to seem plausible.
If the paradox is altered so that there may be multiple barbers in the town, then the paradox may or may not be resolved, depending on the exact phrasing of the initial rules.
If the initial rules state that every man in town must keep himself clean-shaven, either by
- Shaving himself, or
- going to a barber.
(but not both at once), then the paradox is solved. Each barber can be shaved by another barber.
However, if the initial rules describe the responsibilities of the barbers rather than the town's residents in general, then the paradox remains. In this version, the rules state that each barber must shave everyone in town who does not shave himself (and no one else). If Barber A asks Barber B to shave his beard, then Barber A counts as "a person who does not shave himself". But because of this classification, Barber A must shave himself, rather than let Barber B do it for him. However, if Barber A is shaving himself, then he must not shave himself. Either way, Barber A is stuck. Other barbers face the same problem.
A modified version of the barber paradox is frequently encountered in the form of a brain teaser puzzle or joke. The joke is phrased nearly identically to the standard paradox, but omitting a detail that allows an answer to escape the paradox entirely. For example, the puzzle can be stated as occurring in a small town whose barber claims: I shave all and only the men in our town who do not shave themselves. This version identifies the sex of the clients, but omits the sex of the barber, so a simple solution is that the barber is a woman. The barber's claim applies to only "men in our town," so there is no paradox if the barber is a woman (or a gorilla, or a child, or a man from some other town—or anything other than a "man in our town"). Such a variation is not considered to be a paradox at all: the true barber paradox requires the contradiction arising from the situation where the barber's claim applies to himself.
Notice that the paradox still occurs if we claim that the barber is a man in our town with a beard. In this case, the barber does not shave himself (because he has a beard); but then according to his claim (that he shaves all men who do not shave themselves), he must shave himself.
In a similar way, the paradox still occurs if the barber is a man in our town who cannot grow a beard. Once again, he does not shave himself (because he has no hair on his face), but that implies that he does shave himself.
- The Philosophy of Logical Atomism, reprinted in The Collected Papers of Bertrand Russell, 1914-19, Vol 8., p. 228
- Proposition of the Barber's Paradox
- Joyce, Helen. "Mathematical mysteries: The Barber's Paradox." Plus, May 2002.
- Edsger Dijkstra's take on the problem
- The Monist, Vol. 29, No. 3, JULY, 1919, THE PHILOSOPHY OF LOGICAL ATOMISM, page 354