if someone ever tries to tell you something "because godel" direct 'em to this paper. not only are most "popular" uses of "godel incompleteness" dead wrong, but it turns out, a good 2/3 of the "proper" uses of it make it out to be too strong as well.
The standard story is that Godel's second incompleteness theorem stopped Hilbert's program dead in its tracks, because one could not prove the consistency of PA within itself. But a lovely new paper from Artemov argues that this isn't what G2 proved at all! 1/2