Upon rereading your posts, I retract disagreement on “mutually exclusive outcomes”. Instead...
Initially probability function is defined over iterations of probability experiment. You define a different function over all space and time, which you still call “probability”. It surely has properties that you like, but it’s a different function! Please use another name, this is already taken. Or add a disclaimer. Preferably do both. You know how easy it is to confuse people with such things! Definetely, do not start participating in the conversations about probability while talking about your function.
An obvious way to do so is put a hazard sign on “probability” and just not use it, not putting resources into figuring out what “probability” SB should name, isn’t it? For instance, suppose Sleeping Beauty claims “my credence for Tails is 1π”; any specific objection would be based on what you expected to hear.
(And now I realize a possible point why you’re arguing to keep “probability” term for such scenarios well-defined; so that people in ~anthropic settings can tell you their probability estimates and you, being observer, could update on that information.)
As for why I believe probability theory to be useful in life despite the fact that sometimes different tools need to be used: I believe disappearing as a Boltzmann brain or simulated person is balanced out by appearing the same way, dissolving into different quantum branches is balanced out by branches reassembling, and likewise for most processes.
Upon rereading your posts, I retract disagreement on “mutually exclusive outcomes”. Instead...
An obvious way to do so is put a hazard sign on “probability” and just not use it, not putting resources into figuring out what “probability” SB should name, isn’t it? For instance, suppose Sleeping Beauty claims “my credence for Tails is 1π”; any specific objection would be based on what you expected to hear.
(And now I realize a possible point why you’re arguing to keep “probability” term for such scenarios well-defined; so that people in ~anthropic settings can tell you their probability estimates and you, being observer, could update on that information.)
As for why I believe probability theory to be useful in life despite the fact that sometimes different tools need to be used: I believe disappearing as a Boltzmann brain or simulated person is balanced out by appearing the same way, dissolving into different quantum branches is balanced out by branches reassembling, and likewise for most processes.