Ok, now I see your point. It seems you're advocating for intuititionistic logic: you only consider a proposition "true" if you can build a proof for it. Classic

Ok, now I see your point. It seems you're advocating for intuititionistic logic: you only consider a proposition "true" if you can build a proof for it. Classical logics (and, therefore, classical mathematics) assumes that it makes perfect sense to talk about the truth value of a proposition without computing/proving it. Even undecidable ones are either true or false.