Ape in the coat resolves this by abandoning standard probability theory in favour of a scheme in which a single person can simultaneously hold two different probabilities for the same event, to be used when making different decisions.
I don’t think it’s a correct description of what I do. If anything, I resolve this by sticking to probability theory as it is, without making any additional assumptions about personhoods.
First of all, it’s not the same event. In one case we are talking about event “this person sees green”, while in the other—about event “any person sees green”. If distinguishing between this two events and accepting that they may have different probabilities doesn’t count as “abandoning probability theory”, neither is my alternative approach, which is completely isomorphic to it.
Secondly, no theorem or axiom of probability theory claims anything about personhood. People just smuggle in their intuitive idea of it, which may lead to apparently paradoxical results. The only way probability theory can treat personal identities is in terms of possible outcomes. For example in a fair coin toss scenario, “you” is a person who may observe Heads outcome with 1⁄2 probability and Tails outcomes with 1⁄2 probability. But so is any other person that observes the same coin toss! If you and me observe the same coin toss, we are the same entity for the sake of the mathematical model. Probability theory doesn’t distinguish between physical people, or consciousnesses or metaphysical identities. Only between sets of possible outcomes that can be observed. I’ll probably have to elaborate this idea more in a future post.
OK. Perhaps the crucial indication of your view is instead your statement that ‘On the level of our regular day to day perception “I” seems to be a simple, indivisible concept. But this intuition isn’t applicable to probability theory.’
So rather than the same person having more than one probability for an event, instead “I” am actually more than one person, a different person for each decision I might make?
In actual reality, there is no ambiguity about who “I” am, since in any probability statement you can replace “I” by ‘The person known as “Radford Neal”, who has brown eyes, was born in..., etc., etc.’ All real people have characteristics that uniquely identify them. (At least to themselves; other people may not be sure whether “Homer” was really a single person or not.)
So rather than the same person having more than one probability for an event, instead “I” am actually more than one person, a different person for each decision I might make?
No. Once again. Event is not the same. And also not for every decision. You are just as good as “a different person” for every different set of possible outcomes that you have according to the mathematical model that is been used, because possible outcomes is the only thing that matters for probability theory—not the color of your eyes, date of birth etc.
Maybe it would be clearer if you notice, that there are two different mathematical models in use here: one describing probabilities for a specific person (you), and another describing probabilities for any person that sees green—that you may happen to be or not. The “paradox” happens when people confuse these two models assuming that they have to return the same probabilities, or apply the first model when the second has to be applied.
I don’t think it’s a correct description of what I do. If anything, I resolve this by sticking to probability theory as it is, without making any additional assumptions about personhoods.
First of all, it’s not the same event. In one case we are talking about event “this person sees green”, while in the other—about event “any person sees green”. If distinguishing between this two events and accepting that they may have different probabilities doesn’t count as “abandoning probability theory”, neither is my alternative approach, which is completely isomorphic to it.
Secondly, no theorem or axiom of probability theory claims anything about personhood. People just smuggle in their intuitive idea of it, which may lead to apparently paradoxical results. The only way probability theory can treat personal identities is in terms of possible outcomes. For example in a fair coin toss scenario, “you” is a person who may observe Heads outcome with 1⁄2 probability and Tails outcomes with 1⁄2 probability. But so is any other person that observes the same coin toss! If you and me observe the same coin toss, we are the same entity for the sake of the mathematical model. Probability theory doesn’t distinguish between physical people, or consciousnesses or metaphysical identities. Only between sets of possible outcomes that can be observed. I’ll probably have to elaborate this idea more in a future post.
OK. Perhaps the crucial indication of your view is instead your statement that ‘On the level of our regular day to day perception “I” seems to be a simple, indivisible concept. But this intuition isn’t applicable to probability theory.’
So rather than the same person having more than one probability for an event, instead “I” am actually more than one person, a different person for each decision I might make?
In actual reality, there is no ambiguity about who “I” am, since in any probability statement you can replace “I” by ‘The person known as “Radford Neal”, who has brown eyes, was born in..., etc., etc.’ All real people have characteristics that uniquely identify them. (At least to themselves; other people may not be sure whether “Homer” was really a single person or not.)
No. Once again. Event is not the same. And also not for every decision. You are just as good as “a different person” for every different set of possible outcomes that you have according to the mathematical model that is been used, because possible outcomes is the only thing that matters for probability theory—not the color of your eyes, date of birth etc.
Maybe it would be clearer if you notice, that there are two different mathematical models in use here: one describing probabilities for a specific person (you), and another describing probabilities for any person that sees green—that you may happen to be or not. The “paradox” happens when people confuse these two models assuming that they have to return the same probabilities, or apply the first model when the second has to be applied.