*A paradox stated by K. Grelling and L. Nelson in 1908. An adjective is called*autological

*if it has the property denoted by itself. Thus the word 'English' is an English word, 'short' is short, and 'polysyllabic' is polysyllabic. If an adjective is not autological, it is*heterological.

*Thus 'German' is not German, 'long' is not long, and 'monosyllabic' is not monosyllabic. What of the word 'heterological' itself? Is it heterological? It must be either autological or heterological.*(p. 201)

This, I think, is a similar type of problem in the Godel Proof that says that any axiomatic system will have the capacity to generate undecidable statements, and, the corollary, that the consistency of a formal system containing arithmetic cannot be proved by the said system.

Not being a mathematician, and only as a language analyst, I can say that the Grelling-Nelson paradox is rather Anglocentric, and a superficial one at that. And I've never been able to totally accept Godel's Proof for the simple fact that there are these things called "linguistic accidents" like

*little, green ideas dream furiously*.

The Grelling-Nelson paradox is too highly language-specific to be a real paradox within a formal system. It does not consider the real possibility that a given language may have a completely different grammatical structure such that it invalidates their insights completely. For instance, in mathematics alone, one may denote extremely large and extremely small numbers by way of scientific notation: are these numbers autological or heterological? -the question is totally meaningless. In linguistics, the word 'English' may also be denoted as 'Anglophone'; is the word 'Anglophone' English?

If we accept that the word 'Anglophone' is English - and it means 'the English language' in many linguistics textbooks - how do we use the terms

*autological*vs

*heterological*in any productive way?

Now, the Godel Proof, I've read in many maths books that I own that there is often more than one way of constructing a proof. The great Gauss did it all the time where he'd reformulate a statement and his line of reasoning would come out more beautifully and elegantly than other people's proofs. Selberg did the same thing when he and Paul Erdős had a dispute over a certain proof where he was able to bypass Erdős' insight completely.

In the area of physics, it is said that Feynman had an unconvention take on physics, and as a kid he had his own notational system drastically different than the symbolism of maths.

These things are possible because a purely text-based critique (ie, mistaking the text for conceptual level structures) is just so replete with linguistic and logical pitfalls that are often more apparent than real.

Jay

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