Barber Paradox

Paradox
There exists a community, one of whose members is a barber.

This barber operated under an unusual rule: his task was to shave every man in the community who did not shave himself, and only those men.

Who shaves the barber?

If he does not shave himself, then he must shave himself.

But if he shaves himself, he must not shave himself.

Resolution
This paradox has been demonstrated to be an antinomy, and can be resolved by several means, for example:

History
himself used it as an illustration of his paradox, claiming it was invented by an unnamed acquaintance of his.