10 Facts About Russell paradox

The Russell paradox had already been discovered independently in 1899 by the German mathematician Ernst Zermelo.

Russell showed that a version of the paradox could be derived in the axiomatic system constructed by the German philosopher and mathematician Gottlob Frege, hence undermining Frege's attempt to reduce mathematics to logic and questioning the logicist programme.

Two influential ways of avoiding the paradox were both proposed in 1908: Russell's own type theory and the Zermelo set theory.

Further, since set theory was seen as the basis for an axiomatic development of all other branches of mathematics, Russell's paradox threatened the foundations of mathematics as a whole.

Frege then wrote an appendix admitting to the paradox, and proposed a solution that Russell would endorse in his Principles of Mathematics, but was later considered by some to be unsatisfactory.

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In 2001 A Centenary International Conference celebrating the first hundred years of Russell's paradox was held in Munich and its proceedings have been published.

The barber Russell paradox supposes a barber who shaves all men who do not shave themselves and only men who do not shave themselves.

An easy refutation of the "layman's versions" such as the barber Russell paradox seems to be that no such barber exists, or that the barber has alopecia, or is a woman, and in the latter two cases the barber doesn't shave, and so can exist without Russell paradox.

The whole point of Russell's paradox is that the answer "such a set does not exist" means the definition of the notion of set within a given theory is unsatisfactory.

One way that the Russell paradox has been dramatised is as follows: Suppose that every public library has to compile a catalogue of all its books.