(I’m not very familiar with anthropic reasoning, or SSA and SIA specifically.)
In his estimations, Tarsney does not take any anthropic evidence into account, when calculating his credence in solipsism. By doing this, he implicitly assumes the Self-Sampling Assumption.
Could you elaborate on this? Solipsism doesn’t just mean that there’s only one mind that exists, but also that it’s my mind. Here’s Tarsney’s discussion of his estimates:
It seems clear that my credence that my commonsense view of the world has “got things basically right”, metaphysically speaking, should not be greater than 0.9. That is, given how little we have to go on, the lack of expert consensus in basic metaphysics, and trying to correct for the general human tendency toward overconfidence, I should have at least 0.1 credence that the world is in some way fundamentally very different than I take it to be. A good chunk of that credence should go to “some possibility that nobody has ever thought of”. But it also seems overconfident, conditional on my ordinary view of the world being wrong, to have credence greater than 0.9 in that possibility. This leaves at least 1% of my credence to distribute over known revisionary metaphysical hypotheses. And then to get some sense of a lower bound on my credence in solipsism, I should ask first, “Are there any other known revisionary hypotheses that are many orders of magnitude more probable than solipsism?” (to which, it seems to me, the answer is “no”) and second, “Are there thousands or millions of known revisionary hypotheses that are at least roughly as plausible as solipsism?” (to which the answer again seems to be “no”). Taken together, these observations suggest that my credence in solipsism should be at most a few orders of magnitude less than 0.01.
All in all, then, while it would strike me as somewhat unreasonable to assign solipsism a probability greater than 10−2 , it also seems unreasonable to assign it a probability less than 10−9 . To assign any more extreme probability would not display due modesty about our understanding of matters metaphysical.
Also, what about the possibility of infinitely many individuals, which actually seems pretty likely (if you count spatially (or temporally) separated identical individuals separately, or allow the possibility that there could be infinitely many non-identical individuals, maybe increasing without bound in “brain” size)? If you had one of two possibilities, either 1) just you, or 2) infinitely many individuals, your approach would imply that rational credence in solipsism is 0, but solipsism is not a logical certainty conditional on these two hypotheses, so this seems wrong. More generally, it just seems wrong to me that credence in solipsism should approach 0 as the number of (possible?) individuals increases without bound. There should be some lower bound that does not depend on the number of possible individuals (and it could be related to the infinite case, through conditional probabilities). I think this is basically what Tarsney is getting at.
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.
EDIT: I guess you’d need to make more distributional assumptions, since there’s no uniform distribution over infinitely many distinct elements, or you’d draw infinitely many individuals with duplicates from a finite set, and your observations wouldn’t distinguish you from your duplicates.
Adding to this, I think it would follow from your argument that the credence you must assign to the universe having infinitely many individuals must be 0 or 1, which seems to prove too much. You could repeat your argument, but this time with any fixed finite number of individuals instead of 1 for solipsism, and infinitely many individuals as the alternative, and your argument would show that you must assign credence 0 to the first option and so 1 to the infinite.
For each natural number k∈N, and N representing the number of actual people, you could show that
(This is assuming the number of individuals must be countable. I wouldn’t be surprised if the SIA has larger cardinals always dominate in the same way infinity does over each finite number. But there’s no largest cardinal, although maybe we can use the class of all cardinal numbers? What does this even mean anymore? Or maybe we just need to prove that the number of individuals can’t be larger than some particular cardinal.)
(I’m not very familiar with anthropic reasoning, or SSA and SIA specifically.)
Could you elaborate on this? Solipsism doesn’t just mean that there’s only one mind that exists, but also that it’s my mind. Here’s Tarsney’s discussion of his estimates:
Also, what about the possibility of infinitely many individuals, which actually seems pretty likely (if you count spatially (or temporally) separated identical individuals separately, or allow the possibility that there could be infinitely many non-identical individuals, maybe increasing without bound in “brain” size)? If you had one of two possibilities, either 1) just you, or 2) infinitely many individuals,
your approach would imply that rational credence in solipsism is 0, but solipsism is not a logical certainty conditional on these two hypotheses, so this seems wrong. More generally, it just seems wrong to me that credence in solipsism should approach 0 as the number of (possible?) individuals increases without bound. There should be some lower bound that does not depend on the number of possible individuals (and it could be related to the infinite case, through conditional probabilities). I think this is basically what Tarsney is getting at.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.
EDIT: I guess you’d need to make more distributional assumptions, since there’s no uniform distribution over infinitely many distinct elements, or you’d draw infinitely many individuals with duplicates from a finite set, and your observations wouldn’t distinguish you from your duplicates.
Adding to this, I think it would follow from your argument that the credence you must assign to the universe having infinitely many individuals must be 0 or 1, which seems to prove too much. You could repeat your argument, but this time with any fixed finite number of individuals instead of 1 for solipsism, and infinitely many individuals as the alternative, and your argument would show that you must assign credence 0 to the first option and so 1 to the infinite.
P(N=k|I exist and (N=k or N=∞))=0For each natural numberk∈N, andNrepresenting the number of actual people, you could show that
P(N<∞|I exist)=∞∑k=1P(N=k|I exist)≤∞∑k=1P(N=k|I exist and (N=k or N=∞))=0and soAnd henceP(N=∞|I exist)=1.(This is assuming the number of individuals must be countable. I wouldn’t be surprised if the SIA has larger cardinals always dominate in the same way infinity does over each finite number. But there’s no largest cardinal, although maybe we can use the class of all cardinal numbers? What does this even mean anymore? Or maybe we just need to prove that the number of individuals can’t be larger than some particular cardinal.)