The theorem applies beyond elementary arithmetic to any formal system. If we try to be rigorous in that way with our models of the universe, the theorem would s

The theorem applies beyond elementary arithmetic to any formal system. If we try to be rigorous in that way with our models of the universe, the theorem would say that no matter how formally sound our models are they will have to be incomplete, incorrect, or non-provable; that is, we would not be able to rule out the existence of consciousness or figurative pink elephants. (And if they are not formally sound in that way, our models can be safely considered to be incorrect/incomplete simply because they are not formally sound in that way.)