The way I’m thinking about this is “I shuffle a deck of playing cards until it is ordered randomly, then turn over one card.”
I get the 4 of ♥. Am I surprised? In one sense, yes- I couldn’t have told you that I would have drawn that card with anything more than 2% certainty. In another sense, no- I expected that card was as likely as any other card. If I drew the 14 of ♥, then I would be surprised, because my model ascribed 0 probability to that event.
And so it seems like the normal measure of surprise is “can I reject the null hypothesis that this occurred by chance?”. If Sleeping Beauty only has experiences consistent with her model of what will happen, why be surprised, even if those experiences individually have very tiny probabilities of occurring?
That isn’t quite what I’m talking about. Obviously I shouldn’t be surprised when a discrete event with a probability as high as any other discrete event occurs. This isn’t an anthropic issue at all. But I think we can agree that if I buy a lottery ticket and win I should be surprised. But if I copy myself a million times and all copies wake up with lottery tickets (no other tickets having been issued) I don’t think I can even be surprised to be the copy with the winning ticket- since I could tell you at the outset there would be a copy of me holding that ticket.
But if I copy myself a million times and all copies wake up with lottery tickets (no other tickets having been issued) I don’t think I can even be surprised to be the copy with the winning ticket- since I could tell you at the outset there would be a copy of me holding that ticket.
I’m not seeing the relevant difference between this and a million unrelated people holding lottery tickets. Am I missing something?
So obviously your person doesn’t magically transfer from the current copy of you to future copies of you. Rather, those future persons are you because they are psychologically continuous with the present you. Now when you make multiple copies of yourself it isn’t right to say that just one of them will be you. You may never experience both of them but from the perspective of each copy you are their past. So when all million copies of you wake up all of them will feel like they are the next stage of you. All of them will be right. Given that you know there will be a future stage of you that will win the lottery how can that copy (the copy that is the future stage of you that has won the lottery) be surprised? The copy has, in it’s past, a memory of being told that there would be exactly one copy psychologically continuous with his past self. Of course, the winning copy will have some kind of self-awareness “Oh, I’m that copy” but of course it has a memory of expecting exactly that from the copy that won the lottery.
I may need to be providing a more extensive philosophical context about personal identity for this to make sense, I’m not sure.
I don’t think personal identity is a mathematical equivalence relation. Specifically, it’s not symmetric: “I’m the same person you met yesterday” actually needs to read “I was the same person you met yesterday”; “I will be the same person tomorrow” is a prediction that may fail (even assuming I survive that long). This yields failures of transitivity: “Y is the same person as X” and “Z is the same person as X” doesn’t get you “Y is the same person as Z”.
Given that you know there will be a future stage of you that will win the lottery how can that copy (the copy that is the future stage of you that has won the lottery) be surprised?
It’s not the ancestor—he who is certain to have a descendant that wins the lottery—who wins the lottery, it’s that one descendant of him who wins it, and not his other one(s). Once a descendant realizes he is just one of the many copies, he then becomes uncertain whether he is the one who will win the lottery, so will be surprised when he learns whether he is. I think the interesting questions here are
1) Consider the epistemic state of the ancestor. He believes he is certain to win the lottery. There is an argument that he’s justified in believing this.
2) Now consider the epistemic state of a descendant, immediately after discovering that he is one of several duplicates, but before he learns anything about which one. There is some sense in which his (the descendant’s) uncertainty about whether he (the descendant) will win the lottery has changed from what it was in 1). Aside: in a Bayesian framework, this means having received some information, some evidence on which to update. But the only plausible candidate in sight is the knowledge that he is now just one particular one of the duplicates, not the ancestor anymore (e.g., because he has just awoken from the procedure). But of course, he knew that was going to happen with certainty before, so some deny that he learns anything at all. This seems directly analogous to Sleeping Beauty’s predicament.
3) Descendant now learns whether he’s the one who’s won the lottery. Descendant could not have claimed that with certainty before, so he definitely does receive new information, and updates accordingly (all of them do). There is some sense in which the information received at this point exactly cancels out the information(?) in 2).
A couple points:
Of course, Bayesians can’t revise certain knowledge, so the standard analysis gets stuck on square 1. But I don’t see that the story changes in any significant way if we substitute “reasonable certainty(epsilon)” throughout, so I’m happy to stipulate if necessary.
Bayesians have a problem with de se information: “I am here now”. The standard framework on which Bayes’ Theorem holds deals with de re information. De se and de dicto statements have to be converted into de re statements before they can be processed as evidence. This has to be done via various calibrations that adequately disambiguate possibilities and interpret contexts and occasions: who am I, what time is it, and where am I. This process is often taken for granted, because it usually happens transparently and without error. Except when it doesn’t.
I may need to be providing a more extensive philosophical context about personal identity for this to make sense, I’m not sure.
With respect to the descendant “changing their mind” on the probabilility of winning the lottery: when the descendant says “I will win the lottery” perhaps that is a different statement to when the ancestor says “I will win the lottery”. For the ancestor, “I” includes all the ancestor’s descendants. For descendant X, “I” refers to only X (and their descendants, if any). Hence the sense that there is an update occurring is an illusion; the quotation is the same, the referent is not. There need be no information transferred.
But anyway, yes, that’s correct that the referents of the two claims aren’t the same. This could stand some further clarification as to why. In fact, Descendant’s claim makes a direct reference to the individual who uttered it at the moment it’s uttered, but Ancestor’s claim is not about himself in the same way. As you say, he’s attempting to refer to all of his descendants, and on that basis claim identity with whichever particular one of them happens to win the lottery, or not, as the case may be. (As I note above, this is not your usual equivalence relation.) This is an opaque context, and Ancestor’s claim fails to refer to a particular individual (and not just because that individual exists only in the future). He can only make a conditional statement: given that X is whoever it is will win the lottery (or not), the probability that person will win the lottery (or not) is trivial. He lacks something that allows him to refer to Descendant outside the scope of the quantifier. Descendant does not lack this, he has what Ancestor did not have—the wherewithal to refer to himself as a definite individual, because he is that individual at the time of the reference.
But a puzzle remains. On this account, Ancestor has no credence that Descendant will win the lottery, because he doesn’t have the means to correctly formulate the proposition in which he is to assert a credence, except from inside the scope of a universal quantifier. Descendant does have the means, can formulate the proposition (a de se proposition), and can now assert a credence in it based on his understanding of his situation with respect to the facts he knows. And the puzzle is, Descendant’s epistemic state is certainly different from Ancestor’s, but it seems it didn’t happen through Bayesian updating. Meanwhile, there is an event that Descendant witnessed that served to narrow the set of possible worlds he situates himself in (namely, that he is now numerically distinct from any of the other descendants), but, so the argument goes, this doesn’t count as any kind of evidence of anything. It seems to me the basis for requiring diachronic consistency is in trouble.
On further reflection, both Ancestor and each Descendant can consider the proposition P(X) = “X is a descendant & X is a lottery winner”. Given the setup, Ancestor can quantify over X, and assign probability 1/N to each instance. That’s how the statement {”I” will win the lottery with probability 1} is to be read, in conjunction with a particular analysis of personal identity that warrants it. This would be the same proposition each descendant considers, and also assigns probability 1/N to. On this way of looking at it, both Ancestor and each descendant are in the same epistemic state, with respect to the question of who will win the lottery.
Ok, so far so good. This same way of looking at things, and the prediction about probability of descendants, is a way of looking at the Sleeping Beauty problem I tried to explain some months ago, and from what I can see is an argument for why Beauty is able to assert on Sunday evening what the credence of her future selves should be upon awakening (which is different from her own credence on Sunday evening), and therefore has no reason to change it when she later awakens on various occasions. It didn’t seem to get much traction then, probably because it was also mixed in with arguments about expected frequencies.
I don’t think that’s relevant. If a copy would be not surprised to learn that it is the winning copy, does that mean it would be surprised to learn that it is not the winning copy? Or is it sensible that the lower probability event be the higher surprise event?
Of course, the winning copy will have some kind of self-awareness “Oh, I’m that copy” but of course it has a memory of expecting exactly that from the copy that won the lottery.
I think this is where your view breaks down.Each individual should be unsurprised that an individual will win. But each individual should be as surprised that they are the lucky winning copy as a normal person would be surprised that they are the lucky person winning a normal lottery. All you’ve done is reduced the interpersonal distance between the different lottery players, not changed the underlying probabilities- and so while the level of surprise may decrease on other issues (like predicting what the winnings will be used for) it shouldn’t decrease on the location of the winner.
That may make clearer my view, if you word it as “this one shares a cell with the winning ticket” rather than “I won the lottery,” then personhood and identity isn’t an issue besides the physical aspect.
I’m thinking about how those models work together.
Like, if I win the lottery, I should think “Could I be confused? Hallucinating? Deceived? Just lucky?” Seems like, if I win the lottery vs. my clones, I should think the same things. The case that that’s what surprise is about is strong.
In the case of the regular lottery before the draw I do expect someone to win, but that future person will almost certainly not contain any of my memories. When I do win I can point back to my past self that bought the ticket and think “What were the chances he would win?” But in the case of the copies when I point back to myself and ask “What were the chance he would win?”, the answer is clearly “about 1”.
Along the lines of Will’s ‘Hallucinating? Deceived?’ stream of thought we can consider the case where your knowledge that you won the lottery comes from a test which has a 1% chance of false positives every time it is applied. Obviously you would strongly doubt that you were in fact the winner of the lottery even when the test tells you that you are. Hallucinating is far less likely than 1%, deception depends on the circumstance and details and it may be at least be worth a quick reality check to verify that you are not dreaming. This is the sense of ‘surprise’ that Will is considering equivalent to a standard lottery win.
This is not me disagreeing with your position—I upvoted each of your last few comments here. I totally agree with you that you should not be surprised that you win. Before the cloning you were totally expecting to win the lottery. It is only after the cloning and before being told whether ‘you’ won the lottery that you were not expecting the boon.
I don’t consider the whole subjective experience thing to be particularly confusing. It just requires careful expression of what ‘you’ is being discussed and precise description of the conditional probabilities being considered.
The way I’m thinking about this is “I shuffle a deck of playing cards until it is ordered randomly, then turn over one card.”
I get the 4 of ♥. Am I surprised? In one sense, yes- I couldn’t have told you that I would have drawn that card with anything more than 2% certainty. In another sense, no- I expected that card was as likely as any other card. If I drew the 14 of ♥, then I would be surprised, because my model ascribed 0 probability to that event.
And so it seems like the normal measure of surprise is “can I reject the null hypothesis that this occurred by chance?”. If Sleeping Beauty only has experiences consistent with her model of what will happen, why be surprised, even if those experiences individually have very tiny probabilities of occurring?
That isn’t quite what I’m talking about. Obviously I shouldn’t be surprised when a discrete event with a probability as high as any other discrete event occurs. This isn’t an anthropic issue at all. But I think we can agree that if I buy a lottery ticket and win I should be surprised. But if I copy myself a million times and all copies wake up with lottery tickets (no other tickets having been issued) I don’t think I can even be surprised to be the copy with the winning ticket- since I could tell you at the outset there would be a copy of me holding that ticket.
I’m not seeing the relevant difference between this and a million unrelated people holding lottery tickets. Am I missing something?
So obviously your person doesn’t magically transfer from the current copy of you to future copies of you. Rather, those future persons are you because they are psychologically continuous with the present you. Now when you make multiple copies of yourself it isn’t right to say that just one of them will be you. You may never experience both of them but from the perspective of each copy you are their past. So when all million copies of you wake up all of them will feel like they are the next stage of you. All of them will be right. Given that you know there will be a future stage of you that will win the lottery how can that copy (the copy that is the future stage of you that has won the lottery) be surprised? The copy has, in it’s past, a memory of being told that there would be exactly one copy psychologically continuous with his past self. Of course, the winning copy will have some kind of self-awareness “Oh, I’m that copy” but of course it has a memory of expecting exactly that from the copy that won the lottery.
I may need to be providing a more extensive philosophical context about personal identity for this to make sense, I’m not sure.
I don’t think personal identity is a mathematical equivalence relation. Specifically, it’s not symmetric: “I’m the same person you met yesterday” actually needs to read “I was the same person you met yesterday”; “I will be the same person tomorrow” is a prediction that may fail (even assuming I survive that long). This yields failures of transitivity: “Y is the same person as X” and “Z is the same person as X” doesn’t get you “Y is the same person as Z”.
It’s not the ancestor—he who is certain to have a descendant that wins the lottery—who wins the lottery, it’s that one descendant of him who wins it, and not his other one(s). Once a descendant realizes he is just one of the many copies, he then becomes uncertain whether he is the one who will win the lottery, so will be surprised when he learns whether he is. I think the interesting questions here are
1) Consider the epistemic state of the ancestor. He believes he is certain to win the lottery. There is an argument that he’s justified in believing this.
2) Now consider the epistemic state of a descendant, immediately after discovering that he is one of several duplicates, but before he learns anything about which one. There is some sense in which his (the descendant’s) uncertainty about whether he (the descendant) will win the lottery has changed from what it was in 1). Aside: in a Bayesian framework, this means having received some information, some evidence on which to update. But the only plausible candidate in sight is the knowledge that he is now just one particular one of the duplicates, not the ancestor anymore (e.g., because he has just awoken from the procedure). But of course, he knew that was going to happen with certainty before, so some deny that he learns anything at all. This seems directly analogous to Sleeping Beauty’s predicament.
3) Descendant now learns whether he’s the one who’s won the lottery. Descendant could not have claimed that with certainty before, so he definitely does receive new information, and updates accordingly (all of them do). There is some sense in which the information received at this point exactly cancels out the information(?) in 2).
A couple points:
Of course, Bayesians can’t revise certain knowledge, so the standard analysis gets stuck on square 1. But I don’t see that the story changes in any significant way if we substitute “reasonable certainty(epsilon)” throughout, so I’m happy to stipulate if necessary.
Bayesians have a problem with de se information: “I am here now”. The standard framework on which Bayes’ Theorem holds deals with de re information. De se and de dicto statements have to be converted into de re statements before they can be processed as evidence. This has to be done via various calibrations that adequately disambiguate possibilities and interpret contexts and occasions: who am I, what time is it, and where am I. This process is often taken for granted, because it usually happens transparently and without error. Except when it doesn’t.
I hope you do.
With respect to the descendant “changing their mind” on the probabilility of winning the lottery: when the descendant says “I will win the lottery” perhaps that is a different statement to when the ancestor says “I will win the lottery”. For the ancestor, “I” includes all the ancestor’s descendants. For descendant X, “I” refers to only X (and their descendants, if any). Hence the sense that there is an update occurring is an illusion; the quotation is the same, the referent is not. There need be no information transferred.
I didn’t quite follow this. From where to where?
But anyway, yes, that’s correct that the referents of the two claims aren’t the same. This could stand some further clarification as to why. In fact, Descendant’s claim makes a direct reference to the individual who uttered it at the moment it’s uttered, but Ancestor’s claim is not about himself in the same way. As you say, he’s attempting to refer to all of his descendants, and on that basis claim identity with whichever particular one of them happens to win the lottery, or not, as the case may be. (As I note above, this is not your usual equivalence relation.) This is an opaque context, and Ancestor’s claim fails to refer to a particular individual (and not just because that individual exists only in the future). He can only make a conditional statement: given that X is whoever it is will win the lottery (or not), the probability that person will win the lottery (or not) is trivial. He lacks something that allows him to refer to Descendant outside the scope of the quantifier. Descendant does not lack this, he has what Ancestor did not have—the wherewithal to refer to himself as a definite individual, because he is that individual at the time of the reference.
But a puzzle remains. On this account, Ancestor has no credence that Descendant will win the lottery, because he doesn’t have the means to correctly formulate the proposition in which he is to assert a credence, except from inside the scope of a universal quantifier. Descendant does have the means, can formulate the proposition (a de se proposition), and can now assert a credence in it based on his understanding of his situation with respect to the facts he knows. And the puzzle is, Descendant’s epistemic state is certainly different from Ancestor’s, but it seems it didn’t happen through Bayesian updating. Meanwhile, there is an event that Descendant witnessed that served to narrow the set of possible worlds he situates himself in (namely, that he is now numerically distinct from any of the other descendants), but, so the argument goes, this doesn’t count as any kind of evidence of anything. It seems to me the basis for requiring diachronic consistency is in trouble.
On further reflection, both Ancestor and each Descendant can consider the proposition P(X) = “X is a descendant & X is a lottery winner”. Given the setup, Ancestor can quantify over X, and assign probability 1/N to each instance. That’s how the statement {”I” will win the lottery with probability 1} is to be read, in conjunction with a particular analysis of personal identity that warrants it. This would be the same proposition each descendant considers, and also assigns probability 1/N to. On this way of looking at it, both Ancestor and each descendant are in the same epistemic state, with respect to the question of who will win the lottery.
Ok, so far so good. This same way of looking at things, and the prediction about probability of descendants, is a way of looking at the Sleeping Beauty problem I tried to explain some months ago, and from what I can see is an argument for why Beauty is able to assert on Sunday evening what the credence of her future selves should be upon awakening (which is different from her own credence on Sunday evening), and therefore has no reason to change it when she later awakens on various occasions. It didn’t seem to get much traction then, probably because it was also mixed in with arguments about expected frequencies.
I meant from anywhere to the descendant. Perhaps that wasn’t the best wording.
I don’t think that’s relevant. If a copy would be not surprised to learn that it is the winning copy, does that mean it would be surprised to learn that it is not the winning copy? Or is it sensible that the lower probability event be the higher surprise event?
I think this is where your view breaks down.Each individual should be unsurprised that an individual will win. But each individual should be as surprised that they are the lucky winning copy as a normal person would be surprised that they are the lucky person winning a normal lottery. All you’ve done is reduced the interpersonal distance between the different lottery players, not changed the underlying probabilities- and so while the level of surprise may decrease on other issues (like predicting what the winnings will be used for) it shouldn’t decrease on the location of the winner.
That may make clearer my view, if you word it as “this one shares a cell with the winning ticket” rather than “I won the lottery,” then personhood and identity isn’t an issue besides the physical aspect.
I’m thinking about how those models work together.
Like, if I win the lottery, I should think “Could I be confused? Hallucinating? Deceived? Just lucky?” Seems like, if I win the lottery vs. my clones, I should think the same things. The case that that’s what surprise is about is strong.
In the case of the regular lottery before the draw I do expect someone to win, but that future person will almost certainly not contain any of my memories. When I do win I can point back to my past self that bought the ticket and think “What were the chances he would win?” But in the case of the copies when I point back to myself and ask “What were the chance he would win?”, the answer is clearly “about 1”.
Along the lines of Will’s ‘Hallucinating? Deceived?’ stream of thought we can consider the case where your knowledge that you won the lottery comes from a test which has a 1% chance of false positives every time it is applied. Obviously you would strongly doubt that you were in fact the winner of the lottery even when the test tells you that you are. Hallucinating is far less likely than 1%, deception depends on the circumstance and details and it may be at least be worth a quick reality check to verify that you are not dreaming. This is the sense of ‘surprise’ that Will is considering equivalent to a standard lottery win.
This is not me disagreeing with your position—I upvoted each of your last few comments here. I totally agree with you that you should not be surprised that you win. Before the cloning you were totally expecting to win the lottery. It is only after the cloning and before being told whether ‘you’ won the lottery that you were not expecting the boon.
I don’t consider the whole subjective experience thing to be particularly confusing. It just requires careful expression of what ‘you’ is being discussed and precise description of the conditional probabilities being considered.