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.
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]