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Let's Not Forget About Goedel!

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Posted by Richard Ruquist on September 2, 2001 12:29:55 UTC

Goedel showed, ratherproved using math/logic that the following ststement does not follow:

"So it stands that the whole of mathematics is completely derived from abstract, esoteric axioms. "

Bertrand Russell tried to make this statement true. So did Hilbert. But all were unsuccessful becauseof Goedel. The universe does not come just from axioms. Or rather, mathematics does not come just from axioms. In fact, there seems to be much more variety in mathematics than in physical law. It's like the universe used the same math over and over again to develop rather disparate structures, e.g., the laws of similarity.

So if the physical laws are based on a finite set of axioms, then there are laws or theorems that are true but cannot be derived from those axioms. That is what God-el proved. Isn't it amazing that someone named god-god should make room for non-axiomatic truth. That is coincidence for you. Such coincidence seems to be more the rule than the exception. My intuition is that coincidences of this sort comes from Goedel's loophole and is how the universe is guided. It circumvents determinism.

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