I read the beginning and skimmed through the rest of the linked post. It is what I expected it to be.
We are talking about “probability”—a mathematical concept with a quite precise definition. How come we still have ambiguity about it?
Reading E.T. Jayne’s might help.
Probability is what you get as a result of some natural desiderata related to payoff structures. When anthropics are involved, there are multiple ways to extend the desiderata, that produce different numbers that you should say, depending on what you get paid for/what you care about, and accordingly different math. When there’s only a single copy of you, there’s only one kind of function, and everyone agrees on a function and then strictly defines it. When there are multiple copies of you, there are multiple possible ways you can be paid for having a number that represents something about the reality, and different generalisations of probability are possible.
Probability is what you get as a result of some natural desiderata related to payoff structures.
This is a vague gesture to a similarity cluster and not an actual definition. Remove fancy words and you end up with “Probability has something to do with betting”. Yes it does. In this post I even specify exactly what it does. You don’t need to read E.T. Jayne’s to discover this revelation. The definition of expected utility is much more helpful.
When anthropics are involved, there are multiple ways to extend the desiderata, that produce different numbers that you should say, depending on what you get paid for/what you care about, and accordingly different math.
There are always multiple ways to “extend the desiderata”. But more importantly, you don’t have to say different probability estimates depending on what you get paid for/what you care about. This is the exact kind of nonsense that I’m calling out in this post. Probabilities are about what evidence you have. Utilities are about what you care about. You don’t need to use thirder probabilities for per awakening betting. Do you disagree with me here?
When there’s only a single copy of you, there’s only one kind of function, and everyone agrees on a function and then strictly defines it. When there are multiple copies of you, there are multiple possible ways you can be paid for having a number that represents something about the reality, and different generalisations of probability are possible.
How is it different from talking about probability of a specific person to observe an event and probability of any person from a group to observe an event? The fact that people from the group are exact copies doesn’t suddenly makes anthropics a separate magisteria.
Moreover, there are no independent copies in Sleeping Beauty. On Tails, there are two sequential time states. The fact that people are trying to make a sample space out of them directly contradicts its definition.
When we are talking just about betting, one can always come up with its own functions, it’s own way to separate expected utility of an event into “utility” and “probability”. But then their “utilities” will be constantly shifting due to receiving new evidence and “probabilities” will occasionally ignore new evidence, and shift for other reasons. And pointing at this kind of weird behavior is a completely reasonable reaction. Can a person still use such definitions consistently? Sure. But this is not a way to carve reality by its joints. And I’m not just talking about betting. I specifically wrote a whole post about fundamental mathematical reasons, before starting talking about it.
I read the beginning and skimmed through the rest of the linked post. It is what I expected it to be.
Reading E.T. Jayne’s might help.
Probability is what you get as a result of some natural desiderata related to payoff structures. When anthropics are involved, there are multiple ways to extend the desiderata, that produce different numbers that you should say, depending on what you get paid for/what you care about, and accordingly different math. When there’s only a single copy of you, there’s only one kind of function, and everyone agrees on a function and then strictly defines it. When there are multiple copies of you, there are multiple possible ways you can be paid for having a number that represents something about the reality, and different generalisations of probability are possible.
This is surprising to me. Are you up to a a more detailed discussion? What do you think about the statistical analysis and the debunk of centred possible worlds? I haven’t seen these points being raised or addressed before and they are definitely not about semantics. The fact that sequential events are not mutually exclusive can be formally proven. It’s not a matter of perspective at all! We could use the dialogues feature, if you’d like.
This is a vague gesture to a similarity cluster and not an actual definition. Remove fancy words and you end up with “Probability has something to do with betting”. Yes it does. In this post I even specify exactly what it does. You don’t need to read E.T. Jayne’s to discover this revelation. The definition of expected utility is much more helpful.
There are always multiple ways to “extend the desiderata”. But more importantly, you don’t have to say different probability estimates depending on what you get paid for/what you care about. This is the exact kind of nonsense that I’m calling out in this post. Probabilities are about what evidence you have. Utilities are about what you care about. You don’t need to use thirder probabilities for per awakening betting. Do you disagree with me here?
How is it different from talking about probability of a specific person to observe an event and probability of any person from a group to observe an event? The fact that people from the group are exact copies doesn’t suddenly makes anthropics a separate magisteria.
Moreover, there are no independent copies in Sleeping Beauty. On Tails, there are two sequential time states. The fact that people are trying to make a sample space out of them directly contradicts its definition.
When we are talking just about betting, one can always come up with its own functions, it’s own way to separate expected utility of an event into “utility” and “probability”. But then their “utilities” will be constantly shifting due to receiving new evidence and “probabilities” will occasionally ignore new evidence, and shift for other reasons. And pointing at this kind of weird behavior is a completely reasonable reaction. Can a person still use such definitions consistently? Sure. But this is not a way to carve reality by its joints. And I’m not just talking about betting. I specifically wrote a whole post about fundamental mathematical reasons, before starting talking about it.