To determine whether any given subject deserves an entry, Wikipedia uses the criterion of notability. This lead to an interesting question:
Question 1: Whatâ€™s the most notable subject thatâ€™s not notable enough for inclusion in Wikipedia?
Letâ€™s assume for now that this question has an answer (â€œThe Answerâ€), and call the corresponding subject X. Now, we have a second question whose answer is not at all obvious.
Question 2: Is subject X notable merely by being The Answer?
If the answer to Question 2 is â€œnoâ€, then thereâ€™s no problem, and we can all go home.
If the answer to Question 2 is â€œyesâ€, well, we have a contradiction, and in a manner similar to the interesting number paradox, it follows that Question 1 must have no answer, and so every conceivable subject must meet Wikipediaâ€™s notability criterion.
Take that, deletionists!
Hereâ€™s the amusing thing: whether the answer to Question 2 is yes or no depends on where I publish this analysis. If I publish it on my blog and no-one pays any attention, the answer to Question 2 is, most Wikipedians would likely agree, â€œnoâ€.
But suppose I went to great trouble to convene a conference series on The Answer, was able to convince leading logicians and philosophers to take part, writing papers about The Answer, convinced a prestigious journal to publish the proceedings, arranged media coverage, and so on. The Answer would then certainly have exceeded Wikipediaâ€™s notability guidelines, and thus the answer to Question 2 would be “yes”.
In other words, whether this is a paradox or not depends on where it’s been published 🙂
(This line of thought was inspired by a lunchtime conversation two years ago with a group of physicists. I donâ€™t remember who, or Iâ€™d spread the blame.)
Update: A number of people have made comments along the lines of “But aren’t you assuming a well-ordering” / “What if the most notable article isn’t unique” and so on. It’s easy to modify Question 1 to deal with this: all that’s needed is (a) for the set of non-notable subjects to be well-defined; and (b) for there to be some way to pick out a unique one from that set. Point (a) is, of course, debatable, but outside the scope of the game, which starts by assuming that the Notability policy is well-defined to start with. With that, point (b) follows because the set of possible subjects on Wikipedia is a subset of the set of unicode strings, and is thus countable.