Thanks, the second bit you quoted, I rewrote. I agree that sketching the proof that way was not good.
Suppose that hypothetically, Rob proves that crossing the bridge would lead to it blowing up. Then if he crossed, he would be inconsistent. And if so, the troll would blow up the bridge. So Rob can prove that a proof that crossing would result in the bridge blowing up would mean that crossing would result in the bridge blowing up. So Rob would conclude that he should not cross.
This should be more clear and not imply that rob needs to be able to prove his own consistency. I hope that helps.
Okay, now it is clear that you were not presupposing the consistency of the logical system, but its soundness (if Rob proves something, then it is true of the world).
I still get the feeling that embracing hypothetical absurdity is how a logical system of this kind will work by default, but I might be missing something, I will look into Adam’s papers.
Thanks, the second bit you quoted, I rewrote. I agree that sketching the proof that way was not good.
This should be more clear and not imply that rob needs to be able to prove his own consistency. I hope that helps.
Okay, now it is clear that you were not presupposing the consistency of the logical system, but its soundness (if Rob proves something, then it is true of the world).
I still get the feeling that embracing hypothetical absurdity is how a logical system of this kind will work by default, but I might be missing something, I will look into Adam’s papers.