If SIA is valid, than multiverse is true and all possible minds exist.
However, if all possible minds exist, we can't use SIA anymore as the fact of my existence is not the evidence for anything.
As a result, SIA is self-defeating: it can be used only to prove multiverse but we can also prove it without SIA.
We can use untypicality argument similar to SIA: the fact that I exist at all is the evidence that there were many attempts to create me. Examples: the habitability of Earth means that there are many non-habitable planets and fine-tuning of the Universe means that there are many other universes with other physical laws.
Note that untypicality argument is not assumption - it is a theorem. It also doesn't prove infinity of my copies but only very large number of attempts to create, which is practically similar to infinity and can be stretch to "all possible minds exist" if we add that any sufficiently large mind-generating mechanism can't be stopped: non-habitable planets will continue to appear as they don't "know" that one is now habitable.
I am stuck on the following problem:
If the 10100th digit of pi is even then 10
10 blue eyed people and one brown eyed person gets created. Otherwise one blue eyed person and one brown eyed person gets created.
What is my subjective probability of the 10100th digit of pi being even?
If you don't like me talking about probabilities in a deterministic context then pretend that I am asked to bet on whether the 10 100th digit of pi is even and I don't have access to a galaxy-sized supercomputer. I want to know what odds to bet at.
Let us first go over an easier problem:
A particle is initialised spin up in the z direction. Then its spin is measured in the x direction. If the spin is measured to be up then 1010 blue eyed people and one brown eyed person gets created. Otherwise one blue eyed person and one brown eyed person gets created.
If I observe myself to be brown eyed then what is the probability that the particle was measured to be spin up in the x direction?
Here the answer is 50%. To see this, first assume that the Everett Interpretation of quantum mechanics is correct because none of the other interpretations make sense. Then 50% of all the brown eyed people in all the universes in which the measurement took place were in universes in which the particle was measured to be spin up.
Aside: I have cheated a bit here. If there are infinitely many universes then there might be a bit of work to do to make this argument rigorous, which I shall leave as an exercise for the reader.
Anyhow, the reason I am asking this question is because if the deterministic version of the Self Indication Assumption were to turn out to be true then that would be a very strong reason to believe both in the entire Tegmark multiverse hierarchy and in panpsychism. Now there's nothing remotely weird about believing in multiverses.
On the other hand, consider the proposition P: 'atoms are just as conscious as brains'. If P is true then I should be very surprised indeed if I were to observe myself to be a brain rather than an atom.
Since I know so little about the phenomenology of consciousness, I don't have any strong evidence against proposition P except for the fact that I don't observe myself to be an atom. If the deterministic version of the Self Indication Assumption is true then the fact that I don't observe myself to be an atom does not count as evidence against P. So I am forced to assign a fairly high probability to statement P, meanwhile wondering how breathtakingly improbable it is that I am not observing myself to be an atom right now.