To determine whether any given subject deserves an entry, Wikipedia uses the criterion of notability. This lead to an interesting question:

Question 1: What’s the most notable subject that’s not notable enough for inclusion in Wikipedia?

Let’s assume for now that this question has an answer (“The Answer”), 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 “no”, then there’s no problem, and we can all go home.

If the answer to Question 2 is “yes”, 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 Wikipedia’s notability criterion.

Take that, deletionists!

Here’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, “no”.

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 Wikipedia’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 don’t remember who, or I’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.