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)
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)