Same as before, the questions of “what is the probability that today is day 1?” or “what is the probability that this is the first awakening?” are invalid questions which have no answer. It is because these questions cannot be fully interpreted from either perspectives. From first-person perspective the question makes no sense because to me this is indeed the one and only awakening. The date or the sequence of the awakening is only meaningful from a third-person perspective.
This doesn’t seem right. Say there is a calendar in the room next to Beauty’s that indicates the current day. Then, from a first-person perspective, Beauty can refer to the events “the calendar in the room next to mine says it is Monday” or “the calendar in the room next to mine says it is Tuesday”. Even without the calendar in the room next to hers, she could refer to “the world I am in at the current time” and thereby refer to random variables like “the day that the majority of calendars in the world I am in currently say it is”. Uncertainty about these events and random variables is the same as ordinary physical uncertainty (e.g. being uncertain about what color marble is in a particular box).
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?
Agree that the cloning problem is a fine problem to discuss instead of sleeping beauty, and the analysis is mostly the same.
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.
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.
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.
From a first-person perspective, it doesn’t refer to any persons other than “me”.
I think this gets less confusing if we think of an apparently non-anthropic problem. Say a friend has put either a red marble or a blue marble into a box (without showing me what color marble), and puts the box in front of me. Then I look at the box, and think, “I wonder what color marble is in the box”. I can form two events: “the marble in the box in front of me is red” and “the marble in the box in front of me is blue”, and be uncertain about which of these events is true. (These events make formal sense in centered world models)
Other people have boxes containing marbles in front of them, and could also form the events “the marble in the box in front of me is red” and “the marble in the box in front of me is blue”. But there’s no way for me to confuse myself with these other people, or my box with theirs; it’s not like I would accidentally walk into someone else’s room and look at their marble-containing box instead of mine. The box is quite immediate in my own experience, and I can refer to it without referring to any person who isn’t me.
It would be incorrect to say that the event “the marble in the box in front of me is red” refers to many different persons and cannot be in my sample space.
I don’t think I can use repeatable experiments or the principle of indifference to reason about the probability of the marble being blue or red in this non-anthropic experiment, yet I still assign a probability. There are reasons for having probabilities that don’t rely on repeatability or principle of indifference (see: complete class theorem, Cox’s theorem, dutch book arguments, Occam’s razor). It remains an open problem how to assign probabilities in the absence of repeatibility or principle of indifference, but this is a real problem with real consequences rather than a meaningless question.
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.
I wasn’t thinking of the calendar as a perspective, rather as a particular material object, which could even be a mechanical clock. (Events like “the clock reads Monday” are material and are definable relative to a first-person perspective)
I think I agree with your main point, which is that we should avoid perspective-inconsistent propositions (e.g. “I am the first clone”) unless they have a clear translation to some specific perspective. I think these translations are usually pretty easy in these problems, though; they generally have a pretty obvious interpretation as a predicate on centered world models.
We agree that “I am in a blue room” is a valid proposition that an agent should assign a probability to in the cloning case, since it’s entirely first-person. Here’s a cloning problem analogous to sleeping beauty:
1. The experimenter flips a coin.
2. If it comes up heads, you’re put in a blue room. If it comes up tails, you’re cloned once (so there are 2 copies), one copy goes in a green room, and the other goes in a red room.
Before seeing what color your room is, what probability should you assign to the room being blue, green, or red? SSA says blue 1⁄2, green 1⁄4, red 1⁄4; SSA+SIA says each is 1⁄3. I don’t know whether you would recommend a procedure for assigning probabilities in situations like this, and if so what probability your procedure would give here. (In any case, I am guessing that we agree that this problem is not automatically resolved by noting perspective inconsistency, as the only propositions considered are first-person)
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.
I don’t know what you mean by “my room is defined in first-person as well as in third-person (original or clone)”. In all problems involved, the question asked is the color of the wall in front of you, which is entirely first-person (as it is immediate in your experience). Additionally, in all problems involved, the situation you’re in is affected by the actions of the experimenter, who is another person. The experimenter chooses red or green based on facts only known to them (i.e. which is the original and which is the clone), but the experimenter also chooses blue or not-blue based on facts known only to them (i.e. the coin flip). So I don’t see why one question would be valid and the other wouldn’t. (Note that the marble in a box problem is also of this form, where the question is entirely first-person and is affected by some other perspective, specifically my friend’s)
Is there a variant of the doomsday paradox, with numbers painted in rooms, where you think asking what number is in your room is a valid question? (If so, we could set up a problem where the experimenter paints 2 numbers on each room, the first equal to the room’s index (with “lower” rooms always being filled first), and the second equal to the total number of copies. Then we could ask what probability distribution a copy should assign to the second number conditional on knowing the first number. If you use SSA for this you get a doomsday prediction)
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.
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.
In the red/green case the question isn’t clone vs original, it’s whether the wall right in front of you is red or green.
I don’t see why you don’t have to reason from the experimenter’s perspective in the blue/not blue case, since the experimenter is the one deciding where to put people (based on the coin flip).
Basically I see two consistent positions on this set of questions:
Any question about the color of the wall in front of you is valid and can be assigned a probability, since the color is definable in first-person.
A question about the color of the wall in front of you is only valid if reasoning about this color doesn’t require theory of mind about another person.
1 would obviously say that the red/green question is valid. 2 would say that the blue/not blue question is invalid, since whether you end up in a blue room depends on decisions the experimenter makes. (2 would also say that the color of the marble in the box can’t be asked about in the marble problem)
You might have another consistent position but I am having a lot of trouble determining what it is.
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.
This doesn’t seem right. Say there is a calendar in the room next to Beauty’s that indicates the current day. Then, from a first-person perspective, Beauty can refer to the events “the calendar in the room next to mine says it is Monday” or “the calendar in the room next to mine says it is Tuesday”. Even without the calendar in the room next to hers, she could refer to “the world I am in at the current time” and thereby refer to random variables like “the day that the majority of calendars in the world I am in currently say it is”. Uncertainty about these events and random variables is the same as ordinary physical uncertainty (e.g. being uncertain about what color marble is in a particular box).
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?
Agree that the cloning problem is a fine problem to discuss instead of sleeping beauty, and the analysis is mostly the same.
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.
From a first-person perspective, it doesn’t refer to any persons other than “me”.
I think this gets less confusing if we think of an apparently non-anthropic problem. Say a friend has put either a red marble or a blue marble into a box (without showing me what color marble), and puts the box in front of me. Then I look at the box, and think, “I wonder what color marble is in the box”. I can form two events: “the marble in the box in front of me is red” and “the marble in the box in front of me is blue”, and be uncertain about which of these events is true. (These events make formal sense in centered world models)
Other people have boxes containing marbles in front of them, and could also form the events “the marble in the box in front of me is red” and “the marble in the box in front of me is blue”. But there’s no way for me to confuse myself with these other people, or my box with theirs; it’s not like I would accidentally walk into someone else’s room and look at their marble-containing box instead of mine. The box is quite immediate in my own experience, and I can refer to it without referring to any person who isn’t me.
It would be incorrect to say that the event “the marble in the box in front of me is red” refers to many different persons and cannot be in my sample space.
I don’t think I can use repeatable experiments or the principle of indifference to reason about the probability of the marble being blue or red in this non-anthropic experiment, yet I still assign a probability. There are reasons for having probabilities that don’t rely on repeatability or principle of indifference (see: complete class theorem, Cox’s theorem, dutch book arguments, Occam’s razor). It remains an open problem how to assign probabilities in the absence of repeatibility or principle of indifference, but this is a real problem with real consequences rather than a meaningless question.
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.
I wasn’t thinking of the calendar as a perspective, rather as a particular material object, which could even be a mechanical clock. (Events like “the clock reads Monday” are material and are definable relative to a first-person perspective)
I think I agree with your main point, which is that we should avoid perspective-inconsistent propositions (e.g. “I am the first clone”) unless they have a clear translation to some specific perspective. I think these translations are usually pretty easy in these problems, though; they generally have a pretty obvious interpretation as a predicate on centered world models.
We agree that “I am in a blue room” is a valid proposition that an agent should assign a probability to in the cloning case, since it’s entirely first-person. Here’s a cloning problem analogous to sleeping beauty:
1. The experimenter flips a coin.
2. If it comes up heads, you’re put in a blue room. If it comes up tails, you’re cloned once (so there are 2 copies), one copy goes in a green room, and the other goes in a red room.
Before seeing what color your room is, what probability should you assign to the room being blue, green, or red? SSA says blue 1⁄2, green 1⁄4, red 1⁄4; SSA+SIA says each is 1⁄3. I don’t know whether you would recommend a procedure for assigning probabilities in situations like this, and if so what probability your procedure would give here. (In any case, I am guessing that we agree that this problem is not automatically resolved by noting perspective inconsistency, as the only propositions considered are first-person)
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.
I don’t know what you mean by “my room is defined in first-person as well as in third-person (original or clone)”. In all problems involved, the question asked is the color of the wall in front of you, which is entirely first-person (as it is immediate in your experience). Additionally, in all problems involved, the situation you’re in is affected by the actions of the experimenter, who is another person. The experimenter chooses red or green based on facts only known to them (i.e. which is the original and which is the clone), but the experimenter also chooses blue or not-blue based on facts known only to them (i.e. the coin flip). So I don’t see why one question would be valid and the other wouldn’t. (Note that the marble in a box problem is also of this form, where the question is entirely first-person and is affected by some other perspective, specifically my friend’s)
Is there a variant of the doomsday paradox, with numbers painted in rooms, where you think asking what number is in your room is a valid question? (If so, we could set up a problem where the experimenter paints 2 numbers on each room, the first equal to the room’s index (with “lower” rooms always being filled first), and the second equal to the total number of copies. Then we could ask what probability distribution a copy should assign to the second number conditional on knowing the first number. If you use SSA for this you get a doomsday prediction)
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.
Why doesn’t the blue vs. not blue question require an outside perspective to interpret?
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.
In the red/green case the question isn’t clone vs original, it’s whether the wall right in front of you is red or green.
I don’t see why you don’t have to reason from the experimenter’s perspective in the blue/not blue case, since the experimenter is the one deciding where to put people (based on the coin flip).
Basically I see two consistent positions on this set of questions:
Any question about the color of the wall in front of you is valid and can be assigned a probability, since the color is definable in first-person.
A question about the color of the wall in front of you is only valid if reasoning about this color doesn’t require theory of mind about another person.
1 would obviously say that the red/green question is valid. 2 would say that the blue/not blue question is invalid, since whether you end up in a blue room depends on decisions the experimenter makes. (2 would also say that the color of the marble in the box can’t be asked about in the marble problem)
You might have another consistent position but I am having a lot of trouble determining what it is.
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.
[EDIT: retracted]