Posted by: Alexandre Borovik | August 22, 2008

An infinitely bored librarian

Stolen from Richard Elwes:

Matt, having read my recent articles about set-theory, feeds back:

The best “real world” example of Russell’s paradox I’ve seen (I forget where now) is this: A librarian, bored with work, sets about making two indexes of books in their library. In book one, she lists all books which don’t reference themselves. In book two, she lists all books which do reference themselves. But then she thinks: I’ve just created two new books, so I should list them as well. But neither book references itself, so they should both be listed in book one. But by doing this, book one now does reference itself! So book one should really be listed in book two instead. But if she does this, then book one goes back to not referencing itself!

I like it. Much better than the barber one.


  1. I hadn’t heard about the barber, but I like this one better too. Perhaps it is because I can vividly picture my college librarian going through that process (after throwing some people out of the library of course)!

    What would an infinitely bored mathematician do?

  2. Perhaps a bored mathematician would create a third book, to list books which cannot be unambiguously listed in the first two books.

  3. I have also used this example when I had to give a presentation about paradoxes. It proved very effective to get the attention.

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