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I find it ironic that this is the logic used by a group that pretty much universally rejects Pascal's Wager. Also, it wouldn't be the first time humanity has made this particular calculation- when the first atomic bomb was tested at Trinity, Oppenheimer was "pretty sure" it wouldn't cause a neutron chain reaction and ignite the atmosphere in a nuclear hellstorm, but he couldn't guarantee it. Infinite stakes do not necessarily require infinite caution.
Even if you take Pascal's wager seriously, it is not actually very useful. There are multiple religions that each claim their god created the world, with most of them being mutually exclusive. Thus Pascal's wager works about as well as an argument for believing in the Christian God as it does for believing in Allah.
Regarding the atomic bomb, they did the math which showed that a chain reaction was impossible prior to the test. We have no such proof against the dangers of AI. The equivalent would be a paper that shows the theoretical limits of how intelligent LLM's can get, and thus prove that the line will stop going up before we reach the point of AGI.
Pascal's wager is nearly the earliest example of decision theory, and it hardly makes sense to say that the many religions concern simply breaks decision theory. One can do a variety of things to analyze the probability space as well as the payoff space. For an example simplification, suppose there are two possible mutually exclusive levers you could pull, each with some chance of giving you massively large/infinite utility, and P(A pays out)=0.999 while P(B pays out)=0.001. (This is obviously an extreme case, but that's just to build intuition.) Alternatively, one can adjust probabilities such that maybe there's a third mutually exclusive lever that you can pull which has a guaranteed payoff of 1 or whatever. One can make further refinements.
The issue with mutually exclusive religions is that if you pull P(A) and it doesn't pay out, actually it was another faith all along, then you face infinite suffering for being an infidel who foolishly worshipped Jesus as God. You are incentivized to believe in whatever religion has the greatest punishment for nonbelievers to minimize your downside. But then that incentivizes others to make up religions with increasingly worse punishments in the afterlife in order to force you to adhere to the demands of their faith.
It is just not sustainable as there is no way to distinguish between a religion that is made up by humans and one that is actually correct. Playing that game is hopeless from the start.
Interestingly, the base Pascal wager makes sense without any infinite suffering at all. Regardless, there are a variety of ways of handling it, especially if your concern is that Roko (a person) is just making up a basilisk.
This seems to be your real objection, not the multiple religion concern. You think it's just impossible to actually assess anything involved, including probabilities. Presumably, that means it's also impossible for you to assess the probability that atheism is true.
Well yes. But we can prove that many things are true which fly in the face of established religions. For example evolution goes against the Christian creation myth. The sun doesn't actually go to the underworld every night like the ancient Egyptians thought, the earth simply rotates away from it. As far as I can tell, you can repeat this for most religions.
So while I can't prove that atheism is true, I can find arguments that make established religions less likely to be true. If your religion makes claims that turn out to be demonstrably false, then that is fairly solid evidence against it. Even if that was not the case, Pascal's wager still doesn't work. It is not safer for me to subscribe to a religion than it is to be a nonbeliever, as not only are many religions mutually exclusive, several are much harsher to those religions they are directly opposed to than they are to people who simply don't believe.
See, you say
But then you try to argue for no. Both on the probabilistic argument and beyond. You seemed to have embraced the idea that there's no way for you to assess probabilities, but then you say
Even going beyond probabilities, you had said
But now you seem to think there are ways to conclusively show that a religion is false.
Perhaps you'd like to take a chance to try to reconcile some apparent contradictions? I'd be interested in getting to the decision theory question possibly posed by your final sentence, but the contradictions above may make it impossible for us to construct a well-posed decision theory problem.
I suppose I can rephrase it into the kind of problem you are hinting at.
First, let us establish that Pascal's wager attempts to religion literally. The point is that by not being a Christian you risk eternal damnation because biblical Hell might literally be real, while being a believer gets you into Heaven (even though neither appear in the bible). Since we are taking religious texts to be literally true, we can evaluate their credibility by how well they model the world. Any statement or prediction that turns out to be provably wrong is pretty damning for the religion in question and dramatically reduces the risk of it being real and something to worry about. For example, the Abrahamic religions all share a creation myth that is more or less debunked by evolution, a theory which itself has made many correct predictions about the world and has no good evidence against it.
Theoretically, for every religion with a defined doctrine, we can look at the following factors:
If statements or predictions turn out to be wrong, that is an indicator that the religion is not to be taken literally. If religious practices that are supposed to bring you benefit while you are alive actually don't do that, or even cause harm, then that is likewise a point against the religion.
Similarly, if statements and prophecies that were made before we had made the scientific advancements to verify them turn out to be correct, then that makes it more likely the religion is to be taken literally. You would need a way to rank the significance of each statement made to figure out how important it is for the religion, how hard it is to get correct, and to what extent belief in the religion caused the insight in order to find out how likely it is to make the religion real. For religious practices, I would divide them into three tiers from most to least significant:
Generally, I would weight concrete statements higher than vague ones, and wrong statements should matter more than correct ones, as they show that at least part of the religion is wrong and not divine in nature. Meanwhile divine intervention is merely one of several causes for correct statements. The more falsifiable statements turn out to be correct, the greater the likelihood of predictions about the afterlife being real. The more vague and open to interpretation the text is, the less we can say about the afterlife.
This way, we can rank every religion from most believable to least. The most likely religion to be true is the one which has several concrete prophecies with defined timelines that turn out to be correct, alongside myths that accurately describe the world, and whose religious practices demonstrably bring their claimed benefits to believers. But to properly answer Pascals wager we need two more measures.
First is the consequence for being a non-believer. The worse non-believers are treated compared to believers, the more crucial it is that I am part of the religion in case it is real. This is the original premise after all. Second is whether the religion allows me to be part of multiple faiths. If the goal is to optimize my chances in case the afterlife is real, then I ideally want to be a devout member of as many faiths at possible, starting with those that are most likely to be true.
Does this make for a concrete problem? I tried to make my framework as clear as possible, but to actually do this you would have to go through and compare every religion on earth.
I don't actually care all that much about the actual process you use for evaluation of things like probabilities/payoffs (honestly, I don't even care that much about Pascal's wager). The point is that, in principle, one could conceivably do such. Obviously, any particular process is subject to a variety of scrutinies.
There's always going to be some limitation. When I'm coming to my personal beliefs about my own academic field, for example, I certainly don't read every single paper that is published, even though some might be amazing. That doesn't mean I can't ever come to beliefs.
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