I’m very confused. Of course if φ is provable then it’s true. That’s the whole point of using proofs.
But that statement isn’t provable.
Then just assume it as an axiom.
Then the paradox you were describing fires and the system becomes inconsistent.
Yes, but it may be true without being provable.
I’m very confused. Of course if φ is provable then it’s true. That’s the whole point of using proofs.
But that statement isn’t provable.
Then just assume it as an axiom.
Then the paradox you were describing fires and the system becomes inconsistent.
Yes, but it may be true without being provable.