auto? hetero?
Grelling’s Paradox
Kurt Grelling and Leonard Nelson · 1908
The puzzle
A word is autological if it describes itself (“short” is short). It is heterological if it doesn’t (“long” is not long). Is heterological heterological?
Note
If it is, it isn’t; if it isn’t, it is. Like Russell’s paradox in set theory and Berry’s in number, this one runs on self-reference applied to a property whose definition refers back to itself. The standard cure — declare the word self-undefined — saves the system but admits that some perfectly grammatical English sentences refer to nothing. The implication, taken seriously, is that natural-language meaning has gaps a formal theory can describe but cannot really cover. Grelling died in Auschwitz in 1942. Nelson died in 1927. The paradox is usually attributed to both and is sometimes called the Grelling–Nelson antinomy.