What you're describing in the second part of your post is the Principle of Explosion[1]. It does not apply to Godel's argument as his axioms entail no contradic

What you're describing in the second part of your post is the Principle of Explosion[1]. It does not apply to Godel's argument as his axioms entail no contradictions. I'm not sure what you mean by "circular" in this context. However, what people usually mean is an argument where the conclusion is contained in one of the axioms. Godel's proof doesn't explicitly suffer from this but I will say that his fourth axiom, i.e. Good(phi) -> [Necessarily]Good(phi) is cutting it pretty close. [1] http://en.wikipedia.org/wiki/Principle_of_explosion http://en.wikipedia.org/wiki/Principle_of_explosion