it would imply that you should ignore mathematical proofs if the person who came up with the proof only searched for positive proofs and wouldn’t have spend time trying to prove the opposite. (This ties in with the very first section—failing to find a proof is like remaining silent.)
I think this strategy becomes coherent if you update on the claim “fact X is true, here’s its proof” being made? After all, there’s lower probability that person publishes such claim if they fail to find the proof.
(Generalization: it doesn’t matter much on what arguments you update, it matters more what you end up believing.)
The strategy “ignore the arguments” still goes wrong if they’ve published an incorrect mathematical proof, with a flaw you could have spotted. So it’s still clearly wrong in general, even with this adjustment.
I think this strategy becomes coherent if you update on the claim “fact X is true, here’s its proof” being made? After all, there’s lower probability that person publishes such claim if they fail to find the proof.
(Generalization: it doesn’t matter much on what arguments you update, it matters more what you end up believing.)
The strategy “ignore the arguments” still goes wrong if they’ve published an incorrect mathematical proof, with a flaw you could have spotted. So it’s still clearly wrong in general, even with this adjustment.