Very pumped about the book! Very intrigued by the more people than numbers arg 😄 glad you're stealing 'anthropic' back for our side. Strong anthropic principle who?
>Contrast that with atheism: what is the plausible atheistic story on which you get even ℶ2 people, much less Ω people?
All you have to do is imagine that space and time are modeled by hyperreal number systems instead of the reals. There are unsetly many such systems (they can differ by, e.g., arbitrary cardinality), and for each one, the real version of the universe should uniquely extend to a hyperreal version inside that system.[1] All of these universes will look completely indistinguishable when you locally take standard parts, so there's no exotic inductive failure. And they won't be true copies of each other, either (some universes will be strictly larger than others, in terms of cardinality), so this hypothesis sidesteps thorny metaphysical questions about the identity of indiscernibles.
It will be weird that the naturalistic universe has all these redundant-seeming (but cardinally distinguishable) hyperreal duplicates, but less weird than all of the open theoretical pathologies that theism introduces, plus SIA will get completely stuck on how the two bad priors should affect posteriors at all because both hypotheses generate so many people.
[1] For any real-valued function f : R -> R and any hyperreal number system S, there is a unique extension *f : S -> S. I'm pretty sure there's going to be an analogous extension principle for manifolds rather than functions, though I haven't investigated - non-standard differential geometry being something of a backwater of a backwater. Here is a PDF monograph that might discuss this, though I haven't read it: https://u.cs.biu.ac.il/~katzmik/tidg.pdf
If I'm getting the idea correctly, you're positing many different worlds that vary slightly by hyperreals. But why is this better than simply positing that there are uncountably infinite copies of the universe? Which to me seems like one of the best atheistic theories (probably the best is some weird mereological theory on which every brain has unsetly many conscious subsystems).
> But why is this better than simply positing that there are uncountably infinite copies of the universe?
I'm enlisting this machinery just to ensure they aren't true copies, because you might worry that qualitatively identical spatially disconnected universes are in fact numerically identical.
Yeah, I think the two best atheistic proposals are that and weird views of mereology where you get absolutely infinite mind subsets. But I'd still have pretty low credence in those views given atheism. So conditional on SIA plus the legitimacy of the SIA-->absolute infinity, it's good for a Bayes factor of maybe somewhere between 30 and a thousand.
But you'd have to consider how the theoretical costs of this view (which in my view is a bit odd, but not too much so) compare to the theoretical costs of theism.
I suppose, but it's a hypothesis that's very easy to compactly express mathematically. Meanwhile, theism has a ton of famous, deep conceptual problems of its own and which aren't amendable to compact mathematical expression/solution. And you in particular have to posit a lot of weird, arbitrary things like God choosing a strict subset of all possible net-good worlds to instantiate (since you think instantiating all of them would yield inductive failure) without being able to say how he could be doing this in a non-gerrymandered way.
>Though I don't really get it.
Imagine the universe consisted of a single particle moving around in otherwise empty 3d space according to some continuous trajectory or other. We could model this as a function r(t), which maps a single real number (time) to a triplet of real numbers (xyz-coordinates in 3d space, representing the particle's location at that specific time).
If we wanted, we could take this setup and "add" hyperreal numbers (given a hyperreal number system). So in addition to specifying where in space the particle is at time t=5 (i.e., r(5)), we could also talk about where it is at time t=5+ε, where ε is an infinitesimal quantity. If we try to do this, its position here now won't just be a triplet of real numbers, but a triplet of hyperreal numbers (which in this case will differ from its location at time t=5 by an infinitesimal amount/displacement). Of course, ε will not be the only infinitesimal quantity; there will be many others, such as 6ε or ε^2.
Given a hyperreal number system S, our original, *real* function r(t) will uniquely extend to a function r_S(t) which maps S-hyperreal times to S-hyperreal triplets of space coordinates. And there's a sense in which this new function r_S(t) completely "matches" that of r(t): r_S(5) will equal r(5), and furthermore if you take r_S(5+ε) and "shave off" the infinitesimal part of each of the three space coordinates, it will also equal r(5). So we have a hyperreal duplicate of our original setup that in a certain sense duplicates it but adds a bunch of invisibly tiny behavior "in between" - kind of like taking a hair comb and adding a lot of invisibly tiny teeth in between the main ones.
Furthermore, there are many, many systems S that we could choose from: unsetly many, in fact. So we could take one comb and add aleph_1 invisibly tiny teeth in between, and then take a second copy of the original comb and add aleph_2 invisibly tiny teeth in between to that one, etc.
For each hyperreal number system S, there will be a separate universe, with one particle in each universe whose trajectory (a function from time to space) is modeled via S-hyperreals. The behavior of these particles will all agree in the sense that I mentioned: their locations are the exact same at all real-valued times (like t=5), and their locations at times infinitesimally close to a given real time c will also be infinitesimally spatially close to their locations at time c.
Nevertheless, these universes aren't true isomorphic duplicates of each other, because different hyperreal number systems differ in cardinality. So a particle in one universe has a trajectory defined at strictly *more* times, in a set-theoretic sense, than that of another universe's particle.
1. Why would atheistic accounts be unable to provide for multiverses with this many people. It seems like there is no real reason that they cannot, even if it happens that the present arguments don’t provide for them. It just means those atheists are making the wrong argument for atheism. It doesn’t seem clear to me why god would be able to create any more distinct universes than many worlds would provide at the smallest level of separation. I don’t really see how the argument your provide here (imma read the full paper later) counters that.
(by this I mean a many worlds interpretation where the smallest change, so quantum events created different universes, these would seemingly be universes separate and distinct in as small a way as is possible. But maybe they don’t need to be distinct?)
This account seems not only to explain 3 better than the true multiverse, it also seems to be better on Bayesian grounds since we don’t need to through in a second probability on the existence of a divine entity into our credence. It of course also gets out of 2. Maybe this doesn’t work for quantum physics reason but I don’t see an immediate issue.
2. It’s good to create -> so god would create a lot begs the question in what seems to me a fairly obvious way. We have no reason to expect god to behave in a good way unless we are begging the question about the characteristics of that god. Frankly I would expect god not to behave in this way because if god exists it seems he is demonstrably not good.
3. Let me understand this right, your point is that across all possible worlds based on the way we can make variants of any person we have an absolute infinity of persons yeah? But is only true if modal realism is true and those people exist in fact. If modal realism isn’t already true (ie if there aren’t other universes connected to our own) why should we think or care about all these other hypothetical people or factor them into our calculations.
4. I also have to point out that non of this would prove anything at all about the nature of this god. Our credence for any discrete set of religious beliefs, however general should be vanishingly close to 0.
It seems like because of the problem of evil though this god absolutely cannot be the Christian one since none of the arguments people use to try and get out of the problem of evil make any sense. So the only way out as far as I can tell is to accept that noncontradiction doesn’t apply to god a bullet nobody but Descartes has bitten.
1. It's not that they can't it's that they have low antecedent probability given atheism and so lower the likelihood. As a point of comparison, it's not that you can't explain the writing about Thales without positing that he existed--it's just that it's likelier that you'd have the writing if he existed.
2. This is an argument for a perfect God. So we're holding fixed that the being we discuss is perfect. Now, maybe this has a low prior, but that's what it's about.
3. That's not my point. I was talking about the number of possible people which is absolute infinity. SIA implies you should think the number of people that exists = the number of possible people. Thus, it implies you should think absolute infinity people exist.
1. Yeah I’m simply unclear on why that is if all quantum positions supply different worlds, since that seems to supply the maximum um number of discrete worlds unless I’m missing something.
2. Yeah that just seems an insanely low priority probability, almost all these theist arguments predispose the very low credence (to my thinking) belief in a specific kind of deity. The argument may well work without this assumption as well.
3. But where are all these people? That’s my confusion here. If they aren’t in this universe (or a related one) it seems weird that we would regard them as meaningfully having the potential to have been me.
As for god being simple you could also have a maximally evil god. I think we have similar imitations but any specific god set up is just so unlikely. An all good (all powerful, all knowing) god just seems to be impossible given the problem of evil.
Potentially wrong Aside- on further thought it seems like the chances of me existing have little to do with the number of people but merely the presence of people in infinite universes. If I’m only me as a result of these very specific historical conditions of my existence it seems like the brute number of persons doesn’t affect my chances of existence directly. It is actually the # of universes with any number of people present that determines it, the # of people is only related to this probability.
"The self-indication assumption claims that your existence favors theories on which there are more candidates for being your present self."
But there are no other candidates. My present self is the result of a specific and unique set of historical occurrences beginning with my conception by two specific and biologically unique parents at a specific time and place. I either happen or I don't. Adding more people to the world doesn't help, because (a) none of those people are or can be me, and (b) a reality with more (or fewer) people in it would be a different reality than the one that resulted in my current self.
But the one sentence version: you know that you are you. But you don't know which person--given some third party description--you picks out. If there are 100 Earths throughout the universe, based on your current evidence, you don't know which of them you are.
Appreciate the response but I'm still balking at the notion that there is some meaningful "me" that is severable from the unique specific facts that make up my history and identity. I can imagine being another person or having lived own life differently, of course, but even these fantasies are specific to *my* imagination; a truly different person would fantasize differently. As for theoretical exact copies of me on alternate Earths, part of what defines me is that I am aware of myself -- I'm not aware of the copies and cannot access their sensoria so clearly they aren't *exact* copies, they are other people who are not me, however remarkable the resemblance.
"Suppose that God flips a coin. If it comes up tails, ten people get created. If it comes up heads, one person gets created. From this process, you get created. What odds should you give to the coin having come up heads?"
Since I exist to ponder the question, God obviously did create me. If the coin was heads, then I am the only person he created. If tails, he created me and nine other people who are not me. The only way to make tails more likely is to posit a "me" that is somehow separate from a specific physical body -- something like a soul -- and argue that it could have ended up in some completely different body instead, while still, somehow, being the same person.
No, that's not an assumption. It's about the number of people who, given all you know now, you might presently be. It requires no exotic metaphysical assumptions. It just depends on the notion that for all you know now, any of the ten people might be you. So, for instance, you can't rule out your being the first guy.
That's the piece I was quoting from. Really trying not to be dense here, but it's the "any of the ten people might be you" that I'm wrestling with. Are you saying that if I'm in the group of ten, it matters what order God creates me in? Because I would argue I'm the same "me" whether he makes me first or last, and of course he could just create us all simultaneously.
Wanted to give you an answer here so you don't get further confused, as most people do when they encounter the SIA - https://ramblingafter.substack.com/p/is-doomsday-inevitable (I would love if Bentham could take a gander at it - though I know he's really quite busy - and could form a response, or better yet, either (1) understand the flaw in his reasoning or (2) fortify the SIA in a way I've yet to see done)
What about a hypothesis of the form "Whatever mechanism triggered the Big Bang was such that it actually created a huge number of identical copies of our universe."? Now, I'm not sure if absolute infinity Ω really makes sense, but we can just look at different options in more detail.
1.) Ω does make sense. Then "Whatever mechanism triggered the Big Bang was such that it actually created Ω identical copies of our universe." seems like a fairly parsimonious hypothesis. It's maybe not as intuitively motivated as "God is a maximizer so he created as much as possible" (though I personally lack the relevant intuitions about what God would do), but on the other hand it avoids postulating the existence of God which to me feels like it should count in favor of it on simplicity grounds. At least it's not clear which one wins out.
2.) Ω does not make sense. Then fix some cardinality κ and say "Whatever mechanism triggered the Big Bang was such that it actually created κ identical copies of our universe." This is now more ad hoc since it involves this arbitrary-looking κ, but the God hypothesis will be in the same boat since God also had to pick some cardinality κ as we are stipulating that the "natural" choice Ω doesn't make sense.
I suppose this is really very analogous to the axiarchism proposal in your paper, except that it doesn't mention value maximization or something like that.
That's not what standard physics theories say . So I think you'll just have to brutely posit many copies for no reason. That's one of the better atheistic proposals, but it's still costly.
Actually I just realized that this hypothesis contains theism since God is the mechanism which created the universe... But ok, modifying in some obvious way: yes, it's not what the physics says, and it's so far removed from our experimental capacities that we may not even in principle be able to determine it. I think the real question is whether postulating some kind of "simple cosmic seed" that blows up into Ω many copies of our universe is really more costly than theism. I am very confident that it's not much more costly, but with some more modest degree of confidence I would say it might even beat out theism (understood as an infinite, omnibenevolent, omniscient etc. mind).
I do think it's very plausible we live in an infinite multiverse.
I sort of doubt that "exact copies" is even a coherent concept; if reality is just the instantiation of all mathematical possibilities, then any exact copy doesn't exist beyond the instantiation of the original.
I'm a bit unsure myself if exact copies of persons make sense, but upon reflection I do lean towards it being coherent. Like, it seems possible to me that there is a perfectly symmetric house with two inhabitants in either half who are "internally" identical (totally the same thoughts, experiences, etc.) but nevertheless are in some "real", or "metaphysical", or what have you, sense different people.
As I mention in a comment below, you can avoid this issue entirely by enlisting different hyperreal number systems and modeling space and time with them instead of the reals.
Ok, this looks like giving every person little "hyperreal hairs" that are physically invisible but still distinguish them. I.e., some kind of indexicality is baked into the different copies. I was thinking about something possibly similar: just attach an index to each copy. So the universes will be U_α, where α might run over all of Ord if desired. α has no physical meaning (much like the choice of the hyperreal system), it's just a metaphysical appendix to make things discernible. Though perhaps the hyperreal approach has the advantage that there is an intrinsic invariant (cardinality of the spacetime manifold) that distinguishes the U's.
I think the main alternative is that everything possible exists: Tegmark IV, modal realism, stuff like that. Very popular among LessWrongers, and if I'm understanding you correctly, probably more people than a God would create too.
Not more, same number--both absolute infinity. But I think that view collapses induction, doesn't explain most of the other evidence that theism does, and is also just bonkers--in what sense could a person be identical to a mathematical description.
It's more because e.g. someone having a negative experience wouldn't be created by God, right? Or would be less likely to be. So that's strictly more. I get that it might be the same cardinality, but cardinality is the wrong approach to infinities - as you know, Ord's "Evaluating the infinite" argues this, and as you know I'm convinced by it. From a hyperreal perspective, one more just is one more - it's that simple.
"collapses induction" unclear, see e.g. UDASSA. It gets extremely complicated, I don't think much confidence is warranted here. (And also why doesn't your viewpoint collapse induction?)
"in what sense could a person be identical to a mathematical description." if we take a deflationary approach to the concept of existence, like many LessWrongers have done, e.g. Christiano, Garrabrant, etc
Don't hyperreals depend on a measure? But in any case, I'm pretty sure the Ord thing doesn't work nicely with absolute infinites.
Other thing: it's not clear that it's a smaller number. Maybe the right way to think about it isn't "God only creates the good people to create," but "God creates the same collection of people as exist in the modal realist superverse and then makes all of them have fortunate existences."
I’d agree the Ord thing specifically will struggle - as he says in the paper, it’s just a start. It’s more about the larger attitude. The default way of thinking about infinities in real life should not be cardinal. There’s no reason for that, it has no good argument for it that I know of. Hyperreal-style intuitions are just better. Adding one to an infinite amount should make it bigger, intuitively.
I assume that your paper was sent out for peer review. If so, were any of the reviewers trained in physics, math, or statistics? I'd like to know what smart people outside of philosophy think of these SIA-type arguments (which, frankly, seem far-fetched to me, to put it mildly).
I know advanced math in the sense that I did well with it in college and could probably do ok with a brief refresher. That does not mean I am good enough at it to find subtle flaws in complex arguments. I too am curious about what experts in math/stats/physics fields think, not just people who know advanced math.
With the caveat that these things are almost perfectly designed to evince maximum variability of opinions...
I majored in pure math with a strong interest in its fundamentals incl. set theory and Cantor stuff. Followed BB's arguments as they came, learned a lot from it (I had no idea people were trying this kind of thing).
In the end, my assessment is negative. SIA is a framework that seems to work nicely enough in bounded, simple situations like the Sleeping Beauty problem, where you know (by hypothesis) that there is a probabilistic mechanism that puts the observer in a situation or another.
When you give SIA the entire space of conceivable worlds as a workspace, as BB just explained, what you get is not a concrete result, but "bigger than infinity", i.e no concrete infinity is ever big enough.
In science, we don't call this kind of thing an answer - we call it "the approach diverges at this point". Which means it doesn't say anything about the actual universe we live in.
Still, good job trying, and congrats for the publishing! My position hasn't changed though: positive on a mystical ground-of-consciousness view of God, negative on triple-O *and* on deriving it from objective evidence.
Yes to this criticism. The theoretic space of possible world options is infinite. We need to evaluate the contingent nature of OUR universe to evaluate what theoretic models match it. Empiricism, not analytic philosophy, is how to discover the truths about our universe.
If “science”™ is so brain-rotted that it categorically eliminates any sense of a truly infinite infinity, then “science”™ clearly does not correspond to either basic intuition or the mystical experiences of thousands since the beginning of time who have encountered the infinite infinity.
You seem to think the latter is possible, so I wonder why you accept the limitations imposed by “science.”™
I maintain that all of the pro-SIA arguments rest on a faulty assumption. Remove the assumption and it completely falls apart, which is great news because then you no longer get the presumptuous philosopher. (This doesn't mean accepting the SSA either; rather you should reject both.)
I've tried to explain this before, but did a poor job of it; I hope this did a much better job of it:
You should pray, investigate religions, and try even harder to do the right thing--knowing that its benefits are even greater, and you may get to live in paradise forever with those you benefit.
Please correct me if I'm wrong but your proofs/arguments, if they are correct, establish the existence of a god that created the universe. What reason do I have to believe this god would resemble the gods of major religions? For example, that it would care if I pray, that it would want to me "do the right thing" (also how do I know what that is?), or that there is a heaven or hell?
What exactly is it that your arguments demonstrate about god? Apologies I haven't read them very closely.
Right, arguments like this tend to posit "a creator" without any specific attribute. Who's to say it's not trying to maximize suffering, but suffering needs good to know just how bad it is?
Isn't it overwhelmingly plausible that a being that is omnipotent and omnibenevolent would give you an eternal afterlife and not just 80 years of existence?
I don’t know on what basis you make that claim. It just seems eerily similar to leading religions, which seem obviously false to me. I think we’re psychologically aligned with wanting an afterlife to exist which is why religions posit it, and why you’re implying a god would obviously make it.
Ultimately you’re trying to reason about a god that created an incredibly large universe (and potentially a multiverse) with trillions of galaxies and unfathomable empty space. One in which there were no humans for billions of years. One in which there were dinosaurs for hundreds of millions of years. And you think he created it especially with humans in mind? It makes no sense.
The argument doesn't get us to omnipotent or omnibenevolent though. Those traits are assumptions that get dragged in to be compatible with common religions.
It's overwhelmingly implausible to me that the world would look the way it does if there was an omnipotent and omnibenevolent being though
I mean yeah, basically everyone agrees that the problem of evil is a problem. The reason to think that the creator of the multiverse isn't just highly powerful, but perfect, is because the theory is so much simpler than any limited god proposal.
Also, if the argument "only" showed that a limited god exists, this would still be incredibly remarkable.
SIA isn’t a proof for God, it simply describes a statistical likelihood. Large and small infinities are imaginary mathematical concepts but like the square root of -1 don’t exist in the real world - useful yes, but as a proof if God certainly not conclusive.
Congratulations! Also have you thought about pitching that book to Eerdmans - I bet they would love it
Thanks! Btw, have quite enjoyed a lot of your YouTube videos.
I forget which publishers we've talked with.
Very pumped about the book! Very intrigued by the more people than numbers arg 😄 glad you're stealing 'anthropic' back for our side. Strong anthropic principle who?
Thanks!
Congrats on everything!
>Contrast that with atheism: what is the plausible atheistic story on which you get even ℶ2 people, much less Ω people?
All you have to do is imagine that space and time are modeled by hyperreal number systems instead of the reals. There are unsetly many such systems (they can differ by, e.g., arbitrary cardinality), and for each one, the real version of the universe should uniquely extend to a hyperreal version inside that system.[1] All of these universes will look completely indistinguishable when you locally take standard parts, so there's no exotic inductive failure. And they won't be true copies of each other, either (some universes will be strictly larger than others, in terms of cardinality), so this hypothesis sidesteps thorny metaphysical questions about the identity of indiscernibles.
It will be weird that the naturalistic universe has all these redundant-seeming (but cardinally distinguishable) hyperreal duplicates, but less weird than all of the open theoretical pathologies that theism introduces, plus SIA will get completely stuck on how the two bad priors should affect posteriors at all because both hypotheses generate so many people.
[1] For any real-valued function f : R -> R and any hyperreal number system S, there is a unique extension *f : S -> S. I'm pretty sure there's going to be an analogous extension principle for manifolds rather than functions, though I haven't investigated - non-standard differential geometry being something of a backwater of a backwater. Here is a PDF monograph that might discuss this, though I haven't read it: https://u.cs.biu.ac.il/~katzmik/tidg.pdf
If I'm getting the idea correctly, you're positing many different worlds that vary slightly by hyperreals. But why is this better than simply positing that there are uncountably infinite copies of the universe? Which to me seems like one of the best atheistic theories (probably the best is some weird mereological theory on which every brain has unsetly many conscious subsystems).
> But why is this better than simply positing that there are uncountably infinite copies of the universe?
I'm enlisting this machinery just to ensure they aren't true copies, because you might worry that qualitatively identical spatially disconnected universes are in fact numerically identical.
I don’t worry about that
OK, then the copy thing is probably good enough, and the hyperreal stuff is unnecessary. For some reason I thought you did care about that.
Yeah, I think the two best atheistic proposals are that and weird views of mereology where you get absolutely infinite mind subsets. But I'd still have pretty low credence in those views given atheism. So conditional on SIA plus the legitimacy of the SIA-->absolute infinity, it's good for a Bayes factor of maybe somewhere between 30 and a thousand.
But you'd have to consider how the theoretical costs of this view (which in my view is a bit odd, but not too much so) compare to the theoretical costs of theism.
Seems kind of gerrymandered. Though I don't really get it.
I suppose, but it's a hypothesis that's very easy to compactly express mathematically. Meanwhile, theism has a ton of famous, deep conceptual problems of its own and which aren't amendable to compact mathematical expression/solution. And you in particular have to posit a lot of weird, arbitrary things like God choosing a strict subset of all possible net-good worlds to instantiate (since you think instantiating all of them would yield inductive failure) without being able to say how he could be doing this in a non-gerrymandered way.
>Though I don't really get it.
Imagine the universe consisted of a single particle moving around in otherwise empty 3d space according to some continuous trajectory or other. We could model this as a function r(t), which maps a single real number (time) to a triplet of real numbers (xyz-coordinates in 3d space, representing the particle's location at that specific time).
If we wanted, we could take this setup and "add" hyperreal numbers (given a hyperreal number system). So in addition to specifying where in space the particle is at time t=5 (i.e., r(5)), we could also talk about where it is at time t=5+ε, where ε is an infinitesimal quantity. If we try to do this, its position here now won't just be a triplet of real numbers, but a triplet of hyperreal numbers (which in this case will differ from its location at time t=5 by an infinitesimal amount/displacement). Of course, ε will not be the only infinitesimal quantity; there will be many others, such as 6ε or ε^2.
Given a hyperreal number system S, our original, *real* function r(t) will uniquely extend to a function r_S(t) which maps S-hyperreal times to S-hyperreal triplets of space coordinates. And there's a sense in which this new function r_S(t) completely "matches" that of r(t): r_S(5) will equal r(5), and furthermore if you take r_S(5+ε) and "shave off" the infinitesimal part of each of the three space coordinates, it will also equal r(5). So we have a hyperreal duplicate of our original setup that in a certain sense duplicates it but adds a bunch of invisibly tiny behavior "in between" - kind of like taking a hair comb and adding a lot of invisibly tiny teeth in between the main ones.
Furthermore, there are many, many systems S that we could choose from: unsetly many, in fact. So we could take one comb and add aleph_1 invisibly tiny teeth in between, and then take a second copy of the original comb and add aleph_2 invisibly tiny teeth in between to that one, etc.
Wait though won't there still just be one particle but its temporal location is divided up arbitrarily many ways?
For each hyperreal number system S, there will be a separate universe, with one particle in each universe whose trajectory (a function from time to space) is modeled via S-hyperreals. The behavior of these particles will all agree in the sense that I mentioned: their locations are the exact same at all real-valued times (like t=5), and their locations at times infinitesimally close to a given real time c will also be infinitesimally spatially close to their locations at time c.
Nevertheless, these universes aren't true isomorphic duplicates of each other, because different hyperreal number systems differ in cardinality. So a particle in one universe has a trajectory defined at strictly *more* times, in a set-theoretic sense, than that of another universe's particle.
Yeah that seems like one of the better atheistic proposals.
So a number of notes
1. Why would atheistic accounts be unable to provide for multiverses with this many people. It seems like there is no real reason that they cannot, even if it happens that the present arguments don’t provide for them. It just means those atheists are making the wrong argument for atheism. It doesn’t seem clear to me why god would be able to create any more distinct universes than many worlds would provide at the smallest level of separation. I don’t really see how the argument your provide here (imma read the full paper later) counters that.
(by this I mean a many worlds interpretation where the smallest change, so quantum events created different universes, these would seemingly be universes separate and distinct in as small a way as is possible. But maybe they don’t need to be distinct?)
This account seems not only to explain 3 better than the true multiverse, it also seems to be better on Bayesian grounds since we don’t need to through in a second probability on the existence of a divine entity into our credence. It of course also gets out of 2. Maybe this doesn’t work for quantum physics reason but I don’t see an immediate issue.
2. It’s good to create -> so god would create a lot begs the question in what seems to me a fairly obvious way. We have no reason to expect god to behave in a good way unless we are begging the question about the characteristics of that god. Frankly I would expect god not to behave in this way because if god exists it seems he is demonstrably not good.
3. Let me understand this right, your point is that across all possible worlds based on the way we can make variants of any person we have an absolute infinity of persons yeah? But is only true if modal realism is true and those people exist in fact. If modal realism isn’t already true (ie if there aren’t other universes connected to our own) why should we think or care about all these other hypothetical people or factor them into our calculations.
4. I also have to point out that non of this would prove anything at all about the nature of this god. Our credence for any discrete set of religious beliefs, however general should be vanishingly close to 0.
It seems like because of the problem of evil though this god absolutely cannot be the Christian one since none of the arguments people use to try and get out of the problem of evil make any sense. So the only way out as far as I can tell is to accept that noncontradiction doesn’t apply to god a bullet nobody but Descartes has bitten.
1. It's not that they can't it's that they have low antecedent probability given atheism and so lower the likelihood. As a point of comparison, it's not that you can't explain the writing about Thales without positing that he existed--it's just that it's likelier that you'd have the writing if he existed.
2. This is an argument for a perfect God. So we're holding fixed that the being we discuss is perfect. Now, maybe this has a low prior, but that's what it's about.
3. That's not my point. I was talking about the number of possible people which is absolute infinity. SIA implies you should think the number of people that exists = the number of possible people. Thus, it implies you should think absolute infinity people exist.
For stuff about the prior of a good God, see https://benthams.substack.com/p/god-may-be-maximally-simple?utm_source=publication-search
1. Yeah I’m simply unclear on why that is if all quantum positions supply different worlds, since that seems to supply the maximum um number of discrete worlds unless I’m missing something.
2. Yeah that just seems an insanely low priority probability, almost all these theist arguments predispose the very low credence (to my thinking) belief in a specific kind of deity. The argument may well work without this assumption as well.
3. But where are all these people? That’s my confusion here. If they aren’t in this universe (or a related one) it seems weird that we would regard them as meaningfully having the potential to have been me.
As for god being simple you could also have a maximally evil god. I think we have similar imitations but any specific god set up is just so unlikely. An all good (all powerful, all knowing) god just seems to be impossible given the problem of evil.
1. The idea is just there's a conceivable copy of me at different heights for each of the reals and with different rearrangements of particles.
2. Disagree for the resaons linked.
3. They're elsewhere in the multiverse. Note that you don't know which of the universes in the multiverse this one is--so they're all candidates for being your present self. For more see https://benthams.substack.com/p/precisely-defining-the-self-indication?utm_source=publication-search
Potentially wrong Aside- on further thought it seems like the chances of me existing have little to do with the number of people but merely the presence of people in infinite universes. If I’m only me as a result of these very specific historical conditions of my existence it seems like the brute number of persons doesn’t affect my chances of existence directly. It is actually the # of universes with any number of people present that determines it, the # of people is only related to this probability.
See the linked piece where I argue for SIA https://benthams.substack.com/p/the-ultimate-guide-to-the-anthropic
Congrats on the publication. I've read it and you guys did a good job.
Thanks! By the way Daniel, I'd be curious to hear your take on the Menzel wide sets paper https://www.pgrim.org/philosophersannual/34articles/menzelwide.pdf. To what extent do you think it resolves concerns about absolute infinite people existing?
I am unreasonably excited about the book announcement. Are you set on the title yet?
I’m not yet well-enough acquainted with anthropic reasoning to know if I buy the SIA, but this is nonetheless one of the coolest arguments out there.
Tangential: That Jason Stanley video is really the gift that keeps on giving
Truly doing the Lord's work
"The self-indication assumption claims that your existence favors theories on which there are more candidates for being your present self."
But there are no other candidates. My present self is the result of a specific and unique set of historical occurrences beginning with my conception by two specific and biologically unique parents at a specific time and place. I either happen or I don't. Adding more people to the world doesn't help, because (a) none of those people are or can be me, and (b) a reality with more (or fewer) people in it would be a different reality than the one that resulted in my current self.
Also:
"it’s good to create"
Why?
For 1, see https://benthams.substack.com/p/precisely-defining-the-self-indication?utm_source=publication-search
But the one sentence version: you know that you are you. But you don't know which person--given some third party description--you picks out. If there are 100 Earths throughout the universe, based on your current evidence, you don't know which of them you are.
For the other point ,see 4.2 https://benthams.substack.com/p/the-ultimate-guide-to-the-anthropic
Appreciate the response but I'm still balking at the notion that there is some meaningful "me" that is severable from the unique specific facts that make up my history and identity. I can imagine being another person or having lived own life differently, of course, but even these fantasies are specific to *my* imagination; a truly different person would fantasize differently. As for theoretical exact copies of me on alternate Earths, part of what defines me is that I am aware of myself -- I'm not aware of the copies and cannot access their sensoria so clearly they aren't *exact* copies, they are other people who are not me, however remarkable the resemblance.
That's not an assumption, just read the piece
I did read it, but I'm still balking.
"Suppose that God flips a coin. If it comes up tails, ten people get created. If it comes up heads, one person gets created. From this process, you get created. What odds should you give to the coin having come up heads?"
Since I exist to ponder the question, God obviously did create me. If the coin was heads, then I am the only person he created. If tails, he created me and nine other people who are not me. The only way to make tails more likely is to posit a "me" that is somehow separate from a specific physical body -- something like a soul -- and argue that it could have ended up in some completely different body instead, while still, somehow, being the same person.
I meant read this piece to be clear https://benthams.substack.com/p/precisely-defining-the-self-indication?utm_source=publication-search
No, that's not an assumption. It's about the number of people who, given all you know now, you might presently be. It requires no exotic metaphysical assumptions. It just depends on the notion that for all you know now, any of the ten people might be you. So, for instance, you can't rule out your being the first guy.
That's the piece I was quoting from. Really trying not to be dense here, but it's the "any of the ten people might be you" that I'm wrestling with. Are you saying that if I'm in the group of ten, it matters what order God creates me in? Because I would argue I'm the same "me" whether he makes me first or last, and of course he could just create us all simultaneously.
Wanted to give you an answer here so you don't get further confused, as most people do when they encounter the SIA - https://ramblingafter.substack.com/p/is-doomsday-inevitable (I would love if Bentham could take a gander at it - though I know he's really quite busy - and could form a response, or better yet, either (1) understand the flaw in his reasoning or (2) fortify the SIA in a way I've yet to see done)
What about a hypothesis of the form "Whatever mechanism triggered the Big Bang was such that it actually created a huge number of identical copies of our universe."? Now, I'm not sure if absolute infinity Ω really makes sense, but we can just look at different options in more detail.
1.) Ω does make sense. Then "Whatever mechanism triggered the Big Bang was such that it actually created Ω identical copies of our universe." seems like a fairly parsimonious hypothesis. It's maybe not as intuitively motivated as "God is a maximizer so he created as much as possible" (though I personally lack the relevant intuitions about what God would do), but on the other hand it avoids postulating the existence of God which to me feels like it should count in favor of it on simplicity grounds. At least it's not clear which one wins out.
2.) Ω does not make sense. Then fix some cardinality κ and say "Whatever mechanism triggered the Big Bang was such that it actually created κ identical copies of our universe." This is now more ad hoc since it involves this arbitrary-looking κ, but the God hypothesis will be in the same boat since God also had to pick some cardinality κ as we are stipulating that the "natural" choice Ω doesn't make sense.
I suppose this is really very analogous to the axiarchism proposal in your paper, except that it doesn't mention value maximization or something like that.
That's not what standard physics theories say . So I think you'll just have to brutely posit many copies for no reason. That's one of the better atheistic proposals, but it's still costly.
By the way, congrats on the paper, it looks very nice.
Actually I just realized that this hypothesis contains theism since God is the mechanism which created the universe... But ok, modifying in some obvious way: yes, it's not what the physics says, and it's so far removed from our experimental capacities that we may not even in principle be able to determine it. I think the real question is whether postulating some kind of "simple cosmic seed" that blows up into Ω many copies of our universe is really more costly than theism. I am very confident that it's not much more costly, but with some more modest degree of confidence I would say it might even beat out theism (understood as an infinite, omnibenevolent, omniscient etc. mind).
I do think it's very plausible we live in an infinite multiverse.
I sort of doubt that "exact copies" is even a coherent concept; if reality is just the instantiation of all mathematical possibilities, then any exact copy doesn't exist beyond the instantiation of the original.
But also we don't need any of that because there's no proof of infinite observers because the SIA is built atop sand: https://ramblingafter.substack.com/p/is-doomsday-inevitable
I'm a bit unsure myself if exact copies of persons make sense, but upon reflection I do lean towards it being coherent. Like, it seems possible to me that there is a perfectly symmetric house with two inhabitants in either half who are "internally" identical (totally the same thoughts, experiences, etc.) but nevertheless are in some "real", or "metaphysical", or what have you, sense different people.
As I mention in a comment below, you can avoid this issue entirely by enlisting different hyperreal number systems and modeling space and time with them instead of the reals.
Ok, this looks like giving every person little "hyperreal hairs" that are physically invisible but still distinguish them. I.e., some kind of indexicality is baked into the different copies. I was thinking about something possibly similar: just attach an index to each copy. So the universes will be U_α, where α might run over all of Ord if desired. α has no physical meaning (much like the choice of the hyperreal system), it's just a metaphysical appendix to make things discernible. Though perhaps the hyperreal approach has the advantage that there is an intrinsic invariant (cardinality of the spacetime manifold) that distinguishes the U's.
Right.
I think the main alternative is that everything possible exists: Tegmark IV, modal realism, stuff like that. Very popular among LessWrongers, and if I'm understanding you correctly, probably more people than a God would create too.
Not more, same number--both absolute infinity. But I think that view collapses induction, doesn't explain most of the other evidence that theism does, and is also just bonkers--in what sense could a person be identical to a mathematical description.
It's more because e.g. someone having a negative experience wouldn't be created by God, right? Or would be less likely to be. So that's strictly more. I get that it might be the same cardinality, but cardinality is the wrong approach to infinities - as you know, Ord's "Evaluating the infinite" argues this, and as you know I'm convinced by it. From a hyperreal perspective, one more just is one more - it's that simple.
"collapses induction" unclear, see e.g. UDASSA. It gets extremely complicated, I don't think much confidence is warranted here. (And also why doesn't your viewpoint collapse induction?)
"in what sense could a person be identical to a mathematical description." if we take a deflationary approach to the concept of existence, like many LessWrongers have done, e.g. Christiano, Garrabrant, etc
Once we're in the realm of the absolute infinite, not clear that you can take measure in this way.
I'm not sure what you're referring to. Hyperreals aren't a measure.
Don't hyperreals depend on a measure? But in any case, I'm pretty sure the Ord thing doesn't work nicely with absolute infinites.
Other thing: it's not clear that it's a smaller number. Maybe the right way to think about it isn't "God only creates the good people to create," but "God creates the same collection of people as exist in the modal realist superverse and then makes all of them have fortunate existences."
I’d agree the Ord thing specifically will struggle - as he says in the paper, it’s just a start. It’s more about the larger attitude. The default way of thinking about infinities in real life should not be cardinal. There’s no reason for that, it has no good argument for it that I know of. Hyperreal-style intuitions are just better. Adding one to an infinite amount should make it bigger, intuitively.
I assume that your paper was sent out for peer review. If so, were any of the reviewers trained in physics, math, or statistics? I'd like to know what smart people outside of philosophy think of these SIA-type arguments (which, frankly, seem far-fetched to me, to put it mildly).
I know one of the referees and they have graduate training in set theory and statistics.
They definitely knew advanced math.
I know advanced math in the sense that I did well with it in college and could probably do ok with a brief refresher. That does not mean I am good enough at it to find subtle flaws in complex arguments. I too am curious about what experts in math/stats/physics fields think, not just people who know advanced math.
I have a friend with a degree in math and he thinks the argument is good.
With the caveat that these things are almost perfectly designed to evince maximum variability of opinions...
I majored in pure math with a strong interest in its fundamentals incl. set theory and Cantor stuff. Followed BB's arguments as they came, learned a lot from it (I had no idea people were trying this kind of thing).
In the end, my assessment is negative. SIA is a framework that seems to work nicely enough in bounded, simple situations like the Sleeping Beauty problem, where you know (by hypothesis) that there is a probabilistic mechanism that puts the observer in a situation or another.
When you give SIA the entire space of conceivable worlds as a workspace, as BB just explained, what you get is not a concrete result, but "bigger than infinity", i.e no concrete infinity is ever big enough.
In science, we don't call this kind of thing an answer - we call it "the approach diverges at this point". Which means it doesn't say anything about the actual universe we live in.
Still, good job trying, and congrats for the publishing! My position hasn't changed though: positive on a mystical ground-of-consciousness view of God, negative on triple-O *and* on deriving it from objective evidence.
Yes to this criticism. The theoretic space of possible world options is infinite. We need to evaluate the contingent nature of OUR universe to evaluate what theoretic models match it. Empiricism, not analytic philosophy, is how to discover the truths about our universe.
If “science”™ is so brain-rotted that it categorically eliminates any sense of a truly infinite infinity, then “science”™ clearly does not correspond to either basic intuition or the mystical experiences of thousands since the beginning of time who have encountered the infinite infinity.
You seem to think the latter is possible, so I wonder why you accept the limitations imposed by “science.”™
I maintain that all of the pro-SIA arguments rest on a faulty assumption. Remove the assumption and it completely falls apart, which is great news because then you no longer get the presumptuous philosopher. (This doesn't mean accepting the SSA either; rather you should reject both.)
I've tried to explain this before, but did a poor job of it; I hope this did a much better job of it:
https://ramblingafter.substack.com/p/is-doomsday-inevitable
I read this and thought it was quite good
What is the implication of god’s existence for how I should live my life?
Presumably specific religions like Christianity and Islam are wrong. They’re so obviously man-made.
I’m open to a god outside of man-made religions, but not sure the relevance of it to my life.
You should pray, investigate religions, and try even harder to do the right thing--knowing that its benefits are even greater, and you may get to live in paradise forever with those you benefit.
Please correct me if I'm wrong but your proofs/arguments, if they are correct, establish the existence of a god that created the universe. What reason do I have to believe this god would resemble the gods of major religions? For example, that it would care if I pray, that it would want to me "do the right thing" (also how do I know what that is?), or that there is a heaven or hell?
What exactly is it that your arguments demonstrate about god? Apologies I haven't read them very closely.
Right, arguments like this tend to posit "a creator" without any specific attribute. Who's to say it's not trying to maximize suffering, but suffering needs good to know just how bad it is?
Isn't it overwhelmingly plausible that a being that is omnipotent and omnibenevolent would give you an eternal afterlife and not just 80 years of existence?
I don’t know on what basis you make that claim. It just seems eerily similar to leading religions, which seem obviously false to me. I think we’re psychologically aligned with wanting an afterlife to exist which is why religions posit it, and why you’re implying a god would obviously make it.
Ultimately you’re trying to reason about a god that created an incredibly large universe (and potentially a multiverse) with trillions of galaxies and unfathomable empty space. One in which there were no humans for billions of years. One in which there were dinosaurs for hundreds of millions of years. And you think he created it especially with humans in mind? It makes no sense.
The argument doesn't get us to omnipotent or omnibenevolent though. Those traits are assumptions that get dragged in to be compatible with common religions.
It's overwhelmingly implausible to me that the world would look the way it does if there was an omnipotent and omnibenevolent being though
I mean yeah, basically everyone agrees that the problem of evil is a problem. The reason to think that the creator of the multiverse isn't just highly powerful, but perfect, is because the theory is so much simpler than any limited god proposal.
Also, if the argument "only" showed that a limited god exists, this would still be incredibly remarkable.
Nope.
You can't draw those conclusions or recommendations at all.
There's nothing that says that a god created a paradise, or that it even would want people to pray.
It may think praying people are annoying, like begging children. Or don't care.
The fact that there are different religions is an extremely strong indicator that they are not from a god.
It would be so extremely easy for a god to make a religion that would obviously be from a god.
I'd think you should rather reason. As we got a big brain. It would indicate it wanted us to use it.
SIA isn’t a proof for God, it simply describes a statistical likelihood. Large and small infinities are imaginary mathematical concepts but like the square root of -1 don’t exist in the real world - useful yes, but as a proof if God certainly not conclusive.
This doesn't interact with the argument as given.
Congratulations, this is awesome.