> In any rate, "proved true in all [formal] systems" is a mixed-up > of technical terminologies: formal systems prove syntactical theorems, > truths are verified in language structures. The two paradigms are > different and _independent_ : proving in one doesn't logical equate > to the other.
G\"odel's completeness theorem shows that they aren't independent.
-- When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting