# Grelling-Nelson Paradox

> Source: https://ollybritton.com/notes/random/grelling-nelson-paradox/ · Updated: 2022-06-15 · Tags: notes

This came up in a book, I can't remember which one ([Godel, Escher, Bach](https://ollybritton.com/notes/books/godel-escher-bach/) 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.

## Links
* <https://en.wikipedia.org/wiki/Grelling%E2%80%93Nelson_paradox>

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Olly Britton — https://ollybritton.com. Machine-readable index: https://ollybritton.com/llms.txt