I think when you get to any class of hypotheses like “capable of creating unlimited numbers of people” with nonzero probability, you run into multiple paradoxes of infinity.
For example, there is no uniform distribution over any countable set, which includes the set of all halting programs. Every non-uniform distribution this hypothetical superbeing may have used over such programs is a different prior hypothesis. The set of these has no suitable uniform distribution either, since they can be partitioned into countably many equivalence classes under natural transformations.
It doesn’t take much study of this before you’re digging into pathologies of measure theory such as Vitali sets and similar.
You can of course arbitrarily pick any of these weightings to be your “chosen” prior, but that’s just equivalent to choosing a prior over population directly so it doesn’t help at all.
Probability theory can’t adequately deal with such hypothesis families, and so if you’re considering Bayesian reasoning you must discard them from your prior distribution. Perhaps there is some extension or replacement for probability that can handle them, but we don’t have one.
I think when you get to any class of hypotheses like “capable of creating unlimited numbers of people” with nonzero probability, you run into multiple paradoxes of infinity.
For example, there is no uniform distribution over any countable set, which includes the set of all halting programs. Every non-uniform distribution this hypothetical superbeing may have used over such programs is a different prior hypothesis. The set of these has no suitable uniform distribution either, since they can be partitioned into countably many equivalence classes under natural transformations.
It doesn’t take much study of this before you’re digging into pathologies of measure theory such as Vitali sets and similar.
You can of course arbitrarily pick any of these weightings to be your “chosen” prior, but that’s just equivalent to choosing a prior over population directly so it doesn’t help at all.
Probability theory can’t adequately deal with such hypothesis families, and so if you’re considering Bayesian reasoning you must discard them from your prior distribution. Perhaps there is some extension or replacement for probability that can handle them, but we don’t have one.