Sorry for the slow reply as well. For some reason replies from this thread is not showing up in my notifications.
If I say “I’m a man” then it is definitely true and meaningful as the body most immediate to my perception is of a human male. To my wife the same statement is obviously false since she is a woman. It is rather trivial if the subject “I” is defined by a first-person perspective’s center then the statement may not be valid once switched to someone else’s perspective. Of course in real life if I say “I’m a man” my wife would (hopefully) agree. She maybe interpreting the sentence as “My husband is a man”. However “my husband” is still defined by her perspective and the sentence might be invalid to others (e.g. I do not have a husband). Or we can employ a third-person’s perspective and reason as an impartial outsider. The statement may become “Dadadarren is a man.” Here “The person named Dadadarren” is not defined by any perspective center. Notice the name must be used to specify me in third person because for a impartial outsider I am just an ordinary person like everybody else. There is no self apparent “I” anymore. So some feature must be used to specify me among all persons. My argument is that a logic framework must be fully contained within one perspective. E.g. if we use my perspective center to define “I” then we cannot switch to an outsider’s third-person perspective just as we cannot switch to my wife’s perspective. Consequently if my first-person center is used then we are no longer treating every person as ordinary, or belongs to the same reference class, since I’m inherently different from everybody else in this reasoning
First-person perspective center can be used to define not only “I” but also other concepts such as “this”, “here”, “now” and subsequently “today”.
With the above in mind let’s get back to “Today is Tuesday.” As my previous reply had said, my argument is Not that “Today’s Tuesday” is invalid. It is a perfectly meaningful and valid statement. It can be fully understood from the first person perspective just like the statement “I’m a man.” It could simply means on the day that is most immediate to my perception, aka “today”, the calendar says Tuesday. We can also take an outsider’s perspective and change “today” to a day defined by some feature/event. E.g. if the experimenter randomly assigns the color of the wallpaper to be red or blue during the two days in the experiment then “The red day is Tuesday” may also be a valid statement just like “The person named Dadadarren is a man.” I’m arguing that “the probability of today being Monday/Tuesday” is invalid in the setup of the Sleeping Beauty Problem. It’s asking out of the two possible awakenings which is THIS one? “This awakening” or “today’s awakening” is defined by first-person perspective center. But the questions also treats the two awakenings as elements in the same reference class as a third-person would. The question itself involves a perspective switch. It is essentially asking in the eyes of an outside observer which one is my first-person perspective center. Where from a third-person perspective an awakening must be specified by some feature (e.g. the red awakening) since there is no self-apparent “today” or “this awakening”.
It may help to clarify my argument a bit to think about this example. Imagine you are cloned during your sleep last night. The clone is highly accurate and retains your memory well enough such that the clone could not tell he is the new copy. After waking up I argue the question of “The probability of me being the clone/original” is invalid. If the two copies are randomly put into either a red or a blue room. It would be valid to ask “The probability of the copy in the red room being the clone/original.” Since this question is entirely from a third-person perspective (it doesn’t treat one copy as inherently unique “I” as a result has to specify a copy by its feature).
I also want to clarify that I am not arguing “The probability of today being Tuesday”is invalid simply because of its wording. For example, imagine you are put to sleep on Sunday and the experimenters toss a coin. If it lands head they will inject you with a drug that would make you sleep though Monday and wake up Tuesday morning. Otherwise you would wake up on Monday as usual. In this problem when you wake up “the probability of today being Monday/Tuesday” is perfectly valid. The two possibilities reflects the two outcomes of a coin toss. Which can be well understood from a first-person perspective. Compare it to me being clone/original, or “today being Monday/Tuesday” in the sleeping beauty problem, where a third-person perspective is needed to comprehend the possibilities as elements in the same reference class.
I’m not arguing for a communal consciousness among sleeping beauties. In fact it can be said I argue the exact opposite. So it worries me how I gave you that impression. To me consciousness among the awakenings or among different clones are definitely distinct. Or in your words every beauty is a complete person. That’s the reason why there is a self apparent “I” from first-person perspective even without knowing any objective difference between me and others. Whereas from a third-person perspective nobody’s consciousness is inherently unique. So it is better to just ignore consciousness altogether as it is unobservable and unmeasurable to anyone except the first-person anyway.
Hello Jeff. Good seeing you again. Happy new year.
A typical thirder argument follows the Self-Indication Assumption. That this awakening should be regarded as being randomly selected from one of the three possible awakenings. One awakening for Monday-Heads, one for Monday-Tails and another for Tuesday-Tails. The way I understand what your experiment does is, very cleverly, using actually existing participants to represent these possibilities. I.e. today, out of the three awaking participants two of witch would be awake on both days and one would be awake on one day only. So my argument against you is the same as my argument against SIA (or SSA as a matter of fact): in the same logical framework it is wrong to use terms such as [today] or [myself] as self-explanatory concepts while also treat them as in the same reference class of all days and all people. Because [now] or [I] is only meaningful if reasoning from a first-person perspective for they are inherently unique to oneself. If they are treated as unique then it is logically inconsistent to treat them as ordinary time or people. Even though they might be ordinary by objective measures, i.e. in the same reference class as other time and people from a third-person perspective/uncentered reasoning. More specifically applying to your argument, I disagree with assertion C. Just because there are three people awake today does not mean I should regard myself as randomly selected among those three or as if today is randomly selected among Monday or Tuesday.
In this question Monday and Tuesday are not indexical. They are defined by a calendar which could be interpreted as defined by the relative positions of planetary bodies. In this sense the dates are defined by objective events. They can be treated as ordinary compare to one another from a third-person perspective. What is indexical is rather the concept of [today]. Which require a perspective center (first-person) to define. My argument is that first-person and third-person reasoning (or centered and uncentered reasoning) should not be mixed together in the same logic.
Hi, I’ve read your paper on anthropic decision theory. Personally I think that it givens the most complete explaination to bets and decisions related to paradoxes such as sleeping beauty problem. I cited it in my paper and recommended it whenever a discussion about bets in sleeping beauty problem comes up. That being said I feel tackling the anthropic paradoxes as purely decision making problems is very counter-intuitive.
Take the Doomsday argument for example. The explanation you provided here illustrates why someone would bet heavily in favour of doom soon given the reward setup, even when he do not assign a higher probability to it. That his objective is to max average utility. However that seems to be different from what the original doomsday argument is about. In its original form it demonstrates a Bayesian update on my birth rank would shift the probability towards doom soon. My preference towards average or total utility plays no part in its logic. So there is a distinction between actually believing in doom soon and strategically betting on doom soon base on some utility objective. Base on this I think we cannot bypass the probabilities and only discuss decision making in anthropic related paradoxes.
This should have gotten much more attention. I actually find it a crucial part for paradoxes related to anthropic reasoning e.g. sleeping beauty problems, doomsday argument etc. For halfers these disagreement actually happens quite often in anthropic related problems. My opinion is that the disagreement is valid and does not actually violate Aumann’s theorem. However I am against SSA as well as SIA.
Consider this experiment. An alien has abducted you and one of your friends. You are put to sleep. The alien then tosses a fair coin. If it lands on heads it won’t do anything to you. If it lands on tails it will clone you and put the clone into another identical room. The clone process is highly accurate so that the memory is retained. As a result the clone, as well as the original, can not tell if he is old or new. Meanwhile your friend never goes though any cloning process. After waking you up the alien let your friend choose one of the two rooms to enter. Suppose your friend has chosen your room. As a result you guys meet each other inside. How should you reason about the probability of the coin toss? How should your friend reason it?
For my friend the question is non-anthropic thus very simple. If the coin landed heads then 1 out of the 2 rooms would be empty. If the coin landed tails then both rooms would be occupied. Because the room that she randomly chose is occupied she now has new evidence favouring tails. As a result the probability of heads can be calculate by a simply bayesian update to be 1⁄3.
For halfers the question is not too complicated either. After waking up I have no new evidence about the fair coin toss. So I ought to believe the probability of heads is 1⁄2. Because my friend is randomly choosing between two rooms, regardless of the coin toss result the probability of my room being chosen is always half. Therefore seeing my friend gives me no new information about the coin toss either. This means I should keep believing that the probability of heads to be 1⁄2.
Here the disagreement is apparent. Even though the two of us appear to have the same information about the coin toss we assign different probability to the same proposition. To make the matter more interesting nothing I could say would change her mind and vice versa. We can communicate however we like but nobody is going to revise their answer. This may seem strange but it is completely justified. The cause of this disagreement is our different interpretations of who is exactly in this meeting. Remember according to my friends’ reasoning the evidence that causes the probability update is “the chosen room is occupied.” The occupant, in case there are duplicates, could not be specified from her perspective. In other words, as long as there is someone in the room she will reason as such. This is expected since the cloning procedure is highly accurate so there is no objective feature relevant to the coin toss to differentiate each duplicate. However from my first-person perspective I can inherently specify the one whom she is in meeting with. It is me, myself. But this specification is only valid from first-perspective. First-person identity is based on the immediacy to perception, which is primitive. Because perception is imperceivable by others this means my specification is incommunicable. I can keep telling her “this is me” and it would not mean anything to her. As a result the two of us would keep our own answers and remain in disagreement
This disagreement is also valid with a frequentist interpretation, which in my opinion is also easier to understand. The experiment can be repeated many times and the relative frequency can be used to show the correct probability. From my perspective repeating the experiment simply involves me going back to sleep, and wake up again after a coin toss and the potential cloning process. Of course after waking up I may not be the same physical human being just as the case of the first experiment. But this does not matter because in first-person perspective I am defined primitively base on subjective identity instead of objective features or qualities. So I would always regard the one falling asleep on the previous night as part of my subjective
persistent self since it was the center of my perception and my current subjective experience is a continuation of it. To make the procedure easier suppose I can check the previous coin toss result before goingback to sleep again. So each iteration can be summarize as to go to sleep, wake up, and check the coin. Imagine repeating this iteration 1000 times by my count. I would have experienced about 500 heads and tails each. Furthermore if my friend is involved then I would see her about 500 times with about equal number of occurrences after heads or tails. However for these 1000 coin tosses my friend would see an occupied room about 750 times. The extra 250 times would be due to seeing the other duplicate instead of me after tails. It is easy to see our relative frequency of heads with a meeting are indeed different, half for me, a third for her. Of course my friend should be involved in far more repetitions than I do since every duplication of me are indifferent from her perspective so she shall be involved with their repetitions as well. However her relative frequency would remain unchanged by the higher number of iterations.
The disagreement arises because for my friend meeting someone in the room is technically not the same event for me meeting her. This is quite clearly so once the experiment is repeated a large number of times as discussed above. Her seeing someone in the room contains more experiments than me meeting her (750 vs 500). So we are actually assigning probability to different events. In my opinion this means it does not technically violate the theorem. Even though it may seems so superficially.
I appreciate the insight. Something I want to clarify. Point 1,2,3 are not new assumptions but rather derived from the notion that reasonings from different perspectives should not mix. The complete deduction is explained in the pdf. It is quite lengthy so I will try to summarize it at the risk of oversimplifying.
Point 1 for example, when woke up in the experiment, from beauty’s first-person perspective the information available is “I am awake today”. Here “today” is a valid specification of the time since it is from first-person perspective. However from first-person perspective finding oneself awake is a guarantee. So there is no new info. Beauty can also reason from third-person perspective (e.g. by imagine how would an outside observer assign probability with the available info). Here beauty being awake is not a guarantee but “today” is no longer a valid specification of time. So the only info available is “beauty is awake on an unspecific day” i.e. “there is at least one awakening”. There’s no new info either. That’s why “No matter which perspective one choose to reason from there is no new information when beauty wakes up.” Only if we mix the two perspectives together: treating beauty awake as a surprise AND treat “today” as a specific day, then new information can be argued.
For point 2. My argument is not that today being Monday is an invalid observation. I’m arguing if you treat one of the days as inherently special then you should no longer treat the twos potential days as equals. Even though “today” is inherently special from first-person perspective and the two days are ordinary like one another from third-person perspective. To comprehend “the probability of today being Monday” requires one to do both. It uses “today” as one specified day, and it treats Monday and Tuesday as two parallel outcomes in the sample space. This is discussed in section 5 in detail. I also explained in length the difference between such probabilities and probabilities of random experiments such as your example of coin toss. One thing to point out: there is no random experiment deciding if “today” is Monday or Tuesday (or if the duplicated instances are created by memory retained cloning, there is nothing determining if “I” am the original or the clone). So the uncertainty cannot be solely explained from first-person perspective. I really wish if you are interested then give it a look. I look forward to you counter argument.
Point 3 is just a natural following of point 1 and 2. Since there’s no such thing as “the probability of today being Monday/Tuesday”. Then after being told it’s Monday keeping the probability of heads unchanged at 1⁄2 does not violate extant bayesian updating rules.
Also my frequentist argument for 1⁄2 (point 4) is not contained in point 1,2 and 3. To my knowledge it is entirely new. The key is that, considering the importance of a consistent perspective, the repetitions should not be chronologically linear. It should be a nested structure. That is: i.e. using memory wipes, the first level separate the duration of the experiment into two halves, the next level separate each resulting segment into two halves again, so on and so forth. It would be in a form similar to a supertask. Even if the experiment is repeated near infinite number of times it would still have to happen within two days. From beauty’s first-person perspective as the number of repetitions increases, note all these repetitions do not pass though any memory wipe, the relative frequency would approach 1⁄2. (this is discussed in detail in section 3 with betting arguments follows)
As for your betting argument. Forgive my bluntness, it is a common argument for the thirders’ side. Betting argument have the problem of too many underlying assumptions involved. E.g. beauty’s motive, accounting rule, how many bets offered per toss etc. This causes halfers and thirders have little common ground in discussion so they are rarely effective at persuading the opposition. As expected there are many things I do not agree with the argument you presented. However I only wish to point out one thing: only considering the outsider’s view is not enough. An outsider could be in direct communication with beauty and they should still assign different probability to heads. Even with bets involved. This is what I meant by point 6. It is discussed in detail in section 4.
In hindsight I should probably make clear the point forms are not my assumptions but notable conclusions of my argument. They were intended to spark some interest for the pdf. Sorry for any confusion.
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.
At this point I feel any further attempt to explain my position would be at the risk of repeating my previous arguments. The frustration is real because I think my idea is actually very simple. I’m having a bit of struggle to express it. From your reply I feel like we are not exactly engaging each other’s argument on the same page. There must be something fundamental that the two of us are not having the same definition yet we don’t realize. So I will get back to what I meant by first-person and third-person perspective as well as their differences. Maybe that way my reason of why some of the questions being invalid would be a little bit obvious to understand.
First-person perspective to me is the realization that my reasoning is based on my consciousness and perception. One of its perk is self identification based on subjective closeness to perception, which do not need any information. E.g. Twins do not need to know the objective differences between the two to tell themselves apart. For anybody else differences must be used to specify one among the pair (like older vs the younger). A question is perspectively consistent if it can be fully interpreted by one of the perspectives. For everyday probability questions, either perspective would do the job. For example, if you (I assume Jessica) and a guy called Darren are in a experiment where a fair coin is tosses. If heads then only one of the two would be waken up during the experiment whereas tails means both would be awaken. It can be asked from your first-person perspective what is the probability of me waking up in the experiment? Here “me” can be interpreted as the special person most immediate to perception. From third-person perspective, or the perspective of an outsider if you prefer, the two person are in equal positions. It can specify one by their differences (for example their names) and ask what is the probability of Jessica waking up in the experiment? Both questions are fully contained within their own perspectives. Both of which are valid.
But for a question such as “am I the clone or the original?” that’s not the case. It requires first-person perspective to specify an individual by immediacy to perception while also requires third-person perspective to put the two clones in equal positions and differentiate them base on their originality. That’s why it requires us to switch perspectives to attempt to understand it thus invalid.
As for the red/green question. If it is known that the original would be painted red and the clone painted green then asking what color would mine be obviously is asking if I’m the original or clone. Of course the wall in front of me is defined by proximity to perception, but the supposed uncertainty of its color is only because I don’t know who I am from a third-person perspective (original/clone). So we need both perspectives to interpret the question. Compare that to blue/not blue. The wall is still define by proximity to perception and the uncertainty is due to the coin toss. I am perfectly capable of understanding what a coin toss is without having to identity me by some objective differences among a certain reference class. So that question is understandable solely from first-person perspective thus perspectively consistent.
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.
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.
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.
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.
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.
Because to make sense of this question I do not have to think from both perspectives. In the question “I” is whoever that’s most immediate to perception. So it is fully understandable within first-person perspective. Yes the room is painted by another individual but I do not have to use a theory of mind to reason from his perspective to appreciate the uncertainty.
Compare to asking the probability of me being the clone vs the original. From first-person perspective I specify myself only by immediacy to perception. Using differences to differentiate the clones (like clone or original) is third-person thinking. Therefore to understand the question I do have to think from both perspectives. This means it is a perspectively inconsistent question.
Ok, let’s ignore about how are the rooms defined. In the question I am also defined both in first-person as well as in third-person. And the difference is easier to show this way.
The difference is this: for the original problem in your previous comment the uncertainty about red or green is due to the method of assigning the colors are unknown to me. But for the problem I modified the “uncertainty” is due to that I can be either be the original or the clone. The first uncertainty is explainable within the first-person perspective. I don’t know the method. Plain and simple. The “I” in “I don’t know” obviously means the first-person self. While the second kind of “uncertainty” needs both perspectives to interpret. Form first-person there is no uncertainty about who I am: this is me. Distinguishing the two clones basing on their difference, like original or clone, is an outsider’s logic. But if I reason from an outsider’s perspective, and ask if a specific person is the original or clone then the problem is which one is this “specific person”. Obviously that person is the first-person self. Effectively we need to switch perspectives to make sense of the supposed uncertainty. Hence the perspective inconsistency and the reason why I say it is invalid.
In my blog under the doomsday argument section I said asking the probability of my room number (indexed) is not a valid question. The reason is the same as above: to understand the question one needs to switch perspectives. If we keep a constant perceptive the doomsday argument fails. For example from third-person perceptive seeing my room number simply means an ordinary clone with that number exists (instead of a specific clone has that number). And that is no evidence to favour the lower population.
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.
As for the calendar I understand your view. Treating a material object as a perspective is not something I like either, I think it’s just one way to express the argument. Alternatively it can also be seen as something which its evolvement follows that the perspective of an outsider. For beauty to base her decision on the condition of that object is analogous to switching to an outsider’s perspective. Like in sleeping beauty problem there are numerous arguments using monetary awards or bets. Depending on if the bookkeeping is done by an outsider or by beauty herself the conclusion would be completely different. But again my suggestion is that we do not dwell to much on this. Because whether or not the awakenings happens on specific dates, whether or not calendars are significant in the experiment setup, sleeping beauty is still the same problem. The paradox is only caused by the different number of awakenings.
My position to the problem is that the probabilities are for the blue 1⁄2, and others 1⁄4 each. As stated in my argument I shall believe the coin fall with an equal chance. So in case of heads my room would be blue the probability is 1⁄2. If it is tails then the room assigning experiment is exactly like the room painting problem from my previous reply. With no other information I would assume the probability of me being assigned to either room are equal. Hence 1⁄4 each. So far it is pretty similar to SSA’s answer. However I want to point out if the question is modified that in case of tails the original would be put into the green room and the clone goes into the red room then the question becomes invalid (the red or green part, the blue part is still half.) Because in this case my room is defined in first-person as well as in third-person (original or clone). A telltale sign is that the imaginary experiment would involve soul embodiment. For such perspectively inconsistent questions there is no possible answer. But SSA and SIA would still produce an answer with no problem.
If I ask why am I a human being rather than a cow?(here “I” is a first-person definition. So I’m asking why am I experiencing the world from the perspective of a certain primate rather than a bovine.) To me it is pretty obvious logic reasoning wouldn’t able to answer that. Only some sort of metaphysical conjecture or even religious creed could attempt to explain it. But with SSA there is an answer. It would be because there are more humans than cows so it’s more likely that way. If we throw SIA into the mix then it can also be said because I exist it means there are a lot of humans+cows +all other kinds of minds in the universe and possibly multiverses . Of course now the reference class problem rises and the whole thing becomes messy. While in perspectively consistent reasonings I shall simply accept there is no answer and the reference class is never a problem to begin with.
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.
Huh? Beauty might even be able to go into the other room and check the calendar. Everyone else in the world could be dead and she could still go check the calendar. I’m really confused about how talking about this calendar requires a different person’s perspective; there are few things more immediate to Beauty’s first-person experience than a calendar she can just go look at.
Here I don’t mean that beauty has to check the calendar through another person. Think this way. If beauty has a calendar of her own which also goes though the “memory wipe” as she does then for sure it would say it’s Monday. Beauty knows this as well. For the calendar to be indeterminate to beauty it has to be outside of the experiment unaffected by the memory tempering. If we can say the calendar is a valid perspective then to beauty it is an third-person perspective just as the experimenter’s or an outside observers’. That’s what I meant by checking the calendar to determined the date beauty is switching to a third-person perspective.
I personally do not like the version of the problem where the awakenings happen on two specific dates. For sure it makes some arguments easier to express but I feel it also give a false sense where only the outsider’s perspective is valid because only they know the date. I think calendar in the context of this question is just a consensus of a referencing point to account the passing of time, nothing special to it. So beauty could rightfully have her own calendar different from everybody else. However I think these arguments are hard to convey and not really the point of contention anyway. That’s why in my blog I did not specify the dates. I think we can all agree for the experiment the specific dates or the timing of the awakening doesn’t really matter. Only the number of awakenings matters to the answer. So the real question is whether this awakening is the first or the second, (or alternatively if this is the awakening that would always happen or the one that only happens if tails). The concept of first vs second is only meaningful from the third-person perceptive of an outsider not affected by the memory wipe. But using “this awakening” or “today” to specify a time is purely based on immediacy to perception, i.e. first-person. Hence the perspective inconsistency, in another word, the question is formed by using part of the logic from one person and combine it with part of the logic from another.
If I may I want to use a cloning example instead of memory wiping to discuss the difference between these perspectively inconsistent problems and normal non-anthropic problems. Here I’m going to cut the corner and just use one of my example from the footnote. Consider a case where memory retained cloning has created two indistinguishable individuals and you are one of them. Each person is put into an identical room. Someone would randomly choose one out of the two rooms and paint it red and paint the other room blue. It is perfectly valid to ask “what is the probability that I would open my eyes and see a red room (instead of a blue one)?“. I think even though this thought experiment involves anthropic reasoning it is analogous to the marble in box problem you presented. Here the clones are only specified in first-person. Whatever happens to others is not interested to the problem. It keeps a constant perspective and it’s a valid question. The experiment refers to the random choosing of the rooms. To answer the question the experiment can be repeated to count the relative frequency. And the two outcomes of “red room” vs “blue room” to me are indifferent. A perspectively inconsistent question would be “what is the probability of me being the clone in the red room (instead of being the clone in the blue room)?” I know this expression is a bit weird. Here the individuals are defined in first-person as in “me”, but also in third-person as the two clones in different rooms. To make sense of the question I have to combine the perspective of me with the perspective of some observer. That’s whats make the question fallacious. There really is no experiment to the question. Except maybe I can make up a fictitious one where my wandering soul finds one of the clone to get embodied. Then the sample space would be for one person (me) to become two possible persons (the red clone or the blue clone). Even if we use this made up experiment there is no way of repeating it to get a frequentist interpretation. Also because part of the question is from first-person perspective it means not all clones are treated equally (since it treats the first-person as an inherently special individual). It would be self contradicting to treat each clone indifferently in its answer. For example, a common argument would be if all clones guessed “red” then half would be correct so my probability of being the red clone is 1⁄2. This argument only works if the “I” in question is specified in third-person. If I was defined in first-person then I’m already inherently unique and has no one else in my reference class. Basing my answer on averaging me with others makes no sense at all. What I want to stress is that even though the two question looks similar the latter is actually invalid and has no answer. But because the questions are similar we usually just treat the latter as an alternative expression of the former without realizing that. However for questions like “what is the probability of me being the original (instead of being the clone)?” or in the sleeping beauty problem “what is the probability of this awakening being the first (instead of being the second)?” There is no readily available former question. SIA and SSA are just attempts trying to come up with one. In my opinion these are ultimately pointless.
PS: Sorry for the slow reply. Had to take a 14 hour flight with my one year old. Reading your questions made me realise how poorly I expressed myself in the first reply. Really hoping you are still interested in this discussion. I find it really challenging and at the same time forcing me to try to articulate my argument.
As explained earlier in the blog, from my first-person perspective whoever wakes up on the other day is a different person. So from my perspective the amount of time passed is not the same as everyone else’s. That’s why for me this is indeed the first day. To ask about the calendar in the other room is to switch to a third-person’s (who have not experienced a memory wipe) perspective thus the perspective inconsistency. The event of “the calendar in the room next to mine says it is Monday” and “the calendar in the room next to mine says it is Tuesday” refers to two different persons and cannot be both in my sample space. Regarding its difference from an ordinary physical uncertainty I have discussed it in the chapter regarding the doomsday argument. The exact same reason applies here. To summarized it the probability cannot be interpreted in frequentist’s sense because there is no experiment to repeat. Principle of indifference cannot be used either because defining “today” basing on immediacy to perception already violates it. Where as for a physical uncertainty both interpretation works.
If I may make a plea. I find discussing duplication by memory wipes very difficult because it is hard to put into words. IF you agree that duplication by cloning is logically the same problem can we proceed with that route?
I think you are correct that all perspectives are ultimately first-person. That’s why I had to say to reason in third-person is to use a theory of mind to deduct how another person would reason. As a result I guess I’m using the term first-person and third-person in sense of everyday language rather than strict philosophical terminology. I appreciate this insight. Please forgive me in the following paragraphs as I will keep using the terms this way. Not because I don’t agree with you. Just that it makes writing easier.
My main argument is that from first-person perspectives there are unique perk/limitation not applicable to any body else. Such as one do not need any information to specify oneself, and one would always find oneself exists. If I bypass these perks and limitations then my reasoning would be meaningful to others in general. For example twins do not need to know their difference to tell themselves apart. But for everybody else differentiating them require knowing their difference. For the twin it is natural to ask how would others identify me without having to specify which exact person’s perspective among the “others” must he reason from to answer the question. Of course there is nothing wrong in specifying a third person either. In the sleeping beauty problem, we can take the experimenter’s perspective, an observer’s perspective, or even an imaginary person’s perspective, just that their reasoning would be the same. I am not trying to define third-person perspective as the unique perspective of an outside-the-universe observer. As you pointed out that would make uniquely identifying any individual near (if not completely) impossible. Even worse it would make identifying the reference class impossible as well. I feel this identification would ultimately fall back to immediacy to perception. As you suggested in the names case: spatiotemporally close. Which again showing that you are correct in saying all perspective are first-person.
In the case of perspective of a non-mind such as a camera. To be completely honest I feel I do not know enough to contribute an opinion. Coming from a civil engineering background philosophy is not my forte. It is already quite difficult for me to put these not so easily describable ideas down in a second language. Can we reason from the perspective of a camera? I want to say yes? Because we can imagine it has a mind and mind is a non-physical concept so there is no logical contradiction. But again my opinion probably don’t worth two cents. Just want to say that this part I don’t think can change the answer to doomsday argument or the sleeping beauty problem.