I think this interpretation is both intriguing and clarifying, thanks. It suggests that a good framing of the incompleteness theorem is:

Any sufficiently rich system S can be extended by multiple interpretations I, such that all of its provable theorems are true for all of I, but I contains interpretations who disagree on the truth of some unprovable statements of S

I think this interpretation is both intriguing and clarifying, thanks. It suggests that a good framing of the incompleteness theorem is: