In a probability space where you have distinct (non-intersecting) “Monday” and “Tuesday”, it is expected (in the informal sense, outside the broken model) that you’ll observe Tuesday after observing Monday, that upon observing Monday you rule out Tuesday, and that upon observing Tuesday you won’t be able to recognize it as such because it’s already ruled out. “Observer-moments” can be located on the same history, and a probability space that distinguishes them will tear down your understanding of the other observer-moments once you’ve observed one of them and excluded the rest. This model promises you a map disconnected from reality.
It is not the case with a probability space based on possible worlds that after concluding ~X, you expect (in the informal sense) to observe X after that. Possible worlds model is in accordance with this (informal) axiom. Sample space based on “observer-moments” is not.
In a probability space where you have distinct (non-intersecting) “Monday” and “Tuesday”, it is expected (in the informal sense, outside the broken model) that you’ll observe Tuesday after observing Monday, that upon observing Monday you rule out Tuesday, and that upon observing Tuesday you won’t be able to recognize it as such because it’s already ruled out. “Observer-moments” can be located on the same history, and a probability space that distinguishes them will tear down your understanding of the other observer-moments once you’ve observed one of them and excluded the rest. This model promises you a map disconnected from reality.
It is not the case with a probability space based on possible worlds that after concluding ~X, you expect (in the informal sense) to observe X after that. Possible worlds model is in accordance with this (informal) axiom. Sample space based on “observer-moments” is not.