Comment by noslenwerdna
15 hours ago
That is also not how it works. The theorem says that there exist some true statements for which there is no proof. This is assuming the axioms are consistent.
15 hours ago
That is also not how it works. The theorem says that there exist some true statements for which there is no proof. This is assuming the axioms are consistent.
I think you're right, I'm conflating two separate things.
EDIT: I am wrong (it's been a while) but there is nuance.
I said any computer program fails to prove some true statements. In fact, some 'true' statements cannot be proven by any program, as others have said.
But for those statements G, you can prove 'G is true if our system is consistent', just not 'G is true'.
So when we say G is 'true', we are really just asserting the consistency axiom that our computer program is denied.