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nshepperd comments on 0 And 1 Are Not Probabilities - Less Wrong
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Digging up an old thread here, but an interesting point I want to bring up: a friend of mine claims that he internally assigns probability 1 (i.e. an undisprovable belief) only to one statement: that the universe is coherent. Because if not, then mnergarblewtf. Is it reasonable to say that even though no statement can actually have probability 1 if you're a true Bayesian, it's reasonable to internally establish an axiom which, if negated, would just make the universe completely stupid and not worth living in any more?
There's a lot of logic to that. For extremely unlikely possibilities you can often get away with setting their probability to 0 to make the calculations a lot simpler. For possibilities where predicted utility is independent of your actions (like "reality is just completely random") it can also be worthwhile setting their probability to 0 (ie. ignoring them), since they're approximately a constant term in expected utility. These are good ways of approximating actual expected utility so you can still mostly make the right decisions, which bounded rationality requires.