I can try to rephrase what I said, but I honestly have no clue what you mean by putting probabilities in quotes.
2⁄3 is the probability that this Sleeping Beauty is waking up in a world where the coin came up tails. 1⁄2 is the probability that some Sleeping Beauty will wake up in such a world. To the naive reader, both of these things sound like “The probability that the coin comes up tails”.
I put the word “probability” in quotes is because I wanted to talk about the word itself, not the type of logic it refers to. The reason I thought you were talking about different types of logic using the same word was because probability already specifies what you’re supposed to be maximizing. For individual probabilities it could be one of many scoring rules, but if you want to add scores together you need to use the log scoring rule.
To the naive reader, both of these things sound like “The probability that the coin comes up tails”.
Right. One of them is the probability that the coin comes up tails given some starting information (as in a conditional probability, like P(T | S)), and the other is the probability that the coin comes up tails, given the starting information and some anthropic information: P(T | S A). So they’re both “P(T),” in a way.
Hah, so I think in your original comment you meant “asking “but what’s P(T), really?” isn’t helpful,” but I heard “asking “but what’s P(T | S A), really?” isn’t helpful” (in my defense, some people have actually said this).
If this is right I’ll edit it into my original reply so that people can be less confused. Lastly, in light of this there is only one thing I can link to.
I can try to rephrase what I said, but I honestly have no clue what you mean by putting probabilities in quotes.
2⁄3 is the probability that this Sleeping Beauty is waking up in a world where the coin came up tails. 1⁄2 is the probability that some Sleeping Beauty will wake up in such a world. To the naive reader, both of these things sound like “The probability that the coin comes up tails”.
Ah, okay, that makes sense to me now. Thanks.
I put the word “probability” in quotes is because I wanted to talk about the word itself, not the type of logic it refers to. The reason I thought you were talking about different types of logic using the same word was because probability already specifies what you’re supposed to be maximizing. For individual probabilities it could be one of many scoring rules, but if you want to add scores together you need to use the log scoring rule.
Right. One of them is the probability that the coin comes up tails given some starting information (as in a conditional probability, like P(T | S)), and the other is the probability that the coin comes up tails, given the starting information and some anthropic information: P(T | S A). So they’re both “P(T),” in a way.
Hah, so I think in your original comment you meant “asking “but what’s P(T), really?” isn’t helpful,” but I heard “asking “but what’s P(T | S A), really?” isn’t helpful” (in my defense, some people have actually said this).
If this is right I’ll edit it into my original reply so that people can be less confused. Lastly, in light of this there is only one thing I can link to.