state this is:

The barber is a man in town who shaves those and only those men in town who do not shave themselves.

All this seems perfectly logical, until we pose the paradoxical question:

Who shaves the barber?

This question results in a paradox because, according to the statement above, he can either be shaven by:

1. himself, or
2. the barber (which happens to be himself).

However, none of these possibilities is valid. This is because:

• If the barber does shave himself, then the barber (himself) must not shave himself.
• If the barber does not shave himself, then he (the barber) must shave himself.