I count references within each logical possibility and then multiply by their “probability”.
Here’s a super contrived example to explain this. Suppose that if the last digit of pi is between 0 and 3, Sleeping Beauty experiments work as we know them, whereas if it’s between 4 and 9, everyone in the universe is miraculously compelled to interview Sleeping Beauty 100 times if the coin is tails. In this case, I think P(coin heads|interviewed) is 0.4⋅13+0.6⋅1101. So it doesn’t matter how many more instances of the reference class there are in one logical possibility; they don’t get “outside” their branch of the calculation. So in particular, the presumptuous philosopher problem doesn’t care about number of classes at all.
In practice, it seems super hard to find genuine examples of logical uncertainty and almost everything is repeated anyway. I think the presumptuous philosopher problem is so unintuitive precisely because it’s a rare case of actual logical uncertainty where you genuinely cannot count classes.
I’m curious how your conception of probability accounts for logical uncertainty?
I count references within each logical possibility and then multiply by their “probability”.
Here’s a super contrived example to explain this. Suppose that if the last digit of pi is between 0 and 3, Sleeping Beauty experiments work as we know them, whereas if it’s between 4 and 9, everyone in the universe is miraculously compelled to interview Sleeping Beauty 100 times if the coin is tails. In this case, I think P(coin heads|interviewed) is 0.4⋅13+0.6⋅1101. So it doesn’t matter how many more instances of the reference class there are in one logical possibility; they don’t get “outside” their branch of the calculation. So in particular, the presumptuous philosopher problem doesn’t care about number of classes at all.
In practice, it seems super hard to find genuine examples of logical uncertainty and almost everything is repeated anyway. I think the presumptuous philosopher problem is so unintuitive precisely because it’s a rare case of actual logical uncertainty where you genuinely cannot count classes.