These SIA arguments (the arguments that imply an infinite number of people and the existence of God) strike me as so bizarre and counterintuitive that I'm going to withhold judgment until a substantial number of very smart people who've studied them closely come down one way or the other. It's like quantum mechanics is for me. The theory makes no sense to my intuitions, but nearly all physicists accept it, so I trust their judgment over my own gut.
I'm finishing a post demonstrating that SIA is clearly true in the non-duplication situation (where it's equal to standard Bayesian conditioning).
Bentham's argument is wrong in the infinite situation - SIA doesn't scale to infinity. A modification of it does, however (that's the second post I'm finishing).
From what I found when I looked previously, SIA seems to have a decent majority. Although I don't remember exactly where I found that so may be mistaken.
Do you mean that a decent majority agrees that SIA implies the existence of an infinite number of people, as well as the existence of God? That was what I was referring to when I wrote "these SIA arguments".
So... there's unanimous agreement that an infinite number of people exist? I don't know much about philosophy either as a discipline or as a community, but your assertion seems unlikely (of course, I could be misunderstanding your point).
You'll notice a motte-and-bailey thing from "I'm only defending SIA" to "aaand now God must exist." This is a good time, Alex, to trust the instincts you expressed up-thread.
Which version? Bentham accepts a strong version where the more people exist on a theory, the likelier it is you exist. That’s what gets you the claim that the hypothesis that uncountably many people existing makes it much likelier that you exist. Another weaker version just says that the larger a share of possible people exist on a theory, the likelier it is that you exist. The second theory involves just sampling from the set of possible people, and the first is also used to establish that many people possibly exist, rather than taking facts about that as background when updating on the fact you exist.
I don’t think that most people accept his strong version, though perhaps their arguments for it do support it over the weaker version.
I don't think most people have staked out a view on that. But even on the weaker view, because there are lots of possible people, you'll still update in favor of a giant infinite multiverse.
In my example, I’ll use license plates rather than people because we understand license plates better, but I don’t think it makes a difference.
There are a million vacant houses. God flipped a fair coin. If it came up heads, God put a license plate in exactly one house. If it came up tails, God put a license plate in each of the million houses. Every license plate is different. I am informed that the license plate of my vehicle is in a house. What are the odds that the coin came up heads?
P(heads | my license plate) / P(tails | my license plate) =
"You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!" -- Richard Feynman
On SIA, how do we avoid skepticism? There is (at most) one copy of me experiencing my experiences in the real world. But there are potentially infinite centers that are being simulated to have my current experiences. Does SIA give me infinite evidence in favor of theories that include infinite people falsely having my experiences? If so, shouldn't I conclude I'm one of them?
How do I know I'm one of the infinite people experiencing real versions of my experiences and not one of the infinite people experiencing simulated ones?
"Third, does SIA run afoul of the constraint that you can't assign a uniform probability distribution over an infinite set?"
No, this isn't true. You can assign a uniform probability distribution over an infinite set such as a uniform interval within the real numbers with respect to the Lebesgue measure. The issue is that the concept of a uniform distribution isn't even defined without respect to some measure.
You MUST have a finite measure space before assigning a uniform distribution.
Can't you just say that every specific event has probability zero?
Not getting why however non-SIAers take a measure the SIAer can't do as well. Or alternatively say in some cases probabilities are undefined where you can't take a measure.
How do you propose to assign probabilities to being each particular person in an infinite universe? Seems the options are:
1. Think that probabilities are assigned by some normalizable probability function.
2. Think the probability of you being any particular person are zero.
3. Think the probability of you being any particular person are infinitesimal.
I don't like 1, because it implies that you should bet with 99.9999999999999% odds that you're one of the first N people, for some N, even though 0% of people are one of the first N people.
So what you can have is, e.g., non-standard probabilities* + hypercountable additivity to make a God's lottery work. Then, it has some but never all the properties of an uniform distribution: it cannot be independent of the label of each element, because one-to-one correspondence equality gives Cantor's cardinality.
*These numerosities, for finite and infinite subsets of the natural numbers, are very unusual, indeed. Nonetheless, they give a total order of equivalence classes of sets of natural numbers which behaves quite nicely in their arithmetic. So, in a way, it is the fairest and most coherent God's lottery.
Sure, you can say every specific event has probability zero. And then you assign probability 1 to the entire space. But building a sigma algebra from that purely using countable union and intersection and complement only allows you to evaluate the probability of countable subsets (assuming the entire space is uncountable, otherwise you get a contradiction).
It's a valid sigma algebra, but it's very underspecified, because you are unable to evaluate the probability of ANY uncountable subset whose complement is also uncountable.
I clarify that this construction ONLY works of the original total probability space is uncountable. If it's countable, this cannot be done. You need to update your article to specify "countable infinities" not just "infinities" in general.
If you don't care about evaluating probability any sets who are uncountable and whose complements are uncountable, it is fine. Indeed, you would get probability 1 for any complement of a countable subset and probability 0 for any countable subset.
The other thing is that SIA really is just following the completely normal way of doing probability, but applied to ourselves. Like, in your expression of SIA as taking the relative probability between two centers you might be as being independent of other centers, this is exactly how probability normally works when it comes to how we update probabilities as particular outcomes are ruled out. It's completely standard!
But on the infinite persons point, I think more is needed. It's not enough for one theory to say there are infinitely more people, there need to be infinitely more people who you might actually be, as far as you know. Your presentation here seems to skip over this. Have you covered it elsewhere?
Re centers and time slices, what do you think would be the answer to SB if we SB found out she'd also be kept awake for twice as long in the case where she's only woken once?
It seems to me that according to this same logic, one can claim that it's infinitely more probable to be stuck in a time loop experiencing the present moment over and over forever than it is to exist in linear time.
> Thus, you can derive SIA from a very modest principle about how to assign probabilities. You don’t need to think that we’re all souls drawn from some great cosmic soul bank. That has never been what SIA presupposed.
By "modest principle" here you mean this notion of "centers" that ignores the standard condition of mutual exclusivity of the elements of the sample space. That's not modest at all! That's an extremely presumptious and unjustified approach, originating from initially confused framework of possible worlds (See the links below). Yes, if we *just so assume* that one has to apply such approach to probability theoretic reasoning, then SIA is simply a principle of indifference between the centers. But why would we assume such a thing? Why are we supposed to apply principle of indifference between "centers" defined the way you defined them, instead of something else? That's the core question that needs to be answered and which you conveniently ignore.
Sure, you can come up with some mathematical model that describes a certain way to assign some numerical value between 0 and 1 to certain statements. But does this model describe to the way of having confidence in statements that systematically correspond to reality? You can't just sweep this question under the rug with a "modest assumption" label on it - that's what the whole controversy is actually about!
And if one tries to answer this question instead of pretending that it's not there, then we inevitably get something like the notion of souls being drawn from a cosmic soul bank. That's how the universe has to be so that SIA corresponded to it. Still won't work for Sleeping Beauty types of problems, mind you, - they would require an even weirder universe where each individual moment in time is somehow randomly sampled, but regardless.
> This is not, of course, to suggest that an actual agent should be infinitely certain that there are infinite people. You should think there’s some chance that you’re mistaken about anthropics.
You cannot simultaneously believe that one has to be equally uncertain between centers; and that one has to be somehow uncertain between different anthropic theories. In general, the moment you need to appeal to overall uncertainty between theories to justify not taking the prediction of your favored theory at a face value, you acknowledge that your favorite theory is not right.
No it's consistent with mutual exclusivity! The present you being the tuesday waking is mutually exclusive with the present you being the monday one. It only appears otherwise if you assume that there's no self-locating evidence.
You should *never* take the judgments of your favorite first-order theory at face value if you have any anthropic uncertainty. Same with ethics, same with everything--if you aren't sure if your first-order theory is right, your credence should be in the middle.
What is meant by mutual exclusivity is that there is one and only one outcome in every iteration of probability experiment and of those outcomes the sample space for this experiment is made of. This is the general principle of applying probability theory to problems that works without fail. And naturally it's not consistent with treating individual awakenings as outcomes if multiple awakenings can happen during the same iteration of the experiment.
> It only appears otherwise if you assume that there's no self-locating evidence.
There is evidence. And all evidence works according to the principle that I've described. The talk about self-location is an unnecessary confusion. Once again, I'm leaving the link to post where I explain it in detail: https://substack.com/@apeinthecoat/p-190583695
> You should *never* take the judgments of your favorite first-order theory at face value if you have any anthropic uncertainty. Same with ethics, same with everything--if you aren't sure if your first-order theory is right, your credence should be in the middle.
There is a huge difference between the humbleness of generally leaving yourself a possibility of a mistake on basic fallibilistic principles, while actually following your theories where they lead and remembering about second order uncertainty only to excuse your preferred theory from making a crazy prediction, while otherwise proclaiming that this theory is obviously true. You are doing the latter.
I think I largely agree with everything you write in this article, but I still have one concern. Modify God's coin toss where God either creates one physical copy of me or twenty identical physical copies of me with the exact same experiences. If these copies are identical, it is unclear to me if there are twenty centers or one center. After all, maybe consciousness is immaterial and only instantiated once.
I guess the thing I don't understand is what level of difference is required for a center, if any difference is required at all?
There are twenty centers because there are twenty different copies of your experience. Imagine that twenty copies of me are created. Half will be killed in a minute. It seems like I should have a credence of 1/2 that I'll be killed in a minute. But that assumes they're not the same.
Any distinct experiencers or same experiences at different times will be distinct centers.
*Suppose a coin is flipped that creates one person if heads and ten if tails. You are created as a result of this coin flip. The self-indication assumption holds: you ought to think tails is ten times likelier than heads. The coin landing tails will lead to ten times more people existing; it’s thus ten times likelier it will lead to you existing.*
But you've never observed the coin flips, which is the whole problem with this idea. You haven't observed infinite people, and you are mostly just arguing based on categorizing tools and not real things. Infinite is not a real observable thing, but a category used to evaluate sets of things.
Probability only matters based on observing repeatable events over time, and as the amount of events grows higher you can observe a trend that you can use as a general basis for things like risk while still acknowledging individual cases may not meet that pattern. You can't really used unobserved potential probabilities to build the case you want, and the atheists already tried.
Like one could argue the universe is full of infinite planets, meaning special creation is unlikely because there are infinite planets capable of infinite abiogenesis. But the argument is simply we can't observe those things: the universe is potentially infinite but as far as we can see we are the only life that exists, so you file the atheist argument away as weak and relying on further discovery.
The problem is you can't logic or math God into existence, to be blunt.
//Probability only matters based on observing repeatable events over time//
I don't agree with this. The probability of continental drift is very high, even though this isn't repeatable. Instead, we can know it based on it predicting with high likelihood facts about our world. You can have reason to believe one-off events based on strong evidence that doesn't take the form of repeatable predictions.
you can only know about continental drift by measuring repeated movement, you are not trying to logic it out without any observed pheonomena at all, and it’s not probability, its proven by GPS measurements. The problem here is you are not using anything measurable at all nor have seen ancillary events that show what SIA is trying to prove. You can’t use that as a base for any probability at all.
In the coin flip example when you say "The odds I’m person 1=the odds I’m person 2", does this depend on the assumption of a fair coin, or would you still say the odds are equal if it was an unfair coin with a 99% chance of heads (so only person 1 created) and a 1% chance of tails (so persons 2 and 3 created)? If your answer is the latter, I think this is a misleading intuition-pump since more people would likely find it implausible with unbalanced odds, and in the case of a fair coin the seeming plausibility may be because people are unconsciously conflating the 50/50 odds of the coin coming up heads vs tails with the claimed 50/50 odds of being person 1 vs person 2 (or 1 vs 3).
I see from that example that you do think you are 99 times less likely to be any of the individuals in the universe that had 1/99 of being the winner of the die roll, but because there are an infinite number of individuals in that case, the 1/99 factor doesn't matter for the final conclusion. But this would suggest that in Bostrom's "presumptuous philosopher" example where both possible universes contain a finite number of individuals, the SIA doesn't automatically conclude the universe with more individuals is more likely, it would depend on the probability of each type of universe before you took anthropic arguments into account. Is this the general consensus among people who favor SIA or would some favor simple counting of possible individuals?
Also if your view is that we multiply relative likelihood of being an individual in each universe by the probability of that universe, does this only apply in examples where we know the objective probabilities (say because God told us the probabilities he used to decide which type of universe to create), or would you use the same type of calculation in a case where we assign different types of universes different prior subjective probabilities in the "degree of belief" sense?
//But this would suggest that in Bostrom's "presumptuous philosopher" example where both possible universes contain a finite number of individuals, the SIA doesn't automatically conclude the universe with more individuals is more likely//
Yes, that's right, depends on the priors and the ratios. Though normally the example is given so that the ratio of observers is more extreme than the probability skew.
//Also if your view is that we multiply relative likelihood of being an individual in each universe by the probability of that universe, does this only apply in examples where we know the objective probabilities//
No, SIA is an updating rule. It applies like other updating rules, even when you don't know the exact priors.
Is it updating those subjective probabilities purely on theoretical calculations of the number of observers in each hypothetical world, rather than on one's own "location"? As an example, consider the open question about whether complex life could just as easily arise in planetary systems of red dwarf stars or whether various issues in red dwarf systems (like habitable planets being closer to solar flares, the stars mainly emitting lower-energy photons in infrared range, and tidal locking of planets) would make this much less likely. Red dwarfs outnumber yellow dwarf stars like our Sun by about 10 to 1, and they are also much more long-lived so the ratio of potentially habitable years is significantly more lopsided.
So suppose we are considering two hypothetical worlds, a world labeled R&Y where the probability of various evolutionary milestones in a billion year span (including the origin of life) is about the same for a habitable planet in a red dwarf system as in a yellow dwarf system, and world labeled Y where the probability in yellow dwarf systems is much higher than red dwarf systems. We assign worlds R&Y and Y some prior subjective probabilities without taking anthropic issues into consideration, just based on current theories of astrobiology, exoplanet science etc. An SSA advocate will then take note of the fact that we ourselves evolved on a planet orbiting a yellow dwarf star, and update in favor of Y. Would an SIA advocate ignore our own location, and just update in favor of world R&Y based on the idea this would theoretically contain a lot more observers than world Y, with this update being greater the more lopsided the observed ratio between yellow and red dwarfs?
I'm assuming above that R&Y and Y both involve a finite number of observers, but if the answer in that case is that SIA updates in favor of R&Y, what if the hypothetical worlds both contain a countably infinite number of stars and observers? Would the SIA view be that there should then be no anthropic update to the prior probabilities at all? In this case it wouldn't become more SSA-like and update in favor of Y, and it also wouldn't consider anything like the "density" of observers in the two possible infinite universes? (like considering the number of observers in the finite 'observable' region that's had time to causally interact with us since the big bang)
We can’t assume an infinite number of people under a theistic creation because god has an infinite number of options to satisfy his creative urges, and only a small subset of those would be universes. Cf naturalism which only has universes to play with. So if you’re in a universe it’s much more likely it’s naturalistic.
A related issue is that even among algorithms that generate a "universe" of some kind, universes with regular laws that hold for all time have lower algorithmic complexity than ones where the laws differ from one region of spacetime to another (like cellular automata style universe where the update rules can differ at different time increments and different regions of the 'board'). So if God realizes all possible algorithmic universes that contain observers, and all observers are equally likely, then even if we are only considering observers whose experience is just like ours up until now, we should think it's far more likely that our upcoming experiences will be of the "miraculous" breakdown of the laws we remember up until now (this is basically a variant of one of the arguments against our being Boltzmann brains).
Btw, I’d be interested in your view. This also seems to my why fine tuning fails to predict theism. God can realise his visions in an infinite number of ways, and there is no need to have a universe. And for any realisation of his objectives (no matter how precisely defined) given his omnipotence he can always take Realisation 1 and create R2 which is equally good at meeting God’s objectives. And if R2 then R3. So the chances of a fine tuned universe are less under theism given the solution space is unbounded.
If he has infinite universes and infinite non-universes (all of which satisfy his creative urges) the probabilities don’t stack up in favour of theism.
These SIA arguments (the arguments that imply an infinite number of people and the existence of God) strike me as so bizarre and counterintuitive that I'm going to withhold judgment until a substantial number of very smart people who've studied them closely come down one way or the other. It's like quantum mechanics is for me. The theory makes no sense to my intuitions, but nearly all physicists accept it, so I trust their judgment over my own gut.
I'm finishing a post demonstrating that SIA is clearly true in the non-duplication situation (where it's equal to standard Bayesian conditioning).
Bentham's argument is wrong in the infinite situation - SIA doesn't scale to infinity. A modification of it does, however (that's the second post I'm finishing).
From what I found when I looked previously, SIA seems to have a decent majority. Although I don't remember exactly where I found that so may be mistaken.
Do you mean that a decent majority agrees that SIA implies the existence of an infinite number of people, as well as the existence of God? That was what I was referring to when I wrote "these SIA arguments".
Ahhh OK, no, sorry, I just meant the SIA more generally
Yeah, sorry I wasn't clear. I'll edit my original comment.
No one seriously disputes that SIA gives you an infinite update in favor of infinite people.
Marker: I dispute that entirely.
More details in the coming posts.
So... there's unanimous agreement that an infinite number of people exist? I don't know much about philosophy either as a discipline or as a community, but your assertion seems unlikely (of course, I could be misunderstanding your point).
You'll notice a motte-and-bailey thing from "I'm only defending SIA" to "aaand now God must exist." This is a good time, Alex, to trust the instincts you expressed up-thread.
In this post I was clear that I was just defending SIA!
Which version? Bentham accepts a strong version where the more people exist on a theory, the likelier it is you exist. That’s what gets you the claim that the hypothesis that uncountably many people existing makes it much likelier that you exist. Another weaker version just says that the larger a share of possible people exist on a theory, the likelier it is that you exist. The second theory involves just sampling from the set of possible people, and the first is also used to establish that many people possibly exist, rather than taking facts about that as background when updating on the fact you exist.
I don’t think that most people accept his strong version, though perhaps their arguments for it do support it over the weaker version.
I don't think most people have staked out a view on that. But even on the weaker view, because there are lots of possible people, you'll still update in favor of a giant infinite multiverse.
Does SIA follow from Bayesian updating?
In my example, I’ll use license plates rather than people because we understand license plates better, but I don’t think it makes a difference.
There are a million vacant houses. God flipped a fair coin. If it came up heads, God put a license plate in exactly one house. If it came up tails, God put a license plate in each of the million houses. Every license plate is different. I am informed that the license plate of my vehicle is in a house. What are the odds that the coin came up heads?
P(heads | my license plate) / P(tails | my license plate) =
(P(heads) / P(tails)) * P(my license plate | heads) / P(my license plate | tails) =
(0.5 / 0.5) * (1/(number of possible license plates)) / (1,000,000 / (number of possible license plates))
= 1 : 1,000,000
I now see that Bentham's Bulldog used the Bayesian updating argument in a previous post (but without the license plates): https://benthams.substack.com/p/a-new-extremely-strong-argument-for
"You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!" -- Richard Feynman
On SIA, how do we avoid skepticism? There is (at most) one copy of me experiencing my experiences in the real world. But there are potentially infinite centers that are being simulated to have my current experiences. Does SIA give me infinite evidence in favor of theories that include infinite people falsely having my experiences? If so, shouldn't I conclude I'm one of them?
There can be infinite people experiencing your experiences throughout the universe.
How do I know I'm one of the infinite people experiencing real versions of my experiences and not one of the infinite people experiencing simulated ones?
Well it will depend on whether most people are simulated. But if you think you’re not then probably you’re not one of the simulated ones
"Third, does SIA run afoul of the constraint that you can't assign a uniform probability distribution over an infinite set?"
No, this isn't true. You can assign a uniform probability distribution over an infinite set such as a uniform interval within the real numbers with respect to the Lebesgue measure. The issue is that the concept of a uniform distribution isn't even defined without respect to some measure.
You MUST have a finite measure space before assigning a uniform distribution.
Can't you just say that every specific event has probability zero?
Not getting why however non-SIAers take a measure the SIAer can't do as well. Or alternatively say in some cases probabilities are undefined where you can't take a measure.
No. Countably infinite events of probability 0 cannot sum to a probability greater than 0.
If you reject countable additivity?
How do you propose to assign probabilities to being each particular person in an infinite universe? Seems the options are:
1. Think that probabilities are assigned by some normalizable probability function.
2. Think the probability of you being any particular person are zero.
3. Think the probability of you being any particular person are infinitesimal.
I don't like 1, because it implies that you should bet with 99.9999999999999% odds that you're one of the first N people, for some N, even though 0% of people are one of the first N people.
I don't know how to reject countable additivity in this case. 2 and 3 seem to be not possible.
Some discussion here, though I admit that this stuff goes over my head a bit https://plato.stanford.edu/entries/infinity/gods-lottery.html
See here for more on why we might give up countable additivity https://link.springer.com/article/10.1007/s10670-023-00757-5
So what you can have is, e.g., non-standard probabilities* + hypercountable additivity to make a God's lottery work. Then, it has some but never all the properties of an uniform distribution: it cannot be independent of the label of each element, because one-to-one correspondence equality gives Cantor's cardinality.
*These numerosities, for finite and infinite subsets of the natural numbers, are very unusual, indeed. Nonetheless, they give a total order of equivalence classes of sets of natural numbers which behaves quite nicely in their arithmetic. So, in a way, it is the fairest and most coherent God's lottery.
Sure, you can say every specific event has probability zero. And then you assign probability 1 to the entire space. But building a sigma algebra from that purely using countable union and intersection and complement only allows you to evaluate the probability of countable subsets (assuming the entire space is uncountable, otherwise you get a contradiction).
It's a valid sigma algebra, but it's very underspecified, because you are unable to evaluate the probability of ANY uncountable subset whose complement is also uncountable.
And what's wrong with that?
I'm not too bothered with thinking it's importantly underspecified and that you need other principles to get probabilities. I think there are other reasons to think that about probabilities https://benthams.substack.com/p/infinite-ethics-infinite-problems?utm_source=publication-search
I clarify that this construction ONLY works of the original total probability space is uncountable. If it's countable, this cannot be done. You need to update your article to specify "countable infinities" not just "infinities" in general.
You can if you give up countable additivity, as I do https://philarchive.org/archive/BARCAA
If you don't care about evaluating probability any sets who are uncountable and whose complements are uncountable, it is fine. Indeed, you would get probability 1 for any complement of a countable subset and probability 0 for any countable subset.
The other thing is that SIA really is just following the completely normal way of doing probability, but applied to ourselves. Like, in your expression of SIA as taking the relative probability between two centers you might be as being independent of other centers, this is exactly how probability normally works when it comes to how we update probabilities as particular outcomes are ruled out. It's completely standard!
But on the infinite persons point, I think more is needed. It's not enough for one theory to say there are infinitely more people, there need to be infinitely more people who you might actually be, as far as you know. Your presentation here seems to skip over this. Have you covered it elsewhere?
Re centers and time slices, what do you think would be the answer to SB if we SB found out she'd also be kept awake for twice as long in the case where she's only woken once?
Hi! I think you said what I just said. I should have read you first.
Great minds!
It seems to me that according to this same logic, one can claim that it's infinitely more probable to be stuck in a time loop experiencing the present moment over and over forever than it is to exist in linear time.
> Thus, you can derive SIA from a very modest principle about how to assign probabilities. You don’t need to think that we’re all souls drawn from some great cosmic soul bank. That has never been what SIA presupposed.
By "modest principle" here you mean this notion of "centers" that ignores the standard condition of mutual exclusivity of the elements of the sample space. That's not modest at all! That's an extremely presumptious and unjustified approach, originating from initially confused framework of possible worlds (See the links below). Yes, if we *just so assume* that one has to apply such approach to probability theoretic reasoning, then SIA is simply a principle of indifference between the centers. But why would we assume such a thing? Why are we supposed to apply principle of indifference between "centers" defined the way you defined them, instead of something else? That's the core question that needs to be answered and which you conveniently ignore.
Sure, you can come up with some mathematical model that describes a certain way to assign some numerical value between 0 and 1 to certain statements. But does this model describe to the way of having confidence in statements that systematically correspond to reality? You can't just sweep this question under the rug with a "modest assumption" label on it - that's what the whole controversy is actually about!
And if one tries to answer this question instead of pretending that it's not there, then we inevitably get something like the notion of souls being drawn from a cosmic soul bank. That's how the universe has to be so that SIA corresponded to it. Still won't work for Sleeping Beauty types of problems, mind you, - they would require an even weirder universe where each individual moment in time is somehow randomly sampled, but regardless.
> This is not, of course, to suggest that an actual agent should be infinitely certain that there are infinite people. You should think there’s some chance that you’re mistaken about anthropics.
You cannot simultaneously believe that one has to be equally uncertain between centers; and that one has to be somehow uncertain between different anthropic theories. In general, the moment you need to appeal to overall uncertainty between theories to justify not taking the prediction of your favored theory at a face value, you acknowledge that your favorite theory is not right.
https://substack.com/@apeinthecoat/p-190583695
https://substack.com/@apeinthecoat/p-192375740
No it's consistent with mutual exclusivity! The present you being the tuesday waking is mutually exclusive with the present you being the monday one. It only appears otherwise if you assume that there's no self-locating evidence.
You should *never* take the judgments of your favorite first-order theory at face value if you have any anthropic uncertainty. Same with ethics, same with everything--if you aren't sure if your first-order theory is right, your credence should be in the middle.
> No it's consistent with mutual exclusivity!
What is meant by mutual exclusivity is that there is one and only one outcome in every iteration of probability experiment and of those outcomes the sample space for this experiment is made of. This is the general principle of applying probability theory to problems that works without fail. And naturally it's not consistent with treating individual awakenings as outcomes if multiple awakenings can happen during the same iteration of the experiment.
> It only appears otherwise if you assume that there's no self-locating evidence.
There is evidence. And all evidence works according to the principle that I've described. The talk about self-location is an unnecessary confusion. Once again, I'm leaving the link to post where I explain it in detail: https://substack.com/@apeinthecoat/p-190583695
> You should *never* take the judgments of your favorite first-order theory at face value if you have any anthropic uncertainty. Same with ethics, same with everything--if you aren't sure if your first-order theory is right, your credence should be in the middle.
There is a huge difference between the humbleness of generally leaving yourself a possibility of a mistake on basic fallibilistic principles, while actually following your theories where they lead and remembering about second order uncertainty only to excuse your preferred theory from making a crazy prediction, while otherwise proclaiming that this theory is obviously true. You are doing the latter.
I think I largely agree with everything you write in this article, but I still have one concern. Modify God's coin toss where God either creates one physical copy of me or twenty identical physical copies of me with the exact same experiences. If these copies are identical, it is unclear to me if there are twenty centers or one center. After all, maybe consciousness is immaterial and only instantiated once.
I guess the thing I don't understand is what level of difference is required for a center, if any difference is required at all?
There are twenty centers because there are twenty different copies of your experience. Imagine that twenty copies of me are created. Half will be killed in a minute. It seems like I should have a credence of 1/2 that I'll be killed in a minute. But that assumes they're not the same.
Any distinct experiencers or same experiences at different times will be distinct centers.
*Suppose a coin is flipped that creates one person if heads and ten if tails. You are created as a result of this coin flip. The self-indication assumption holds: you ought to think tails is ten times likelier than heads. The coin landing tails will lead to ten times more people existing; it’s thus ten times likelier it will lead to you existing.*
But you've never observed the coin flips, which is the whole problem with this idea. You haven't observed infinite people, and you are mostly just arguing based on categorizing tools and not real things. Infinite is not a real observable thing, but a category used to evaluate sets of things.
Probability only matters based on observing repeatable events over time, and as the amount of events grows higher you can observe a trend that you can use as a general basis for things like risk while still acknowledging individual cases may not meet that pattern. You can't really used unobserved potential probabilities to build the case you want, and the atheists already tried.
Like one could argue the universe is full of infinite planets, meaning special creation is unlikely because there are infinite planets capable of infinite abiogenesis. But the argument is simply we can't observe those things: the universe is potentially infinite but as far as we can see we are the only life that exists, so you file the atheist argument away as weak and relying on further discovery.
The problem is you can't logic or math God into existence, to be blunt.
The point I make in this article is generally about updating, not just about coin flips. For more, see https://benthams.substack.com/p/a-new-extremely-strong-argument-for?utm_source=publication-search
//Probability only matters based on observing repeatable events over time//
I don't agree with this. The probability of continental drift is very high, even though this isn't repeatable. Instead, we can know it based on it predicting with high likelihood facts about our world. You can have reason to believe one-off events based on strong evidence that doesn't take the form of repeatable predictions.
you can only know about continental drift by measuring repeated movement, you are not trying to logic it out without any observed pheonomena at all, and it’s not probability, its proven by GPS measurements. The problem here is you are not using anything measurable at all nor have seen ancillary events that show what SIA is trying to prove. You can’t use that as a base for any probability at all.
But I’m not doing that either. I’m basing it on the phenomenon that I exist
No you are basing it on theoretical concepts like “the multiverse existing,” and that infinite people exist. Neither of which you observe.
In the coin flip example when you say "The odds I’m person 1=the odds I’m person 2", does this depend on the assumption of a fair coin, or would you still say the odds are equal if it was an unfair coin with a 99% chance of heads (so only person 1 created) and a 1% chance of tails (so persons 2 and 3 created)? If your answer is the latter, I think this is a misleading intuition-pump since more people would likely find it implausible with unbalanced odds, and in the case of a fair coin the seeming plausibility may be because people are unconsciously conflating the 50/50 odds of the coin coming up heads vs tails with the claimed 50/50 odds of being person 1 vs person 2 (or 1 vs 3).
Assumption of a fair coin. Though I talk about how it would work if the probabilities were different in the die roll case.
I see from that example that you do think you are 99 times less likely to be any of the individuals in the universe that had 1/99 of being the winner of the die roll, but because there are an infinite number of individuals in that case, the 1/99 factor doesn't matter for the final conclusion. But this would suggest that in Bostrom's "presumptuous philosopher" example where both possible universes contain a finite number of individuals, the SIA doesn't automatically conclude the universe with more individuals is more likely, it would depend on the probability of each type of universe before you took anthropic arguments into account. Is this the general consensus among people who favor SIA or would some favor simple counting of possible individuals?
Also if your view is that we multiply relative likelihood of being an individual in each universe by the probability of that universe, does this only apply in examples where we know the objective probabilities (say because God told us the probabilities he used to decide which type of universe to create), or would you use the same type of calculation in a case where we assign different types of universes different prior subjective probabilities in the "degree of belief" sense?
//But this would suggest that in Bostrom's "presumptuous philosopher" example where both possible universes contain a finite number of individuals, the SIA doesn't automatically conclude the universe with more individuals is more likely//
Yes, that's right, depends on the priors and the ratios. Though normally the example is given so that the ratio of observers is more extreme than the probability skew.
//Also if your view is that we multiply relative likelihood of being an individual in each universe by the probability of that universe, does this only apply in examples where we know the objective probabilities//
No, SIA is an updating rule. It applies like other updating rules, even when you don't know the exact priors.
Is it updating those subjective probabilities purely on theoretical calculations of the number of observers in each hypothetical world, rather than on one's own "location"? As an example, consider the open question about whether complex life could just as easily arise in planetary systems of red dwarf stars or whether various issues in red dwarf systems (like habitable planets being closer to solar flares, the stars mainly emitting lower-energy photons in infrared range, and tidal locking of planets) would make this much less likely. Red dwarfs outnumber yellow dwarf stars like our Sun by about 10 to 1, and they are also much more long-lived so the ratio of potentially habitable years is significantly more lopsided.
So suppose we are considering two hypothetical worlds, a world labeled R&Y where the probability of various evolutionary milestones in a billion year span (including the origin of life) is about the same for a habitable planet in a red dwarf system as in a yellow dwarf system, and world labeled Y where the probability in yellow dwarf systems is much higher than red dwarf systems. We assign worlds R&Y and Y some prior subjective probabilities without taking anthropic issues into consideration, just based on current theories of astrobiology, exoplanet science etc. An SSA advocate will then take note of the fact that we ourselves evolved on a planet orbiting a yellow dwarf star, and update in favor of Y. Would an SIA advocate ignore our own location, and just update in favor of world R&Y based on the idea this would theoretically contain a lot more observers than world Y, with this update being greater the more lopsided the observed ratio between yellow and red dwarfs?
I'm assuming above that R&Y and Y both involve a finite number of observers, but if the answer in that case is that SIA updates in favor of R&Y, what if the hypothetical worlds both contain a countably infinite number of stars and observers? Would the SIA view be that there should then be no anthropic update to the prior probabilities at all? In this case it wouldn't become more SSA-like and update in favor of Y, and it also wouldn't consider anything like the "density" of observers in the two possible infinite universes? (like considering the number of observers in the finite 'observable' region that's had time to causally interact with us since the big bang)
We can’t assume an infinite number of people under a theistic creation because god has an infinite number of options to satisfy his creative urges, and only a small subset of those would be universes. Cf naturalism which only has universes to play with. So if you’re in a universe it’s much more likely it’s naturalistic.
That just seems like a different argument.
And though he has infinite ways to create, it's likely he'd create the maximum number he could because that's better.
A related issue is that even among algorithms that generate a "universe" of some kind, universes with regular laws that hold for all time have lower algorithmic complexity than ones where the laws differ from one region of spacetime to another (like cellular automata style universe where the update rules can differ at different time increments and different regions of the 'board'). So if God realizes all possible algorithmic universes that contain observers, and all observers are equally likely, then even if we are only considering observers whose experience is just like ours up until now, we should think it's far more likely that our upcoming experiences will be of the "miraculous" breakdown of the laws we remember up until now (this is basically a variant of one of the arguments against our being Boltzmann brains).
I don't think God makes every laws--he makes every possible person and puts them in the best world for them.
Btw, I’d be interested in your view. This also seems to my why fine tuning fails to predict theism. God can realise his visions in an infinite number of ways, and there is no need to have a universe. And for any realisation of his objectives (no matter how precisely defined) given his omnipotence he can always take Realisation 1 and create R2 which is equally good at meeting God’s objectives. And if R2 then R3. So the chances of a fine tuned universe are less under theism given the solution space is unbounded.
If he has infinite universes and infinite non-universes (all of which satisfy his creative urges) the probabilities don’t stack up in favour of theism.
It is not possible that there are infinite people. But, there could be an arbitrarily huge number of people as far as we know.
Many theories of physics imply that there are infinite people; you shouldn't rule such possibilities out categorically.
Are you not categorically ruling out—or saying there is infinite evidence against—theories of physics that do not predict infinite people?
Yes but not a priori--a posteriori, based on the surprising fact that I exist.
The point is that, if there is >0 probability that an infinite people theory holds, then we are overwhelmingly likely in it.