I think this highlights our difference at least in the numerical sense in this example.
Yes! This is one of the few objective disagreements we have and I’m very excited to figure it out!
You seem to treat different awakenings of Alice as if they were different people in attempts to preserve the similarity between memory erasure sleeping beauty type of problems and fissure type of problems. While I notice that these problems are different.
The difference is that in Sleeping Beauty P(Heads|Monday) = 1⁄2 while in Fissure, where non-fissured person is always in Room1 and fissured people are randomly assigned either Room1 or Room2, P(Heads|Room1) = 2⁄3. Is it our crux?
I maintain the memory erasure and fission problem are similar because I regard the first-person identification equally applies to both questions. Both the inherent identifications of “NOW” and “I” are based on the primitive perspective. I.E., to Alice, today’s awakening is not the other day’s awakening, she can naturally tell them apart because she is experiencing the one today.
I don’t think our difference comes from the non-fissured person always stays in Room1 while the fissure person are randomly assigned either Room 1 or Room 2. Even if the experiment is changed, so that the non-fissured person is randomly assigned among the two rooms, and the fissured person with the original left body always stays in Room 1 and the fissured person with the original right body always in Room 2 my answer wouldn’t change.
Our difference still lies in the primitivity of perspective. In this current problem by cousin-it, I would say Alice should not update the probability after meeting Bob, because from her first-person perspective, the only thing she can observe is “I see Bob (today)” vs “I don’t see Bob (today)”, and her probability shall be calculated accordingly. She is not in the vantage point to observe whether “I see Bob on one of the two days” vs “I don’t see Bob on any of the two days”, so she should not update that way.
to Alice, today’s awakening is not the other day’s awakening, she can naturally tell them apart because she is experiencing the one today.
Well, sure but nothing is preventing her from also realizing that both of the awakenings are happening to her, not some other person. That both today’s and tomorrow awakening are casually connected to each other even if she has her memory erased, contrary to the fissure problem where there are actually two different people in two rooms with their own causal history hence forth.
I would say Alice should not update the probability after meeting Bob, because from her first-person perspective, the only thing she can observe is “I see Bob (today)” vs “I don’t see Bob (today)”, and her probability shall be calculated accordingly. She is not in the vantage point to observe whether “I see Bob on one of the two days” vs “I don’t see Bob on any of the two days”, so she should not update that way.
Alice is indeed unable to observe the event “I didn’t see Bob at all”. Due to the memory erasure she can’t distinguish between “I don’t observe Bob today but will observe him tomorrow/observed him yesterday” and “I do not observe Bob in this experiment at all”. So when Alice doesn’t see Bob she keeps her credence at 50%.
But why doesn’t she also observe “I see Bob on one of the two days”, if she sees Bob on a specific day? Surely today is one of the two days. This seems like logical necessity.
Suppose there is no Bob. Suppose:
The Beauty is awakened on Monday with 50% chance. If she wasn’t awakened a fair coin is tossed. On Tails the Beauty is awakened on Tuesday.
Do you also think that the Beauty isn’t supposed to update in favor of Tails when she awakes in this case?
This post highlights my problem with your approach: I just don’t see a clear logic dictating which interpretation to use in a given problem—whether it’s the specific first-person instance or any instance in some reference class.
When Alice meets Bob, you are saying she should construe it as “I meet Bob in the experiment (on any day)” instead of “I meet Bob today” because—”both awakening are happening to her, not another person”. This personhood continuity, in your opinion, is based on what? Given you have distinguished the memory erasure problem from the fission problem, I would venture to guess you identify personhood by the physical body. If that’s the case, would it be correct to say you regard anthropic problems utilizing memory erasures fundamentally different from problems with fissures or clones? Entertain me this, what if the exact procedural is not disclose to you, then what? E.g. there is a chance that the “memory erasure” is actually achieved by creating a clone of Alice and wake that clone on Monday, then destroy it. Then wake the original on Tuesday. What would Alice’s probability calculation then? Anything changes if the fissure is used instead of cloning? What would Alice’s probability of Tails when she sees Bob when she is unsure of the exact procedure?
Furthermore you are holding that if saw Bob, Alice should interpret “I have met Bob (on some day) in the experiment”. But if if she didn’t see Bob, she shall interpret “I haven’t met Bob specifically for Today”. In another word, whether to use “specifically today” or “someday” depends on whether or not she sees Bob or not. Does this not seem problematic at all to you?
I’m not sure about what you mean in your example, Beauty is awakened on Monday with 50% chance, if she is awaken then what happens? Nothing? The experiment just ends, perhaps with a non-consequential fair coin toss anyway? If she is not awakened then if the coin toss is Tails then she wakes on Tuesday? Is that the setup? I fail to see there is any anthropic elements in this question at all. Of course I would update the probability to favour Tails in this case upon awakening. Because that is new information for me. I wasn’t sure that I would find myself awake during the experiment at all.
This personhood continuity, in your opinion, is based on what?
Causality. Two time states of a single person a causally connected, while two clones are not. Probability theory treats independent and non-independent events differently. The fact that it fits the basic intuition for personal identity is a nice bonus.
If that’s the case, would it be correct to say you regard anthropic problems utilizing memory erasures fundamentally different from problems with fissures or clones?
Yes it would. I find the fact that these problems are put in the same category of “anthropic problems” quite unfortunate as they have testably different probability theoretic properties. For example for Sleeping Beauty correct position is double halfism, while for fissure—lewisian halfism.
Entertain me this, what if the exact procedural is not disclose to you, then what? E.g. there is a chance that the “memory erasure” is actually achieved by creating a clone of Alice and wake that clone on Monday, then destroy it. Then wake the original on Tuesday. What would Alice’s probability calculation then? Anything changes if the fissure is used instead of cloning? What would Alice’s probability of Tails when she sees Bob when she is unsure of the exact procedure?
Okay, that sounds as an interesting problem. Let’s formulate it like this:
Alice if put to sleep then the coin is tossed. On Heads she is awaken on Monday. On Tails another coin is tossed:
Either she is awakened both on Monday and on Tuesday with memory erasure
Or fissure happens. Alice1 is awakened on Monday, Alice2 is awakened on Tuesday
What do we have probability wise, on an awakening on the unknown day?
50% for Heads, 50% for Tails, 25% fissure, 25% memory erasure, 12.5% to be Alice1/Alice2
Now, suppose Alice meets Bob, who is awaken on a random day. Bob updates 2⁄3 in favor of Tails as he meets an Alice in the experiment with 75% probability.
But for a particular Alice the probability to meet Bob in the experiment is only 1⁄4 + 2⁄8 + 1⁄8 = 5⁄8
So her probability that the initial coin is Heads:
Now, I think in this particular case there is not much difference between fissure and cloning. There would apparently be difference if we were talking about a person who was about to participate in the experiment, instead of a person in the middle of it. Because current participator can be in the state of uncertanity whether she is a clone or not, while future participator is pretty sure the she is not going to be a clone, thus can omit this possibility from the calculations.
But yeah, I should probably write a separate post about such scenarios, after I’m done with the Sleeping Beauty case.
Furthermore you are holding that if saw Bob, Alice should interpret “I have met Bob (on some day) in the experiment”. But if if she didn’t see Bob, she shall interpret “I haven’t met Bob specifically for Today”. In another word, whether to use “specifically today” or “someday” depends on whether or not she sees Bob or not. Does this not seem problematic at all to you?
As a matter of fact, it doesn’t. You seem to be thinking that I’m switching between two different mathematical models here. But actually, we can use a single probability space.
“I see Bob in the experiment” is equal to “I see Bob on either Monday or Tuesday” it’s an event that consist of two outcomes: “seeing Bob on Monday” and “seeing Bob on Tuesday”. When an outcome is realized it means that every event which this outcome is part of is realized. So when Alice sees Bob on Monday she both observes “I see Bob on Monday” and “I see Bob in the experiment”. And, likewise, when Alice sees Bob on Tuesday. Just one observation of Bob on any day of the experiment is enough to be certain that Bob was observed on either Monday or Tuesday.
On the other hand, “I don’t see Bob in the experiment” happens only when Bob was neither observed on Monday, nor on Tuesday. Not observing him only on one day isn’t enough. To observe this event Alice has to accumulate information between two days.
All this is true, regardless of whether there is memory erasure or not. What is different with memory erasure is that now Alice is made unable to accumulate information between days. So she can’t observe event “I don’t see Bob in the experiment”. However, she is still perfectly able to observe event “I see Bob in the experiment”. She is supposed to update her credence for Heads based on it. And until her memory is erased she can act on this information.
What if problematic, on the other hand, is the “today”, “this awakening” and similar categories which can’t be formally mathematically specified in Sleeping Beauty. This is the reason why probability of an event “today is Monday” is undefined, “today” is not just some variable that takes a specific value from the {Monday, Tuesday}, on Tails it have to be both! It’s not a fixed thing throughout the experiment and so reasoning as if it is leads to confusion and paradoxes.
I fail to see there is any anthropic elements in this question at all. Of course I would update the probability to favour Tails in this case upon awakening. Because that is new information for me. I wasn’t sure that I would find myself awake during the experiment at all.
As I keep saying, this whole “anthropic problems” category is silly to begin with. All of these are just plain probability theory problems. And these two problems are isomorphic to each other. If being awaken on Tails is twice as likely than being awaken on Heads, awakening is an evidence in favor of Tails. If meeting Bob is twice as likely on Tails than on Heads, then meeting Bob is an evidence in favor of Tails. The same basic principle that gives you answer in one problem gives you the answer to the other. You don’t need to search for any “anthropic elements” in these problems. The math works the same way.
Yes! This is one of the few objective disagreements we have and I’m very excited to figure it out!
You seem to treat different awakenings of Alice as if they were different people in attempts to preserve the similarity between memory erasure sleeping beauty type of problems and fissure type of problems. While I notice that these problems are different.
The difference is that in Sleeping Beauty P(Heads|Monday) = 1⁄2 while in Fissure, where non-fissured person is always in Room1 and fissured people are randomly assigned either Room1 or Room2, P(Heads|Room1) = 2⁄3. Is it our crux?
I maintain the memory erasure and fission problem are similar because I regard the first-person identification equally applies to both questions. Both the inherent identifications of “NOW” and “I” are based on the primitive perspective. I.E., to Alice, today’s awakening is not the other day’s awakening, she can naturally tell them apart because she is experiencing the one today.
I don’t think our difference comes from the non-fissured person always stays in Room1 while the fissure person are randomly assigned either Room 1 or Room 2. Even if the experiment is changed, so that the non-fissured person is randomly assigned among the two rooms, and the fissured person with the original left body always stays in Room 1 and the fissured person with the original right body always in Room 2 my answer wouldn’t change.
Our difference still lies in the primitivity of perspective. In this current problem by cousin-it, I would say Alice should not update the probability after meeting Bob, because from her first-person perspective, the only thing she can observe is “I see Bob (today)” vs “I don’t see Bob (today)”, and her probability shall be calculated accordingly. She is not in the vantage point to observe whether “I see Bob on one of the two days” vs “I don’t see Bob on any of the two days”, so she should not update that way.
Well, sure but nothing is preventing her from also realizing that both of the awakenings are happening to her, not some other person. That both today’s and tomorrow awakening are casually connected to each other even if she has her memory erased, contrary to the fissure problem where there are actually two different people in two rooms with their own causal history hence forth.
Alice is indeed unable to observe the event “I didn’t see Bob at all”. Due to the memory erasure she can’t distinguish between “I don’t observe Bob today but will observe him tomorrow/observed him yesterday” and “I do not observe Bob in this experiment at all”. So when Alice doesn’t see Bob she keeps her credence at 50%.
But why doesn’t she also observe “I see Bob on one of the two days”, if she sees Bob on a specific day? Surely today is one of the two days. This seems like logical necessity.
Suppose there is no Bob. Suppose:
The Beauty is awakened on Monday with 50% chance. If she wasn’t awakened a fair coin is tossed. On Tails the Beauty is awakened on Tuesday.
Do you also think that the Beauty isn’t supposed to update in favor of Tails when she awakes in this case?
This post highlights my problem with your approach: I just don’t see a clear logic dictating which interpretation to use in a given problem—whether it’s the specific first-person instance or any instance in some reference class.
When Alice meets Bob, you are saying she should construe it as “I meet Bob in the experiment (on any day)” instead of “I meet Bob today” because—”both awakening are happening to her, not another person”. This personhood continuity, in your opinion, is based on what? Given you have distinguished the memory erasure problem from the fission problem, I would venture to guess you identify personhood by the physical body. If that’s the case, would it be correct to say you regard anthropic problems utilizing memory erasures fundamentally different from problems with fissures or clones? Entertain me this, what if the exact procedural is not disclose to you, then what? E.g. there is a chance that the “memory erasure” is actually achieved by creating a clone of Alice and wake that clone on Monday, then destroy it. Then wake the original on Tuesday. What would Alice’s probability calculation then? Anything changes if the fissure is used instead of cloning? What would Alice’s probability of Tails when she sees Bob when she is unsure of the exact procedure?
Furthermore you are holding that if saw Bob, Alice should interpret “I have met Bob (on some day) in the experiment”. But if if she didn’t see Bob, she shall interpret “I haven’t met Bob specifically for Today”. In another word, whether to use “specifically today” or “someday” depends on whether or not she sees Bob or not. Does this not seem problematic at all to you?
I’m not sure about what you mean in your example, Beauty is awakened on Monday with 50% chance, if she is awaken then what happens? Nothing? The experiment just ends, perhaps with a non-consequential fair coin toss anyway? If she is not awakened then if the coin toss is Tails then she wakes on Tuesday? Is that the setup? I fail to see there is any anthropic elements in this question at all. Of course I would update the probability to favour Tails in this case upon awakening. Because that is new information for me. I wasn’t sure that I would find myself awake during the experiment at all.
Causality. Two time states of a single person a causally connected, while two clones are not. Probability theory treats independent and non-independent events differently. The fact that it fits the basic intuition for personal identity is a nice bonus.
Yes it would. I find the fact that these problems are put in the same category of “anthropic problems” quite unfortunate as they have testably different probability theoretic properties. For example for Sleeping Beauty correct position is double halfism, while for fissure—lewisian halfism.
Okay, that sounds as an interesting problem. Let’s formulate it like this:
Alice if put to sleep then the coin is tossed. On Heads she is awaken on Monday. On Tails another coin is tossed:
Either she is awakened both on Monday and on Tuesday with memory erasure
Or fissure happens. Alice1 is awakened on Monday, Alice2 is awakened on Tuesday
What do we have probability wise, on an awakening on the unknown day?
50% for Heads, 50% for Tails, 25% fissure, 25% memory erasure, 12.5% to be Alice1/Alice2
Now, suppose Alice meets Bob, who is awaken on a random day. Bob updates 2⁄3 in favor of Tails as he meets an Alice in the experiment with 75% probability.
But for a particular Alice the probability to meet Bob in the experiment is only 1⁄4 + 2⁄8 + 1⁄8 = 5⁄8
So her probability that the initial coin is Heads:
P(H1|MeetsBob)=P(MeetsBob|H1)P(H1)/P(MeetsBob)=1/2∗1/2∗8/5=40%
Now, I think in this particular case there is not much difference between fissure and cloning. There would apparently be difference if we were talking about a person who was about to participate in the experiment, instead of a person in the middle of it. Because current participator can be in the state of uncertanity whether she is a clone or not, while future participator is pretty sure the she is not going to be a clone, thus can omit this possibility from the calculations.
But yeah, I should probably write a separate post about such scenarios, after I’m done with the Sleeping Beauty case.
As a matter of fact, it doesn’t. You seem to be thinking that I’m switching between two different mathematical models here. But actually, we can use a single probability space.
“I see Bob in the experiment” is equal to “I see Bob on either Monday or Tuesday” it’s an event that consist of two outcomes: “seeing Bob on Monday” and “seeing Bob on Tuesday”. When an outcome is realized it means that every event which this outcome is part of is realized. So when Alice sees Bob on Monday she both observes “I see Bob on Monday” and “I see Bob in the experiment”. And, likewise, when Alice sees Bob on Tuesday. Just one observation of Bob on any day of the experiment is enough to be certain that Bob was observed on either Monday or Tuesday.
On the other hand, “I don’t see Bob in the experiment” happens only when Bob was neither observed on Monday, nor on Tuesday. Not observing him only on one day isn’t enough. To observe this event Alice has to accumulate information between two days.
All this is true, regardless of whether there is memory erasure or not. What is different with memory erasure is that now Alice is made unable to accumulate information between days. So she can’t observe event “I don’t see Bob in the experiment”. However, she is still perfectly able to observe event “I see Bob in the experiment”. She is supposed to update her credence for Heads based on it. And until her memory is erased she can act on this information.
What if problematic, on the other hand, is the “today”, “this awakening” and similar categories which can’t be formally mathematically specified in Sleeping Beauty. This is the reason why probability of an event “today is Monday” is undefined, “today” is not just some variable that takes a specific value from the {Monday, Tuesday}, on Tails it have to be both! It’s not a fixed thing throughout the experiment and so reasoning as if it is leads to confusion and paradoxes.
As I keep saying, this whole “anthropic problems” category is silly to begin with. All of these are just plain probability theory problems. And these two problems are isomorphic to each other. If being awaken on Tails is twice as likely than being awaken on Heads, awakening is an evidence in favor of Tails. If meeting Bob is twice as likely on Tails than on Heads, then meeting Bob is an evidence in favor of Tails. The same basic principle that gives you answer in one problem gives you the answer to the other. You don’t need to search for any “anthropic elements” in these problems. The math works the same way.