Absolutely, but that's not the interesting part. The problem boils down to the fact that any kind of formal proof system is only "truth-preserving machinery"; that is, you can't get out something "truer" than what you put in. It doesn't introduce new truths into the world, it just permutes existing ones so that different facets of them are clear.
But when you're trying ask big questions about the nature of truth itself, a proof doesn't get you very far! You're trying to get at the thing that has to be assumed as a prior or axiom in order for the proof machinery to do what it does. Given our current understanding of the universe, a proof in any formal system can never tell you "why" the thing that it proved was true. Just how it got there.
But when you're trying ask big questions about the nature of truth itself, a proof doesn't get you very far! You're trying to get at the thing that has to be assumed as a prior or axiom in order for the proof machinery to do what it does. Given our current understanding of the universe, a proof in any formal system can never tell you "why" the thing that it proved was true. Just how it got there.