As the offer gets bigger, it is more likely to be a lie, mistake, or misunderstanding.
Offer A: “If you drive me to San Francisco, I’ll pay you twenty dollars.”
Offer B: “If you drive me to San Francisco, I’ll pay you a billion dollars.”
Offer C: “If you drive me to San Francisco, I’ll pay you with this gemstone.” (Which looks like a very valuable diamond to you.)
Offer D: “If you drive me to San Francisco, I’ll pay you 3↑↑↑3 dollars.”
Offer A is credible — but you’re being underpaid; at least make them pay the tolls too.
Offer B is conceivable, but not readily believable. The chance that someone is going to pay you a billion dollars to drive them to SF is very, very low. Perhaps they’re just lying to you. Or maybe you misheard them over the noise of traffic. Maybe they actually said “If you [build a robot car that can] drive me to San Francisco, I’ll pay you a billion dollars [to acquire your company]” and you didn’t hear the bracketed parts.
Offer C is likewise conceivable, and you probably even heard them right. But you’re probably mistaken about reality — the gemstone is probably moissanite or cubic zirconia or something other than diamond.
Offer D is not conceivably possible. Either they are just making stuff up, or someone is confused about what ↑ means, or you’ve been tricked and they really said “three, um um um, three doll hairs”.
But what about Pascal’s Muggle? If you want to cancel out 3↑↑↑3 by multiplying it with a comparably small probability, the probability has to be incredibly, incredibly, small; smaller than a Bayesian can update after 13 billion years of viewing evidence. So where did that small number come from? If the super-exponenctial smallness came from priors, then you can’t update away from it reasonably—you’re always going to believe the proposition is false, even if given an astronomical amount of evidence. Are you biting the bullet and saying that even if you find yourself in a universe where this sort of thing seems normal and like it will happen all the time, you will say a priori this this apparently normal stuff is impossible?
There are claims for which believing the claim would require more confidence than I have in my own thought processes. That is, if I think I have evidence for X, I should first doubt whether my thinking has run astray and ceased to be connected to reality, rather than going ahead and believing X.
After all, it’s not just the claim that can be true or false. My reasoning can run truly or falsely too. There are circumstances under which self-doubt is the correct mental motion: “The fact that I am about to believe this claim is itself evidence. What has been true about others who have come to believe claims like this one?”
Example: Occasionally, a human will come to believe that God is telling them to go murder a bunch of people. As far as anyone can tell, they have all been wrong. And the world would be better off if each of them had thought, “Huh, everyone else who’s ever come to this conclusion turned out to be wrong. I wonder if maybe I’m having a schizophrenia or something?”
As the offer gets bigger, it is more likely to be a lie, mistake, or misunderstanding.
Offer A: “If you drive me to San Francisco, I’ll pay you twenty dollars.”
Offer B: “If you drive me to San Francisco, I’ll pay you a billion dollars.”
Offer C: “If you drive me to San Francisco, I’ll pay you with this gemstone.” (Which looks like a very valuable diamond to you.)
Offer D: “If you drive me to San Francisco, I’ll pay you 3↑↑↑3 dollars.”
Offer A is credible — but you’re being underpaid; at least make them pay the tolls too.
Offer B is conceivable, but not readily believable. The chance that someone is going to pay you a billion dollars to drive them to SF is very, very low. Perhaps they’re just lying to you. Or maybe you misheard them over the noise of traffic. Maybe they actually said “If you [build a robot car that can] drive me to San Francisco, I’ll pay you a billion dollars [to acquire your company]” and you didn’t hear the bracketed parts.
Offer C is likewise conceivable, and you probably even heard them right. But you’re probably mistaken about reality — the gemstone is probably moissanite or cubic zirconia or something other than diamond.
Offer D is not conceivably possible. Either they are just making stuff up, or someone is confused about what ↑ means, or you’ve been tricked and they really said “three, um um um, three doll hairs”.
But what about Pascal’s Muggle? If you want to cancel out 3↑↑↑3 by multiplying it with a comparably small probability, the probability has to be incredibly, incredibly, small; smaller than a Bayesian can update after 13 billion years of viewing evidence. So where did that small number come from? If the super-exponenctial smallness came from priors, then you can’t update away from it reasonably—you’re always going to believe the proposition is false, even if given an astronomical amount of evidence. Are you biting the bullet and saying that even if you find yourself in a universe where this sort of thing seems normal and like it will happen all the time, you will say a priori this this apparently normal stuff is impossible?
There are claims for which believing the claim would require more confidence than I have in my own thought processes. That is, if I think I have evidence for X, I should first doubt whether my thinking has run astray and ceased to be connected to reality, rather than going ahead and believing X.
After all, it’s not just the claim that can be true or false. My reasoning can run truly or falsely too. There are circumstances under which self-doubt is the correct mental motion: “The fact that I am about to believe this claim is itself evidence. What has been true about others who have come to believe claims like this one?”
Example: Occasionally, a human will come to believe that God is telling them to go murder a bunch of people. As far as anyone can tell, they have all been wrong. And the world would be better off if each of them had thought, “Huh, everyone else who’s ever come to this conclusion turned out to be wrong. I wonder if maybe I’m having a schizophrenia or something?”