“It would seem weird (and maybe even contradictory?) to disobey a proof that you would take a certain action, so wouldn’t the most sensible option be to just obey the proof?”
You lost me here. Either the proof is valid and you will take the action, there is no “option” there. Or the proof has a flaw and you can do whatever you want. In which case there is no proof and no case for doing what it purports to prove.
The importance of this question doesn’t involve whether or not there is an “option” in the first case or what you can or can’t do in the second. What matters is whether, hypothetically, you would always obey such a proof or would potentially disobey one. The hypothetical here matters independently of what actually happens because the hypothetical commitments of an agent can potentially be used in cases like this to prove things about it via Lob’s theorem. Another type of in which how an agent would hypothetically behave can have real influence on its actual circumstances is Newcomb’s problem. See this post.
You lost me here. Either the proof is valid and you will take the action, there is no “option” there. Or the proof has a flaw and you can do whatever you want. In which case there is no proof and no case for doing what it purports to prove.
The importance of this question doesn’t involve whether or not there is an “option” in the first case or what you can or can’t do in the second. What matters is whether, hypothetically, you would always obey such a proof or would potentially disobey one. The hypothetical here matters independently of what actually happens because the hypothetical commitments of an agent can potentially be used in cases like this to prove things about it via Lob’s theorem.
Another type of in which how an agent would hypothetically behave can have real influence on its actual circumstances is Newcomb’s problem. See this post.