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I stumbled across the following tidbit while reading Godel, Escher, Bach last night: heterological adjectives! It’s a formulation of Russell’s Paradox, but in the English language.

Suppose I present you with the following two adjectives:

autological: an adjective that describes itself

heterological: an adjective that does not describe itself

For example, ‘short’ is an autological word, but ‘long’ is not. I think my favorite autological word (and these are the far rarer of the two) is ‘attributive’ - the word itself attributes meaning to it’s modified noun.

And here’s the brain-teaser of the day. What if we ask the following question: “Is ‘heterological’ heterological?”

If ‘heterological’ is itself heterological, then it certainly describes itself. But that would make ‘heterological’ autological. But we just said it was heterological!

If ‘heterological’ is not heterological, then it is autological (they’re antonyms afterall). So then ‘heterological’ describes itself. So then ‘heterological’ is heterological. Contradiction!

So we wind up with the following: ‘heterological’ is heterological if and only if ‘heterological’ is not heterological.

Just a Wednesday morning’s musings.