As you may know, my Full Nonindexical Conditioning (FNC) approach (see http://www.cs.utoronto.ca/~radford/anth.abstract.html) uses the third-person perspective for all inference, while emphasizing the principle that all available information should be used when doing inference. In everyday problems, a third-person approach is not distinguishable from a first-person approach, since we all have an enormous amount of perceptions, both internal and external, that are with very, very high probability not the same as those of any other person. This approach leads one to dismiss the Doomsday Argument as invalid, and to adopt the Thirder position for Sleeping Beauty.
You argue against approaches like FNC by denying that one should always condition on all available information. You give an example purporting to show that doing so is sometimes wrong. But your example is simply mistaken—you make an error somewhat analogous to that made by many people in the Monte Hall problem.
Here is your example (with paragraph breaks added for clarity):
Imagine you are on an exotic island where all families have two children. The island is having their traditional festival of boys’ day. On this day it is their custom for each family with a boy to raise a flag next to their door. Tradition also dictates in case someone knocks on the door then only a boy can answer. You notice about 3⁄4 of the families has raised a flag as expected. It should be obvious that if you randomly choose a family with flags then the probability of that family having two boys is 1⁄3. You also know if
you knock on the door a boy would come to answer it so by seeing him there is no new information.
But not so fast. When you see the boy you can ask him “are you the older or the younger child?”. Say he is the older one. Then it can be stated that the older child of the family is a boy. This is new information since I could not know that just by seeing the flag. If both children are boys then the conditional probability of the older kid being a boy is one. If only one child is a boy then the conditional probability of the older kid being a boy is only half. Therefore this new evidence favours the former. As a result the probability of this family having 2 boys can be calculated by bayesian updating to increase to be 1⁄2. If the child is the younger kid the same reason can still be applied due to symmetry. Therefore even before knocking on the door I should conclude the randomly chosen family’s probability of having 2 boys is 1⁄2 instead of 1⁄3.
This is absurd. This shows specifying the child base on ad hoc details is clearly wrong. For the same reason I should not specify today or this awakening by ad hoc details observed after waking up, such as the color of the paper.
Your mistake here is in asking the boy “are you the older or younger child?” and then reasoning as if an “older” answer to this question is the same as a “yes” answer to the question “is the older child in this family a boy?”.
If you actually ask a neighbor “is the older child in that family a boy?”, and get the answer “yes”, then it WOULD be correct to infer that the probability of the younger child also being a boy is 1⁄2. But you didn’t do that, or anything equivalent to that, as can be seen from the fact that the question you actually asked cannot possibly tell you that the older child is a girl.
The correct analysis is as follows. Before knowing anything about the family, there are four equally likely possibilities, which we can write as BB, BG, GB, GG, where the first B or G is the sex of the younger child, and the second is the sex of the older child. When you see the flag on the family’s house, the GG possibility is eliminated, leaving BB, BG, GB, all having probability 1⁄3. When a boy answers the door, the probabilities stay the same. After you ask whether the boy is the younger or older child, and get the answer “older”, the likelihood function over these three possibilities is 1⁄2, 0, 1, which when multiplied by 1⁄3, 1⁄3, 1⁄3 and renormalized gives probability 1⁄3 to BB and probability 2⁄3 to GB, with zero probability for BG (and GG). If instead the answer is “younger”, the result is probability 1⁄3 for BB and 2⁄3 for BG.
There is nothing odd or absurd here. Conditioning on all available information is always the right thing to do (though one can ignore information if one knows that conditioning on it won’t change the answer).
Professor Neal, first of all I want to thank you for your input in this discussion. I’m an U of T graduate from 2010, so getting a reply from you means a lot to me.
Of course I have read your paper on the FNC approach. As you said it treats all interference from a third-person perspective. I think we have a disagreement about why for everyday problem third-person and first-person perspectives do not cause a difference in answer. According to FNC approach it is because that we have enormous amount of details information available that there is another person with the same perception would be virtually impossible. So the answer from both perspectives should be extremely close or for all practical purposes: equal. I think the reason is because for everyday probability problems third-person identity is obvious and they are not related with questions of self-existence. The main differences between the two perspectives is that first-person identity is inherently obvious but third-person identity is not. Also from first-person perspective self-existence is a guaranteed observation while from third-person perspective no one’s existence is a guarantee. So for everyday problems none of these two points matters. So the reasoning from either perspectives would be the same. And we can arbitrarily switch perspectives without worrying about a change in the answer.
I completely agree with your analysis on the island problem. The example is trying to repeat the argument of Technicolor Beauty by Titelbaum yet arriving at an obviously incorrect answer. In fact when I was writing the example I was thinking about the Boy or Girl Paradox. But it makes perfect sense that it reminds others about the Monty Hall problem. Since from both problems the key to the answer is not about what information do we have but rather about how we got the information. As you have pointed out in the island problem the process of knowing the information “the older kid is a boy” was twisted and we get a wrong answer. In the Monty Hall problem the key is not the empty door shown but that the host knows which doors are empty and is selecting among those rather than just randomly selecting a door to show us. Yet in the technicolor argument the information available is conceptualized as an static description that “I am awake on a blue day.” without discussing how is that obtained. And that how is exactly where the paradox is at. If I treat me as a randomly selected individual from all actually exist individuals then seeing the color blue doesn’t really matter in calculation and we get halfer’s position. If I treat me as a randomly selected individual from all potential individuals then seeing blue matters and we get thirder’s position. It is only due to our habit of interpreting the language that the argument concludes thirders are correct. After all, if the color does not matter why purposely say I am awake on a blue day.
In my opinion FNC is definitely superior to SIA because it does not out right uses first-person identity in an otherwise third-person argument. However it still need an assumption about how all the details of perceptions are obtained from a third-person perspective. Because the same details and information functions differently in calculation depending on the process.
In my opinion we should always keep the perspectives separate. Then there is no assumption involved. The details I see in first-person that are not relevant to the coin toss would not need to be kept in mind in our calculation.
I’m not sure what you’re saying in this reply. I read your original post as using the island problem to try to demonstrate that there are situations in which using probabilities conditional on all the available information gives the wrong answer—that to get the right answer, you must instead ignore “ad hoc” information (though how you think you can tell which information is “ad hoc” isn’t clear to me). My reply was pointing out that this example is not correct—that if you do the analysis correctly, you do get the right answer when you use all the information. Hence your island problem does not provide a reason not to use FNC, or to dismiss the Technicolor Beauty argument.
In the Technicolor Beauty variation, the red and blue pieces of paper on the wall aren’t really necessary. Without any deliberate intervention, there will just naturally be numerous details of Beauty’s perceptions (both of the external world and of her internal thoughts and feeling) which will distinguish the days. Beauty should of course reason correctly given all this information, but I don’t see that there are any subtle aspects to “how” she obtains the information. She looks at the wall and sees a blue piece of paper. I assume show knows that the experimenter puts a red or blue piece of paper on the wall. What is supposed to be the issue that would make straightforward reasoning from this observation invalid?
I think we agreed that FNC reasons from a third-person perspective, which i would say SIA attempted to do so as well. From this perspective all clones are in indifferent positions. Of course from a clone’s first-person perspective the process of knowing the color was simply opening my eyes and saw a piece of blue paper. But from a third-person perspective, where no clone is inherently special, it remains a question of how come the details in discussion is from one particular clone’s observation rather than from any other (potential) clone’s. Here a process is missing explaining how is that clone chosen.
As you have pointed out in the island problem this process is crucial in the calculation. The fact of “older child is boy” can be the answer to the question of “Is this boy the younger or the older child” or “Is the older child a boy or a girl”. Different questions imply different processes of how the fact was learnt and the calculation would be different. The island problem assumed latter question thus used the wrong process and got the absurd answer. Similarly for the technicolor beauty problem that fact that “awake on blue day” can either be the answer to “what color was assigned to this day?” or “is there an awakening on the blue day?”. In the technicolor beauty argument the question was chosen to be the latter. There is no justification for this. With this question implies an imaginary process from the third-person perspective: from all days the blue day is specified, then it is checked to see if there is an awakening in it. This is the process SIA assumes in the first-place. Of course its conclusion would confirm thirder’s answer. So the technicolor beauty is just showing SIA would lead to a thirder conclusion, nothing more. In another word, only thirders should conclude the probability of heads to be 1⁄3 after considering the color of the paper. The argument attempts to show even if someone initially assigns equal probability to heads and tails he should update his answer to 1⁄3 after seeing the paper. It is incorrect. For example a supporter of SSA would say beauty after waking up must be in one of the three positions: 1H,1T, 2T (here the number of 1 or 2 means first or second day and H or T means heads or tails.), the respective probability according to SSA is 1⁄2, 1⁄4, 1⁄4. Regardless of which situation she’s in the likelihood of seeing blue would always be 1⁄2. So he would still conclude the probability of heads as 1⁄2. That is because according to SSA the process of learning about the blue paper (from third-person perspective) is different. Here an awakening is first chosen among all awakening(s) and the color of that day just turns out to be blue by chance. Applying technicolor beauty’s argument in this case and say he should update to 1⁄3 would be making the exact mistake the island problem did. In effect after considering the paper color thirders would still be thirders and halfers should remain halfers. Meaning the color is inconsequential to the problem.
I agree using all information available, though not necessary in most cases, would give the correct answer. But here the process of which clone’s detailed observation is chosen to be used in third-person argument, which is the key information to calculation, is assumed. Then it is no longer safe to say FNC must be correct. In my opinion the supposed missing process is trying to link first-person and third-person perspectives. The link would cause perspective inconsistency thus there should be no such process to begin with. The perspectives should just be kept separate.
As for the so called “Ad hoc” information it’s my mistake to just use made up terms and not defining them. When we deal with everyday problems there are always some detailed information with no effect one the answer that we automatically ignore them in the calculation. These are details that are not related to the subject matter at hand, eg being the older kid has no effect on the sex of the child; and played no part in the process of how we get to know relevant evidences, e.g. being the older kid does not change the chance of him coming to the door. These are what I refer to as Ad-hoc informations because they cannot be pre-specified in an observation. As in the island problem the kid at the door just happens to be the older one. If I was predetermined to meet the older child then I have to use this info and specify him as such in the calculation and the answer should then be rightly half. Other example of Ad-hoc information could include how does the boy look, what is he wearing, which day of the week was he born in or any other detailed information you can get about him. I think it is best practice if we just ignore these. As using these info to specify the boy in front of you would lead to mistakes in calculation. But as you have shown in the first reply they can be used if we pay attention to the process of how are these information learnt (or what questions does these details answer). So I am mistaken to say these info cannot be used. Just that correctly using these information would not make any changes to the answer.
I think I can put more structure into my argument comparing the island problem to technicolor beauty.
The Island Problem
While the statement “the older child is a boy” is factually true it can be learnt by two different processes.
Process 1:
First a boy is specified among all boy(s). One can ask: “is this boy the younger or the older child?”. Then it found out that he is actually the older.
Process 2:
First the older child is specified among all children. One can ask: “is the older child a boy or a girl?”. Then it found out that the older child is actually a boy.
As you have pointed out in the first reply the correct process is Process 1. However in the island problem the calculation was done according to Process 2. That is why its answer is wrong.
The Technicolor Problem
While the statement “I’m awake on a blue day” is factually true it can also be learnt by two different processes.
Process 1:
First an awakening is specified among all awakening(s). One can ask: “is this awakening a blue or a red awakening?” As beauty opens her eyes it is found out that it’s the blue one.
Process 2:
First the blue day is specified among all days. One can ask “is there an awakening on the blue day?”. Then it is found out that there is indeed an awakening on the blue day.
Technicolor beauty used Process 2 in its calculation without any justification. To me Process 1 is describing what actually took place. Before opening my eyes, I can ask “is this awakening red or blue?” and expect to find the answer after opening my eyes. I cannot ask “is there an awakening on the blue day?” and expect to find an answer. What if the paper turns out to be red? Shall I retrospectively change the question to ask about the red day instead?
To me the justification would be treating today as a randomly chosen day among the two days. Then Process 2 would be the correct description. However that is exactly what SIA assumes in the first place. SIA would lead to thirder’s answer regardless if there are papers involved. People thinking the coin fell with equal chance would disagree and say Process 1 is the correct one to use. Using which their probability, even after considering the papers, would still remain at half. So the added detail of different colors would be inconsequential to the problem after all.
I can sort of see what you’re getting at here, but to me needing to ask “what question was being asked?” in order to do a correct analysis is really a special case of the need to condition on all information. When we know “the older child in that family is a boy”, we shouldn’t condition on just that fact when we actually know more, such as “I asked a neighbour whether the older child is a boy or girl, and they said ‘a boy’”, or “I encountered a boy in the family and asked if they were the older one, and they said ‘yes’”. Both these more detailed descriptions of what happened imply (assuming truthfulness) that the older child is a boy, but they contain more information than that statement alone, so it is necessary to condition on that information too.
For Technicolor Beauty, the statement (from Beauty’s perspective) “I woke up and saw a blue piece of paper” is not the complete description. She actually knows sometime like “I woke up, felt a bit hungry, with an itch in my toe, opened my eyes, and saw a fly crawling down the wall over a blue piece of paper, which fluttered at bit because the air conditioning was running, and I remembered that the air duct is above that place, though I can’t see it behind the light fixture that I can see there, etc.”. I argue that she should then condition on the fact that somebody has those perceptions and memories, which can be seen as a third-person perspective fact, though in ordinary life (not strange thought experiments involving AIs, or vast cosmological theories) this is equivalent to a first-person perspective fact. So one doesn’t get different answers from different perspectives, and one needn’t somehow justify disagreeing with a friend’s beliefs, despite having identical information.
I see what you mean. I agree that we know more than just “the older child of the family is a boy”. The “more” would be the process of how I come to know it. To me what’s special about the island problem is that when trying to express what I know into a simply statement such as “the older child is a boy” any information about the process is lost. Therefore it left us with an ambiguity about the process thats up to interpretation. This is exactly what happens in the Boy or Girl paradox as well. If there is any lesson then it should be conditioning on a statement such as “someone with all those detailed perception and memory exists” is a rather delicate matter. Is this someone specified first and then all the details about her explored? Or is all these details spelled out first and someone with these details was found to be exist? SSA and SIA would give different answers from a third-person perspective. But from first-person perspective the process is clear. It is the former. That someone is specified based on immediacy to perception, i.e. that someone is this one. And then all the details about me are found out though my experience. Therefore the perspective consistency argument would not change its answer basing on any details observed after waking up.
As for the disagreement, more preciously the “agree to disagree”, between friends while in communication. I’m aware it is a rather peculiar case. SIA and FNC would not result in that which can certainly be used as a argument favouring them. But in my opinion it can be quite simply explained by perspective differences. Of course basing on my experience with paradoxes relating to anthropic reasoning, nothing is simple. So I understand if others find it hard to accept.
What I mean by “someone with those memories exists” is just that there exists a being who has those memories, not that I in particular have those memories. That’s the “non-indexical” part of FNC. Of course, in ordinary life, as ordinarily thought of, there’s no real difference, since no one but me has those memories.
I agree that one could imagine conditioning on the additional piece of “information” that it’s me that has those memories, if one can actually make sense of what that means. But one of the points of my FNC paper is that this additional step is not necessary for any ordinary reasoning task, so to say it’s necessary for something like evaluating cosmological theories is rather speculative. (In contrast, some people seem to think that SSA is just a simple extension of the need to account for sampling bias when reasoning about ordinary situations, which I think is not correct.)
SSA conditions on more “information” than that an observer with your observations exists; specifically, it conditions on the fact that a randomly selected observer has your observations, which automatically implies that an observer with your observations exists. (I put “information” in quotes because this is only information if you accept something like SSA)
As you may know, my Full Nonindexical Conditioning (FNC) approach (see http://www.cs.utoronto.ca/~radford/anth.abstract.html) uses the third-person perspective for all inference, while emphasizing the principle that all available information should be used when doing inference. In everyday problems, a third-person approach is not distinguishable from a first-person approach, since we all have an enormous amount of perceptions, both internal and external, that are with very, very high probability not the same as those of any other person. This approach leads one to dismiss the Doomsday Argument as invalid, and to adopt the Thirder position for Sleeping Beauty.
You argue against approaches like FNC by denying that one should always condition on all available information. You give an example purporting to show that doing so is sometimes wrong. But your example is simply mistaken—you make an error somewhat analogous to that made by many people in the Monte Hall problem.
Here is your example (with paragraph breaks added for clarity):
Imagine you are on an exotic island where all families have two children. The island is having their traditional festival of boys’ day. On this day it is their custom for each family with a boy to raise a flag next to their door. Tradition also dictates in case someone knocks on the door then only a boy can answer. You notice about 3⁄4 of the families has raised a flag as expected. It should be obvious that if you randomly choose a family with flags then the probability of that family having two boys is 1⁄3. You also know if
you knock on the door a boy would come to answer it so by seeing him there is no new information.
But not so fast. When you see the boy you can ask him “are you the older or the younger child?”. Say he is the older one. Then it can be stated that the older child of the family is a boy. This is new information since I could not know that just by seeing the flag. If both children are boys then the conditional probability of the older kid being a boy is one. If only one child is a boy then the conditional probability of the older kid being a boy is only half. Therefore this new evidence favours the former. As a result the probability of this family having 2 boys can be calculated by bayesian updating to increase to be 1⁄2. If the child is the younger kid the same reason can still be applied due to symmetry. Therefore even before knocking on the door I should conclude the randomly chosen family’s probability of having 2 boys is 1⁄2 instead of 1⁄3.
This is absurd. This shows specifying the child base on ad hoc details is clearly wrong. For the same reason I should not specify today or this awakening by ad hoc details observed after waking up, such as the color of the paper.
Your mistake here is in asking the boy “are you the older or younger child?” and then reasoning as if an “older” answer to this question is the same as a “yes” answer to the question “is the older child in this family a boy?”.
If you actually ask a neighbor “is the older child in that family a boy?”, and get the answer “yes”, then it WOULD be correct to infer that the probability of the younger child also being a boy is 1⁄2. But you didn’t do that, or anything equivalent to that, as can be seen from the fact that the question you actually asked cannot possibly tell you that the older child is a girl.
The correct analysis is as follows. Before knowing anything about the family, there are four equally likely possibilities, which we can write as BB, BG, GB, GG, where the first B or G is the sex of the younger child, and the second is the sex of the older child. When you see the flag on the family’s house, the GG possibility is eliminated, leaving BB, BG, GB, all having probability 1⁄3. When a boy answers the door, the probabilities stay the same. After you ask whether the boy is the younger or older child, and get the answer “older”, the likelihood function over these three possibilities is 1⁄2, 0, 1, which when multiplied by 1⁄3, 1⁄3, 1⁄3 and renormalized gives probability 1⁄3 to BB and probability 2⁄3 to GB, with zero probability for BG (and GG). If instead the answer is “younger”, the result is probability 1⁄3 for BB and 2⁄3 for BG.
There is nothing odd or absurd here. Conditioning on all available information is always the right thing to do (though one can ignore information if one knows that conditioning on it won’t change the answer).
Professor Neal, first of all I want to thank you for your input in this discussion. I’m an U of T graduate from 2010, so getting a reply from you means a lot to me.
Of course I have read your paper on the FNC approach. As you said it treats all interference from a third-person perspective. I think we have a disagreement about why for everyday problem third-person and first-person perspectives do not cause a difference in answer. According to FNC approach it is because that we have enormous amount of details information available that there is another person with the same perception would be virtually impossible. So the answer from both perspectives should be extremely close or for all practical purposes: equal. I think the reason is because for everyday probability problems third-person identity is obvious and they are not related with questions of self-existence. The main differences between the two perspectives is that first-person identity is inherently obvious but third-person identity is not. Also from first-person perspective self-existence is a guaranteed observation while from third-person perspective no one’s existence is a guarantee. So for everyday problems none of these two points matters. So the reasoning from either perspectives would be the same. And we can arbitrarily switch perspectives without worrying about a change in the answer.
I completely agree with your analysis on the island problem. The example is trying to repeat the argument of Technicolor Beauty by Titelbaum yet arriving at an obviously incorrect answer. In fact when I was writing the example I was thinking about the Boy or Girl Paradox. But it makes perfect sense that it reminds others about the Monty Hall problem. Since from both problems the key to the answer is not about what information do we have but rather about how we got the information. As you have pointed out in the island problem the process of knowing the information “the older kid is a boy” was twisted and we get a wrong answer. In the Monty Hall problem the key is not the empty door shown but that the host knows which doors are empty and is selecting among those rather than just randomly selecting a door to show us. Yet in the technicolor argument the information available is conceptualized as an static description that “I am awake on a blue day.” without discussing how is that obtained. And that how is exactly where the paradox is at. If I treat me as a randomly selected individual from all actually exist individuals then seeing the color blue doesn’t really matter in calculation and we get halfer’s position. If I treat me as a randomly selected individual from all potential individuals then seeing blue matters and we get thirder’s position. It is only due to our habit of interpreting the language that the argument concludes thirders are correct. After all, if the color does not matter why purposely say I am awake on a blue day.
In my opinion FNC is definitely superior to SIA because it does not out right uses first-person identity in an otherwise third-person argument. However it still need an assumption about how all the details of perceptions are obtained from a third-person perspective. Because the same details and information functions differently in calculation depending on the process.
In my opinion we should always keep the perspectives separate. Then there is no assumption involved. The details I see in first-person that are not relevant to the coin toss would not need to be kept in mind in our calculation.
I’m not sure what you’re saying in this reply. I read your original post as using the island problem to try to demonstrate that there are situations in which using probabilities conditional on all the available information gives the wrong answer—that to get the right answer, you must instead ignore “ad hoc” information (though how you think you can tell which information is “ad hoc” isn’t clear to me). My reply was pointing out that this example is not correct—that if you do the analysis correctly, you do get the right answer when you use all the information. Hence your island problem does not provide a reason not to use FNC, or to dismiss the Technicolor Beauty argument.
In the Technicolor Beauty variation, the red and blue pieces of paper on the wall aren’t really necessary. Without any deliberate intervention, there will just naturally be numerous details of Beauty’s perceptions (both of the external world and of her internal thoughts and feeling) which will distinguish the days. Beauty should of course reason correctly given all this information, but I don’t see that there are any subtle aspects to “how” she obtains the information. She looks at the wall and sees a blue piece of paper. I assume show knows that the experimenter puts a red or blue piece of paper on the wall. What is supposed to be the issue that would make straightforward reasoning from this observation invalid?
I think we agreed that FNC reasons from a third-person perspective, which i would say SIA attempted to do so as well. From this perspective all clones are in indifferent positions. Of course from a clone’s first-person perspective the process of knowing the color was simply opening my eyes and saw a piece of blue paper. But from a third-person perspective, where no clone is inherently special, it remains a question of how come the details in discussion is from one particular clone’s observation rather than from any other (potential) clone’s. Here a process is missing explaining how is that clone chosen.
As you have pointed out in the island problem this process is crucial in the calculation. The fact of “older child is boy” can be the answer to the question of “Is this boy the younger or the older child” or “Is the older child a boy or a girl”. Different questions imply different processes of how the fact was learnt and the calculation would be different. The island problem assumed latter question thus used the wrong process and got the absurd answer. Similarly for the technicolor beauty problem that fact that “awake on blue day” can either be the answer to “what color was assigned to this day?” or “is there an awakening on the blue day?”. In the technicolor beauty argument the question was chosen to be the latter. There is no justification for this. With this question implies an imaginary process from the third-person perspective: from all days the blue day is specified, then it is checked to see if there is an awakening in it. This is the process SIA assumes in the first-place. Of course its conclusion would confirm thirder’s answer. So the technicolor beauty is just showing SIA would lead to a thirder conclusion, nothing more. In another word, only thirders should conclude the probability of heads to be 1⁄3 after considering the color of the paper. The argument attempts to show even if someone initially assigns equal probability to heads and tails he should update his answer to 1⁄3 after seeing the paper. It is incorrect. For example a supporter of SSA would say beauty after waking up must be in one of the three positions: 1H,1T, 2T (here the number of 1 or 2 means first or second day and H or T means heads or tails.), the respective probability according to SSA is 1⁄2, 1⁄4, 1⁄4. Regardless of which situation she’s in the likelihood of seeing blue would always be 1⁄2. So he would still conclude the probability of heads as 1⁄2. That is because according to SSA the process of learning about the blue paper (from third-person perspective) is different. Here an awakening is first chosen among all awakening(s) and the color of that day just turns out to be blue by chance. Applying technicolor beauty’s argument in this case and say he should update to 1⁄3 would be making the exact mistake the island problem did. In effect after considering the paper color thirders would still be thirders and halfers should remain halfers. Meaning the color is inconsequential to the problem.
I agree using all information available, though not necessary in most cases, would give the correct answer. But here the process of which clone’s detailed observation is chosen to be used in third-person argument, which is the key information to calculation, is assumed. Then it is no longer safe to say FNC must be correct. In my opinion the supposed missing process is trying to link first-person and third-person perspectives. The link would cause perspective inconsistency thus there should be no such process to begin with. The perspectives should just be kept separate.
As for the so called “Ad hoc” information it’s my mistake to just use made up terms and not defining them. When we deal with everyday problems there are always some detailed information with no effect one the answer that we automatically ignore them in the calculation. These are details that are not related to the subject matter at hand, eg being the older kid has no effect on the sex of the child; and played no part in the process of how we get to know relevant evidences, e.g. being the older kid does not change the chance of him coming to the door. These are what I refer to as Ad-hoc informations because they cannot be pre-specified in an observation. As in the island problem the kid at the door just happens to be the older one. If I was predetermined to meet the older child then I have to use this info and specify him as such in the calculation and the answer should then be rightly half. Other example of Ad-hoc information could include how does the boy look, what is he wearing, which day of the week was he born in or any other detailed information you can get about him. I think it is best practice if we just ignore these. As using these info to specify the boy in front of you would lead to mistakes in calculation. But as you have shown in the first reply they can be used if we pay attention to the process of how are these information learnt (or what questions does these details answer). So I am mistaken to say these info cannot be used. Just that correctly using these information would not make any changes to the answer.
I think I can put more structure into my argument comparing the island problem to technicolor beauty.
The Island Problem
While the statement “the older child is a boy” is factually true it can be learnt by two different processes.
Process 1:
First a boy is specified among all boy(s). One can ask: “is this boy the younger or the older child?”. Then it found out that he is actually the older.
Process 2:
First the older child is specified among all children. One can ask: “is the older child a boy or a girl?”. Then it found out that the older child is actually a boy.
As you have pointed out in the first reply the correct process is Process 1. However in the island problem the calculation was done according to Process 2. That is why its answer is wrong.
The Technicolor Problem
While the statement “I’m awake on a blue day” is factually true it can also be learnt by two different processes.
Process 1:
First an awakening is specified among all awakening(s). One can ask: “is this awakening a blue or a red awakening?” As beauty opens her eyes it is found out that it’s the blue one.
Process 2:
First the blue day is specified among all days. One can ask “is there an awakening on the blue day?”. Then it is found out that there is indeed an awakening on the blue day.
Technicolor beauty used Process 2 in its calculation without any justification. To me Process 1 is describing what actually took place. Before opening my eyes, I can ask “is this awakening red or blue?” and expect to find the answer after opening my eyes. I cannot ask “is there an awakening on the blue day?” and expect to find an answer. What if the paper turns out to be red? Shall I retrospectively change the question to ask about the red day instead?
To me the justification would be treating today as a randomly chosen day among the two days. Then Process 2 would be the correct description. However that is exactly what SIA assumes in the first place. SIA would lead to thirder’s answer regardless if there are papers involved. People thinking the coin fell with equal chance would disagree and say Process 1 is the correct one to use. Using which their probability, even after considering the papers, would still remain at half. So the added detail of different colors would be inconsequential to the problem after all.
I can sort of see what you’re getting at here, but to me needing to ask “what question was being asked?” in order to do a correct analysis is really a special case of the need to condition on all information. When we know “the older child in that family is a boy”, we shouldn’t condition on just that fact when we actually know more, such as “I asked a neighbour whether the older child is a boy or girl, and they said ‘a boy’”, or “I encountered a boy in the family and asked if they were the older one, and they said ‘yes’”. Both these more detailed descriptions of what happened imply (assuming truthfulness) that the older child is a boy, but they contain more information than that statement alone, so it is necessary to condition on that information too.
For Technicolor Beauty, the statement (from Beauty’s perspective) “I woke up and saw a blue piece of paper” is not the complete description. She actually knows sometime like “I woke up, felt a bit hungry, with an itch in my toe, opened my eyes, and saw a fly crawling down the wall over a blue piece of paper, which fluttered at bit because the air conditioning was running, and I remembered that the air duct is above that place, though I can’t see it behind the light fixture that I can see there, etc.”. I argue that she should then condition on the fact that somebody has those perceptions and memories, which can be seen as a third-person perspective fact, though in ordinary life (not strange thought experiments involving AIs, or vast cosmological theories) this is equivalent to a first-person perspective fact. So one doesn’t get different answers from different perspectives, and one needn’t somehow justify disagreeing with a friend’s beliefs, despite having identical information.
I see what you mean. I agree that we know more than just “the older child of the family is a boy”. The “more” would be the process of how I come to know it. To me what’s special about the island problem is that when trying to express what I know into a simply statement such as “the older child is a boy” any information about the process is lost. Therefore it left us with an ambiguity about the process thats up to interpretation. This is exactly what happens in the Boy or Girl paradox as well. If there is any lesson then it should be conditioning on a statement such as “someone with all those detailed perception and memory exists” is a rather delicate matter. Is this someone specified first and then all the details about her explored? Or is all these details spelled out first and someone with these details was found to be exist? SSA and SIA would give different answers from a third-person perspective. But from first-person perspective the process is clear. It is the former. That someone is specified based on immediacy to perception, i.e. that someone is this one. And then all the details about me are found out though my experience. Therefore the perspective consistency argument would not change its answer basing on any details observed after waking up.
As for the disagreement, more preciously the “agree to disagree”, between friends while in communication. I’m aware it is a rather peculiar case. SIA and FNC would not result in that which can certainly be used as a argument favouring them. But in my opinion it can be quite simply explained by perspective differences. Of course basing on my experience with paradoxes relating to anthropic reasoning, nothing is simple. So I understand if others find it hard to accept.
What I mean by “someone with those memories exists” is just that there exists a being who has those memories, not that I in particular have those memories. That’s the “non-indexical” part of FNC. Of course, in ordinary life, as ordinarily thought of, there’s no real difference, since no one but me has those memories.
I agree that one could imagine conditioning on the additional piece of “information” that it’s me that has those memories, if one can actually make sense of what that means. But one of the points of my FNC paper is that this additional step is not necessary for any ordinary reasoning task, so to say it’s necessary for something like evaluating cosmological theories is rather speculative. (In contrast, some people seem to think that SSA is just a simple extension of the need to account for sampling bias when reasoning about ordinary situations, which I think is not correct.)
SSA conditions on more “information” than that an observer with your observations exists; specifically, it conditions on the fact that a randomly selected observer has your observations, which automatically implies that an observer with your observations exists. (I put “information” in quotes because this is only information if you accept something like SSA)