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points by rcpt 3 days ago | 0 comments

Godel says that there are statements that are true but have no proof within that system. It's not about algorithms.

I'm saying it'd be funny if Riemann were true but not proveable.

Though I guess it's actually funnier. If Riemann were false then there would be a counterexample, so it's clearly within existing axioms.

So if one can prove that Riemann isn't proveable in our current axioms then it has to be true.

[–] plagiarist 3 days ago

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.