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.
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.