Gödel's Theorem

1. In any formal system adequate for number theory there exists an undecidable formula (namely a formula which is not provable and whose negation is not provable). It is sometimes added that the undecidable formula is true.

2. A corollary to the theorem is that the consistency of a formal system adequate for number theory cannot be proved within the system. The bearing of these results on epistemological problems remains uncertain, but it has been suggested that they should not be rashly called upon to establish the primacy of some act of intuition that would dispense with formalization.