I'd say it's because the process of updating probabilities in light of new evidence involves multiplication, which yields you nothing new for 0 and 1. It's not resetting values of variables.
> Does Cromwell's Rule mean that I have to believe that Hillary Clinton is the PotUS at least a little, because otherwise I will never be able to believe it if she ever gets elected president?
Yes. And the justification for that is that there's tiny but non-zero possibility that she may really be the president, and it's your senses that deceive you. Perhaps you're the protagonist of your own's Truman Show. Or perhaps it's some peculiarity in your brain that prevents you from accepting who the real president is. Integrating other evidence around you, you can assign ridiculously low probabilities to these scenarios, but you can't assume zero probability. After all, there exist people with such problems, and they tend to end up in treatment when someone realizes what's going on with them.
And the nice thing about it, that not using 0 and 1 makes the whole thing add up to reality in an elegant fashion. Adding 0 and 1 breaks that.
>> And the nice thing about it, that not using 0 and 1 makes the whole thing add up to reality in an elegant fashion. Adding 0 and 1 breaks that.
I really don't see the "elegance" in having to accept that I may be in a strange mental state were reality is unkonwable, in order to describe reality.
I mean, at the end of the day, if you follow down that path you find yourself having to argue that Hillary Clinton might, actually, be the PotUS, and I may be brain damaged or something, you never know. That's just absurd and there's no practical point in it. It's just a waste of time.
> Does Cromwell's Rule mean that I have to believe that Hillary Clinton is the PotUS at least a little, because otherwise I will never be able to believe it if she ever gets elected president?
Yes. And the justification for that is that there's tiny but non-zero possibility that she may really be the president, and it's your senses that deceive you. Perhaps you're the protagonist of your own's Truman Show. Or perhaps it's some peculiarity in your brain that prevents you from accepting who the real president is. Integrating other evidence around you, you can assign ridiculously low probabilities to these scenarios, but you can't assume zero probability. After all, there exist people with such problems, and they tend to end up in treatment when someone realizes what's going on with them.
And the nice thing about it, that not using 0 and 1 makes the whole thing add up to reality in an elegant fashion. Adding 0 and 1 breaks that.