If there are two theories: there is finite number of actual observers in the universe and there is infinite number of them which includes all possible observers—then SIA strongly prefer infinite version.
However, we can use “I exist” for update only once. Now if someone asks second question—which of two theories is more likely, there is one civilization per galaxy on average and there are 100 civilizations per galaxy, there is no update from SIA. So SIA is a used ticket. However, we can still used SSA if we define exact reference class like: here is two galaxies and one is 10 times larger than another, there I am more likely to be?
I think that my line of reasoning here is close to yours, but I will read your next posts in the sequence after finish this comment.
I think that SIA proves infinite universe and after that stops working. After that we can compare different regions of the multiverse but have to take into account their size and concentration of observers in them. (assuming that we solve the way how we count infinities).
The alternative I found, D-SIA, does extend to infinite universes but isn’t strongly fond of them (it likes large worlds, but doesn’t have an infinite update towards infinite worlds).
If there are two theories: there is finite number of actual observers in the universe and there is infinite number of them which includes all possible observers—then SIA strongly prefer infinite version.
However, we can use “I exist” for update only once. Now if someone asks second question—which of two theories is more likely, there is one civilization per galaxy on average and there are 100 civilizations per galaxy, there is no update from SIA. So SIA is a used ticket. However, we can still used SSA if we define exact reference class like: here is two galaxies and one is 10 times larger than another, there I am more likely to be?
As I argued here, C-SIA (counting SIA) argues for infinite numbers of observers and then breaks in worlds with infinite numbers of observers.
That seems a reducio against C-SIA, not an argument for infinite universes!
(D-SIA, the alternative I’m arguing for, deals fine with infinite universes, but involves some more choices on our parts).
I think that my line of reasoning here is close to yours, but I will read your next posts in the sequence after finish this comment.
I think that SIA proves infinite universe and after that stops working. After that we can compare different regions of the multiverse but have to take into account their size and concentration of observers in them. (assuming that we solve the way how we count infinities).
The alternative I found, D-SIA, does extend to infinite universes but isn’t strongly fond of them (it likes large worlds, but doesn’t have an infinite update towards infinite worlds).