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Posted by Richard Ruquist on July 22, 2001 17:27:39 UTC

Rational fundamentals certainly exist. And the universe may be describable, mostly, by a finite number of them. If string-loop-quantum gravity research succeeds we will find such a set of rational fundamentals.

But if the universe obeys mathematics, that is if the universe is rational, then the laws of physics will be mathematical, but we cannot derive every possible solution from the axioms of the laws of physics. My understanding is that Goedel has shown that there will always be correct solutions or theorems that are a consequence of the laws of physics but which cannot be derived from its fundamental axioms.

There are examples in math right now of "conjectures" that from computer analysis and the like appear to be correct but are not yet derived from basic math theory. Gradually, some of them are being proven. Goedel essentially said that there are conjectures that cannot be proven ever, and apparently he proved that statement. Chaitin has investigated something like the number of provable conjectures versus the number of unprovable ones and claims the the latter far outnumber the former

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