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Gödel proved the incompleteness of Arithmetic.  Specifically, he demonstrated that in any axiomatic system capable of Arithmetic there are statements that can neither be proved or disproved within the axioms.

To fully understand what that meant and means requires an understanding of what Logic and Mathematics were 'on about' from around 1870 to l933.  To (greatly) simplify, Frege, Hilbert, Russell, Whitehead, & All That Crew were attempting to construct an intellectual tool that would always, when correctly used, derive a True and Valid answer.  

Gödel's Proof = You Can't.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Wed Jan 2nd, 2008 at 10:56:09 PM EST
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