Editing Russell's paradox (section)

== Applied versions ==
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There are some versions of this paradox that are closer to real-life situations and may be easier to understand for non-logicians. For example, the [[barber paradox]] supposes a barber who shaves all men who do not shave themselves and only men who do not shave themselves. When one thinks about whether the barber should shave himself or not, a similar paradox begins to emerge.<ref>{{Cite web |title=barber paradox |url=https://www.oxfordreference.com/display/10.1093/oi/authority.20110803095446216 |access-date=2024-02-04 |website=Oxford Reference |language=en }}</ref>

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 is not a man, 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.

One way that the paradox has been dramatised is as follows: Suppose that every public library has to compile a catalogue of all its books. Since the catalogue is itself one of the library's books, some librarians include it in the catalogue for completeness; while others leave it out as it being one of the library's books is self evident. Now imagine that all these catalogues are sent to the national library. Some of them include themselves in their listings, others do not. The national librarian compiles two master catalogues—one of all the catalogues that list themselves, and one of all those that do not.<ref name=":0">{{Cite journal |last=Moorcroft |first=Francis |date=Spring 1998 |title=Paradoxes |url=https://doi.org/10.5840/tpm1998293 |journal=The Philosophers' Magazine |issue=2 |pages=63 |doi=10.5840/tpm1998293 |via=Philosophy Documentation Center (pdoc)|url-access=subscription }}</ref>

The question is: should these master catalogues list themselves? The 'catalogue of all catalogues that list themselves' is no problem. If the librarian does not include it in its own listing, it remains a true catalogue of those catalogues that do include themselves. If he does include it, it remains a true catalogue of those that list themselves. However, just as the librarian cannot go wrong with the first master catalogue, he is doomed to fail with the second. When it comes to the 'catalogue of all catalogues that do not list themselves', the librarian cannot include it in its own listing, because then it would include itself, and so belong in the other catalogue, that of catalogues that do include themselves. However, if the librarian leaves it out, the catalogue is incomplete. Either way, it can never be a true master catalogue of catalogues that do not list themselves.<ref name=":0" />