The Library of Babel is a short story by Jorge Luis Borges describing its own title. The Library is an entire world completely filled by hexagonal rooms of bookshelves, containing all the possible permutations of 25 symbols - 22 letters, plus the period, comma, and space - that could be contained in books that are precisely 410 pages long, 40 lines per page, 80 symbols per line. Every possible book that fits these parameters is somewhere in the Library, exactly once. Somewhere, there is a book containing nothing but four hundred and ten pages of MCVMCVMCV, but also the Encyclopedia Britannica, Shakespeare's First Folio, and a book that describes how to construct a perpetual-motion machine.
And, of course, a book whose title page is from the First Folio (by MCV), but the rest of which is from a faulty version of the Britannica that contains a description of a perpetual-motion machine. Thus, the Library contains all truth - but also all falsehood.
Obviously, somewhere, there is an index - a catalogue, explaining where all the books containing truth can be found, and one in every language, no less. But of course there are also a countless number of flawed indices, many of which have simply misplaced a period or substituted a word, but many of which are seemingly flawless except that where they say you should be able to find your own biography there is actually a copy of Finnegan's Wake. How, then, can you tell the true from the false?
You can start by picking an apparent index and looking it up in itself. If it's not there, you obviously can't trust it, because if it is true it should be listed in the book! Moreover, if it gives you a wrong location, you can't trust it, either. This is the easiest thing to begin with - any index which cannot account for itself is not a reliable index.
When you have an index that satisfies this basic condition, you can check the reliability of the rest of the list to make sure that all the books it contains are where it says they are. Then you must test the reliability of those books to make sure that they actually contain what they say they contain in the title; if any of these books are themselves indices (more than likely, for a library of this scope), this means testing a number of their contents for accuracy as well, ad infinitum if it goes that far.
Difficult, you say? Yes. Impossible? Necessary, if you wish to believe you know anything.
I hate hitting people with frying pans, but... if you haven't realized what this entire entry is a metaphor for yet, well, the majority of the rest of this blog is probably not for you.
As for Godel... he can wait until later.