I think I'm missing something with the Löb's theorem example.
If [A()=5⇒U()=5]∧[A()=10⇒U()=0] can be proved under the theorem, then can't [A()=10⇒U()=10]∧[A()=5⇒U()=0] also be proved? What's the cause of the asymmetry that privileges taking $5 in all scenarios where you're allowed to search for proofs for a long time?
I think I'm missing something with the Löb's theorem example.
If [A()=5⇒U()=5]∧[A()=10⇒U()=0] can be proved under the theorem, then can't [A()=10⇒U()=10]∧[A()=5⇒U()=0] also be proved? What's the cause of the asymmetry that privileges taking $5 in all scenarios where you're allowed to search for proofs for a long time?