So if a the territory is branching , the map.should, too.
Of course not. The territory can be made of rocks and dirt, but it doesn’t mean that the map also has to be.
That’s a disadvantage, because the same map can’t represent any territory.
I’m not saying that it represents every territory. I’m saying that it represents a more general class of territories without loosing any advantages of the framework of possible worlds.
In the post I’ve even specifically outlined what are the territories that my framework can represent:
“So the territory that probability is in the map of is...”
All the processes in the real world, such that my knowledge state about them works like a weighted sample of n elements.
( there may be an ontological neutral way of doing probability calculations, but it’s not a map, for that reason....more of a tool)
Now it seems that you are finally starting to get it. It is a map, of course, but that’s really beside the point. If you want to put it in a separate category of “tools” (as if a map is not a tool?) then whatever suits your needs. Yes, what I’m doing is providing an ontologically neutral framework for probability theory that works better than a framework of possible worlds.
The problem is the implied ontology.
Once again, no ontology is actually implied. It’s absolutely trivial to describe behavior of indetermenistic processes in terms of probability experiment. I’m concentrating on deterministic cases simply because they are trickier.
If there is a referent for it in the territory, it is entirely reasonable to say “possible worlds exist”.
I’m not saying that it’s unreasonable to say, conditionally on using this term. I’m saying that usage of the term, to begin with, is a bad idea as it keeps leading people doing probability theory astray.
Is it really a win to admit the substance of existing possible worlds, but under a different name?
When your goal is to separate the substance from the harmful rubbish, it absolutely is a win.
Good overall, but you are making a serious mistake: confusing single halfism, with double halfism.
SSA is a generalized single halfism reasoning. It’s very obviously wrong in Sleeping Beauty as it implies that if the Beauty knows that she is awakened on Monday, she expects that there is 3⁄2 chance that the coin is Heads. Generally if you actually do the math, SSA can’t produce correct betting odds for Sleeping Beauty problem. It’s, in a sense, even worse than SIA for SB, but ultimately both of them are based on the flawed and unjustified framework of “centred possible worlds”.
Double halfism is the correct approach and has no problem with correct betting odds. All your argument in favor of halfism are, in fact, double halfer reasoning. However you mistakenly credit them to SSA.