Meta:
I find this situation quite ironic. From my perspective, I painstakingly cited and answered your comments piece by piece even though you didn’t engage much neither with the arguments in my posts nor with any of my replies.
I’m not sure how I could have missed “parts where you try to communicate the structure of the question”. The only things which I haven’t directly cited in your previous comment are:
Beside which, the Sleeping Beauty problem explicit uses the word.
and
As defined, a universe state either satisfies or does not satisfy a proposition. If you’re referring to propositions that may vary over space or time, then when modelling a given situation you have two choices
Which I neither disagree nor have any interesting to add.
Universe states can be distinguished by time information, and in problems like this where time is part of the world-model, they should be. The mathematical structure of a probability space has nothing to do with it, as the mathematical formalism doesn’t care what the elements of a sample space are.
Which does not have any argument in it. You just make statements without explaining why they are supposed to be true. I obviously do not agree that in Sleeping Beauty case our model should be treating time states as individual outcomes. But simply proclaming this disagreement doesn’t serve any purpose after I’ve already presented comprehensive explanation why we can’t lawfully reason about time states in this particular case as if they are mutually exclusive outcomes, which you, once again, failed to engage with.
I would appreciate if you addressed this meta point because I’m honestly confused about your perspective on this failure of our communication.
Meta ended.
No, I specifically was referring to the Sleeping Beauty
If you were specifically referring to Sleeping Beauty problem then your previous comment doesn’t make sense.
Either you are logically pinpointing any sample space for at least some problem, and then you can say that any non-empty set fits this description.
Or you are logically pinpointing sample space specifically for the Sleeping Beauty problem, then you can’t dismiss the condition of mutually exclusivity of outcomes which are relevant to the particular application of the sample space.
Frankly it feels as if people are not even trying to sell environmentalism to republicans. There are so many low hanging fruits here:
Russia is the main beneficiary of global warming! Don’t let the commies win!
Is pollution making your kids trans? No one was trans before the industrial revolution and now everyone is! We need to stop it before the western civilization collapses!
Leftists just pretend to fight global warming to virtue signal, but they are too much of pussies to have anything done. We need real action to protect the natural resources of our country!