TimS comments on Welcome to Less Wrong! (2012) - Less Wrong
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If there is no empirical evidence either way about a belief, how would one go about destroying it? Beliefs pay rent in anticipated experience, not anticipated actions.
In short, the religious person has adopted a terminal value of being a nicer person, but is confused an thinks this is an instrumental value in pursuit of the "real" terminal value of implementing the desires of a supernatural being. Epistemic rationality has no more to say about this terminal value than about any other terminal value.
One way you could go about destroying a belief like that is to use Ockham's Razor: sure, it's possible that all kinds of unfalsifiable beliefs are true, but why should you waste time in believing any of them, if they have no effect on anything ?
However, if the believer has some subjective evidence for the belief -- f.ex., if he personally experienced the gods talking to him -- then this attack cannot work. In this case, would you still say that his belief is "indestructible" ?