I do not understand the validity of this statement:
There is no possible plan you can devise, no clever strategy, no cunning device, by which you can legitimately expect your confidence in a fixed proposition to be higher (on average) than before.
Given a temporal proposition A among a set of other mututally exclusive temporal propositions {A, B, C...}, demonstrating B, C, and other candidates do not meet the evidence so far while A meets the evidence so far does raise our confidence in the proposition *continuing to hold*. This is standard Bayesian inference applied to temporal statements.
For example, we have higher confidence in the statement “the sun will come up tomorrow” than the statement “the sun will not come up tomorrow”, because the sun has come up in the past, whereas it has not not come up comparably fewer times. We have relied on the prior distribution to make confident statements about the result of an impending experiment, and can constrain our confidence using the number of prior experiments that conform to it—further, every new experiment that confirms “the sun will come up” makes it harder to argue that “the sun will not come up” because the latter statement now has to explain *why* it failed to apply in the prior cases as well as why it will work now.
It would seem quantifying the prior distribution against a set of mutually-exclusive statements thus *is* a valid strategy for raising confidence in a specific statement.
Maybe I’m misinterpreting what “fixed proposition” means here or am missing something more fundamental?
I do not understand the validity of this statement:
Given a temporal proposition A among a set of other mututally exclusive temporal propositions {A, B, C...}, demonstrating B, C, and other candidates do not meet the evidence so far while A meets the evidence so far does raise our confidence in the proposition *continuing to hold*. This is standard Bayesian inference applied to temporal statements.
For example, we have higher confidence in the statement “the sun will come up tomorrow” than the statement “the sun will not come up tomorrow”, because the sun has come up in the past, whereas it has not not come up comparably fewer times. We have relied on the prior distribution to make confident statements about the result of an impending experiment, and can constrain our confidence using the number of prior experiments that conform to it—further, every new experiment that confirms “the sun will come up” makes it harder to argue that “the sun will not come up” because the latter statement now has to explain *why* it failed to apply in the prior cases as well as why it will work now.
It would seem quantifying the prior distribution against a set of mutually-exclusive statements thus *is* a valid strategy for raising confidence in a specific statement.
Maybe I’m misinterpreting what “fixed proposition” means here or am missing something more fundamental?