While I agree with your conclusion in some sense you are using the wrong notion of probability. The people who feel there is a right answer to the sleeping beauty case aren’t talking about the kind of formally defined count over situations in some formal model. If that’s the only notion of probability then you can’t even talk about the probabilities of different physical theories being true.
The people who think there is a sleeping beauty paradox believe there is something like the rational credence one should have in a proposition given your evidence. If you believe this then you have a question to answer. What kind of credence should sleeping beauty have in the coin landing heads given she has the evidence of remembering being enrolled in the experiment and waking up this morning.
In my analysis of the issue I ultimately come to essentially the same conclusion that you do (it’s an ill-posed problem) but an important feature of this account is that it requires **denying** that there is a well-defined notion that we refer to when we talk about rational credence in a belief.
This is a conclusion that I feel many rationalists will have a hard time swallowing. Not the abstract view that should shut up about probability and just look at decisions. Rather, the conclusion that we can’t insist the person who (despite strong evidence to the contrary) that it’s super likely that god exists is being somehow irrational because there isn’t even necessarily a common notion of what kind of possible outcomes count for making decisions, e.g., if they only value being correct in worlds where there is a deity they get an equally valid notion of rational credence which makes their belief perfectly rational.
While I agree with your conclusion in some sense you are using the wrong notion of probability. The people who feel there is a right answer to the sleeping beauty case aren’t talking about the kind of formally defined count over situations in some formal model. If that’s the only notion of probability then you can’t even talk about the probabilities of different physical theories being true.
The people who think there is a sleeping beauty paradox believe there is something like the rational credence one should have in a proposition given your evidence. If you believe this then you have a question to answer. What kind of credence should sleeping beauty have in the coin landing heads given she has the evidence of remembering being enrolled in the experiment and waking up this morning.
In my analysis of the issue I ultimately come to essentially the same conclusion that you do (it’s an ill-posed problem) but an important feature of this account is that it requires **denying** that there is a well-defined notion that we refer to when we talk about rational credence in a belief.
This is a conclusion that I feel many rationalists will have a hard time swallowing. Not the abstract view that should shut up about probability and just look at decisions. Rather, the conclusion that we can’t insist the person who (despite strong evidence to the contrary) that it’s super likely that god exists is being somehow irrational because there isn’t even necessarily a common notion of what kind of possible outcomes count for making decisions, e.g., if they only value being correct in worlds where there is a deity they get an equally valid notion of rational credence which makes their belief perfectly rational.