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points by plagiarist 3 days ago | 0 comments
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.
[–] skew-aberration 3 days ago
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.

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