Gödel, Escher, Bach: Grelling's Paradox

'Gödel, Escher, Bach' (Douglas R. Hofstadter).

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[2bsirius]

OK..I cheated. SORRY!

If Russell's paradox is shifted into the world of words and grammar, then Grelling's paradox results. Coining the word "heterological", defined as "a word which does not describe itself", creates the same situation as exploring the set of all sets that do not contain themselves. The word heterological describes itself IF it does not describe itself.

The Oxford Dictionary of Philosophy entry

So Jprotevi is spot on! 5*s

[jhip87]

I don't want to talk about this at length, and what you say may indeed be true of some paradoxes, but certainly not all. The Liar Paradox, for instance, or Russell's, Berry's, or Curry's, have all expanded our knowledge of mathematics and language immensely.

[insidetrip101]

@Abracadabra208

I think you mean that you can not talk about everything at the same time and in the same respect: "If everyone who does not shave themself is shaved by the barber, then who shaves the barber?"

[dolofonos]

It is perfectly possible make a false statement; yet we marvel at the paradox.

"Imagine an unstoppable and an immovable object in coexistence." The Universe did not just explode because there is no natural law that says I cannot declare an absurdity.

[Abracadabra208]

One could supply a classically based answer to the paradox and simply state that the question itself is nonsense, akin to asking what is north of the North Pole or what there was "before" time began. A priori, truth cannot contradict truth.

[Bakmoon]

@toogoodbw Because if the word "heterological" isn't heterological, then it doesn't describe itself. But if it doesn't describe itself then by definition it is heterological.

[toogoodbw]

I don't understand why the answer isn't a simple "No. The word 'heterological' is not heterological."

[jmarkmusic]

@jmarkmusic oops: `T and `F... same idea.

[jmarkmusic]

Let's have ~T!=F and ~F!=T and lets have `T=F and `F=T. T=T and F=F. Let's also have ~T=`F and ~F=`T. Heterological is heterological is both ~T and ~F. END OF DISCUSSION, MATHEMATICIANS! I WIN AT MATH. This is the art of infinite reckoning in a nutshell.

[zeekoprop]

Let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition 'F(F(fx))', in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(f(x)) and the outer one has the form Y(O(fx)). Only the letter 'F' is common to the two functions, but the letter by itself signifies nothing. This immediately becomes clear if instead of 'F(Fu)' we write '(do) : F(Ou) . Ou = Fu'. Russel's paradox resolved.

[ariastoteles]

A marvelous paradox!

[Paulginz]

@SarahStarmer The Banach-Tarski paradox (you can take a sphere, chop it up into 5 pieces and reassemble the pieces into 2 spheres of the same size as the original) is a nice example of paradox that isn't based on self-reference.