Eliezer, I think I’m starting to see what you’re getting at a little more with your second definition (“an ideal Bayesian seeing a probabilistic opportunity to destroy a belief (downgrade its probability) by following a path of investigation”). But I’m still not entirely sure whether I would agree with the two points in your post that I originally took issue with.
If I come up with a reason to doubt the probability I previously assigned to some outcome, then, because (as an ideal Bayesian) I shouldn’t expect to change the probability assigned to something as a result of new evidence, I should presumably revise my probability estimate down immediately—before seeing any evidence at all. But once that’s done, whether or not the doubt warrants further investigation, or still needs in some sense to be resolved still seems an open issue. To be honest, I’m not even entirely sure what “resolution” would mean in this context any more. (Unless, perhaps, you simply mean the initial downgrading of probability?)
Eliezer, I think I’m starting to see what you’re getting at a little more with your second definition (“an ideal Bayesian seeing a probabilistic opportunity to destroy a belief (downgrade its probability) by following a path of investigation”). But I’m still not entirely sure whether I would agree with the two points in your post that I originally took issue with.
If I come up with a reason to doubt the probability I previously assigned to some outcome, then, because (as an ideal Bayesian) I shouldn’t expect to change the probability assigned to something as a result of new evidence, I should presumably revise my probability estimate down immediately—before seeing any evidence at all. But once that’s done, whether or not the doubt warrants further investigation, or still needs in some sense to be resolved still seems an open issue. To be honest, I’m not even entirely sure what “resolution” would mean in this context any more. (Unless, perhaps, you simply mean the initial downgrading of probability?)