So, really, you end up with an undefined positive number if the number of beliefs becomes infinite. This number could either be very very big or very very small.
At that point, you would have to rely on arguing that Atheism provides more utility while you are alive than the Heaven and Hell beliefs do, which would again be a difficult argument to make.
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Welcome to the forum.
Infinity can't be a small number, but any number divided into infinity becomes numerically indistinguishable from zero.
So if we have say, five religions and we apply pascals wager we stand a 20% chance of being correct, if none are correct then Atheism is the correct choice.
Your options with Atheism are 50% correct and 20% wrong. It's either correct or it isn't. Your odds with being an Atheist are much greater.
If we have infinite choices of religions, and we choose one of them we stand mathematically close to zero percent chance of choosing correctly, whereas with Atheism the odds are still exactly the same.
For what it's worth, if we break this down into comprehensible numbers, there are apparently about 4,200 religions and spiritual systems. Some are a bit wonky in my opinion, but hey Catholics, amirite?
So lets use 4,200 for your check on Pascals wager.
This gives you a .023% chance of choosing the correct religion for an afterlife plan.
Again, Atheism remains at 50% correct, or .023% that it's wrong.
You will recognize this as BAD MATH
, hopefully. Since the odds on Atheist being correct actually go up as the odds on it being wrong go down.
It's more like the odds are (for five religions) 80% vs 20% and (for 4,200 religions) 99.977% correct vs .023%
If we use
vs Pascals wager, we get the only choice worth making is Atheism. The odds on choosing the one true religion out of infinity choices is numerically indistinguishable from zero.
*edit: ascii code for infinity didn't work. Replaced with image.