Grelling-Nelson Paradox
This came up in a book, I can’t remember which one ( [[Gödel, Escher, Bach]]N maybe?). It’s a paradox based on the word “heterological”.
A word is said to be autological if it describes itself, e.g.:
- English
- word
- noun
- pentasyllabic
- unhyphenated
And a word is said to be heterological if it doesn’t describe itself, e.g.:
- long
- hyphenated
- monosyllabic
The paradox asks, “is heterological a heterological or an autological word”?
- If heterological is a heterological word, then it does not describe itself, which is the meaning of ‘heterological’. Therefore it is an autological word, which is a contradiction.
- If heterological is an autological word, then it does describe itself. Therefore it is an autological word. But if it is an autological word, it must be heterological, which is a contradiction.