Editing Barber paradox (section)

== History ==

This paradox is often incorrectly attributed to [[Bertrand Russell]] (e.g., by [[Martin Gardner]] in ''Aha!''). It was suggested to Russell as an alternative form of [[Russell's paradox]],<ref name=atomism/> which Russell had devised to show that [[set theory]] as it was used by [[Georg Cantor]] and [[Gottlob Frege]] contained contradictions. However, Russell denied that the Barber's paradox was an instance of his own:

{{Quotation|That contradiction [Russell's paradox] is extremely interesting. You can modify its form; some forms of modification are valid and some are not. I once had a form suggested to me which was not valid, namely the question whether the barber shaves himself or not. You can define the barber as "one who shaves all those, and those only, who do not shave themselves". The question is, does the barber shave himself? In this form the contradiction is not very difficult to solve. But in our previous form I think it is clear that you can only get around it by observing that the whole question whether a class is or is not a member of itself is nonsense, i.e. that no class either is or is not a member of itself, and that it is not even true to say that, because the whole form of words is just noise without meaning.|Bertrand Russell, ''The Philosophy of Logical Atomism''<ref name=atomism/>}}

This point is elaborated further under [[Russell's paradox#Applied versions|Applied versions of Russell's paradox]].