Embed Notice

4/5

An easy refutation of the ”layman's versions” such as the barber 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 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. Note the difference between the statements ”such a set does not exist” and ”it is an empty set”. It is like the difference between saying "There is no bucket" and saying ”The bucket is empty”.

A notable exception to the above may be the Grelling–Nelson paradox, in which words and meaning are the elements of the scenario rather than people and hair-cutting. Though it is easy to refute the barber's paradox by saying that such a barber does not (and cannot) exist, it is impossible to say something similar about a meaningfully defined word. 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.