Comment by skew-aberration

Godel sentences are only true if you assume consistency. And once you add that axiom, the computer can prove them too.

G 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.