Ah, the old irresistible force acting upon immovable object argument.
This seems (dis)solvable by representing changing beliefs as shifting probability mass around. You might argue that after you’ve worked your way through the proof of T step by step, you’ve moved the bulk of probability mass to T (with respect to priors that don’t favor either T or ~T too much). But if it were enough, we would expect to see all of the following: 1) people are always certain of their conclusions after they’ve done the math once; 2) people don’t find errors in proofs that have been published for a long time; 3) there’s no perceived value in checking each other’s proofs; 4) If there is a certain threshold of complexity or length after which people would stop becoming certain of their conclusions, nobody has reached it yet.
None of this is true in our word, which supports the hypothesis that a non-trivial amount of probability mass gets stuck along the way, subjectively this manifests in you acknowledging the (small, but non-negligible) possibility of having erred in each part of the proof.
Now, the proper response to TM would be to shift your probability according to the weight of Ms. Math’s authority, which is not absolute. If you’re uncomfortably uncertain afterwards, you just re-examine your evidence paying more attention the hardest parts, and squeeze some more probability juice either way until you either are certain enough or until you spot an error.
Ah, the old irresistible force acting upon immovable object argument.
This seems (dis)solvable by representing changing beliefs as shifting probability mass around. You might argue that after you’ve worked your way through the proof of T step by step, you’ve moved the bulk of probability mass to T (with respect to priors that don’t favor either T or ~T too much). But if it were enough, we would expect to see all of the following: 1) people are always certain of their conclusions after they’ve done the math once; 2) people don’t find errors in proofs that have been published for a long time; 3) there’s no perceived value in checking each other’s proofs; 4) If there is a certain threshold of complexity or length after which people would stop becoming certain of their conclusions, nobody has reached it yet.
None of this is true in our word, which supports the hypothesis that a non-trivial amount of probability mass gets stuck along the way, subjectively this manifests in you acknowledging the (small, but non-negligible) possibility of having erred in each part of the proof.
Now, the proper response to TM would be to shift your probability according to the weight of Ms. Math’s authority, which is not absolute. If you’re uncomfortably uncertain afterwards, you just re-examine your evidence paying more attention the hardest parts, and squeeze some more probability juice either way until you either are certain enough or until you spot an error.