I think we’ve had this discussion before, but let me try one more time...
You say, “And the “probability I am the Orignal” is not a valid concept. “I” is an identification not based on anything but my first-person perspective. Whether “I” am the Orignal or the Clone is something primitive, not analyzable. Any attempt to justify this probability requires additional postulates such as equating “I” to a random sample of some sort.”
But to me, this means throwing out the whole notion of probability as a subjective measure of uncertainty. Perhaps you’re fine with that, but it also means throwing out all use of probability in scientific applications, such as evaluating the probability that a drug will work and/or have side effects—because the practical use of such evaluations is to conclude that “I” will probably be cured by that drug, which is a statement you have declared meaningless. Maybe you’re assuming that some “additional postulate” will fix that, but if so, I don’t see why something similar wouldn’t also render the probability that “I” am the Original in your problem meaningful.
I think an underlying problem here is an insistence on overly abstract thought experiments. You’re assuming that the subject of the experiment cannot simply walk out the door of the room they’re in and see whether they’re in the same place where they went to sleep (in which case they’re the Original), or in a different place. They can also do all sorts of other things, whose effects for good or bad may depend on whether or not they are the Original (before they figure this out). They will in general need some measure of uncertainty in making decisions of this sort—they can’t simply say that self-locating probabilities are meaningless, when implicitly they will be using them to decide. This is all true even if they in fact decide to cooperate with the experimenter and do none of this.
The assumption that the experiment must proceed in the manner as it is abstractly described severs all connection between the answers being proposed and the real world. There is then nothing stopping anyone from proposing that the probability of Heads is 1⁄2, or 3⁄4, or 2⁄7 - since none of these have consequences—and similarly the probability of “I am the Original” can be anything you like, or be meaningless, if you treat the person making the judgement as an abstract entity constrained to do nothing but what they’re supposed to do in the problem statement, rather than as a real person.
I don’t think rejecting self-locating probability means totally rejecting probability as a measure of uncertainty. Because self-locating probability only applies to very specific anthropic problems. E.g.
An incubator creates two observers, the first in a blue room and the second in a red room. Given I am one of the created observers but don’t know if I am the first or the second. What is the probability that I will see blue when I turn on the lights?
Some people put me and another person into two rooms. One Blue, one red but the process is random or unknown to me. Before turning on the light what is the probability that I am in the blue room?
My position is that the two problems are fundamentally different, only problem 1 is what has been referred to as self-locating probability in anthropic paradoxes. The entire experiment is known from a god’s eye view. The uncertainty is which of the two observers is ME. ME (as well as Now or Here) are not some physical or observable identification but primitive concepts due to reasoning from a first-person perspective. So there is no reasonable way to attach a probability to it.
Problem 2 is different. I know which person is ME all along. The uncertainty is not about which is me but what happened to me. About the room assignment process. This whole problem can be described from a god’s eye view and is still comprehensible. I.E. “dadadarren and another person has been put into two rooms respectively, what is the probability that dadadarren is in the blue room?” So even though it askes which room I am in, it is different from the self-locating probabilities being discussed in anthropic problems. Probabilities like this are obviously valid.
You probably think this distinction is not meaningful. So saying self-locating probabilities are invalid would lead to all probability as a measure of uncertainty being invalid. But that is not the argument I am making. Granted, for some metaphysical views, the is no difference between the two types. E.g. the Many-Worlds Interpretation considers the self-locating probability as the source of probability. So my argument is not compatible with the MWI, i.e. it is a counter-argument against MWI.
Also, I am not making assumptions that the copies cannot go outside or ask others whether they are the Original. And they can certainly get into situations where the outcome depends on whether they are the original or the clone. I am arguing in such situations when a decision is involved, given my objective is about MY own benefit (as in the benefit of the “I” in self-locating probability) then there is no singular rational decision. Rational decisions only exist if the objective is about the collective benefit (total or average) of the copies, or a random sample from these copies. Yet it is hard to argue “maximizing MY own benefit” is disconnected from reality, something a real person will not do.
I think we’ve had this discussion before, but let me try one more time...
You say, “And the “probability I am the Orignal” is not a valid concept. “I” is an identification not based on anything but my first-person perspective. Whether “I” am the Orignal or the Clone is something primitive, not analyzable. Any attempt to justify this probability requires additional postulates such as equating “I” to a random sample of some sort.”
But to me, this means throwing out the whole notion of probability as a subjective measure of uncertainty. Perhaps you’re fine with that, but it also means throwing out all use of probability in scientific applications, such as evaluating the probability that a drug will work and/or have side effects—because the practical use of such evaluations is to conclude that “I” will probably be cured by that drug, which is a statement you have declared meaningless. Maybe you’re assuming that some “additional postulate” will fix that, but if so, I don’t see why something similar wouldn’t also render the probability that “I” am the Original in your problem meaningful.
I think an underlying problem here is an insistence on overly abstract thought experiments. You’re assuming that the subject of the experiment cannot simply walk out the door of the room they’re in and see whether they’re in the same place where they went to sleep (in which case they’re the Original), or in a different place. They can also do all sorts of other things, whose effects for good or bad may depend on whether or not they are the Original (before they figure this out). They will in general need some measure of uncertainty in making decisions of this sort—they can’t simply say that self-locating probabilities are meaningless, when implicitly they will be using them to decide. This is all true even if they in fact decide to cooperate with the experimenter and do none of this.
The assumption that the experiment must proceed in the manner as it is abstractly described severs all connection between the answers being proposed and the real world. There is then nothing stopping anyone from proposing that the probability of Heads is 1⁄2, or 3⁄4, or 2⁄7 - since none of these have consequences—and similarly the probability of “I am the Original” can be anything you like, or be meaningless, if you treat the person making the judgement as an abstract entity constrained to do nothing but what they’re supposed to do in the problem statement, rather than as a real person.
I don’t think rejecting self-locating probability means totally rejecting probability as a measure of uncertainty. Because self-locating probability only applies to very specific anthropic problems. E.g.
An incubator creates two observers, the first in a blue room and the second in a red room. Given I am one of the created observers but don’t know if I am the first or the second. What is the probability that I will see blue when I turn on the lights?
Some people put me and another person into two rooms. One Blue, one red but the process is random or unknown to me. Before turning on the light what is the probability that I am in the blue room?
My position is that the two problems are fundamentally different, only problem 1 is what has been referred to as self-locating probability in anthropic paradoxes. The entire experiment is known from a god’s eye view. The uncertainty is which of the two observers is ME. ME (as well as Now or Here) are not some physical or observable identification but primitive concepts due to reasoning from a first-person perspective. So there is no reasonable way to attach a probability to it.
Problem 2 is different. I know which person is ME all along. The uncertainty is not about which is me but what happened to me. About the room assignment process. This whole problem can be described from a god’s eye view and is still comprehensible. I.E. “dadadarren and another person has been put into two rooms respectively, what is the probability that dadadarren is in the blue room?” So even though it askes which room I am in, it is different from the self-locating probabilities being discussed in anthropic problems. Probabilities like this are obviously valid.
You probably think this distinction is not meaningful. So saying self-locating probabilities are invalid would lead to all probability as a measure of uncertainty being invalid. But that is not the argument I am making. Granted, for some metaphysical views, the is no difference between the two types. E.g. the Many-Worlds Interpretation considers the self-locating probability as the source of probability. So my argument is not compatible with the MWI, i.e. it is a counter-argument against MWI.
Also, I am not making assumptions that the copies cannot go outside or ask others whether they are the Original. And they can certainly get into situations where the outcome depends on whether they are the original or the clone. I am arguing in such situations when a decision is involved, given my objective is about MY own benefit (as in the benefit of the “I” in self-locating probability) then there is no singular rational decision. Rational decisions only exist if the objective is about the collective benefit (total or average) of the copies, or a random sample from these copies. Yet it is hard to argue “maximizing MY own benefit” is disconnected from reality, something a real person will not do.