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thomblake comments on How confident is your atheism? - Less Wrong
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Christianity isn't a single proposition though. There is a lot of content there. A lot of unverified content.
The probability that you should believe Christianity because of some fear of hell (act on your worry) is something less than the probability that there is a God times the probability that God had a son given that there is a God times the probability that Jesus was the one and only son of God given that God had a son times the probability that there are souls given all of the above times the probability that God sends these souls somewhere GAOTA times the probability that God sends people who don't believe in him to Hell GAOTA.
Some of those things are pretty likely given the prior statement, but several of them are non-obvious.
And if you are going to act on a belief in a general diety... well, what policy do you take? He may only punish believers. He may only punish people who wear shoes. He may only grant souls to pillows and only send red pillows to heaven, blue pillows to hell, and all others (including mixes) to purgatory. Diety-space is HUGE and complex propositions without strong evidence are almost always wrong.
I am not even sure "Lots of humans believe it" counts as evidence. Is it more likely that something is true, given that lots of people believe it? I think the inverse is true: if something is true it is more likely that lots of people will believe it. But P(B|A)!=P(A|B)
I know you were speaking loosely, but you can't just multiply probabilities when they're not made independent.
That's false.
Let's say that we have 3 sets of propositions, A, B, and C. A is 40% likely. B is 90% likely if A is the case and 1% likely if A is not the case. C is 10% likely if B is not the case, 50% likely if A and B are both true, and 5% likely if B is true but A isn't.
B and C are clearly dependent variables. Nevertheless, simple math tells us that C is 8.17% likely, all other things being equal. Since Christianity is only true if all of the relevent propositions are true (as opposed to the scenario above) you can just multiply the probabilities together. (Unlike our A, B, C scenario, which also required some amount of addition.) You just multiply the probability within the conditional: that if God has a son that his one and only son is Jesus, rather than simply the probability that Jesus existed or that Jesus was the son of God. If Christianity could be true without Jesus being the one son of God, then addition would be required along with the multiplication, but this is not the case as the belief "Christianity" implies a zero-probability for these scenarios.
I somehow didn't notice the "given all of the above" shorthand.