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Grelling-Nelson paradox

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The Grelling-Nelson paradox is a verbal paradox formulated in 1908 by Kurt Grelling[?] and Leonard Nelson[?] and sometimes mistakenly attributed to German philosopher and mathematician Herman Weyl[?]. It is a reformulation of the Barber paradox and Russell's paradox.

The paradox deals with the made-up words "autological" and "heterological". A word is called autological if it applies to itself. For example "short" is autological, since the word "short" is short. "Sophisticated" is also autological. Words that are not autological are called heterological. "Long" is a heterological word, for example. The obvious question arises: is "heterological" heterological? There is no consistent answer: if it is, then it isn't; if it isn't, then it is -- think it through.

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