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Posted by Mark on July 18, 2003 19:11:48 UTC

I may be wrong here (that's what the "?" was for in the title), but doesn't Godel's proof actualy state that any formal system of logic is incomplete, hence there will always be "more truth out there" than can be proved by any arbitrary formal system...?

For example: for every formal system founded on A1, A2, A3, ... An axioms, there exists a sentence which can neither be proved true nor false within this formal system, hence logic/mathematics is insufficient to prove every aspect of reality. There will always be questions that must go on unanswered, no matter how knowledgeable and advanced the system of logic.

I don't recall the mention of required paradoxes & contradictions. In fact a system of logic requiring contradictions is itself illogical and absurd. Contradictions inherently collapse any proof, and are the ultimate downfall of any logic system if they cannot be discarded. However, I may be sadly mistaken... What do you say?

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