1. : elaborating on why I think Tarsney implicitly assumes SSA:
You are right, that Tarsney does not take any anthropic evidence into account. Therefore it might be more accurate to say, that he forgot about anthropics/does not think it is important. However it just so happens, that assuming the Self-Sampeling Assumption would not change his credence in solipsism at all. If you are a random person from all actual persons, you can not take your existence as evidence how many people exist. So by not taking anthropic reasoning into account, he gets the same result as if he assumed the Self-Sampeling Assumption.
2. Does’t the Self-Indicaion Assumption say, that the universe is almost surely infinite?
Yes, that is the great weakness of the SIA. You are also completely correct, that we need some kind of more sophisticated mathematics if we want to take into account the possibility of infinite people. But also if we just consider the possibility if very many people existing, the SIA yields weird results. See for example Nick Bostroms thought experiment of the presumptuous philosopher (copy-pasted the text from here):
It is the year 2100 and physicists have narrowed down the search for a theory of everything to only two remaining plausible candidate theories, T1 and T2 (using considerations from super-duper symmetry). According to T1 the world is very, very big but finite, and there are a total of a trillion trillion observers in the cosmos. According to T2, the world is very, very, very big but finite, and there are a trillion trillion trillion observers. The super-duper symmetry considerations seem to be roughly indifferent between these two theories. The physicists are planning on carrying out a simple experiment that will falsify one of the theories. Enter the presumptuous philosopher: “Hey guys, it is completely unnecessary for you to do the experiment, because I can already show to you that T2 is about a trillion times more likely to be true than T1 (whereupon the philosopher runs the God’s Coin Toss thought experiment and explains Model 3)!”
Your evidenceless prior on the number of individuals must be asymptotically 0 (except for a positive probability for infinity), as the number increases, or else the probabilities won’t sum to one. Maybe this solves some of the issue?
Of course, we have strong evidence that the number is in fact pretty big as Tarsney points out, based on estimates of how many conscious animals have existed so far. And your prior is underdetermined.
1. : elaborating on why I think Tarsney implicitly assumes SSA:
You are right, that Tarsney does not take any anthropic evidence into account. Therefore it might be more accurate to say, that he forgot about anthropics/does not think it is important. However it just so happens, that assuming the Self-Sampeling Assumption would not change his credence in solipsism at all. If you are a random person from all actual persons, you can not take your existence as evidence how many people exist. So by not taking anthropic reasoning into account, he gets the same result as if he assumed the Self-Sampeling Assumption.
2. Does’t the Self-Indicaion Assumption say, that the universe is almost surely infinite?
Yes, that is the great weakness of the SIA. You are also completely correct, that we need some kind of more sophisticated mathematics if we want to take into account the possibility of infinite people. But also if we just consider the possibility if very many people existing, the SIA yields weird results. See for example Nick Bostroms thought experiment of the presumptuous philosopher (copy-pasted the text from here):
It is the year 2100 and physicists have narrowed down the search for a theory of everything to only two remaining plausible candidate theories, T1 and T2 (using considerations from super-duper symmetry). According to T1 the world is very, very big but finite, and there are a total of a trillion trillion observers in the cosmos. According to T2, the world is very, very, very big but finite, and there are a trillion trillion trillion observers. The super-duper symmetry considerations seem to be roughly indifferent between these two theories. The physicists are planning on carrying out a simple experiment that will falsify one of the theories. Enter the presumptuous philosopher: “Hey guys, it is completely unnecessary for you to do the experiment, because I can already show to you that T2 is about a trillion times more likely to be true than T1 (whereupon the philosopher runs the God’s Coin Toss thought experiment and explains Model 3)!”
Your evidenceless prior on the number of individuals must be asymptotically 0 (except for a positive probability for infinity), as the number increases, or else the probabilities won’t sum to one. Maybe this solves some of the issue?
Of course, we have strong evidence that the number is in fact pretty big as Tarsney points out, based on estimates of how many conscious animals have existed so far. And your prior is underdetermined.