>>11383542Godel says that, within any axiomatic system*, there are true statements which cannot be proven true by using any of the axioms, so I guess the converse holds as well? i.e. if P is such a statement, then not P is by definition false, but if we could prove that not P is false, then we could prove that P is true, a contradiction to Godel. But perhaps this only works if you assume the excluded middle, I'm not sure.
*obviously there are caveats to this, and I'm simplifying for a 4chan post.
