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cinc's avatar

I think this argument gets some crucial stuff about probability and infinities wrong.

"if fewer than Beth 2 people exist, then 0% of possible people exist, which would make the odds of my existence in particular zero"

Having a measure of zero doesn't imply non-existence, impossibility, or anything meaningful at all about the probability of your existence. A measure of zero simply means the size of the set of actually existing people is negligible in comparison to the set of all possible people. Your argument is kind of like saying the probability of selecting .2523 from [0, 1] is 0 because "0% of numbers exist" - it's 0 because its measure is 0. Or you could consider the subset of rational numbers within the set of all reals - same issue. I'm actually not sure if you're suggesting you randomly select a person from the set of all possible people and integrate over the subset of actually existing people, or if you're suggesting you integrate over the entire range. But either way, it doesn't make much sense. To get meaningful probabilities, you have to look at ranges. Given this sample space, you have to use PDF, not simple division. And, if you want to integrate over the entire space, we need to use a nonuniform distribution, otherwise you violate normalization. This means not every person has the same probability of existing.

Since the sample space you're using is uncountably infinite, you're suggesting humans are not discrete objects. I'm not really sure how that works. But even if humans weren't discrete, I still have no idea what it would mean to say a powerset of an infinity of people exist. Power sets of infinities are abstractions - it's not sensible to say that Beth 2 people actually exist.

If God can somehow make cardinal infinities of persons, then why would this ever stop? If even making countably infinite persons isn't a limit on him, and he can make powersets of infinities of people, then he can take the power set ad infinitum. This seems to lead to a contradiction - he's going to make the maximum number of people, but there is no maximum number of people.

This raises the question as to where all these people are. The number of people has clearly varied over time - it hasn't been constant at some maximum. The universe is mostly devoid of life. So, where are all these Beth 2 people? Is God keeping some infinite vat of souls? If so, then you run into exactly the same problem as before. If God selects some soul from the vat to exist at any given time, you again have measure zero.

I think you rightly point out God would maximize life. But then anthropic reasoning points in exactly the opposite direction you're claiming - the universe is hostile to life. We certainly don't observe Beth 2 people. Your claims go against empirical observation. And, as I mentioned before, the very existence of humans suggests God isn't real: https://link.springer.com/article/10.1007/s11841-009-0137-0

Regardless, and I think most crucially, these probabilities simply aren't meaningful. Your existence is determined by initial conditions in conjunction with nomological laws, not someone selecting a random person out of a set of Beth 2 possible people. Your existence is not a random event, so all of this probabilistic reasoning is irrelevant.

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Marlon's avatar

Sure, I'll give anthropics a try. What's the worst that could happen? :v

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