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Undecidable words

January 14th, 2005 (01:58 pm)
current mood: twisted

My sister-in-law gave me a copy of Weird and Wonderful Words for Christmas. Today I found this gem:

autological of an adjective, having the property that it describes. The antonym is heterological. Thus, the adjective sesquipedelian is autological, the adjective infinitesimal is heterological.

Now, as a math geek, I can't see a word like this, which is all about self-reference, without trying to apply it to itself. So, the question is, is "autological" autological? The mathematician's answer is that it's undecidable: "autological" is autological if and only if it has the property that it describes--in other words, if and only if it's autological. Since there's no external reference here, you have a choice of axioms: either it is or it isn't; it's up to you. (This is an extremely handwavy proof of undecidability, but hey.)

The common-sense answer, of course, is that, no, it's not autological, because there's no particular reason to say it is: "autological" is heterological.

The really interesting question is, what about "heterological"? If "heterological" is autological, then it has the property it names, so it's heterological, so it's not autological. On the other hand, if "heterological" is heterological, then it doesn't have the property it names, so it's not heterological. So the sentence "The word 'heterological' is heterological" is neither true nor false.

So much more entertaining than "This sentence is false.". :-)

Comments

Posted by: Amy Knauer / Violet Coleson (violet_amy)
Posted at: January 14th, 2005 09:32 pm (UTC)

If you are interested in how phrases came to be, another good book to read is Devious Derivations: Popular Misconceptions -- And More Than 1,000 True Origins of Common Words and Phrases by Hugh Rawson.

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