Goedel's "incompleteness theorem" says that a purely formal deductive system (ie, a purely rationalistic system) is not closed. D'uh.
A purely formal deductive system does not have any facts drawn from reality. A system of knowledge is not closed unless it's got facts drawn from reality. Incorporate facts of reality into your purely formal deductive system and presto! you've no longer got a purely formal deductive system.
Goedel is an absolute genius for realizing that pure rationalism does not admit the facts of reality into its system. But he is an absolute asshat for confusing a pure rationalism with actual knowledge, and declaring that knowledge is therefore not "closed".
