Editing Grelling–Nelson paradox (section)

==={{anchor|Heterological}}Paradoxical cases===
{{unreferenced |section|date=August 2023}}
The Grelling–Nelson paradox arises when we consider the adjective "heterological". One can ask: Is "heterological" a heterological word? If the answer is "no", then "heterological" is autological. This leads to a contradiction, for in this case "heterological" does not describe itself: it must be a heterological word. But if the answer is "yes", then "heterological" is heterological.  This again leads to a contradiction, because if the word "heterological" describes itself, it is autological.

* Is "heterological" a heterological word?
** no → "heterological" is autological → "heterological" describes itself → "heterological" is heterological, ''contradiction''
** yes → "heterological" is heterological → "heterological" does not describe itself → "heterological" is not heterological, ''contradiction''

The paradox can be eliminated, without changing the meaning of "heterological" where it was previously well-defined, by modifying the definition of "heterological" slightly to hold all nonautological words except "heterological". But "nonautological" is subject to the same paradox, for which this evasion is not applicable because the rules of English uniquely determine its meaning from that of "autological".  A similar slight modification to the definition of "autological" (such as declaring it false of "nonautological" and its synonyms) might seem to correct that, but the paradox still remains for synonyms of "autological" and "heterological" such as "self-descriptive" and "non-self-descriptive", whose meanings also would need adjusting, and the consequences of those adjustments would then need to be pursued, and so on. Freeing English of the Grelling–Nelson paradox entails considerably more modification to the language than mere refinements of the definitions of "autological" and "heterological", which need not even be in the language for the paradox to arise. The scope of these obstacles for English is comparable to that of [[Russell's paradox]] for mathematics founded on sets.