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.
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.
[edited]
It could be, but Bostrom suggested stronger explanation: you spent more time in slower lanes.
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.