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.



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