The Barber Paradox
One of the most famous questions of 20th century philosophy is The Barber paradox, usually attributed to British philosopher Bertrand Russell. The Barber paradox highlights a fundamental problem in mathematics, exposing an inconsistency in the basic principles on which mathematics is founded. It seems strange to many that Russell, a thinker who devoted most of his early career to finding mathematical truths that provided annswers to the great philosophical question like “Where did we come from?” “Is there a God?” “Does life have any meaning?” and “Who put the bing in wallah wallah bing bong?”
In the latter part of his life however, Russell’s quest for the truth took him in another direction and one of the results of this is the logic problem of The Barber Paradox.
The question asks us to consider the following situation:
In a village, the barber shaves everyone who does not shave himself, but no one else.
Now we are asked to answer the question “Who shaves the barber?”
No matter how we try to answer this question we get into trouble (allegedly). If we say that the barber shaves himself, then we are in trouble. The barber shaves only those who do not shave themselves, so if he shaves himself then he doesnt shave himself, which is self-contradictory.
If we say that the barber does not shave himself, problems arise from that. The barber shaves everyone who does not shave himself, so if he doesnt shave himself then he shaves himself, which is again absurd.
Even if we try to get clever, saying that the barber is a woman, we do not evade the paradox. If the barber is a woman, then she either shaves herself (and so is one of the people not shaved by the barber), or does not shave herself (and so is one of the people shaved by the barber. You may note here a typical mathematician’s irrationality creeping in; a woman (unless she is Greek) does not need to shave her face and thus cannot be part of the logic problem.
Both cases, then, are impossible; the barber can neither shave himself nor not shave himself.
But what really makes Russell’s logic problem absurd is the ridiculous limits set on the logic.
It must have occurred to you all now that the barber had a beard.