BARBER PARADOX

Posted on April 4, 2014

A paradox is a statement that apparently contradicts itself and yet might be true. Most logical paradoxes are known to be invalid  arguments but are still valuable in promoting critical thinking . One of the more interesting paradox i came across is the barber’s paradox because that an apparently plausible scenario is logically impossible. The paradox itself is as follows –

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 that “The barber is a man in town who shaves all those, and only those, men in town who do not shave themselves.”

From this, asking the question “Who shaves the barber?” results in a paradox because according to the statement above, he can either shave himself, or go to the barber (which happens to be himself). However, neither of these possibilities are valid: they both result in the barber shaving himself, but he cannot do this because he shaves only those men “who do not shave themselves” . Can you arrive at a solution to this problem ?