This reminds me of the old joke about induction in mathematics. Maybe it could be adapted as follows:

Claim: Every Wikipedia page ever made is notable.

Proof: Suppose at least one Wikipedia page that is not notable exists. Choose the one whose length in characters is smallest. Then surely this page is notable for being the short non-notable Wikipedia page ever created, making it quite notable, indeed. We have reached a contradiction and hence the proof is complete.

Or something like that.

Why does it have to the the shortest page? The logic is flawed.

In the 'interesting number paradox' the smallest non-interesting number is chosen. By convention every ordered set has a smallest element which is arbitrarily chosen.

The logic is flawed for the main reason that partitioning sets in any non-objective manner and then drawing conclusions from that is folly, which is the point of such so-called paradoxes.

I tend to think of "interestingness" as a fuzzy property that is at or near 1 on the obviously interesting integers {0, 1, ...} and approaches 0 as N -> infinity. But that obviously doesn't alter the fact that "interestingness" is extremely subjective.

Another cool paradox is the one surrounding "the smallest positive integer that cannot be expressed using twenty or fewer English words".

It's not the shortest page on wikipedia, just the shortest non-notable page. (As in "shortest(non-notable page)", not "(shortest, non-notable)page".)

English associativity sucks.

Indeed. I never noticed how ambiguous it is until I took a class where I tried to teach a computer to understand it.

Yet somehow, we still communicate. I guess that says something interesting about our evolution.

On a related note, how many linguists does it take to change a broken light bulb? Two. One to decide what it should change into, and one to find out what kind of bulb emits broken light.

You mean it's interesting how irregular natural languages are, but those are the ones we use instead of well-defined ones? Yeah, I guess it is interesting. But then again, nature comes before science, right? (Well, not if you asked a string theorist.) We're trying to impose logical systems where they do not exist, like reliable computers built on top of unreliable transistors (or relays, or vacuum tubes, for that matter). Heck, we even mix countable and uncountable, continuity and discreteness. We count two rocks and therefore we think we can have exactly two meters of something.

Why can't we just be well-defined formal systems? :/

Which one would you start by, then? You have to at least order them in some way to discard them one by one.

Is proof-by-induction different from proof-by-contradiction?

Yes, completely different.

Proof by contradiction means that you start by assuming the opposite of what you wish to prove, and then logically arriving at a contradiction. The existence of a contradiction implies that your premises were false, and since your premise was the opposite of what you wanted to prove, what you wished to prove must be true.

Proof by induction works by showing that a particular case (usually the first/smallest case) is true, and then showing that the fact that one case is true implies that the next case is also true. In other words, prove that your statement is true for n=1, and then prove that if the statement is true for m, it is also true for m+1. Since it's true for n=1, that implies it's true for n+1=2, and since it's true for n=2, that implies it's true for n+1=3, and so on, and thus you have proven that it's true for all n larger than your original case. Of course, it doesn't have to be that n implies n+1 -- it can be n-1, or any other variant, the point is that it chains up and leads to all values being proven.

I like the one about all positive integers being interesting better. There, at least you have to break out the fuzzy logic to debate the "proof"'s value.

There is probably a tie for shortest Wikipedia non-notable page at 0 characters. Filtering out 0s, we get a bunch of 1-character pages not worth ordering. Also, the distinction is always changing, since non-notable Wikipedia pages are always changing (page blanks, vandalism) and being deleted. The fact that the "shortest page" distinction is being passed around promiscuously to a bunch of different crappy pages means that it's a pretty meaningless one.

This is reminiscent of Hofstadter's desire for a book of reviews of itself (http://en.wikipedia.org/wiki/Douglas_Hofstadter#Columnist).

Wikipedia tries to keep its integrity, but I think sometimes they need to be more reasonable. Someone ought to create a complement to wikipedia which allows people to add things like this and other non-spam articles which wikipedia editors won't tolerate.

I guess not surprisingly, I attempted to write a book of reviews of itself once. The idea still lingers in my mind, and I'd suspect that after a handful of years I'll pull it out and finish it. (I think the idea will be to mark the book as a "50th anniversary edition" of itself, and have the entire thing just be a history of forwards to the book from various known literary critics, documenting the critical reception of the book throughout history. It's a very conceited idea.)

It's already been written: The Book of the Book by Idries Shah (1969).

http://www.amazon.com/Book-Idries-Shah/dp/090086012X

Somehow, http://xkcd.com/545/ and http://xkcd.com/446/ seem appropriate to mention here.

Hint: Check the alt text

> It can be looked at both as metahumor and as a piece of postmodern art.

I think this is more of a recursive humor than metahumor.

True, false classification. (Metahumor would be humor about humor.)

Well, it's a wiki page, so anybody can edit it and fix stuff like that.

Well, according to wikipedia, in which metahumor redirects to meta-joke:

Meta-joke refers to three somewhat different, but related categories: "self-referential jokes", "jokes about jokes" (see meta-) also known as metahumor, and "joke templates".

Recursive humor would be a subclass of self-referential jokes, going by the definition for self-referential jokes as given by (what else?) Wikipedia.

This kind of meta-joke is a joke in which the joke itself, or rather a familiar class of jokes, is part of the joke.

There should be a wiki page about the creation of the Wikiid page (which apparently got deleted?). Surely that's relevant?

It has been suggested that this page or section be merged with Wikiid.

Well there is:

http://deletionpedia.dbatley.com/w/index.php?title=Main_Page

Nah, it didn't catch it.

Looks like a few people are vandalizing stuff - which is pretty awesome and should definitely be added to the page's "history" at some point - but for a reference point, the page looked like this when I submitted it: http://en.wikipedia.org/w/index.php?title=User:Diikiw/Wikiid...

Anyone can make a page notable enough to avoid deletion. Fill it with well written, relevant and verifiable materials and its fine.

"Within Wikipedia, notability refers to whether or not a topic merits its own article." (emphasis added) http://en.wikipedia.org/wiki/Wikipedia:Notability

Topics are notable; articles are not. If a topic is non-notable in the real world, nothing written on Wikipedia should change that.

You miss the point. The concept is that Wikipedia itself is a notable web site. The question became: was it possible to make a page that cited no source outside of Wikipedia, yet managed to create relevant content by citing Wikipedia?

The answer was no, but I still hold that Wikipedia's belief that it can manage to stay NPOV when it's selective about what it deems relevant or not is a deluded one, and one of the most damning parts of the web site.