[eis]

> These theorems apply to any system of axioms that are rich enough to state the liar's paradox.

Isn't that circular reasoning or tautological though? Rephrased: any system that can state something that these theorems apply to, can have the theorems applied to.

I think the word "rich" is too inaccurate in this context. It is not clear why there can't be a more "rich" system which does not suffer from this issue and can't state the liars paradox.

[qnleigh]

Yeah rich is a vague word here. Really we're trying to say 'if a set of axioms can express provability, and can get a sentence to refer to itself, then it can state the liar sentence. And once it can state the liar sentence, then the rest of Gödel's argument follows.' There's no circularity.