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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 Hermann Weyl. It is thus occasionally called "Weyl's paradox," as well as sometimes "Grelling's paradox." Justice of attribution has increasingly encouraged the first name, however. It is closely related (and analogous) to several other well known paradoxes, in particular the Barber paradox, the Liar paradox, and Russell's paradox.
Definition
Define the adjectives "autological" and "heterological" as follows:
- A word is autological if and only if it describes itself. For example "short" is autological, since the word "short" is short. "Sophisticated" and "polysyllabic" are also autological.
- A word is heterological if and only if it does not describe itself. Hence "long" is a heterological word, as is "monosyllabic".
Since autological and heterological are opposites, all words are members of either the set of "autological" words, or the set of "heterological" words.
The paradox is this: is the word "heterological" heterological? There is no consistent answer: if it is, then it isn't; if it isn't, then it is.
Assume the word "heterological" is autological. By definition of autological, the word "heterological" must apply to itself; that is, the word "heterological" must be heterological. However, if "heterological" is heterological, then by definition of heterological, it does not describe itself; that is, the word "heterlogical" is not heterological.
Examples
Heterological words
Autological words
External links
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