There are no frequencies in this problem; it is a one-time experiment.
Probability is logically prior to frequency estimation
That’s not what I said; I said that probability theory is logically prior to decision theory.
If your “probability” has zero application because your decision theory uses “likeliness weights” calculated an entirely different way, I think something has gone very wrong.
Yes; what’s gone wrong is that you’re misapplying the decision theory, or your decision theory itself breaks down in certain odd circumstances. Exploring such cases is the whole point of things like Newcomb’s problem and Functional Decision Theory. In this case, it’s clear that Beauty is going to make the same betting decision, with the same betting outcome, on both Monday and Tuesday (if the coin lands Tails). The standard betting arguments use a decision rule that fails to account for this.
I think if you’ve gone wrong somewhere, it’s in trying to outlaw statements of the form “it is Monday today.”
See my response to Dacyn below (“Classical propositions are simply true or false...”). Classical propositions do not change their truth value over time.
There are no frequencies in this problem; it is a one-time experiment.
One can do things multiple times.
See my response to Dacyn below (“Classical propositions are simply true or false...”). Classical propositions do not change their truth value over time.
I tried to get at this in the big long paragraph of “‘Monday’ is an abstraction, not a fundamental.” There is no such thing as a measurement of absolute time. When someone says “no, I mean to refer to the real Monday,” they are generating an abstract model of the world and then making their probability distributions within that model. But then there still have to be rules that cash your nice absolute-time model out into yucky relative-time actual observables.
It’s like Solomonoff induction. You have a series of data, and you make predictions about future data. Everything else is window dressing (sort of).
But it’s not so bad. You can have whatever abstractions you want, as long as they cash out to the right thing. You don’t need time to actually pass within predicate logic. You just need to model the passage of time and then cash the results out.
It’s also like how probability distributions are not about what reality is, they are about your knowledge of reality. “It is Monday” changes truth value depending on the external world. But P(It is Monday | Information)=0.9 is a perfectly good piece of classical logic. In fact, this exactly the same as how you can treat P(H)=0.5, even though classical propositions do not change their truth value when you flip over a coin.
I dunno, putting it that way makes it sound simple. I still think there’s something important in my weirder rambling—but then, I would.
There are no frequencies in this problem; it is a one-time experiment.
That’s not what I said; I said that probability theory is logically prior to decision theory.
Yes; what’s gone wrong is that you’re misapplying the decision theory, or your decision theory itself breaks down in certain odd circumstances. Exploring such cases is the whole point of things like Newcomb’s problem and Functional Decision Theory. In this case, it’s clear that Beauty is going to make the same betting decision, with the same betting outcome, on both Monday and Tuesday (if the coin lands Tails). The standard betting arguments use a decision rule that fails to account for this.
See my response to Dacyn below (“Classical propositions are simply true or false...”). Classical propositions do not change their truth value over time.
One can do things multiple times.
I tried to get at this in the big long paragraph of “‘Monday’ is an abstraction, not a fundamental.” There is no such thing as a measurement of absolute time. When someone says “no, I mean to refer to the real Monday,” they are generating an abstract model of the world and then making their probability distributions within that model. But then there still have to be rules that cash your nice absolute-time model out into yucky relative-time actual observables.
It’s like Solomonoff induction. You have a series of data, and you make predictions about future data. Everything else is window dressing (sort of).
But it’s not so bad. You can have whatever abstractions you want, as long as they cash out to the right thing. You don’t need time to actually pass within predicate logic. You just need to model the passage of time and then cash the results out.
It’s also like how probability distributions are not about what reality is, they are about your knowledge of reality. “It is Monday” changes truth value depending on the external world. But P(It is Monday | Information)=0.9 is a perfectly good piece of classical logic. In fact, this exactly the same as how you can treat P(H)=0.5, even though classical propositions do not change their truth value when you flip over a coin.
I dunno, putting it that way makes it sound simple. I still think there’s something important in my weirder rambling—but then, I would.