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The following excerpt is from Godel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter.

Divide the adjectives in English into two categories: those which are self-descriptive, such as "pentasyllabic", "awkwardnessful", and "recherché", and those which are not, such as "edible", "incomplete", and "bisyllabic". Now if we admit "non-self-descriptive" as an adjective, to which class does it belong? If it seems questionable to include hyphenated words, we can use two terms invented specially for this paradox: autological (= "self-descriptive"), and heterological (= "non-self-descriptive"). The question then becomes: "Is 'heterological' heterological?" Try it!

What Hofstadter is describing is a famous variation of Russell's Paradox known as The Grelling-Nelson Paradox. Both Hofstadter and Grelling seem to be concerned with how one should classify "heterological", and makes no mention of which of the two categories "autological" falls into. So my question then, is "autological" an autological adjective, or a heterological adjective? Or is the answer to this question yet another paradox implied by Grelling's original question about "heterological"?

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Just as you can view the question of the self-descriptiveness of "non-self-descriptive" as a form of the liar's paradox ("this statement is false") you can similarly view the question of whether "autological" is autological along the lines of "this statement is true."

The traditional analysis is that such statements can be taken as either true or false, without contradiction either way. Thus it's valid to say that "autological" is autological, or that it is not autological, and no contradiction will arise.

I believe I once read that due to esoteric reasons in formal logic, such statements were (either by convention or deeper reasons) taken to be true — but I cannot currently find a reference for this. (I believe Tarski or Smullyan may have claimed as such?) In that case, one should take "autological" to, in fact, be autological. I will look some more to see if I can find a reference for this (and the reasons) but perhaps somebody else will beat me to it.

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    George Lakoff wrote a paper on it back in the early 70s, as I recall. He pointed out that there is as much difficulty assigning truth values to positive as to negative truth descriptions.
    – jlawler
    May 22, 2019 at 14:11
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No instance of an adjective is self-descriptive, it always describes other instances of words. This is the classical sign/meaning confusion. Word-forms are not descriptive, they are collections of instances and always follow the instance (hence dictionaries need citations). Problem solved.

Few words, like "I" said by myself for example, are self descriptive, and then not bijective, that is, I am not just the sound that I omit and the sound is not my own posession, but then what is?

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