The Librarian Paradox

Though I'm sure this isn't something new for many of you, The Librarian Paradox is new to me:

A librarian is wandering round her library one day and comes across a shelf of catalogues. There are catalogues of novels, poems, essays and so on, and some of these catalogues, she discovers, list themselves, while others do not.

In order to simplify the system, the hard-working (and rigorously logical) librarian makes two more catalogues. One lists all those catalogues that list themselves; the other lists all those that don't. Once she has completed this task, she has a problem: should the catalogue which lists all the other catalogues which do not list themselves, be listed in itself? If it is listed, then by definition it should not be listed. However, if it is not listed, then by definition it should be.

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paradox not

that's why we have metadata... something which refers to something doesn't need to refer to itself... some people think these sorts of paradoxes are fun to contemplate: I never invite those people to my parties.

AKA Russell's paradox

This is a alternative setting for what's usually known by mathematicians as "Russell's paradox", a classic problem in set theory. Wikipedia has a fairly good summary at

http://en.wikipedia.org/wiki/Russell's_paradox

Another amusing variation I heard of was of a math student who dedicated his thesis to all those who did not dedicate their theses to themselves.

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