Can something be both true and unprovable without being a self-referential Godel sentence? I assume most statements that aren't self-referential are independent, like the continuum hypothesis with ZFC.
replyGodel sentences are only true if you assume consistency. And once you add that axiom, the computer can prove them too.
replyG is independent of your original system T (cannot be proven true or false).
If you create T+ with added consistency axiom, then G is true and provable.
But G is never true and unprovable in the same system.
It's a lot like is/ought or theology.