SIA should be suspect because ultimately probability is just a fancy way of counting and if you phrased this just as a matter of counting possibilities this isn't really convincing.
I think the problem here is, much like with sleeping beauty, ultimately just a confusion about what it is you are counting. If you are trying to count the fraction of experiences that are like being woken up for beauty where the coin is heads divided by all such experiences that gives you one result -- and could be called probability in a sense. OTOH if you count the number of configurations of the whole world divided by the number where the coin is heads you get a different result.
Same thing here. You are just counting two different things.
--
More generally, if you accept the kind of reasoning a la SIA you end up having to say that you should be certain that theories which predict infinite numbers of people are infinitely more likely than ones which don't. And then what about uncountable cardinalities (nothing about these theories require the observers to be in same 'universe').
Yes, you should think the universe is infinitely big. I agree with this and in fact defended it in this very article. In this article I gave an argument for SIA which is, I think, convincing. Not sure what you mean about probability just being a fancy way of counting or why that discredits SIA.
Regarding the infinite universe the problem is that for any specific cardinality you get that the universe is essentially certainly larger than that.
But now you can't even talk about the set of all people since it's not going to be a set but a proper class with virtual certainty and something seems wrong about that.
Ahh but now you get into a paradox because the whole notion of probability -- which you used to reach this result -- is defined into terms of a probability space which itself takes every outcome to be a set. So probability reasoning can't be used to talk about the probability of results like this.
What? Why? Like, if you think Beth 2 existing is possible you should have some view about how to reason about that. Can you spell out what the paradox is?
>. They are currently 50/50 between humanity having tons of people and it having just two people, but reason in the following way: “if civilization lasts super long, it’s unlikely that we’re the first two people—for we could be any of the people. In contrast, if there are only two people in total, then we’re guaranteed to be the two people. Therefore, if we ever discover that we’re the first two people we’ll get extremely strong evidence that humanity doesn’t last long.”
This is just accepting the reasoning of SIA. All you've done here is combine the reasoning that you take to establish SIA with the assumption of it's falsity so of course you can derive absurd conclusions.
What, no? If you know that there are a lot of people but don't know your birth rank, you should split your credence across the possible birth ranks and think it unlikely that you're late.
Wait if you are thinking of it that way you can't simultaneously have them think it's likely that there aren't many people and that conditional on them procreating there will be many people.
This example seems kinda poorly defined so maybe you could explain it in more detail.
stage 1: they don't know their birth rank. So they think it's super unlikely they're the first two people if the first two people have lots of offspring
stage 2: they find out that they're the first two people. Because that's guaranteed if the first two people don't have offspring but unlikely (per stage 1) if they do, they have strong evidence that the first two people won't have many offspring. But now they know they're the first two people, so they get strong evidence that they themselves won't have many offspring. From this, lazy adam and such follows.
I've been reading through a lot of your old articles on SIA (after your recent one) and I've finally put together why this whole thing seems strange.
Both of these examples seem to fail for the exact same reason: it doesn't seem meaningful to assume that we are just samples from God's soul storage.
On Serpent's Advice, let's think about our cases. Either Adam and Eve are first, or Adam and Eve have many kids in the future. Those kids are in the future, and thus no matter what, Adam and Eve are still first. That Adam and Eve being first becomes retroactively less likely if they have kids in the future is just an absurd proposition on its face.
Lazy Adam is the exact same thing. The information that "causes" the paradox is the Snake's information about the future and the retrocausality that makes it supposedly less likely for Adam and Eve to have been "picked" first after they have many kids. But they were either picked first or they weren't. It's like being surprised that a flip of a coin came up HTHHTTHHTHT. That sequence I wrote has a likelihood of 1/(2^11) but it shouldn't surprise anyone that it was picked. It's the same problem with SIA. It assumes that individuals are somehow picked from a set of possible observers. P(I exist|many exist) and P(I exist|only I exist) are the same because both are 1. I exist.
You mention elsewhere that conditional compartmentalization suffers from a simple money pump, but these all fail for the same reason. My experiences are my experiences and they will always be extremely unlikely if considered from the past. They are no more or less unlikely when something happens, because something always had to happen.
Like with your Sleeping Beauty example in the article, I don't get why that's the choice. Like this is just a meaningless statement: Before 3, you reason that it being Monday today is twice as likely if the coin came up heads. Let's look at 3rd party observer probabilities of each of the categories:
P(Heads) = 1/2, P(Monday|Heads) = 1, P(Tuesday|Heads) = 0, P(Monday|Tails) = 1, P(Tuesday|Tails) = 1. (there will always be both Monday and Tuesday when you get tails), P(Monday)=1 (there will always be monday), P(Tuesday)=1/2 (only on tails do you get Tuesday)
P(H|Monday) = P(Monday|Heads)*P(Heads)/P(Monday)
P(H|Monday) = 1*1/2/1 = 1/2
The probability of heads given it is monday is still 1/2 as you should expect given a fair coin. I don't know what you mean that the probability Monday is today is 2x as likely. Is it that P(Monday|Heads) is 2x P(Monday|Tails)? That's wrong because there will always be Monday awakening if you flip Heads or Tails.
So our probability of Tails by itself remains 1/2, but our probability of Tails given we are awake is 2/3 because we are awake more times when it is Tails. None of these are contradictory.
Your money pump seems confused. Did you mean you get $1 if it comes up tails? Also a money pump is supposed to be a case where the probability leads to you losing money. So if CC leads to earning money that would mean it's more correct than whoever is offering the betting odds.
//Both of these examples seem to fail for the exact same reason: it doesn't seem meaningful to assume that we are just samples from God's soul storage.//
//On Serpent's Advice, let's think about our cases. Either Adam and Eve are first, or Adam and Eve have many kids in the future. Those kids are in the future, and thus no matter what, Adam and Eve are still first. That Adam and Eve being first becomes retroactively less likely if they have kids in the future is just an absurd proposition on its face.//
This just follows from Bayes theorem. At stage 1, they don't know they're firs.t Many kids and few kids hypotheses are equally likely. Then, they learn they're first. That got low odds conditional on many people, high odds conditional on few. If you learn something that you found antecedently improbable on one theory and antecedently probable on another, you update.
Otherwise you get predictable updating: after you learn your birth rank, either your credence in tails goes up or doesn't change. It can't go down.
//My experiences are my experiences and they will always be extremely unlikely if considered from the past.//
I'm not sure what money pump you're talking about or what this is supposed to be about it.
//The probability of heads given it is monday is still 1/2 as you should expect given a fair coin. I don't know what you mean that the probability Monday is today is 2x as likely. //
There are 3 options: 1 today is Monday and the coin will come up heads. 2. Today is Monday and the coin will come up tails. 3. the coin has come up tails. My claim 1=2 in lieklihood and 2=3, so tails is 2x likelier than heads.
The third party probabilities are just looking at the odds of events occurring, but they ignore the self-locating evidence. They leave out the probabilies concerning what day it is today. So they just beg the question in favor of CC.
Then separately on your money pumps one. First on this:
//here are 3 options: 1 today is Monday and the coin will come up heads. 2. Today is Monday and the coin will come up tails. 3. the coin has come up tails. My claim 1=2 in lieklihood and 2=3, so tails is 2x likelier than heads.
The third party probabilities are just looking at the odds of events occurring, but they ignore the self-locating evidence. They leave out the probabilies concerning what day it is today. So they just beg the question in favor of CC.//
If you are looking for P(Monday|awake) let's find it.
We again need to split awake into its constituent parts
1*1/3+0*0+1*1/3+0*1/3 or 2/3rds. Sure I agree that the likelihood of it being Monday upon awakening is 2x the likelihood of it being Tuesday upon awakening.
Again there is no problem in using probability while maintaining P(Heads) = P(Tails) = 1/2 or that P(Monday)=1 and P(Tuesday)=1/2. All that changes is the information you're using to condition the result.
You're right that none of this depends on "self-locating evidence". It does incorporate the likelihood of a date occurring given certain information though, as I show above. I don't see how this is "begging the question". This is just utilizing the information we know correctly.
On the money pump:
//After five minutes, CCers will think that tails is likelier than heads. After all, tails predicts more total experiences are had, so it’s likelier that your present set of experiences would be had. But before five minutes, CCers will think heads and tails are equally likely. So, during the first five minutes, offer each person a bet that the coin came up heads, so that they get 55 cents if it came up heads and lose 45 cents if it came up tails. Then, after five minutes, they think heads is twice as likely as tails. So, for five cents, offer to cancel their earlier bet. CCers will take this, and thus predictably lose.//
This still relies on the idea that anything that happens will make you surprised in the outcome. But that suffers from the same problem that you should spend your life dumbfounded staring at a random number generator because of how unlikely any given number was to be generated.
//This just follows from Bayes theorem. At stage 1, they don't know they're firs.t Many kids and few kids hypotheses are equally likely. Then, they learn they're first. That got low odds conditional on many people, high odds conditional on few. If you learn something that you found antecedently improbable on one theory and antecedently probable on another, you update.
Otherwise you get predictable updating: after you learn your birth rank, either your credence in tails goes up or doesn't change. It can't go down.//
Let's look at the situation.
1. Adam and Eve do not know their birth order. They do not know if they are 1,2 out of 1,000,000 or 1,2 out of 2.
2. You say that being 1,2 out of 1,000,000 is less likely than 1,2 out of 2.
3. But look at what is consistent in both. They are 1 and 2! That doesn't change. The probability is and has to be 1 because that is the outcome itself. Can you state with a straight face that they are less likely to be 1 and 2 when both scenarios have them as 1 and 2?
Think about it in time order. Their position being "unlikely" can only occur when they choose to have kids and thus create the remaining billion+ souls. But that choice comes after their creation. If they choose not to have children, they are 1 and 2 at 100% likelihood.
Let's work through this. Let's refer to Adam and Eve first as X=1.
P(X=1|no children)=1
P(no children|X=1)*P(X=1)/P(no children) = 1
But at some point when they were created they have to have no children (because they haven't had children yet). So:
P(no children|X=1) = 1 and P(no children) = 1
1*P(X=1)/1 = 1
or P(X=1) = 1
By the very construction of the problem Adam and Eve are first. There is no case in which they aren't first.
While I admit that I don’t care too much about this, I appreciate that you care. 🙂
SIA should be suspect because ultimately probability is just a fancy way of counting and if you phrased this just as a matter of counting possibilities this isn't really convincing.
I think the problem here is, much like with sleeping beauty, ultimately just a confusion about what it is you are counting. If you are trying to count the fraction of experiences that are like being woken up for beauty where the coin is heads divided by all such experiences that gives you one result -- and could be called probability in a sense. OTOH if you count the number of configurations of the whole world divided by the number where the coin is heads you get a different result.
Same thing here. You are just counting two different things.
--
More generally, if you accept the kind of reasoning a la SIA you end up having to say that you should be certain that theories which predict infinite numbers of people are infinitely more likely than ones which don't. And then what about uncountable cardinalities (nothing about these theories require the observers to be in same 'universe').
Yes, you should think the universe is infinitely big. I agree with this and in fact defended it in this very article. In this article I gave an argument for SIA which is, I think, convincing. Not sure what you mean about probability just being a fancy way of counting or why that discredits SIA.
Regarding the infinite universe the problem is that for any specific cardinality you get that the universe is essentially certainly larger than that.
But now you can't even talk about the set of all people since it's not going to be a set but a proper class with virtual certainty and something seems wrong about that.
That's why you should think it's bigger than any cardinality--just like there's no cardinality of all truths because there's no set.
Ahh but now you get into a paradox because the whole notion of probability -- which you used to reach this result -- is defined into terms of a probability space which itself takes every outcome to be a set. So probability reasoning can't be used to talk about the probability of results like this.
What? Why? Like, if you think Beth 2 existing is possible you should have some view about how to reason about that. Can you spell out what the paradox is?
>. They are currently 50/50 between humanity having tons of people and it having just two people, but reason in the following way: “if civilization lasts super long, it’s unlikely that we’re the first two people—for we could be any of the people. In contrast, if there are only two people in total, then we’re guaranteed to be the two people. Therefore, if we ever discover that we’re the first two people we’ll get extremely strong evidence that humanity doesn’t last long.”
This is just accepting the reasoning of SIA. All you've done here is combine the reasoning that you take to establish SIA with the assumption of it's falsity so of course you can derive absurd conclusions.
What, no? If you know that there are a lot of people but don't know your birth rank, you should split your credence across the possible birth ranks and think it unlikely that you're late.
Wait if you are thinking of it that way you can't simultaneously have them think it's likely that there aren't many people and that conditional on them procreating there will be many people.
This example seems kinda poorly defined so maybe you could explain it in more detail.
stage 1: they don't know their birth rank. So they think it's super unlikely they're the first two people if the first two people have lots of offspring
stage 2: they find out that they're the first two people. Because that's guaranteed if the first two people don't have offspring but unlikely (per stage 1) if they do, they have strong evidence that the first two people won't have many offspring. But now they know they're the first two people, so they get strong evidence that they themselves won't have many offspring. From this, lazy adam and such follows.
I've been reading through a lot of your old articles on SIA (after your recent one) and I've finally put together why this whole thing seems strange.
Both of these examples seem to fail for the exact same reason: it doesn't seem meaningful to assume that we are just samples from God's soul storage.
On Serpent's Advice, let's think about our cases. Either Adam and Eve are first, or Adam and Eve have many kids in the future. Those kids are in the future, and thus no matter what, Adam and Eve are still first. That Adam and Eve being first becomes retroactively less likely if they have kids in the future is just an absurd proposition on its face.
Lazy Adam is the exact same thing. The information that "causes" the paradox is the Snake's information about the future and the retrocausality that makes it supposedly less likely for Adam and Eve to have been "picked" first after they have many kids. But they were either picked first or they weren't. It's like being surprised that a flip of a coin came up HTHHTTHHTHT. That sequence I wrote has a likelihood of 1/(2^11) but it shouldn't surprise anyone that it was picked. It's the same problem with SIA. It assumes that individuals are somehow picked from a set of possible observers. P(I exist|many exist) and P(I exist|only I exist) are the same because both are 1. I exist.
You mention elsewhere that conditional compartmentalization suffers from a simple money pump, but these all fail for the same reason. My experiences are my experiences and they will always be extremely unlikely if considered from the past. They are no more or less unlikely when something happens, because something always had to happen.
Like with your Sleeping Beauty example in the article, I don't get why that's the choice. Like this is just a meaningless statement: Before 3, you reason that it being Monday today is twice as likely if the coin came up heads. Let's look at 3rd party observer probabilities of each of the categories:
P(Heads) = 1/2, P(Monday|Heads) = 1, P(Tuesday|Heads) = 0, P(Monday|Tails) = 1, P(Tuesday|Tails) = 1. (there will always be both Monday and Tuesday when you get tails), P(Monday)=1 (there will always be monday), P(Tuesday)=1/2 (only on tails do you get Tuesday)
P(H|Monday) = P(Monday|Heads)*P(Heads)/P(Monday)
P(H|Monday) = 1*1/2/1 = 1/2
The probability of heads given it is monday is still 1/2 as you should expect given a fair coin. I don't know what you mean that the probability Monday is today is 2x as likely. Is it that P(Monday|Heads) is 2x P(Monday|Tails)? That's wrong because there will always be Monday awakening if you flip Heads or Tails.
We can check our other outcome as well:
P(T|Tuesday) = P(Tuesday|T)*P(T)/P(Tuesday) = (1*1/2)/(1/2) =1
So we correctly get no information about the coin if we find out it's Monday, and we correctly learn the coin must be tails if it's Tuesday.
Let's say on awakening you are asked to bet whether the coin is tails.
We're trying to find P(T|awake). Well what does that mean. Let's decompose awake. Here are our cases:
P(T|Monday&Heads)*P(awake|Monday&Heads) + P(T|Tuesday&Heads)*P(awake|Tuesday&Heads) + P(T|Monday&Tails)*P(awake|Monday&Tails) + P(T|Tuesday&Tails)*P(awake|Tuesday&Tails) =
0*1/3+0*0+1*1/3+1*1/3 or 2/3rds.
So our probability of Tails by itself remains 1/2, but our probability of Tails given we are awake is 2/3 because we are awake more times when it is Tails. None of these are contradictory.
Your money pump seems confused. Did you mean you get $1 if it comes up tails? Also a money pump is supposed to be a case where the probability leads to you losing money. So if CC leads to earning money that would mean it's more correct than whoever is offering the betting odds.
//Both of these examples seem to fail for the exact same reason: it doesn't seem meaningful to assume that we are just samples from God's soul storage.//
Not an assumption https://benthams.substack.com/p/precisely-defining-the-self-indication?utm_source=publication-search
//On Serpent's Advice, let's think about our cases. Either Adam and Eve are first, or Adam and Eve have many kids in the future. Those kids are in the future, and thus no matter what, Adam and Eve are still first. That Adam and Eve being first becomes retroactively less likely if they have kids in the future is just an absurd proposition on its face.//
This just follows from Bayes theorem. At stage 1, they don't know they're firs.t Many kids and few kids hypotheses are equally likely. Then, they learn they're first. That got low odds conditional on many people, high odds conditional on few. If you learn something that you found antecedently improbable on one theory and antecedently probable on another, you update.
Otherwise you get predictable updating: after you learn your birth rank, either your credence in tails goes up or doesn't change. It can't go down.
//My experiences are my experiences and they will always be extremely unlikely if considered from the past.//
I'm not sure what money pump you're talking about or what this is supposed to be about it.
//The probability of heads given it is monday is still 1/2 as you should expect given a fair coin. I don't know what you mean that the probability Monday is today is 2x as likely. //
There are 3 options: 1 today is Monday and the coin will come up heads. 2. Today is Monday and the coin will come up tails. 3. the coin has come up tails. My claim 1=2 in lieklihood and 2=3, so tails is 2x likelier than heads.
The third party probabilities are just looking at the odds of events occurring, but they ignore the self-locating evidence. They leave out the probabilies concerning what day it is today. So they just beg the question in favor of CC.
The money pumps I give here https://benthams.substack.com/p/money-pump-arguments-destroy-non?utm_source=publication-search
Then separately on your money pumps one. First on this:
//here are 3 options: 1 today is Monday and the coin will come up heads. 2. Today is Monday and the coin will come up tails. 3. the coin has come up tails. My claim 1=2 in lieklihood and 2=3, so tails is 2x likelier than heads.
The third party probabilities are just looking at the odds of events occurring, but they ignore the self-locating evidence. They leave out the probabilies concerning what day it is today. So they just beg the question in favor of CC.//
If you are looking for P(Monday|awake) let's find it.
We again need to split awake into its constituent parts
P(Monday|Monday&Heads)*P(awake|Monday&Heads) + P(Monday|Tuesday&Heads)*P(awake|Tuesday&Heads) + P(Monday|Monday&Tails)*P(awake|Monday&Tails) + P(Monday|Tuesday&Tails)*P(awake|Tuesday&Tails) =
1*1/3+0*0+1*1/3+0*1/3 or 2/3rds. Sure I agree that the likelihood of it being Monday upon awakening is 2x the likelihood of it being Tuesday upon awakening.
Again there is no problem in using probability while maintaining P(Heads) = P(Tails) = 1/2 or that P(Monday)=1 and P(Tuesday)=1/2. All that changes is the information you're using to condition the result.
You're right that none of this depends on "self-locating evidence". It does incorporate the likelihood of a date occurring given certain information though, as I show above. I don't see how this is "begging the question". This is just utilizing the information we know correctly.
On the money pump:
//After five minutes, CCers will think that tails is likelier than heads. After all, tails predicts more total experiences are had, so it’s likelier that your present set of experiences would be had. But before five minutes, CCers will think heads and tails are equally likely. So, during the first five minutes, offer each person a bet that the coin came up heads, so that they get 55 cents if it came up heads and lose 45 cents if it came up tails. Then, after five minutes, they think heads is twice as likely as tails. So, for five cents, offer to cancel their earlier bet. CCers will take this, and thus predictably lose.//
This still relies on the idea that anything that happens will make you surprised in the outcome. But that suffers from the same problem that you should spend your life dumbfounded staring at a random number generator because of how unlikely any given number was to be generated.
Starting from this one:
//This just follows from Bayes theorem. At stage 1, they don't know they're firs.t Many kids and few kids hypotheses are equally likely. Then, they learn they're first. That got low odds conditional on many people, high odds conditional on few. If you learn something that you found antecedently improbable on one theory and antecedently probable on another, you update.
Otherwise you get predictable updating: after you learn your birth rank, either your credence in tails goes up or doesn't change. It can't go down.//
Let's look at the situation.
1. Adam and Eve do not know their birth order. They do not know if they are 1,2 out of 1,000,000 or 1,2 out of 2.
2. You say that being 1,2 out of 1,000,000 is less likely than 1,2 out of 2.
3. But look at what is consistent in both. They are 1 and 2! That doesn't change. The probability is and has to be 1 because that is the outcome itself. Can you state with a straight face that they are less likely to be 1 and 2 when both scenarios have them as 1 and 2?
Think about it in time order. Their position being "unlikely" can only occur when they choose to have kids and thus create the remaining billion+ souls. But that choice comes after their creation. If they choose not to have children, they are 1 and 2 at 100% likelihood.
Let's work through this. Let's refer to Adam and Eve first as X=1.
P(X=1|no children)=1
P(no children|X=1)*P(X=1)/P(no children) = 1
But at some point when they were created they have to have no children (because they haven't had children yet). So:
P(no children|X=1) = 1 and P(no children) = 1
1*P(X=1)/1 = 1
or P(X=1) = 1
By the very construction of the problem Adam and Eve are first. There is no case in which they aren't first.