Here, you dropped this from the last bullet point at the end :)
A very clear walkthrough of full nonindexical conditioning. Thanks! I think there’s still a big glaring warning sign that this could be wrong, which is the mismatch with frequency (and, by extension, betting). Probability is logically prior to frequency estimation, but that doesn’t mean I think they’re decoupled. 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.
I think if you’ve gone wrong somewhere, it’s in trying to outlaw statements of the form “it is Monday today.”
Suppose on Monday the experimenters will give her a cookie after she answers the question, and on Tuesday the experimenters will give her ice cream. Do you really want to outlaw “in 5 minutes I will get a cookie” as a valid thing to have beliefs about?
In fact, I think you got it precisely backwards—probability distributions come from the assigner’s state of information, and therefore they must be built off of what the assigner actually knows. I don’t have access to some True Monday Detector, I only have access to my internal sense of time. “Now” is fundamental, “Monday” is the higher level construct. Similarly, I don’t have an absolute position sense—my probability distribution over things must always use relative coordinates (even if it’s “relative to the zero reading on this gauge here”) because there are no absolute coordinates available to me. I don’t have access to my mystical True Name, so I don’t know which of several duplicates is the Real Me unless I can describe it in relative terms like “the one who came first”—therefore “me” is fundamental, “the original Charlie” is the higher-level construct.
Anyhow, once you allow temporal information you go back to trying to trying to figure out what your model should say when you demand a MEE constraint on Monday vs. Tuesday.
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.
Here, you dropped this from the last bullet point at the end :)
A very clear walkthrough of full nonindexical conditioning. Thanks! I think there’s still a big glaring warning sign that this could be wrong, which is the mismatch with frequency (and, by extension, betting). Probability is logically prior to frequency estimation, but that doesn’t mean I think they’re decoupled. 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.
I think if you’ve gone wrong somewhere, it’s in trying to outlaw statements of the form “it is Monday today.”
Suppose on Monday the experimenters will give her a cookie after she answers the question, and on Tuesday the experimenters will give her ice cream. Do you really want to outlaw “in 5 minutes I will get a cookie” as a valid thing to have beliefs about?
In fact, I think you got it precisely backwards—probability distributions come from the assigner’s state of information, and therefore they must be built off of what the assigner actually knows. I don’t have access to some True Monday Detector, I only have access to my internal sense of time. “Now” is fundamental, “Monday” is the higher level construct. Similarly, I don’t have an absolute position sense—my probability distribution over things must always use relative coordinates (even if it’s “relative to the zero reading on this gauge here”) because there are no absolute coordinates available to me. I don’t have access to my mystical True Name, so I don’t know which of several duplicates is the Real Me unless I can describe it in relative terms like “the one who came first”—therefore “me” is fundamental, “the original Charlie” is the higher-level construct.
Anyhow, once you allow temporal information you go back to trying to trying to figure out what your model should say when you demand a MEE constraint on Monday vs. Tuesday.
MEE constraint?
“mutually exclusive and exhaustive.” Usually just means the probabilities of AND-ing them is zero, and the total probability is one.
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.