Grelling-Nelson paradox

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 related (and analogous) to several other well known paradoxes, in particular the Barber paradox, the Liar paradox, and Russell's paradox. Also see blardy.

Definition

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

1. 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.
2. 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.

If "heterological" is heterological, as "heterological" is by definition an autological word, it is thus not heterological. If not, then "heterological" has the property it designates and therefore it is heterological. Hence, "heterological" is heterological iff it is not heterological.

Examples

Heterological words

• Abbreviated
• Adverb — or any other part of speech word except 'Noun', 'Adjectival' or 'Adverbially', or the neologism 'to verb'
• Purple
• Female
• Carcinogenic
• Plural
• Phonetic
• Misspelled

Autological words

• Pentasyllabic
• Adjectival
• Slang, originally
• Pronounceable
• Legible
• Confusionful
• Wee
• English
• Verbify
• Obfuscating
• e-text —as it appears on the internet edition of Wikipedia
• Listed item —in the present context
• Final —in the present context

External links

• Autological words