I agree that it is necessary to distinguish between "I" and physical person.
In my model, "I" is a thought process about anthropics and "physical person" is everything else around it: octopus, or biped or a computer. The question I want to learn is how this thought process is distributed between different bodies and what it means. Physical person is external observable to the thought process, no more different than a coin or a ball in urn.
Imagine that Sleeping beauty was given one more drug, so on Tuesday she can't think about anthropics. She know this. After her awakening, she starts to think if she is on Monday on Tuesday. But as she know that she thinks about self-location, she know that she can think about anthropics and thus she is Monday.
What I did here, I made the whole problem to be seen from God's eye. But to do so, I introduced the notion of the "thought process of a qualified observer", that is one who is (now) thinking about anthropic. It is close, I think, to EY's functional decision theory.
This gives new versions of SSA and SIA:
For SSA: "I am randomly selected from all qualified observers in every reference class." ("I" means here an instance of thought process.)
For SIA: "If I am in rare position, it means that there were many attempts to create me".
In my opinion, the indexical "I" has an intrinsically clear meaning: the first-person. There is no point in further deconstructing it. Each of us inherently knows which person "I" is because the subjective experience is due to it, the rest of the world is perceived by interaction with it. As a concept, it cannot be further reduced or explained by logic or reasoning. I'm ok with you treating it as a thought process, but it doesn't have to be about anthropics. It is something far simpler and basic.
Anthropic problems lead to paradoxes because they are formulated using specific first-person perspectives. This allows the problem to be set up without using any particular physical person/time.
In the original sleeping beauty problem, there could be 2 awakenings. But the question doesn't specify which physical one is being considered. By saying "as Beauty wakes up in the experiment", the awakening is specified by Beauty's first-person perspective (the one happening "now"). So the problem is really only understandable from this perspective. And to comprehend the question we have to imagine being Beauty in that scenario. Thus it could only be answered from this first-person perspective.
In your modified version, the two awakenings are distinguishable. Now we can understand it by imagining being Beauty in her situation. We can also comprehend which day is being questioned by taking an outsider view: "the day Beauty is able to think about anthropics". So it can be solved either way, from beauty's first-person OR from a god's eye view. That is actually the case for most probability problems. Which is why people want to solve anthropic problems from a god's eye view too. Because it worked so well before.
For the original sleeping beauty problem, solving it from a gods' eye view is impossible because the question uses the first-person perspective like "now" or "I". So additional assumption is needed to change them into something meaningful from the god's eye view. That is where SSA or SIA kicks in: they change the first-person "I" or "now" into a random sample, to be incorporated into god's eye view reasoning.
Because in your modified version the awakenings are distinguishable thus can be perfectly understood from an outsider's view, SSA or SIA is not needed to answer it. "Beauty wakes up on the day she's able to think about anthropics, aka Monday" is no new information and the probability stays put at 1/2. So unless we want to treat every problem as an anthropic problem, there is really no need to bring up SSA or SIA here.
Ok, it looks like I start to understand your point of view.
Imagine that there is a Devil, which could manipulate the "measure" of any observer (e.g. by secretly creating a number of observer's copies or adding more juice into observer's existence, the method doesn't matter here.) Neither observer, nor objective God's eye can't distinguish any difference.This will screw any attempts of Sleeping beauty to calculate probabilities, as there is no mapping between objective and subjective probabilities. Surely, SB assumes that there is no devil or it could be predicted as some form of bias, but how can she be sure?
Returning to what I said in the comment above, surely I meant that there are several instances of SB, like one more on Wednesday and only one on Wed can't think about anthropics, so the choice from several similar copies remains, but it should be limited to copies who actually thinking about anthropic. As someone said in comment about this idea: "Now you updating of the fact that you are updating!" Exactly this.
My view (at least before devil idea) is that we can solve most paradoxes about anthropics or at least replace them with uncertainties about our own believes. E..g in form of claims that "there is 50 per cent chance that Doomsday argument is true".
We also could test experimentally if anthropic reasoning works by looking at smaller examples from our own life. Like situations similar to the claim: "Cars in the next lane really do go faster" or that my birthday looks like to be a randomly chosen from the whole year duration.
In my opinion, "the next lane goes faster" is not really an anthropic problem. If we treat lane choosing as the experiment, there could be other factors affecting one's decision other than speed. So one lane could seem more preferable, making it busier thus slower. Or at the very least, as suggested above, joining a lane make it slower.
Nick Bostrom giving an anthropic explanation is not a surprise either. By treating anthropic as Observation Selection Effect, anthropics appear everywhere. Even for a simple toss of a fair coin, we could think how this particular toss is selected from all the tosses performed by me in my lifetime, or even from all the tosses performed by all observers in this universe.
Observation Selection Effect is fixated on reasoning about two things: 1. The fact that I exist (now). 2. The fact that I am this particular physical observer (experiencing the current moment). SSA and SIA try to provide ways to understand them and draw information from them. In my opinion, those things have no explanation. They can only be accepted as primitively given, a reasoning starting point.
Interestingly, if I think about a random coin presented to me, I think about the chances that it is biased coin, and dismiss them as most coins in the universe are not biased and most of observations of coins are observations of unbiased coins. So I use something like selection of my observation from all observations in the universe to get a prior about if the coin is biased. And I do it almost unconsciously, it is built-in calculation of what is normal.
I have found it useful to replace all references to "I" or "you" in anthropic problems with specifications of instances of actors or robots running a decision procedure. This extends to treating, e.g., utility as a variable in these decision procedures.
I think it is a good stratergy. It will highlight the paradoxes in anthropics are due to the involvement of indexicals such as "I" or "now" in the argument.
I didn't use decision process to discuss anthropics because it involves defining the subject of utility. How one specify it involves assumptions that already determines the answer. For example is a program running on two independent instance considered the same actor? Should the results be pooled together upon evaluation? etc.
How one specify it involves assumptions that already determines the answer.
That is the beauty of an operation specification. My motto is: If you can't program it you don't understand it. :-))
This is another attempt to promote my approach to anthropic paradoxes. I framed the argument differently hopefully making it more clear. Please refer to my website for more.
In the strict indexical sense, "I" just means the first person. However we also often interpret it as the physical person uttering the word and usually equate the two meanings, "I am this physical person" after all. But there is a caveat. The equivalency is bound by the perspective.
The first person meaning of "I" is restricted to its own viewpoint, from other perspectives only the physical meaning can be used. If I hear you say "I'm hungry", to me the only correct way of interpreting it would be the physical person "[insert reader name] is hungry", not that "I am hungry" (as in "dadadarren is hungry"). We do this sort of transcoding naturally all the time.
What's more subtle is this should also apply to "god's eye view" (or "view from nowhere" if you prefer). If we try to be objective and reason from a god's eye view, then we shouldn't be using the first-person "I" at all. For it would only refer to the imaginary impartial observer, not any particular person.
But we keep using the two meanings interchangeably in anthropic problems. Effectively jumping back and forth between our natural viewpoints and the god's eye view. This is the cause of paradoxes and why different camps have trouble communicating.
One major contention in anthropics is whether or not "I exist" can be used as evidence to support certain theories. (Which exact theory, such as more observers, big universe, or "fine-tuning" is a separate matter. ) One camp suggests it does not support any theory because "I would always find myself exist". The other camp disagrees arguing that is claiming "My existence is guaranteed to happen". Which is obviously untrue. So "I exist" is valid evidence. Both camps are unconvinced by the opponent's argument.
The key difference between the two camps is they are using different meanings of "I". When the former argues "I would always find myself exist", they are using the strictly indexical, first-person meaning of "I". i.e. No matter whose perspective we choose to take, we will always conclude the first person exists. It does not have any specific physical person in mind.
On the contrary, when the opponents say 'I exist' is not guaranteed. They are using the other interpretation. Here it is not about the first-person, but that specific physical human being. A particular person's existence is of course not guaranteed, so it shall be considered new information. This argument is taking a god's eye view instead.
To cut to the chase: I think "I exist" is not valid evidence. The first-person interpretation above is right, while the physical interpretation has some missing links.
But before getting into it, I want to clear a common misconception: that "I always find myself exist" is an argument based on SSA. That is not true. It is a very simple conclusion once we keep to the first person meaning of "I". SSA is an additional assumption carefully made to not contradict it. Nevertheless, SSA is ultimately wrong.
Let's look at this in the context of the Doomsday Argument. It claims once considering my birth rank among all humans, the rational forecast of our species' future population shall be greatly reduced. Because I am more likely to be a typical person, aka, to be considered as a randomly selected sample from all human beings.
Doomsday Argument does not consider "I exist" as evidence. So it is using the first-person sense of "I" here. From a first-person perspective, the basic logic of the forecast is as follows: "At the very start, I realize I am this physical being. Then I find out there are other similar physical beings. Let's call all these similar things "human". Some humans are born before me, others after. I want to make a rational estimate of how many will come after me."
Notice in the above analysis there is no place for the uncertainty of "among all human beings, which one is me?". "I'm this one" is evident right from the beginning. What the Doomsday Argument does is take a god's eye view, look at all human beings impartially, then raise the question "among all these people which one is me(I)?". But from the god's eye view, the first person meaning of "I" is not usable. Some additional thing is needed to complete the logic. So SSA specifies a physical person by random sampling, then assumes that particular person is equivalent to the first-person "I".
This assumption lacks any rational backing whatsoever. It misguides us to use the indexical "I" and that physical person interchangeably. It conceals the random jump between the first-person perspective and the god's eye view in reasoning. And eventually leads to the paradoxical conclusion.
How about we consider "I exist" as valid evidence? As mentioned before, that means it is interpreting the statement by the physical person. In the case of the Doomsday Argument for example, "I exist" would suggest a greater number of humans.
But there is a missing link. Why update the belief about the world based on this particular physical person's existence? Why not do so based on someone else's existence/nonexistence?
For example, why say "Since [insert reader name] exists there are probably more observers than it seems?" instead of saying "Since Obama's son does not exist there are probably fewer observers?" What justifies this kind of special attention to that particular person?
The most intuitive response would be "Because I am that particular person". Of course, I shall give it special attention. But, this response is actually using the first-person meaning of "I". If one endorses this use, then "I exist" would always be true therefore cannot confirm any theory. Here it needs an explanation that can be used from a god's eye view instead of the first-person "I".
This is where SIA kicks in. It assumes the first person "I" is equivalent to the physical observer selected by random sampling. The sampling process is constructed so the sample's existence is evidence for more observers (e.g. a random sample from all potential observers). This makes the probability update using "I exist" as evidence feasible.
Consequently, this also means all the criticisms against SSA above - lack of rational backing, allows the interchanging use of the indexical and physical person, etc - also stand for SIA.
SSA and SIA's similarities matter far more than their discrepancies. The only difference is, SSA's sampling process is constructed so that it does not affect the assessment of "I exist" while SIA does. In a sense, SIA makes more errors yet it is more consistent. It applies to all probability operations while SSA only applies to parts. Yet substituting the first-person "I" with a random sample is where both mistakes lie.
Anthropic problems are special because they are formulated using specific first-person perspectives. (This is more obvious in the sleeping beauty problem. "when you wake up in the experiment". The awakening being questioned is identified by beauty's first-person experience with indexical concepts such as "now" or "today" instead of any objective measure) Using observer selection effects such as SSA or SIA to substitute the indexicals and solve it from a god's eye view is a misguided attempt due to habit. They shall be solved by thinking from that perspective in question. Doing so means there's no uncertainty such as "which observer is the first person I". The first person has no reference class nor can it be regarded as some random selection outcome.