> Take the proof that the square root of 2 is irrational. The proof relies on a contradiction that arises if one assumes the root is rational, but one can imagi

> Take the proof that the square root of 2 is irrational. The proof relies on a contradiction that arises if one assumes the root is rational, but one can imagine a logic system where such a contradiction does not imply that the original assumption is false. How possible, you say? It's all math, where one is allowed any starting assumptions, and works out the implications of those. The truth or falsity of that statement in a model is independent of who observes that model. The only “social construct” you’ve described is which model to use by default — literally, a notation convention, nothing semantic. > But, there is something deeply satisfying about thinking that contradictions are (or should be) impossible in our universe, and so this "proof" seems solid. Our universe either does or doesn’t, depending on which model best represents it — we’re only debating what assumption to make about an unknown.