At Manifest, you proposed that we can get enough people by adopting the Tegmark view that every mathematical structure is instantiated. I was interpreting you as disagreeing with my claim that anthropic reasoning tells us that there are infinite people—too many to be a set—which what we discussed at Manifest wouldn’t address.

My worry about the Tegmark view—aside from the fact that it doesn’t really explain most of the other facts favoring theism—is that I think it undermines induction. If every mathematical structure is instantiated then there however many worlds there are where induction works, there are that many worlds where five seconds from now induction completely breaks. You proposed that the simpler worlds could be more common, but I think this doesn’t really work—if two infinites are the same cardinality, unless one is a subset of the other, I don’t think there are ways to compare them.

One way to see this is that any two infinite sets of the same cardinality (the same points will apply to collections to big to be sets) can be paired 1 to 1. But this means that if you assign everyone a status as in an inductive world or not in an inductive world, it would be possible to make every single world have mostly people from non-inductive worlds just by moving them around. This makes it hard to see coherently how one maintains that probably induction will work in their world.

(I’m also not sure if the Tegmark view gets enough people—maybe it only gets a number equal to the number of functions or something, which I think is only Beth 3, but I could be wrong).