I think there are some serious issues with the first two arguments. For the watchman case, the watchman is watching the room and has a chance to see it empty. But you don't have a similar option, because there's no way you could possibly come to realize you don't exist; if you're even observing at all, every possible world in which you don't exist is immediately ruled out. If you fix the watchman's description such that he also has no chance to witness it empty - maybe he's told that heads means you appear in his room and tails means you appear in his room and a million other people appear outside - then it would also be reasonable for him to be totally 50/50 once you appear, right?
The bigger issue I have, though, is with the second one. It seems just false to say the total share of people coming from larger families is greater than the total share of people coming from smaller ones! That seems like a totally contingent fact - if you had a world of ten families where nine had two children and one had six children, then most people would be from small families. And further, it does seem totally reasonable to think that the odds you came from a big family depend on facts about how large other families tend to be. If I find out that the average family in my world has three kids, I would assume I probably had two siblings. It would super weird to me if someone *didn't* think that mattered. Of course, it doesn't matter in a metaphysical sense - it's not like other people having more children causes my parents to have more children, except maybe by increasing the social pressure to do likewise. But if I'm assuming my parents are probably typical, then why not look at what size typical families are?
Also, this seems open to another super strong objection (imo) to the SIA and thirding, which is that it requires affirming that it's sometimes reasonable to believe one thing today even though you know you'll have good reason to believe another thing tomorrow. You can imagine a situation where God flips a coin and puts me in a small family if it's heads and a big family if it's tails. Before the flip, I should definitely think the odds are 50/50. But once I wake up as a newborn, I should immediately update towards tails in your view, right? But then it just seems inconceivable to me that I shouldn't updates towards tails *before* the flip, knowing that I will inevitably do that update later. Is there a good explanation for how this could be made coherent?
Re watchman, the thing that's weird is that there's some event in the world that may or may not occur. Whichever of you has more evidence should just defer to the other. So the question is which one's guess is better?
The claim is that all else equal a bigger family is likelier. So if a coin is flipped, if it comes up heads, your parents had a big family, tails a small one, you should think it came up heads. But alternatives to SIA hold that this is contingent on the number of people other than you. I think this addresses your last case.
I definitely think the watchman is in a position to make a better guess, but that's because the situation is set up in such a way that he has a chance to see an empty room and you don't; if the situation were equalized to make it so that he never had any chance to see any empty room, he wouldn't have any more information than you do and SSA-like reasoning would be the reasonable heuristic for him too. I actually think that's a good argument *for* SSA, but at the very least it shows the dynamic you're talking about is sensitive to the specifics of the situation - whether the watchman's reasoning mirrors the general SSA approach or the general SIA approach depends on the way the situation is constructed, not on some general fact about epistemology.
For the second issue though, I still don't see how this avoids the paradox I'm talking about. Before the coin flip, your credence should obviously be 50/50. But if you should update towards heads the moment you wake up, and you know you're going to wake up after the coin toss no matter what, then why shouldn't you update your credence before the coin flip? If I know beyond a shadow of a doubt that something will happen tomorrow that increases my credence in heads, then it seems almost analytically true that I should increase that credence now. But that can't be right in this situation, because I know my initial credence is correct. So the only option, imo, is rejecting the claim that waking up can increase my credence by itself.
If the watchman is in a position to make a better guess, why shouldn't you just defer to his guess?
In sleeping beauty, you will change your mind tomorrow but that's because tomorrow you'll have less evidence about the current time. You tomorrow won't know it's the day after the coin flip. And because it might be the third day, there's no impermissible updating.
It would be reasonable to trust the watchman if they're in a position to make a better guess, sure. But that position isn't some inherent feature of a non-anthropic perspective. It's just a result of how the situation is set up. You could alter the situation easily to make it so the watchman was in the same epistemic position you are, or in a better position that gave you reason to diverge from the SIA assumption. So the mere fact that you should defer to them here doesn't imply anything overall.
Otherwise, I still don't think it would make sense to abandon the 50/50 credence just because you lose information after waking up - presumably, when you wake up, you know that you've lost that information, so why not just stay firm on the credence you had when you had more information? If I know that I used to know more, and when I knew more, I believed X, then I should believe X even if I no longer know what it is that led to me to believe it.
Wait so then why shouldn't they defer to the watchmen in your case?
The reason they shouldn't defer to their past self is that they have misleading evidence currently, where they are in a position epistemically indistuinguishable from an observer with more evidence.
The watchman in my case has no more information than you do, because he'll see you pop into existence regardless of how the coin lands. So he would give the "SSA-ish" advice that your credence should be 50/50. Maybe you should defer to him, but the point is that his judgment would no longer confirm the SIA. Whether the watchman is worth deferring to and whether he'll tell you to defer towards the SSA versus the SIA is dependent on how the situation is described.
I'm not sure what you mean when you say "epistemically indistinguishable from an observer with more evidence." They have the evidence they knew they'd have before the coin flip, and that's what throws things off.
What do you think of the following anthropic argument against certain forms of theism:
1. I currently know that I'm on earth.
2. If certain forms of theism are true, I exist finitely on earth and infinitely in heaven, so the probability that I would currently know that I'm on earth are 0%.
3. If naturalism is true, there is a non-zero chance that I'd currently know that I'm on earth.
4. Therefore, the fact that I currently know that I'm on earth is evidence strongly favouring naturalism over this specific form of theism.
This argument could also be run based on any time-sensitive knowledge, making a ridiculously strong case against a form of theism where I exist finitely on earth and infinitely in heaven (or maybe hell, given that I'm making this argument).
Do you think that the easy way out is to reject premise 3 because of Huemer's immortality stuff and also the anthropic argument FOR theism showing that the probability of my existence on naturalism is plausibly 0?
Thanks for the link this seems super interesting. Could another response also be to suggest that the future is finite? I don’t currently know of anyone who seriously thinks this but it seems like a way to save the probabilities for naturalism.
You’ve probably answered this before too somewhere else, but to deal with this could I just appeal to the fact that I’m really not sure whether there actually are Beth 2 possible people, or how many possible people there are at all? If I split my credences across there being different numbers of possible people it seems that I should no longer think that there’s a 0% chance that I’d exist.
Or even I could say that, since the evidence for naturalism is overwhelming (I’m not sure I really think this but I’m interested in seeing ways out for the naturalist), then this is good evidence that the number of possible people is finite (because this makes the probability of my existence non-zero). Is this the right move to make for a naturalist?
Watchman and you have different probability spaces and receive different evidence. The fact that SIA treats these situation the same way is not a point in its favor.
> Bigger families
The initial premise is wrong. Like in Doomsday argument, SSA makes stupid assumption and then you use compensatorial assumption of SIA to make it less stupid. Well, how about not making stupid assumptions in the first place?
> The first Carlsmith result: moving boulders with your mind (and other illicit causation and dependency)
It's an argument against SSA, not in favor of SIA. And Carlsmith also mentions a SIA analogue of save the puppy. He personally doesn't find as bad but it's his personal views. I don't see why we should accept either of them.
> The second Carlsmith result
Another point not in favor of SIA. Observing your survival is actual evidence about the coin toss, because you couldn't be sure to observe this no matter what. Meanwhile if you are not created you have no opportunity to observe or not observe something. Once again, different possible observables - different evidence that you get, therefore different estimates.
> The third Carlsmith result
Another point against SSA, not in favor of SIA. SIA, meanwhile, has the opposite problem of assuming that infinite observers is the most probable case and then not being able to work in it.
> But surely finding out that prior to birth, one pondered anthropics for a few seconds, does not affect how one should reason about anthropics.
It absolutely does! Remember, only SIA treats death and non existence as the same. If you can observe your own non existence the situation is quite different from when you can't. That's why SIA somewhat works with the intuition of souls.
//Watchman and you have different probability spaces and receive different evidence. The fact that SIA treats these situation the same way is not a point in its favor.//
Which of you knows more?? Whichever has extra evidence, the other one should defer to.
//The initial premise is wrong. Like in Doomsday argument, SSA makes stupid assumption and then you use compensatorial assumption of SIA to make it less stupid. Well, how about not making stupid assumptions in the first place?//
You keep assuming falsely that my arguments are just addressing SSA. No part of my argument assumed that alternatives to SIA must be SSA. Every plausible view should say you're more likely to be part of bigger families, all else equal, because they have a greater share of people.
//It's an argument against SSA, not in favor of SIA. And Carlsmith also mentions a SIA analogue of save the puppy. He personally doesn't find as bad but it's his personal views. I don't see why we should accept either of them.//
Well maybe read the bit where I explain why this applies to every view other than SIA!! The modified version of save the puppy isn't that bad imo in isn't any different from other cases, so doesn't give you a reason to update.
//Another point not in favor of SIA. Observing your survival is actual evidence about the coin toss, because you couldn't be sure to observe this no matter what. Meanwhile if you are not created you have no opportunity to observe or not observe something. Once again, different possible observables - different evidence that you get, therefore different estimates.//
Well at this point you couldn't have survived. Remember, the relevant difference is whether other people who were not you were created and then killed. You can just bite the bullet here, but that's very implausible.
//Another point against SSA, not in favor of SIA. SIA, meanwhile, has the opposite problem of assuming that infinite observers is the most probable case and then not being able to work in it.//
Again, read more carefully, where I explain why this applies to every view other than SIA.
//It absolutely does! Remember, only SIA treats death and non existence as the same. If you can observe your own non existence the situation is quite different from when you can't. That's why SIA somewhat works with the intuition of souls.//
The weird results of SIA shouldn't start being acceptable if we thought for like 5 minutes about anthropics prior to birth.
I'm going to think about these, but here's an argument against SIA*. Suppose God randomly chooses an integer between 1 and 3 with equal probability. If it's 1, he does nothing and creates nothing. If it's 2, he creates you specifically (not just any person) and gives you a red jacket. If it's 3, he creates you specifically plus 999 other people, and gives ten of you guys red jackets, the rest blue. You discover (somewhat redundantly) that you exist and have a red jacket.
Let EVEN be the probability that God picked an even number (i.e., 2), and let E be your evidence that you exist and have a red jacket. On your view, you want to say the prior on EVEN is 1/3, but SIA leads you to update to 11/1001. So E disconfirms EVEN. On the other hand, imagine that E were false. This is true iff you didn't exist or didn't have a red jacket. If you didn't exist, God would've picked the odd number 1 with probability 1. If you existed but had a blue jacket, God would've picked the odd number 3 with probability 1. In either case, the posterior of EVEN would be 0. So ~E also (maximally) disconfirms EVEN, relative to our background assumptions. This violates conservation of evidence.
* This is actually more an argument against a specific reading of SIA, wherein you have a prior, guided by physical chances, that assigns non-identically-1 probability to scenarios in which you don't exist, and which you take SIA to be an update procedure upon.
SIA doesn't do that updating. If two theories both entail that you, in particular, exist, they are equal, for then your reference class is just one person--you.
If the theories are “God picked an odd number” and “God picked an even number,” then they don’t both entail that I exist. Only the second one does. Still, though, I think your basic objection is right - I’m not in an epistemically indistinguishable situation from the other people in case 3, since there only I have been guaranteed existence if God had counterfactually chosen 2. Thanks for the correction.
But I think if you remove the “created me specifically” part from the setup, it may still go through. Conditional on me not existing on this truncated setup that refers to no one's specific identity, we should arguably go with 1/3 credence on EVEN, which will still lead to violating conservation of evidence. I think you'll reply that this point isn't true - that if I don't exist, then smaller worlds are in fact more likely, since larger worlds which have more people in them will have more opportunities for one of them to be me. (That's what I was trying to block with the "created me specifically" part.) I guess this seems metaphysically dubious to me. But maybe this is question-begging.
Alternatively, though, I could try taking my original example and just try making it more symmetric. Imagine God has in mind a thousand possible people labeled P_1 through P_1000, but whose specific labels God always keeps hidden. He rolls a 1001-sided die. If it's N (1 <= N <= 1000), he creates person P_N specifically and gives them a red jacket. If it's 1001, he creates all P_N's, then gives ten of them red jackets, the rest blue, and informs all of them they're one of the P_N's. Next, I wake up and find that I have a red jacket. Let K be my actual secret number, unknown to me. Regardless of whether I exist and have a red jacket, I have evidence against the hypothesis that God rolled K.
I don't really understand how your objection is supposed to work in this revised thought experiment. It's true that the various die outcomes mention me specifically, but only in a way that they're symmetric with respect to other possible people, and I have no way of knowing which of those possible people I'm supposed to be.
Right, so then SIA would tell you to be indifferent between odd and even--both entail that I exist.
In the modified case, well for one, there can't be a violation of conservation of expected evidence because you didn't exist previously! Upon finding out that you exist, you update in favor of some theories, but that's perfectly kosher. Given that I exist, by credence in it being 1 should go down, for instance, relative to a third party who didn't know I exist. This isn't violation of expected evidence.
When you say "we should arguably go with 1/3 credence on EVEN, which will still lead to violating conservation of evidence," who are you talking about? There is no me to bet prior to the experiment!
In regards to your last example, you get evidence that God rolled K. If God rolled K, the number of people with my evidence is 1, while if he rolled 1001, then it's less, because only 10 people have my evidence, including the red jacket.
>When you say "we should arguably go with 1/3 credence on EVEN, which will still lead to violating conservation of evidence," who are you talking about? There is no me to bet prior to the experiment!
I agree! This is in general why I think it makes no sense to put a prior of less than 1 on my own (current) existence. If you put a prior of less than 1 on it, who are you talking about who's doing that? As mentioned in the footnote of my first comment, that's part of the formulation I'm trying to attack. But if you do in fact already think this, then maybe what I'm saying doesn't/didn't apply to you.
>In regards to your last example, you get evidence that God rolled K. If God rolled K, the number of people with my evidence is 1, while if he rolled 1001, then it's less, because only 10 people have my evidence, including the red jacket.
Suppose my number secretly happens to be 1, without me finding out. Of the 1010 possible people with evidence subjectively indistinguishable from mine, only one of them lives in a world where God rolled 1. So my credence on rolling 1 should go down from 1/1001 to 1/1010. Since 1 is symmetric (relative to my evidence) with respect to every other number <= 1000, it follows that my credence on God rolling my number should be 1/1010. Waking up with a red jacket disconfirms God rolling my number.
On the other hand, if I didn't exist, God definitely didn't roll my number. If I had a blue jacket, God definitely rolled 1001, which is not my number. Thus, not waking up with a red jacket also disconfirms God rolling my number!
//I agree! This is in general why I think it makes no sense to put a prior of less than 1 on my own (current) existence. If you put a prior of less than 1 on it, who are you talking about who's doing that? As mentioned in the footnote of my first comment, that's part of the formulation I'm trying to attack. But if you do in fact already think this, then maybe what I'm saying doesn't/didn't apply to you.//
It's true that I definitely exist. But this doesn't mean that it's necessary that I exist or that my prior, before observing that I exist, in my existence should be one. I think this is the wrong way to think about priors--maybe I'll write an essay about this at some point. There are lots of cases where you couldn't have otherwise existed but get evidence for a hypothesis--e.g. the firing squad case.
//Suppose my number secretly happens to be 1, without me finding out. Of the 1010 possible people with evidence subjectively indistinguishable from mine, only one of them lives in a world where God rolled 1. //
Sure, if you don't know which one you are, then you should think that the theory that 1010 people exist is better. Once you know who you are, you'll rule out all theories that don't entail that particular person exists. But I'm not sure what the objection is supposed to be.
>It's true that I definitely exist. But this doesn't mean that it's necessary that I exist or that my prior, before observing that I exist, in my existence should be one. I think this is the wrong way to think about priors--maybe I'll write an essay about this at some point. There are lots of cases where you couldn't have otherwise existed but get evidence for a hypothesis--e.g. the firing squad case.
I realize that's your position. My point was that it's not clear how you square this view with your objection about not being able to coherently conditionalize on yourself not existing in order to get around one of my examples violating conservation of evidence.
>Sure, if you don't know which one you are, then you should think that the theory that 1010 people exist is better. Once you know who you are, you'll rule out all theories that don't entail that particular person exists. But I'm not sure what the objection is supposed to be.
My objection is that conservation of evidence is violated. My evidence E (= "I exist and my jacket is red") can't disconfirm the hypothesis "God rolled my number" along with its negation also disconfirming that hypothesis. But it does do that on your theory, for the reason I spelled out in my last comment:
P(God rolled my number|E) = ∑ (God rolled n|E & my number is n)*P(my number is n|E)
= ∑ 1/1010 * 1/1000
= 1/1010
< 1/1001
where the sum goes from n = 1 to 1000. The fact that (God rolled n|E & my number is n) = 1/1010 comes from SIA: if my number happens to be n (for any valid n), of the 1010 possible people with my exact evidence, only one of them lives in a world where God rolled n. (It's true that on the setup I can only really be at most two of them, but I have no idea which two and neither do the other test subjects; everything is symmetric.) And on the other hand, the negation of E is totally incompatible with God rolling my number.
Note that you can't respond that conditionalizing on my number being n breaks the symmetry. Conditionalizing on a hypothesis being true is different from conditionalizing on knowledge of the hypothesis being true. Only the latter breaks the symmetry, whereas the former is what I'm using.
I think there are some serious issues with the first two arguments. For the watchman case, the watchman is watching the room and has a chance to see it empty. But you don't have a similar option, because there's no way you could possibly come to realize you don't exist; if you're even observing at all, every possible world in which you don't exist is immediately ruled out. If you fix the watchman's description such that he also has no chance to witness it empty - maybe he's told that heads means you appear in his room and tails means you appear in his room and a million other people appear outside - then it would also be reasonable for him to be totally 50/50 once you appear, right?
The bigger issue I have, though, is with the second one. It seems just false to say the total share of people coming from larger families is greater than the total share of people coming from smaller ones! That seems like a totally contingent fact - if you had a world of ten families where nine had two children and one had six children, then most people would be from small families. And further, it does seem totally reasonable to think that the odds you came from a big family depend on facts about how large other families tend to be. If I find out that the average family in my world has three kids, I would assume I probably had two siblings. It would super weird to me if someone *didn't* think that mattered. Of course, it doesn't matter in a metaphysical sense - it's not like other people having more children causes my parents to have more children, except maybe by increasing the social pressure to do likewise. But if I'm assuming my parents are probably typical, then why not look at what size typical families are?
Also, this seems open to another super strong objection (imo) to the SIA and thirding, which is that it requires affirming that it's sometimes reasonable to believe one thing today even though you know you'll have good reason to believe another thing tomorrow. You can imagine a situation where God flips a coin and puts me in a small family if it's heads and a big family if it's tails. Before the flip, I should definitely think the odds are 50/50. But once I wake up as a newborn, I should immediately update towards tails in your view, right? But then it just seems inconceivable to me that I shouldn't updates towards tails *before* the flip, knowing that I will inevitably do that update later. Is there a good explanation for how this could be made coherent?
Re watchman, the thing that's weird is that there's some event in the world that may or may not occur. Whichever of you has more evidence should just defer to the other. So the question is which one's guess is better?
The claim is that all else equal a bigger family is likelier. So if a coin is flipped, if it comes up heads, your parents had a big family, tails a small one, you should think it came up heads. But alternatives to SIA hold that this is contingent on the number of people other than you. I think this addresses your last case.
I definitely think the watchman is in a position to make a better guess, but that's because the situation is set up in such a way that he has a chance to see an empty room and you don't; if the situation were equalized to make it so that he never had any chance to see any empty room, he wouldn't have any more information than you do and SSA-like reasoning would be the reasonable heuristic for him too. I actually think that's a good argument *for* SSA, but at the very least it shows the dynamic you're talking about is sensitive to the specifics of the situation - whether the watchman's reasoning mirrors the general SSA approach or the general SIA approach depends on the way the situation is constructed, not on some general fact about epistemology.
For the second issue though, I still don't see how this avoids the paradox I'm talking about. Before the coin flip, your credence should obviously be 50/50. But if you should update towards heads the moment you wake up, and you know you're going to wake up after the coin toss no matter what, then why shouldn't you update your credence before the coin flip? If I know beyond a shadow of a doubt that something will happen tomorrow that increases my credence in heads, then it seems almost analytically true that I should increase that credence now. But that can't be right in this situation, because I know my initial credence is correct. So the only option, imo, is rejecting the claim that waking up can increase my credence by itself.
If the watchman is in a position to make a better guess, why shouldn't you just defer to his guess?
In sleeping beauty, you will change your mind tomorrow but that's because tomorrow you'll have less evidence about the current time. You tomorrow won't know it's the day after the coin flip. And because it might be the third day, there's no impermissible updating.
It would be reasonable to trust the watchman if they're in a position to make a better guess, sure. But that position isn't some inherent feature of a non-anthropic perspective. It's just a result of how the situation is set up. You could alter the situation easily to make it so the watchman was in the same epistemic position you are, or in a better position that gave you reason to diverge from the SIA assumption. So the mere fact that you should defer to them here doesn't imply anything overall.
Otherwise, I still don't think it would make sense to abandon the 50/50 credence just because you lose information after waking up - presumably, when you wake up, you know that you've lost that information, so why not just stay firm on the credence you had when you had more information? If I know that I used to know more, and when I knew more, I believed X, then I should believe X even if I no longer know what it is that led to me to believe it.
Wait so then why shouldn't they defer to the watchmen in your case?
The reason they shouldn't defer to their past self is that they have misleading evidence currently, where they are in a position epistemically indistuinguishable from an observer with more evidence.
The watchman in my case has no more information than you do, because he'll see you pop into existence regardless of how the coin lands. So he would give the "SSA-ish" advice that your credence should be 50/50. Maybe you should defer to him, but the point is that his judgment would no longer confirm the SIA. Whether the watchman is worth deferring to and whether he'll tell you to defer towards the SSA versus the SIA is dependent on how the situation is described.
I'm not sure what you mean when you say "epistemically indistinguishable from an observer with more evidence." They have the evidence they knew they'd have before the coin flip, and that's what throws things off.
What do you think of the following anthropic argument against certain forms of theism:
1. I currently know that I'm on earth.
2. If certain forms of theism are true, I exist finitely on earth and infinitely in heaven, so the probability that I would currently know that I'm on earth are 0%.
3. If naturalism is true, there is a non-zero chance that I'd currently know that I'm on earth.
4. Therefore, the fact that I currently know that I'm on earth is evidence strongly favouring naturalism over this specific form of theism.
This argument could also be run based on any time-sensitive knowledge, making a ridiculously strong case against a form of theism where I exist finitely on earth and infinitely in heaven (or maybe hell, given that I'm making this argument).
Do you think that the easy way out is to reject premise 3 because of Huemer's immortality stuff and also the anthropic argument FOR theism showing that the probability of my existence on naturalism is plausibly 0?
I've addressed that argument here https://benthams.substack.com/p/three-niche-philosophical-objections
Thanks for the link this seems super interesting. Could another response also be to suggest that the future is finite? I don’t currently know of anyone who seriously thinks this but it seems like a way to save the probabilities for naturalism.
Doesn’t work if you accept sia
You’ve probably answered this before too somewhere else, but to deal with this could I just appeal to the fact that I’m really not sure whether there actually are Beth 2 possible people, or how many possible people there are at all? If I split my credences across there being different numbers of possible people it seems that I should no longer think that there’s a 0% chance that I’d exist.
Yeah, I think this is right. But you should think there are Beth 2 possible peopel or more https://benthams.substack.com/p/for-an-unrestricted-self-indication
https://benthams.substack.com/p/the-anthropic-argument-for-theism
Or even I could say that, since the evidence for naturalism is overwhelming (I’m not sure I really think this but I’m interested in seeing ways out for the naturalist), then this is good evidence that the number of possible people is finite (because this makes the probability of my existence non-zero). Is this the right move to make for a naturalist?
> Only SIA accords with non-anthropic evidence
Watchman and you have different probability spaces and receive different evidence. The fact that SIA treats these situation the same way is not a point in its favor.
> Bigger families
The initial premise is wrong. Like in Doomsday argument, SSA makes stupid assumption and then you use compensatorial assumption of SIA to make it less stupid. Well, how about not making stupid assumptions in the first place?
> The first Carlsmith result: moving boulders with your mind (and other illicit causation and dependency)
It's an argument against SSA, not in favor of SIA. And Carlsmith also mentions a SIA analogue of save the puppy. He personally doesn't find as bad but it's his personal views. I don't see why we should accept either of them.
> The second Carlsmith result
Another point not in favor of SIA. Observing your survival is actual evidence about the coin toss, because you couldn't be sure to observe this no matter what. Meanwhile if you are not created you have no opportunity to observe or not observe something. Once again, different possible observables - different evidence that you get, therefore different estimates.
> The third Carlsmith result
Another point against SSA, not in favor of SIA. SIA, meanwhile, has the opposite problem of assuming that infinite observers is the most probable case and then not being able to work in it.
> But surely finding out that prior to birth, one pondered anthropics for a few seconds, does not affect how one should reason about anthropics.
It absolutely does! Remember, only SIA treats death and non existence as the same. If you can observe your own non existence the situation is quite different from when you can't. That's why SIA somewhat works with the intuition of souls.
//Watchman and you have different probability spaces and receive different evidence. The fact that SIA treats these situation the same way is not a point in its favor.//
Which of you knows more?? Whichever has extra evidence, the other one should defer to.
//The initial premise is wrong. Like in Doomsday argument, SSA makes stupid assumption and then you use compensatorial assumption of SIA to make it less stupid. Well, how about not making stupid assumptions in the first place?//
You keep assuming falsely that my arguments are just addressing SSA. No part of my argument assumed that alternatives to SIA must be SSA. Every plausible view should say you're more likely to be part of bigger families, all else equal, because they have a greater share of people.
//It's an argument against SSA, not in favor of SIA. And Carlsmith also mentions a SIA analogue of save the puppy. He personally doesn't find as bad but it's his personal views. I don't see why we should accept either of them.//
Well maybe read the bit where I explain why this applies to every view other than SIA!! The modified version of save the puppy isn't that bad imo in isn't any different from other cases, so doesn't give you a reason to update.
//Another point not in favor of SIA. Observing your survival is actual evidence about the coin toss, because you couldn't be sure to observe this no matter what. Meanwhile if you are not created you have no opportunity to observe or not observe something. Once again, different possible observables - different evidence that you get, therefore different estimates.//
Well at this point you couldn't have survived. Remember, the relevant difference is whether other people who were not you were created and then killed. You can just bite the bullet here, but that's very implausible.
//Another point against SSA, not in favor of SIA. SIA, meanwhile, has the opposite problem of assuming that infinite observers is the most probable case and then not being able to work in it.//
Again, read more carefully, where I explain why this applies to every view other than SIA.
//It absolutely does! Remember, only SIA treats death and non existence as the same. If you can observe your own non existence the situation is quite different from when you can't. That's why SIA somewhat works with the intuition of souls.//
The weird results of SIA shouldn't start being acceptable if we thought for like 5 minutes about anthropics prior to birth.
I'm going to think about these, but here's an argument against SIA*. Suppose God randomly chooses an integer between 1 and 3 with equal probability. If it's 1, he does nothing and creates nothing. If it's 2, he creates you specifically (not just any person) and gives you a red jacket. If it's 3, he creates you specifically plus 999 other people, and gives ten of you guys red jackets, the rest blue. You discover (somewhat redundantly) that you exist and have a red jacket.
Let EVEN be the probability that God picked an even number (i.e., 2), and let E be your evidence that you exist and have a red jacket. On your view, you want to say the prior on EVEN is 1/3, but SIA leads you to update to 11/1001. So E disconfirms EVEN. On the other hand, imagine that E were false. This is true iff you didn't exist or didn't have a red jacket. If you didn't exist, God would've picked the odd number 1 with probability 1. If you existed but had a blue jacket, God would've picked the odd number 3 with probability 1. In either case, the posterior of EVEN would be 0. So ~E also (maximally) disconfirms EVEN, relative to our background assumptions. This violates conservation of evidence.
* This is actually more an argument against a specific reading of SIA, wherein you have a prior, guided by physical chances, that assigns non-identically-1 probability to scenarios in which you don't exist, and which you take SIA to be an update procedure upon.
SIA doesn't do that updating. If two theories both entail that you, in particular, exist, they are equal, for then your reference class is just one person--you.
If the theories are “God picked an odd number” and “God picked an even number,” then they don’t both entail that I exist. Only the second one does. Still, though, I think your basic objection is right - I’m not in an epistemically indistinguishable situation from the other people in case 3, since there only I have been guaranteed existence if God had counterfactually chosen 2. Thanks for the correction.
But I think if you remove the “created me specifically” part from the setup, it may still go through. Conditional on me not existing on this truncated setup that refers to no one's specific identity, we should arguably go with 1/3 credence on EVEN, which will still lead to violating conservation of evidence. I think you'll reply that this point isn't true - that if I don't exist, then smaller worlds are in fact more likely, since larger worlds which have more people in them will have more opportunities for one of them to be me. (That's what I was trying to block with the "created me specifically" part.) I guess this seems metaphysically dubious to me. But maybe this is question-begging.
Alternatively, though, I could try taking my original example and just try making it more symmetric. Imagine God has in mind a thousand possible people labeled P_1 through P_1000, but whose specific labels God always keeps hidden. He rolls a 1001-sided die. If it's N (1 <= N <= 1000), he creates person P_N specifically and gives them a red jacket. If it's 1001, he creates all P_N's, then gives ten of them red jackets, the rest blue, and informs all of them they're one of the P_N's. Next, I wake up and find that I have a red jacket. Let K be my actual secret number, unknown to me. Regardless of whether I exist and have a red jacket, I have evidence against the hypothesis that God rolled K.
I don't really understand how your objection is supposed to work in this revised thought experiment. It's true that the various die outcomes mention me specifically, but only in a way that they're symmetric with respect to other possible people, and I have no way of knowing which of those possible people I'm supposed to be.
Right, so then SIA would tell you to be indifferent between odd and even--both entail that I exist.
In the modified case, well for one, there can't be a violation of conservation of expected evidence because you didn't exist previously! Upon finding out that you exist, you update in favor of some theories, but that's perfectly kosher. Given that I exist, by credence in it being 1 should go down, for instance, relative to a third party who didn't know I exist. This isn't violation of expected evidence.
When you say "we should arguably go with 1/3 credence on EVEN, which will still lead to violating conservation of evidence," who are you talking about? There is no me to bet prior to the experiment!
In regards to your last example, you get evidence that God rolled K. If God rolled K, the number of people with my evidence is 1, while if he rolled 1001, then it's less, because only 10 people have my evidence, including the red jacket.
>When you say "we should arguably go with 1/3 credence on EVEN, which will still lead to violating conservation of evidence," who are you talking about? There is no me to bet prior to the experiment!
I agree! This is in general why I think it makes no sense to put a prior of less than 1 on my own (current) existence. If you put a prior of less than 1 on it, who are you talking about who's doing that? As mentioned in the footnote of my first comment, that's part of the formulation I'm trying to attack. But if you do in fact already think this, then maybe what I'm saying doesn't/didn't apply to you.
>In regards to your last example, you get evidence that God rolled K. If God rolled K, the number of people with my evidence is 1, while if he rolled 1001, then it's less, because only 10 people have my evidence, including the red jacket.
Suppose my number secretly happens to be 1, without me finding out. Of the 1010 possible people with evidence subjectively indistinguishable from mine, only one of them lives in a world where God rolled 1. So my credence on rolling 1 should go down from 1/1001 to 1/1010. Since 1 is symmetric (relative to my evidence) with respect to every other number <= 1000, it follows that my credence on God rolling my number should be 1/1010. Waking up with a red jacket disconfirms God rolling my number.
On the other hand, if I didn't exist, God definitely didn't roll my number. If I had a blue jacket, God definitely rolled 1001, which is not my number. Thus, not waking up with a red jacket also disconfirms God rolling my number!
//I agree! This is in general why I think it makes no sense to put a prior of less than 1 on my own (current) existence. If you put a prior of less than 1 on it, who are you talking about who's doing that? As mentioned in the footnote of my first comment, that's part of the formulation I'm trying to attack. But if you do in fact already think this, then maybe what I'm saying doesn't/didn't apply to you.//
It's true that I definitely exist. But this doesn't mean that it's necessary that I exist or that my prior, before observing that I exist, in my existence should be one. I think this is the wrong way to think about priors--maybe I'll write an essay about this at some point. There are lots of cases where you couldn't have otherwise existed but get evidence for a hypothesis--e.g. the firing squad case.
//Suppose my number secretly happens to be 1, without me finding out. Of the 1010 possible people with evidence subjectively indistinguishable from mine, only one of them lives in a world where God rolled 1. //
Sure, if you don't know which one you are, then you should think that the theory that 1010 people exist is better. Once you know who you are, you'll rule out all theories that don't entail that particular person exists. But I'm not sure what the objection is supposed to be.
>It's true that I definitely exist. But this doesn't mean that it's necessary that I exist or that my prior, before observing that I exist, in my existence should be one. I think this is the wrong way to think about priors--maybe I'll write an essay about this at some point. There are lots of cases where you couldn't have otherwise existed but get evidence for a hypothesis--e.g. the firing squad case.
I realize that's your position. My point was that it's not clear how you square this view with your objection about not being able to coherently conditionalize on yourself not existing in order to get around one of my examples violating conservation of evidence.
>Sure, if you don't know which one you are, then you should think that the theory that 1010 people exist is better. Once you know who you are, you'll rule out all theories that don't entail that particular person exists. But I'm not sure what the objection is supposed to be.
My objection is that conservation of evidence is violated. My evidence E (= "I exist and my jacket is red") can't disconfirm the hypothesis "God rolled my number" along with its negation also disconfirming that hypothesis. But it does do that on your theory, for the reason I spelled out in my last comment:
P(God rolled my number|E) = ∑ (God rolled n|E & my number is n)*P(my number is n|E)
= ∑ 1/1010 * 1/1000
= 1/1010
< 1/1001
where the sum goes from n = 1 to 1000. The fact that (God rolled n|E & my number is n) = 1/1010 comes from SIA: if my number happens to be n (for any valid n), of the 1010 possible people with my exact evidence, only one of them lives in a world where God rolled n. (It's true that on the setup I can only really be at most two of them, but I have no idea which two and neither do the other test subjects; everything is symmetric.) And on the other hand, the negation of E is totally incompatible with God rolling my number.
Note that you can't respond that conditionalizing on my number being n breaks the symmetry. Conditionalizing on a hypothesis being true is different from conditionalizing on knowledge of the hypothesis being true. Only the latter breaks the symmetry, whereas the former is what I'm using.