Let us say, we have a credence of cs in solipsism, before taking into account any anthropic evidence. If solipsism is true, there is only 1 person, and if solipsism is false, there are Np persons. From the observation, that we are indeed a person ourselves, this leads us to a credence of cs⋅1cs⋅1+(1−cs)⋅Np=11+Npcs−Np≈csNp in solipsism.
cs is the probability that there’s only one mind, not also that it’s my mind, right? Maybe I’m being pedantic, but solipsism already implies that this mind is mine, so this was kind of confusing to me. I thought you were using cs to refer to Tarsney’s range, but it seems you’re referring to a more general hypothesis (of which solipsism is a special case, with the mind being me).
With S= there’s only one mind (whether mine or not),
I think the way you put it makes sense, and if you put the number in, you get to the right conclusion. The way I think about this is slightly different, but (I think) equivalent:
Let {Hn} be the set of all possible Persons, and {pn} the probability of them existing. The probability, that you are the person Hmis pm∑npn. Lets say some but not all possible people have red hair. She subset of possible people with red hair is {Hs}⊆{Hn}. Then the probability, that you have red hair is:∑sps∑npn.
In my calculations in the post, the set of all possible people is the one solipsistic guy, and Np people in the non-solipsistic universe. (with their probability of existence being cs and (1−cs) ). So the probability, that you are in a world, where solipsism is true, is cscs1+(1−cs)Np.
cs is the probability that there’s only one mind, not also that it’s my mind, right? Maybe I’m being pedantic, but solipsism already implies that this mind is mine, so this was kind of confusing to me. I thought you were using cs to refer to Tarsney’s range, but it seems you’re referring to a more general hypothesis (of which solipsism is a special case, with the mind being me).
With S= there’s only one mind (whether mine or not),
P(S|I exist)=P(I exist|S)P(S)P(I exist|S)P(S)+P(I exist|notS)P(notS)=P(I exist|S)csP(I exist|S)cs+P(I exist|notS)(1−cs)What are each of the probabilities here supposed to be? P(I exist|S)=1N,P(I exist|notS)=NpN, where N= the number of possible people?
I think the way you put it makes sense, and if you put the number in, you get to the right conclusion. The way I think about this is slightly different, but (I think) equivalent:
Let {Hn} be the set of all possible Persons, and {pn} the probability of them existing. The probability, that you are the person Hm is pm∑npn. Lets say some but not all possible people have red hair. She subset of possible people with red hair is {Hs}⊆{Hn}. Then the probability, that you have red hair is:∑sps∑npn.
In my calculations in the post, the set of all possible people is the one solipsistic guy, and Np people in the non-solipsistic universe. (with their probability of existence being cs and (1−cs) ). So the probability, that you are in a world, where solipsism is true, is cscs1+(1−cs)Np.