“Probabilities” are a mathematical construct that can be used to represent multiple things, but in Bayesianism the first option is the most common.
Which world gets to be real seems arbitrary.
It’s the one observations come from.
Most possible worlds are lifeless, so we’d have to be really lucky to be alive.
Typically probabilistic models only represent a fragment of the world, and therefore might e.g. implicitly assume that all worlds are lived-in. The real world has life so it’s ok to assume we’re not in a lifeless world.
We have no information about the process that determines which world gets to be real, so how can we decide what the probability mass function p should be?
Often you require need some additional properties, e.g. ergodicity or exchangeability, which might be justified by separation-of-scale and symmetry and stuff.
P represents your uncertainty over worlds, so there’s no “right” P (except the one that assigns 100% to the real world, in a sense). You just gotta do your best.
“Probabilities” are a mathematical construct that can be used to represent multiple things, but in Bayesianism the first option is the most common.
It’s the one observations come from.
Typically probabilistic models only represent a fragment of the world, and therefore might e.g. implicitly assume that all worlds are lived-in. The real world has life so it’s ok to assume we’re not in a lifeless world.
Often you require need some additional properties, e.g. ergodicity or exchangeability, which might be justified by separation-of-scale and symmetry and stuff.
P represents your uncertainty over worlds, so there’s no “right” P (except the one that assigns 100% to the real world, in a sense). You just gotta do your best.