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Best sentence I've read this week:
In short, Godel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved.
-Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter
(I'm only about a quarter through the book, but one of the morals I am gleaning is that *everything* is an axiomatic system. Of course, if you've taken more than a certain threshold of math classes, you're convinced of that anyway.)
In short, Godel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved.
-Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter
(I'm only about a quarter through the book, but one of the morals I am gleaning is that *everything* is an axiomatic system. Of course, if you've taken more than a certain threshold of math classes, you're convinced of that anyway.)
