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Re: Godel's Theorem

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Posted by Harvey on September 23, 2003 19:48:58 UTC

I might add, I hypothesize, that even logic and mathematics have 'cause and effect' as a result of Godel's proof of indeterminacy. That is, with any sufficiently rich formal axiomatic system, there must exist theorems that cannot be proven true. This creates an asymmetry between mathematical cause (axiom) and mathematical effect (theorem) since if there were no indeterminacy (i.e., we could prove all theorems of a sufficiently rich formal axiomatic system), then the theorems could be the cause of the axioms since you could (in principle) take all the theorems that are true for the axiomatic system and 'prove' all the axioms of those theorems. This would mean that the axioms would be 'theorems' and the theorems would be 'axioms'. Or, conversely, you only have axioms in mathematics (or you only have theorems) which is ludicrous since if all you have is axioms then nothing is proven, and if you only have theorems, then nothing is conjecture. Perhaps Godel's theorem is a fundamental rule of logic and math such that indeterminancy is primary? Due to Godel's theorem I doubt indeterminacy will go away in quantum physics. In my view, indeterminacy encompasses a deep truth.

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