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Grelling-Nelson paradox

From Academic Kids

The Grelling-Nelson paradox is a semantic 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 Grelling's paradox. Justice of attribution has increasingly encouraged the present name, however. It is closely analogous to several other well known paradoxes, in particular the Barber paradox and Russell's paradox.

Contents

Definition

Define the adjectives "autological" and "heterological" as follows:

  1. A word is autological (or blardy) if and only if it describes itself. For example "short" is autological, since the word "short" is short. "Sophisticated" and "polysyllabic" are also autological.
  2. A word is heterological if and only if it does not describe itself. Hence "long" is a heterological word, as is "monosyllabic".

All words are members of either the set of "autological" words, or the set of "heterological" words (although it may not always be obvious which is correct).

The paradox is this: is the word "heterological" heterological? There is no consistent answer: if "heterological" is heterological, then it is an autological word, thus it is not heterological. If "heterological" is not heterological, then it must be autological, which means it describes itself, and is therefore heterological. Hence, "heterological" is heterological iff it is not heterological.

Examples

Heterological words

Autological words

External links

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