As a statistician, one of my main concerns with the Self-Indication Assumption (SIA) is that it treats ‘I exist’ as if it were a typical piece of evidence for updating our hypotheses, whereas from my own vantage point, my existence is guaranteed (probability 1). Hence, we do not truly have an independent observation. Let me try to be more clear:
Given universe A with billions of people and universe B with a gazillion of people the fact that "I exist" is not independent of the worlds being considered. The existence of observers is tied to the structure of each possible world, making "I exist" a given rather than an independent piece of evidence.
Again even more clear (hopefully):
Under SIA, we assign higher probability to World B because it has more observers, making our existence seem more likely in that world. However:
The observation that "I exist" isn't a random variable sampled from a distribution over observers. Instead, it is a given that applies equally in either world, conditional on the subject being able to make observations.
In other words it seems to me that the probability of "I exist" is 1 in both worlds, conditional on our own capacity to reason, so it cannot provide additional evidence to differentiate between them.
This undermines the usual machinery of Bayesian inference, which presumes we have evidence that can vary depending on which hypothesis is true. Here, the evidence ‘I exist’ does not really vary from my standpoint: it’s guaranteed if I’m around to observe it. Consequently, it seems like it does not provide additional, independent information to discriminate between Universe A and Universe B.
It sounds like the view you'd adopt would be compartmentalized conditionalization--your only evidence is that your experiences are had, the numbers don't matter. But CC is super crazy and violates Bayesian conditionalization https://benthams.substack.com/p/compartmentalized-conditionalization
Interesting. Given that these anthropic arguments are partly based on statistical principles, I wonder if there have been any published works by people whose training was primarily in statistics, as opposed to people who are primarily philosophers. If so, was there any consensus from the statistical community?
Well, seeing as there are no published works on the anthropic argument, there are none by people who know about statistics. I know someone who thinks it works and has a degree in math. Many SIA boosters know a lot about math--most are philosophers, but that's just because SIA is a philosophical subject. Some technical areas of philosophy involve quite a lot of math.
>Thus, if naturalism is true, then if there are L people total, there are L people who are deceived, just as there are L people who aren’t deceived. Your credence in you being deceived should thus be undefined.
This doesn't follow. I'm not sure Bayesians even allow undefined probabilities, at least in the case of an ideal reasoner and non-super-mathematically-pathological propositions like "I am not being deceived" (as opposed to "this uniformly distributed random variable on the interval [0,1] belongs to this specific Vitali set I constructed via the Axiom of Choice"). But regardless of that technicality, just because the world is such that you can't meaningfully apply the principle of indifference or whatever anthropic principle to resolve a certain question, it doesn't automatically follow that you need to be skeptical in any sense about that question. Maybe you can fall back to other epistemic principles in cases like these, e.g., phenomenal conservatism.
It's also not obvious why the atheist can't get around all this by simply proposing some non-theistic axiological competitor that posits the same collection of worlds being created as you think God would create - i.e., the overall metaphysics of world creation is "just" that the best collection of worlds gets created full-stop, with no intermediary agent who's responsible for this. And so if you think that only induction-friendly hypotheses are in the running, and you think theism is induction-friendly due to the worlds that it would generate, this one should also be induction-friendly because it generates the same ones.
Finally, it's extraordinarily mysterious *how* God chooses which set of net-positive anti-inductive worlds he actualizes. Why would he choose one and not the other? Is it random? But we have no theory of probability that's going to work well to model this given the cardinalities involved, so it's "random" in the haziest possible sense (not to mention how weird it is to suggest an omniscient agent choosing something randomly, as if he doesn't know the outcome in advance, and as if there's some Metaphysical Random Number Generator/"MNRG" that is doing stuff outside of any universe and independently of his will and as if the same mystery doesn't adhere to the MNRG's process). In fact, if almost all worlds are inductive, shouldn't we have essentially 100% credence that the next induction I try to apply will succeed, instead of something appropriately lower like 99%? You might reply that we should go by the proportion of observer-moments within each universe where induction succeeds rather than across universes, but why? Putting aside that this sounds more like an SSA approach than SIA, if it's because the proportions are undefined like what you write about the atheistic multiverse hypothesis above, then you agree with my earlier point there - in cases where we can't reason this way because the math doesn't work out, we can just fall back to other principles. And indeed, even ignoring this weirdness, I should still be 100% certain that I'm not in an anti-inductive universe in general, which most would reject.
Always nice to hear from you Mark. Yes, I agree that the atheist can *in principle* have an explanation that mirrors the theist's explanation. However, it's hard to see what the plausible story is regarding how this will work out. The axiarchist explanation works, but I think axiarchism has other problems--I don't think, for instance, that there's a unique best collection of things.
I think if you adopt PC, then you get a defeater for your seemings if there are infinite deceived people. If the world is such that each galaxy has 1,000 deceived people and only 1 non-deceived people, it seems irrational to be highly confident that you're the non-deceived person in your galaxy.
This is how we treat other probabilities. If there are aleph null people both with red and green shirts, your credence in having a green shirt should be undefined. It seems that your credence regarding being deceived should work similarly--if there are some number of people both with and without some property, it seems that your credence in you having the property doesn't depend on the specific content of the property.
//Finally, it's extraordinarily mysterious *how* God chooses which set of net-positive anti-inductive worlds he actualizes.//
Well, God makes every *person* be in a world ideal for their flourishing. But for every particular person, it's unlikely the world ideal for their flourishing involves induction breaking. Thus, every person should think induction won't work.
There are some probabilistic hurdles here, but if there's a guy on our team who likes us having reliable cognitive faculties, and cares about us, the situation is considerably better.
Probably won't reply because I have too many commenters, but happy to discuss this more when we next chat.
>The axiarchist explanation works, but I think axiarchism has other problems--I don't think, for instance, that there's a unique best collection of things.
I would in fact agree, but you can still try to mirror whatever theism is doing. Instead of saying there's an optimal being psychologically choosing among collections of world to actualize, you can instead say there's an unintelligent axiological principle non-psychologically "choosing" among collections of world to actualize. You can ask how it's doing that, but as one of the things I tried to gesture at in my comment, God's process must also be also very mysterious indeed in order to make your thoughts about induction work out!
>I think if you adopt PC, then you get a defeater for your seemings if there are infinite deceived people. If the world is such that each galaxy has 1,000 deceived people and only 1 non-deceived people, it seems irrational to be highly confident that you're the non-deceived person in your galaxy.
You're offering a fallback principle: even if there are infinite observer-moments overall (i.e., across the totality of existence or the multiverse) such that X and infinite observer-moments such that ~X, so that we can't meaningfully compute any truly total proportions, we might still be able to reason about proportions within universes (or even galaxies, but I'll just stick with the descriptor "universes" for short to encompass anything like that) and go from there. But this won't apply to the mathematical multiverse hypothesis. Given any numerical proportion R of successful inductive inferences, there will be the same number/cardinality/whatever of universes where the proportion of successful inductive inferences in that universe is R. Worse, there will be just as many universes where *there is no well-defined proportion of inductive inferences*! So I don't think this strategy fits cleanly enough to constitute a defeater, and maybe we're allowed to use other fallback principles that don't rely on looking at proportions at all.
>Well, God makes every *person* be in a world ideal for their flourishing. But for every particular person, it's unlikely the world ideal for their flourishing involves induction breaking. Thus, every person should think induction won't work.
I thought you believed God has to do some very specific picking and choosing here -otherwise it seems there would be a uniquely optimal collection of worlds to actualize (namely, all the net positive ones, or all the ones where everyone is in their ideal flourishing situation, or something like that). Or am I misunderstanding what you wrote? And if you do think that, then the mystery of how to make sense of him doing this kicks in.
For example, if hypothetically you thought he chose some cardinality C of net-positive anti-inductive worlds and some larger cardinality D of net-positive inductive worlds, where D is larger than C (which is supposed to ensure all the people reasoning anthropically are justified in their reliance on induction), why would he choose C and D instead of C+1 and D+1? Wouldn't the latter be even better? So that's where I thought you might have to rely on some notion of random choice, which struck me as problematic in this context.
What about past-future symmetry and the philosophy of time? I believe in B-theory and block universe and that the future is just as real as the past. A lot of the defenses of SIA are things like "wouldn't it be weird if we had very high credences about improbable future events". But that weirdness has to do with the weirdness of knowing what happens in the future and then how we can choose our actions based on that knowledge. This is something explored in the philosophy of time travel and maybe something you should look into.
Good question! The weirdness of knowing future events doesn't come from any fact about time. It comes more broadly from a principle about how evidence works. Your credence in some chancy event should equal its objective probability, unless you have evidence that it will turn out some way. That evidence takes the form of something that you've observed which is likelier to happen if the theory is true than if it's false.
Now, this rules out having your credence in an event depend on its future consequences. For you to have evidence now, there must be stuff you've observed which affects your judgment. If some event will happen in the future, and the present will look the same no matter how it turns out, then by definition you can't have future evidence about how it will turn out.
But the principle is broader! Consider:
A coin is flipped. If it is going to come up tails, a million years ago, a hundred faraway galaxies were destroyed. If it is going to come up heads, they weren't.
In this case, you should similarly have a credence of .5 in the coin coming up heads. Because you haven't observed whether the galaxies are destroyed, you have no evidence to nudge you away from your 50% credence in the coin coming up heads.
In short: the argument doesn't depend on anything about time. It depends on a principle about evidence. This broader principle entails the future oriented principle I gave in the article, but is broader, and it doesn't require treating the future and past differently.
I've read a lot of your work on this subject and I guess I still struggle to nail down exactly what is meant by "possible person" in general here. Are we talking about possible subjects of experience, or possible entities as described in a third-person sense, or something else? You say the SIA says you should think that there are more people who you currently might be - but isn't there just one person I currently might be, the particular entity I actually am? I guess if you believe in souls, then you could imagine being "slotted into" various different bodies with different contingent features, but if you think you just are this particular arrangement of psychophysical states in a necessary sense, then I guess I would see that as my "one red shirt" as opposed to everyone else's blue shirts (or infinitely many shirts of infinitely many different colors, I guess). If God said "I flipped a coin and either produced the particular arrangement of psychophysical states that comprise you, or that particular arrangement plus a million more," then obviously I wouldn't think I had any information one way or the other. But I guess that's how I see *all* of these thought experiments breaking down, so I must be missing something.
What matters is the number of people you might presently be. You know you are you, but you don't know which person (de re) you is (de se). Like, suppose that there are two identical copies of the mind behind Both Sides Brigade across the universe. Your current evidence doesn't tell you which of them you currently are.
I have no clue how this is supposed to solve the thought experiments. Like, take the Elga case I gave. One person is created, a coin is flipped, and if it comes up tails, 999 other people get created. You have to give up one of the following 4:
1) If you're created and know the coin comes up tails, the odds are 1/1000 that you're the first person.
2) You should follow Bayesian updating (even if you give this one up, the problems generally reappear).
3) After learning you're the first person, you shouldn't think at 1,000:1 odds that the coin will come up heads.
4) If you're created by this and don't know your birth rank, you should think tails is 1,000 times likelier than heads.
I don't know how your comments are supposed to inform which of these we're supposed to give up.
The question about duplicate minds is tricky for me because it seems to imply some sort of essential subjectivity that I'm not sure I accept - if there really were two collections of identical psychophysical states, then I guess I would doubt there's any particular answer to the question of "which one I am." Is the idea that many of these possible people are exact pyschophysical duplicates of other possible people?
Similarly, quoting you on this: "Suppose that we’re considering two theories—one of them says there’s one possible person who exists, the other says there are two possible people who both exist. Assume they’re equally externally credible. By Elga’s reasoning, the odds you’re the first person and only one person exists = the odds you’re the first person and two people exist = the odds you’re the second person and two people exist."
I just don't quite understand what it would be mean for me to exist "as the first person" versus exist "as the second person." Is the idea that there are just two "open slots" for personhood that each could be filled with any set of psychophysical states? Because then I don't see what's meaningful about saying I was in "the first slot" versus "the second slot." If I was created in a room with the other possible person, how could we figure out which one of us was the first person versus the second? Or are the two possible people two possible sets of psychophysical states, like Frank the Human and Glorbus the Alien? And I wake up, knowing I exist but not knowing whether I'm the alien or the human? That makes more sense to me, but then I don't see what the import is once I realize I *am* Frank the Human (or Glorbus the Alien) like I've realized that I am the person I am now. Shouldn't my credence return to 50/50 based on the two options left open?
Ultimately, I guess that's what I feel like I'm missing. If I know that I exist, then I also know that I am *necessarily* who I am - even if I can't "put a name" on who that person is in an external sense, it feels like I can still say "Well, I know that I am whoever this particular possible person is, so the likelihood of me being any other possible person is zero." I could even just give myself a sort of indexical name like THISMAN and then I don't see why all these cases don't reduce to the red shirt versus blue shirt example where the red shirt is THISMAN-ness. I'm sure I'm missing something, but that's always been my stumbling block!
The relevant kind of uncertainty is about epistemic probability. Thus, whether origin essentialism is true doesn't matter--even if it's metaphysically impossible that you're the person other than you are, you're not sure which person you are.
The part of your argument that seems to be doing the most work is the statement that "there’s no plausible atheistic account of reality on which Beth 2 people come to exist." But why is that? If that's the total number of possible people that could theoretically exist, why is theism necessary to instantiate it?
It seems to be too quick to go from "there are sizes of infinity greater than aleph nought" to "the set of people could have a cardinality greater than aleph nought."
I think it's pretty plausible that there couldn't be more than continuum-many spatial locations in a single space. Why? I think when we try to explain what it is for something to be a spatial location, it's natural to start saying stuff that presupposes that spatial locations--at least within a single "space"--have a structure that corresponds to the real numbers. While you can define bigger sets (eg, the power set of the reals) it's not at all clear they have the right internal structure to number the spatial locations.
I'm tempted to say similar stuff about people and their individuation conditions; I think we need to hear more about the metaphysics of persons before conceding that we're not talking nonsense in countenancing the possibility that the number of people is some large cardinal.
See section 4.3, titled "Maybe there are only aleph null possible people," (though commenting without reading the article isn't blameworthy as the article is quite long).
Having read it, I think it basically presupposes a non naturalist conception of persons, even though I know you don't think you're doing that. The (or at least, an) alternative to souls is not arbitrary arrangements of points, but rather arrangements of points that play certain functional roles (they stick together, and their movements over time can be explained in terms of utility maximization...and certainly much more). The idea that for each truth there's a possible mind that thinks that truth is plausible if you think of minds as part of the irreducible furniture of the universe, but much less so if you think of them as emergent entities. I want to hear about how you'd have to arrange the basic stuff to get the functional profile of mind who only ever has the thought "cheese is tasty." I don't think it can be done.
What do you make of the Pruss argument and the USIA argument? Seems like you can just keep duplicating worlds. Even if you think you can't have identical copy worlds, just by varying a points/fields in the brain, you can get to Beth 2.
I mean, I don't know how exactly to make a brain of most configurations, but it seems possible to make one thinking only that cheese is tasty.
I don't see why I should think duplicating gets me from one cardinality of infinity to another. Take the natural numbers: 1, 2, 3...
Now duplicate them! 1,1, 2,2, 3,3...
We still have aleph nought items in our list.
I feel like I need to see a construction of the set of possible people that explains why if you try to put it into correspondence with the naturals, you're guaranteed to miss some possible people.
I see how that works if you think for each member of some set whose cardinality is already granted to be greater than the naturals, there's a possible person thinking about that member and only that member.
But as for the brain thing, if you think thinking "cheese is tasty" is an intrinsic property of a brain (eg, it instantiates certain qualia), then sure. This is Chalmers' view, I think. And plenty of non naturalists. But if you're more naturalistically inclined, you'll think you need to do a lot of work to tell a story about how the brain is casually embedded in its environment in a way that lets it have cheese thoughts at all. I tend to think that in telling that story, you'll be forced to attribute it a bunch more thoughts besides.
If you duplicate 1 Beth 1 times, you will, in fact, have Beth 1 numbers. You won't have Beth 1 *distinct* numbers, but the total number of numbers that you produce will be Beth 1. SIA favors theories on which there are more clones. The number of distinct people is irrelevant.
Do you think it would be possible for there to be, say, Beth 2 rocks in a giant multiverse? If not, why not? If so, why are people different?
The reason to think that the set of people can't be put in correspondence with the naturals is that there are more people than the naturals as shown by the arguments!
I think talking about the truths arguments won't be fruitful as it's the worst of the three.
You might think there could be worlds (maybe even this one!) where time and space and physics are better modeled with some hyperreal number system than the reals. And there are such systems with arbitrary cardinality, and these universes won't merely reduce to a union of a large number of utterly disconnected sub-universes.
Okay, so I'm going to do the thing you're probably quite bored of at this point... which is to express my reservations about SIA. Now I'm not a philosopher, just a guy with a science/computation background that's getting a bit rusty. But let's try!
> According to SIA, if a theory predicts 10 times as many people exist as another theory, so long as for all you know you might be any of the people, then it’s 10 times as likely you would come to exist.
Let's call this the Big Claim. First, my gut feeling from this is that SIA proves too much. The number of people in the universe is (in principle) measurable; if SIA means I can get a best estimate from my measures, then go into a quiet room, think hard for a while, repeat the process ten times, and then I should rationally hold that there are 10^10 times more people than I first measured (as long as I can think of a theory that allows it).... my gut feeling is that however convincing the arguments for SIA, something must have gone wrong somewhere. With all due respect to thought experiments, it's just too much concrete and unlikely information to be springing forth from just thinking about it.
Tentative thought: maybe I'd draw a line between strong and weak anthropics. Let's define anthropics as reasoning about probabilities while holding uncertain which observer in the system you are (let's call this indexicality). In some simpler cases, the question can be rephrased without reference to indexicality, by counting total observations among a given distribution of possible scenarios. In those cases I think it works out and you get a reasonable answer. But in more complicated cases, the question can't be rephrased without reference to "I am X" questions. In that case I'm not sure statistics are even possible, because as far as I know statistics are done over possible worlds, but whether I am John or Bob is not a fact of the world. John is John, Bob is Bob, and "I" is just a pronoun indicating the perspective of whoever is speaking right now, it's not a separate variable that can take either value. Mabye something like this could explain why simpler cases work out, without having to accept the stronger and weirder conclusions.
Let's look concretely at the "doomsday" scenario. In that case, the objective odds of the fair coin are by definition 50%; if you repeat the experiment 1000 times, you expect in average 500 heads and 500 tails. But the 500 tails will be observed 1000 times each, whereas each heads is observed only once. (We call an "observation" the moment a guy gets told the rules and wonders for the first time what the coin's value is in his timeline.) So from the perspective of a randomly chosen observation, the odds are 1 heads to 1000 tails, and the anthropic reasoning works out. Each observer was more likely to be observing from the branch that had more people in it. But note that we got there by rephrasing in a way that doesn't talk about "I am X", just by counting observations.
Now, maybe I haven't thought enough about it, but I don't see a way to get from conceding this, to the Big Claim above. In the Doomsday scenario, we know ahead of time distribution of probabilities according to which the two sub-scenarios happen, and the different participants are instantiated or not. This is then held constant throughout the thought experiment.
If we try to apply this to the actual universe, the strict equivalent would be: assume that the universe was created through some (possibly probabilistic) process, which is amenable to rational investigation. Now, whatever that process was, we don't get a choice; it's in the past, and we can't influence it (assuming no causal loops). So this process must have had a definite distribution of possible worlds with their probabilities, which is a given in the system, even if it's unknown to us. If we apply the "doomsday" reasoning to that scenario, what we learn is that, within that given distribution of possible created universes, we're more likely to be observing this from one of the more populated branches. As far as I can tell, that's all that the reasoning allows us to derive.
And that is a far cry from Big Claim above! It even directly contradicts it, because it says that whatever measure we can make of the number of people in the universe, *that* is likely to be within the upper range of possibilities, not only in this world, but also among all the worlds that could have been created by the same process.
In other words, we get the well-known weak anthropic principle back. Among all possible universes, we're likelier to be asking "why am I here" from one of the more populated ones. So even if we can think of theories where the universe would have 10 or 10^10 times more people than it appears to have, this actually gives us evidence *against* them.
Sorry for the long post, still trying to grapple with these reasonings. Not even sure if I've taken a well-known non-SIA position, or something else.
The proposal is that the people are in the multiverse, not that they're all on Earth. SIA doesn't have any preference regarding where the people are distributed.
For now I tentatively side with Ape in the Coat, from the thread where you debated with him:
> Probability is a mathematical function and it's domain is event space. If your statement can not be interpreted as well-defined event of probability experiment, then you can't assign probability value to it.
OK I guess that's where we disagree. I don't think "I am Bob" is an event, or functions like an event enough that you can assign probabilities to it, in the general case. Bob is just Bob, and Alice is Alice, and however much Bob thinks "I am Bob", there is no alternate world where he actually is Alice. So, if you can't assign sensible probabilities to something, then it's no wonder that Bayesian conditionalization fails.
On the other hand, in carefully designed thought experiments where people are pre-indexed according to some rules, even though "I am person #1" is not an event, questions like "in which modal branch am I likely to find myself" can be rephrased in objective terms by counting possible observations across the system. So in those cases you can get a cogent response to an anthropic-sounding question.
The same applies to the simple counter-example you gave in another thread, "I exist, therefore my parents had reproductive sex" sounds anthropic, but is not irreducibly so; if Bob thinks this, then it just amounts to the ordinary inference "Bob exists, therefore his parents had reproductive sex".
I'm sympathetic to your anthropic argument for God. I was a committed thirder on the Sleeping Beauty problem for years before I heard about the SIA, and I'm fond of technical quasi-mathematical arguments, and I am predisposed by disposition and upbringing to be theist.
I do, however, have at least a couple concerns.
(1) You broach in your post the possibility of infinitely many copies of the same person. It seems to me that the anthropic argument you make pushes us inevitably to believe in a God who created not just me, but very many copies of me. This clashes with my "Occam's razor" intuition that such profligate duplication (rather than diversification) is bizarre and unnatural to hypothesize. I could lean into Scott Alexander's "There is no cosmic unemployment rate" and say that haeccities don't exist so you can't actually make multiple copies of me... but I'm not sure that this works even if haeccities don't exist. Even if there's no such thing as "this" electron and "that" electron, after all, we can still have "two electrons".
(2) There are naturalistic accounts that would give us your unfathomably many people. They're unnatural and bizarre and I don't believe them, but I'd continue to disbelieve them even if I were persuaded that there is no God, so that provides (infinitely strong?) evidence against SIA. For example, on the Mathematical Universe Hypothesis, every mathematically possible universe exists with the same ontology as our physical reality, so every possible person exists. Moreover, by considering the direct sum of arbitrarily large numbers of copies of the same mathematical universe (a very common construction), we can end up with more copies of me than any cardinality of ZFC allows for. Does SIA provide infinitely strong evidence for the Mathematical Universe Hypothesis? Really?
(3) The mathematical formalism seems like it may be imposing more on reality than is actually there. Beth-2 really isn't that special of a cardinal. Why shouldn't we have more, or fewer, people? If people come into existence in sequence, should we index them by an ordinal instead of a cardinal? But there's something more fundamental than both of these issues, and that's that I don't think ZFC is the One True Model of mathematics. In NFU, for example, you can in fact describe the set of all people (or all groups, or all topological spaces, or...) regardless of its cardinality! The power set of a set might end up smaller than the original set, Cantor's paradox notwithstanding. I think you can even have a set of all true statements, though that might require some more delicacy. Even without such a radical step, nonstandard models of ZFC, or ZFC with large cardinal axioms, or ZFC with negations of large cardinal axioms, may land you with different beliefs about "how many people it's possible for there to be" and therefore "how many people there are". But the underlying nature of reality shouldn't depend on what math you use to model it, while your intuitions about how many people there are seem fairly model-dependent.
1) Even if you can't have exact duplicates, the Lewis argument shows there are at least Beth 2 people. So the argument still works. Regarding Ockham's razor, I think Ockham's razor only applies to fundamental entities (this has been discussed by Jonathan Schaffer a bit). If a coin got flipped a while ago, that created a lot of different kinds of things if tails, and a few kinds if heads, I don't think parsimony gives you reason to think it likely came up tails.
2) Well, it may be that if you came to think that there was no God you'd have to give up SIA. Nonetheless, SIA is the best view. Like, it can be that view A has strong arguments in its favor, but it works poorly with view B. The fact that accepting view B would make you give up view A wouldn't tell us if view A is plausible--its plausibility may give you a reason to reject view B. I think SIA updates you in favor of the Tegmark view, but it's independently implausible (for reasons I explain in the article, in the section about Tegmark's view).
3) As I say, I think that there are more than Beth 2 possible people. I think there's no set of all possible people, and I argue for that.
I'm afraid I don't know enough about set theory to comment very intelligently on some of what you say. Though I think Cantor's theorem is pretty well established purely by logic, and my comments in the section about why you shouldn't think there are aleph null people should be applicable.
(1) What do you mean by "fundamental entities"? I agree with you that if a fair coin would create more entities on one flip than the other, parsimony shouldn't commit me to the flip that ends up with fewer entities.
But to my mind, there's something of a clash between my intuition about Occam's razor and the anthropic principle. Occam's razor seems to want me to postulate the simplest explanation compatible with my experience, and SIA seems to want me to postulate the explanation-that-produces-the-most-people-like-me compatible with my experience. But the simplest explanation compatible with my experience is not that there are infinitely many duplicates or near-duplicates of me that I will never interact with or observe in any way.
(2) I don't think I expressed what I meant to clearly, probably because I am not yet clear on what I want to express. I first became exposed to the anthropic argument for God by your articles, and I'm still wrestling with my intuitions about them. SIA seems plausible to me. A cosmos with only finitely many (or only aleph null) people seems plausible to me. It seems, though, that if your syllogism doesn't have some hidden error, I should either give SIA probability 0 (by a Bayesian modus tollens) or a denumerable count of people probability 0 (by a Bayesian modus ponens). That seems sufficiently overconfident that it makes me want to revisit my thirder status, or else figure out why a limited SIA doesn't force me to grant a global one, or something.
(3) I read your argument, including its allusions to proper classes of people, and you can ignore my yammering about ordinals if you want. But I think you should be disturbed that you're making a set-theoretic argument that there's no set of all people (not for well-definedness reasons, but for cardinality reasons)! That means the theory you are using to make your argument isn't powerful enough to apprehend the state of the world that actually obtains!
Cantor's Theorem is indeed a well-established result, and I'm not disputing its correctness inside of ZFC. It does depend, though, on the restricted axiom (schema) of comprehension: given any set X and any formula phi(x), the set {x in X : phi(x)}. In NFU, though, this axiom requires further qualifications before it can be used, and thus Cantor's Theorem itself is a more qualified statement. (Intuitively, formulas like "x is not an element of x" have a suspicious sort of self-reference to them, and so we don't allow them to appear willy-nilly in our formulae.) If you're curious about why this is a sane perspective and what happens when you develop it, I'm happy to refer to you Randall Holmes's book https://randall-holmes.github.io/head.pdf.
But my general point isn't that Beth 2 doesn't exist, and it isn't that you should want a weakly stratified set-theoretic universe; I merely maintain that ZFC is a convenient rather than a canonical framework for reasoning, and you want to be careful with your infinities.
1) A fundamental entity is one that isn't explained by deeper entities.
Occam's razor is about priors, SIA is about updating from your existence. But as I think the coinflip case demonstrates, your priors shouldn't disfavor created entities.
2)
//It seems, though, that if your syllogism doesn't have some hidden error, I should either give SIA probability 0 (by a Bayesian modus tollens) or a denumerable count of people probability 0 (by a Bayesian modus ponens).//
I don't think this is right. You can have, say, credence in SIA of .9 and credence in finite people of .1. Your credence conditional on SIA (and you not being confused) of there being finite people should be 0, but you shouldn't be certain of SIA.
3) Yeah, I agree there are puzzles of how math works with things that are not sets. I'm not in a position to sort that out. Worst case scenario, I'd just accept that the collection of possible people was a set of some big size.
(1) Anyone in a position to update based on priors is also positioned to update based on existence. So both Occam's razor and SIA upweight and downweight various hypotheses before you've engaged meaningfully with the world at large, right?
(2) You are correct! I was being sloppy. All I demonstrated is that if your syllogism holds, then SIA and a denumerable population are almost disjoint possibilities.
...
What do you make of the following argument?
(a) God exists (because of SIA, and psychophysical harmony, and fine-tuning, and whatever else)
(b) From God's perspective, SIA affirms that He should expect as many beings like Him as are possible. Therefore, unless there's an ontological/necessity argument that God is unique, there should be infinitely many Gods.
(c) By Aumann's Theorem or something similar, we too should believe there are infinitely many Gods.
Regarding 1) yes, but this is totally normal. Even non-SIA views will do this--your existence will give you evidence for views on which you exist. But those are on average more complicated than views on which you don't. There's nothing probabilistically illicit about having priors that favor A and updating in favor of ~A.
Regarding 2) first of all, I think (c) would be false, as de se evidence can't be treated the same way as non-de-se evidence. Also, I don't think b) is right, as God is supposed to be omniscient, and directly acquainted with every truth. He doesn't figure things out by inference to the best explanation.
Probably can't reply to your response to this as I'm a bit busy.
(1) I mean, sure, if we take any brand of anthropic reasoning seriously then both Occam's razor and anthropic reasoning apply, and it's not illicit that it should be so. The a priori versus a posteriori distinction doesn't seem super meaningful to me when every reasoner can make the same posteriori arguments. My point is that the conclusion is reached with such confidence, despite seeming unnatural on other grounds, that I am forced to be suspicious of the method.
(2) A Christian or conventional monotheist does hold that God directly apprehends all truth in a de se sort of way, but I don't see why you should grant the same. Why should we expect God to have a kind (rather than degree) of knowledge so radically different from ours? Still, I agree that if God can directly apprehend His own uniqueness that He doesn't need to make reference to any SIA argument. Should He be surprised that He is unique?
I see that the distinction between de-se and non-de-se evidence exists, but I'm disquieted that I and God might both be sure that He exists, and yet draw different conclusions from that exact fact about whether other gods also exist.
Like, here's a toy example that doesn't have so much metaphysical nonsense. God flips a coin. If it comes up heads, He creates ten men in red shirts and one man in a blue shirt, and if it comes up tails He creates ten men in blue shirts and one man in a white shirt. Each white room has doors leading to each other white room. I wake up, and find that I have a red shirt. I now believe that heads is ten times as likely as tails by SIA. I then open one of the doors and see a man in a blue shirt on the other side. I should now (I claim) revert to even odds between heads and tails, since seeing this other man was ten times as likely if the coin came up tails as heads.
Right?
(I guess you can't respond because you are busy. Thanks for chatting! I expect I'll comment more on later posts)
Doesn't SIA prove too much? Since I'm American, wouldn't it be more likely that America is secretly 50x larger than it is purported to be, and the population similarly larger to inflate the probability that I am American - and that this is essentially a wide conspiracy?
So, it's a little complicated, but the basic answer is no.
What SIA tells you to think there are more of is people you might presently be. Now, you know you're an American, so it tells you to think there are infinite Americas throughout the multiverse. This is discussed a bit in section 4.7.
Thus, the theory tells you to think that there are many Americas in that sense through believing in a multiverse. For people other than those you might be, SIA gives no reason to think they're in America.
It could be that every possible person is created in America. This view will get an update in its favor, but will also have a similarly low prior--if all of reality is just one location repeated, given the infinite locations that could be repeated, it's infinitely unlikely that the location would be America.
Now, if you conclude that every possible person is created, SIA will hold that you should think a maximally large share of them are in America, though this just seems like the right result. And the math here gets messy as doing precise comparisons of infinities is a nightmare.
I'd like a highlight a theory I came upon recently that is consistent with both fine-tuning and the SIA, but which does not require a first mover.
Isn't it amazing how complicated humans are? They must have been designed by an intelligent creator. Actually, there's a known mechanism that complexity develops through gradual accumulation.
Isn't it interesting how the big bang came from a singularity, and that black holes are singularities? What would it imply if production of singularities created universes just slightly different from their parent universe?
It would imply that there are indeed infinite people, and actually infinite universes as well.
One very interesting implication of the theory is that intelligent life is selected for because they have a tendency to create and harness black holes for energy production. Assuming the universe is positive utility, it seems like we have a moral duty to advance technological progress in order to create many more universes like our own.
First off, I don't really buy the arguments about cardinality because the relationship between mathematics and reality is rather fuzzy when we start talking about infinities.
But in any case, this theory certainly moots your point about deceived people because Boltzmann brains cannot develop black holes. In this theory, the universe selects for intelligent life that is capable of rationally interacting with the natural world, which Boltzmann brains and illogical minds are not.
Regarding the fine-tuning multiverse arguments:
> The process required for generating multiple universes is complex and requires fine-tuning of its own
I see this as the equivalent of the first-mover problem in that the theory explains how universes are created but can't explain how the process itself began. But theism also has this.
> Second, the multiverses have to be very improbable in a variety of ways! There’s fine-tuning of the laws, constants, and initial conditions—so it has to be able to vary all of them.
Also about how the process itself originated, so I view this as part of the first objection. Nevertheless, cosmological evolution does provide an mechanism for how these laws and constants are tuned - every child universe is a slight variation of the parent universe, perhaps affected by things like the mass of the black hole and what enters their event horizons.
> Third, a multiverse might lead to the proliferation of Boltzmann brains
Covered above, cosmological evolution does not select for Boltzmann brains
> Therefore, the multiverse can’t explain the most troubling kind of fine-tuning—fine-tuning for low entropy.
Black holes are hard to create when entropy is high, therefore universes select for low entropy.
> The multiverse is analogous to explaining why there’s a book like Shakespeare’s that exists somewhere by saying that there are an infinite number of monkeys typing on typewriters
Random selection wouldn't create Shakespeare, but a genetic algorithm would certainly be able to produce something like it.
> Fourth, even if a multiverse explains why we exist, it doesn’t explain fine-tuning for scientific discovery.
It does, because scientific discovery leads to the production of black-holes: https://phys.org/news/2023-12-ways-black-holes-energy-source.html. Isn't it weird that small black holes are theoretically the most efficient form of energy production in the universe?
> This is because God would be likely to create a multiverse.
The conditional probability is that if your god existed, he would be likely to create a multiverse, but this relies on that very particular type of god existing in the first place, which is unlikely.
> Similarly, for the multiverse to eliminate the force of fine-tuning, the odds of a multiverse has to be high on atheism.
The odds of the multiverse is high under atheism actually, because if universes are optimizing for universe creation, you naturally get a never-ending expansion of child universes.
Anyways, I think it's pretty ironic that your name references Thomas Huxley but you are arguing in favor of intelligent design over evolution.
The point about Boltzmann brains isn't that every universe will inevitably produce deceived people. It's that almost every universe with enough people to be supported anthropically will result in deception. It obviously doesn't do to dismiss a sound argument just by saying that math is fuzzy in its application to reality, when the right theory of anthropics tells you to be certain that theree are infinite people.
I obviously believe in evolution.
All the points about fine-tuning are confused, but I don't have the time to type out a detailed reply.
I agree that there are infinite numbers of people, what I disagree with is about whether the scope of that infinity matters. What I mean by the application of math to reality is fuzzy is specifically when speaking about different kinds of infinities.
The point I make about deceived people is in response to this particular point:
> But if there are infinite deceived people, and no more non-deceived people than deceived people, then you should have no confidence in the reliability of your cognitive faculties.
However, if reliable cognitive faculties are selected for then you should expect there to be many more non-deceived people than deceived people. Universes actually actively select against production of deceived people since that would require a different type of fine-tuning, but the result is totally useless for creation of singularities. Therefore you can be confident that you are actually non-deceived under cosmological evolution.
Doesn’t this lead to parody arguments though? Like someone coming up with a theory about a leprechaun making infinite people is now more likely cause you exist?
Yes. One consequence of SIA is that otherwise bad theories that predict many people beat good theories that predict few. But this is a general consequence whenever a view scores explains one kind of evidence poorly.
You're a brave man! I share your intuition that infinitesimal probabilities make sense, but to talk about probabilities like 1/Beth 2, you need the full machinery of the surreal numbers, not just petty infinitesimals like the hyperreals! Unfortunately, I'm not aware of a satisfactory development of surreal integration, much less of an exhaustive theory of surreal probability. I get nervous when my formalisms lag so far behind my intuition.
The SIA is easy not to buy. It applies probability to an event where probability doesn't make sense.
A coin flip being heads or tails might create Jack or Jill from the ether. The birth of a person, in reality, is not due to any such purely 'random' factors. The kind of conclusions that SIA draws are what are typically described as being "Not even wrong".
SIA thought experiments refer to an abstract possibility for a human being created, often referencing thought experiments where people are created out of nothing in a room. But in the real world, people only exist through a natural cycle of reproduction that happens due to predictable events. Thought experiments about people being suddenly created or not created due to one singular decision do not offer appreciable insights for how the world works.
Well, for each of the thought experiments, you can imagine replacing the spontaneous creation with people being born through natural process. Also, thought experiments can be informative even if they're not realistic--the way to reason about creation of people doesn't depend on whether they were created through the childbirth process or spontaneously.
If you used the natural process of reproduction instead of spontaneous creation, then the conclusions normally drawn for SIA would seem obviously unsupported by the evidence. The person waking up in a room could reason that there are probably some number of humans that exist to avoid the problems of unavoidable incest from a very small (less than 500) population, assuming that they were healthy. But there would be no strong reason to think there must be a million, a billion, or infinitely more humans, because some tribe could continue having kids and then someone would possible wake up in a room one day.
I’m not sure I follow why any of this (or what I directly observe) necessarily suggests god is perfectly “good” versus any of the countless other ways god could be.
Thanks. I’ll re-read it and post my further questions about the perfect goodness of things there.
Edit: I guess my confusion was due to the following sentence, which makes it seems like your argument hinges to some extent on god being good:
> It’s good to create a person and give them a good life, so God would create, in his infinite power and goodness, some ungodly (Godly?) number of people.
Well, the argument raises the probability of a good God. If a good God, something that lots of people believe in, predicts some fact about the world better than most other theories, that fact is evidence for the theory.
I'm not convinced about SIA. I would think each coin toss creates a world of equal weight, so your weight in one room is 50% and in the other room 50%*N/N = 50%.
It depends on whether you are assigned to your room top down or bottom up.
If you follow the bottom up route, then you'd expect to end up in a universe derived from all possible multiverses.
(Thanks for writing this by the way - I'm nearing the end of Leslie's "Universes" and this is the next thing I wanted to explore.)
But that produces the result that if you find yourself as the first person, in a case where many people will be created if a coin that will be flipped comes up tails, you should be super confident that the coin will come up heads.
Didn't understand your reply. Is this what you meant?
"But that produces the result that if you find yourself IN the first ROOM, in a case where many people WOULD HAVE BEEN created if a coin that HAD BEEN flipped CAME up tails, you should be super confident that the coin HAD come up heads."
But that's trivially true: if you KNEW you were in the first room, then obviously it was heads.
No! Suppose that one person is created. Then a coin is flipped. If it comes up tails, a bunch of people get created. If you split your credence across the coinflips, then after updating on being the first person, you get near certainty that the fair coin will come up heads. See also section 3.1.
Just tell me what you think about the scenario I gave. What should your credences be after learning you're the first person?
Re Adam and Eve, the point is they don't know they're the first two people. After learning it, so long as they follow conditionalization, they get a massive update in favor of there being few people.
If the example involves a human putting black and white balls in an urn it's obvious that normal combinatorial arithmetic applies.
An equivalent example using a god and people raises are all sorts of questions with unknowable answers like whether he's building rooms on Earth or creating worlds and how awareness finds its way into bodies.
If all universes/worlds were equal weight we'd all be quantum Boltzmann brains.
When you find out you're the first person you've already defeated the odds so it's reasonable to assume H is now 1,000 times likelier than ~H. (By selecting a person who's beaten 1000:1 odds we're in the realm of fiction - normal reality needn't apply in this artificial linked scenario.)
Do you think the King of England wakes up everyday and thinks: there are 8 billion people in the world, I can't possibly be King of England!
[Or Philip Goff thinks there are a gazillion self-aware particles in the universe, how come I'm human?]
PS: I'm perfectly happy with SIA within a single level in the multiverse, but not sure it can be automatically applied over multiple levels, but I'm still thinking about this. Artificial and Adam and Eve scenarios are questionably multi-level.
My main problem with this argument is that SIA / SSA is the wrong lens to use to determine the likelihood of initial causes and conditions.
You use a lot of coin flips as examples. That’s good for explaining SIA, but says nothing about the probability of theism being true. Mainly because the fact of whether or not god exists is nothing like a fair coin.
Imagine instead a cosmic lottery, picking balls randomly from a cosmic urn. Every time a red ball with the number “2” is picked, a million universes come into existence, but if any other ball comes up, only one universe comes into existence.
Given that you are a person who exists in a universe, which number do you think came up? The correct answer is that you have no way of knowing.
Without knowing the number of balls in the urn, how many are red, how many have the number “2”, how many drawings there are, etc. you simply don’t have enough information to calculate odds of anything. Maybe there are infinite drawings. Maybe all the balls in the urn are blue. Or maybe there’s just one ball in the urn, and it’s a red 2.
Before the coin flip metaphor is of any use, you need to know more about the likelihood of scenarios on offer in the first place, and you can’t use the anthropic argument to determine that.
As for all the evidence: You appear to conflate the chances of a scenario being true with the amount of evidence each scenario produces after the fact. But obviously, nothing that happens after the fact can change the initial chances of it happening.
We discussed/disagreed on The Sleeping Beauty problem a while back, in a discussion that sharpened my view on it. (Thanks.)
Basically, even if your chances of being right about a claim improves with tails, that’s not because the odds of tails being true have changed. It's because tails gives you more opportunities to be right. And, because the guess is about its own preconditions, you will be right more often if you choose the answer that, when true, allows you to be right more often.
This extrapolates to pretty much every thought experiment where you're supposed to deduce the outcome of a coin toss based on a single, non-conclusive observation.
I have other issues with the argument as well: I think you're unintentionally strawmanning modal realism and Tegmark; I suspect your play with infinities muddies the difference between cardinality and probability; I think even if you're right, a good god is not the only plausible explanation … but that's for another day.
If god creates only non-deluded people, then there are a lot of not created people. There are infinite ways to be deluded for every way you are not deluded, so the set of deluded people is the superset of non-deluded people and therefore has higher cordiality. Therefore by anthropic argument God doesn't exist and everyone is deluded.
> A world with God and other good stuff is better than a world with God alone because it has more good stuff. Now, if you count a world with God and other good stuff as a thing, then that thing is better than God alone, but God remains the best non-composite thing—the best single thing that doesn’t involve stitching together a bunch of different things.
That would require God be less than infinite good, otherwise ∞ + x = ∞.
> The anthropic argument claims that anthropic theory—specifically, SIA—raises the likelihood of theism. It’s not about whether God would create in the first place; it’s about how many people would be created by God vs. atheism. Thus, talking about whether God would create at all is changing the subject.
This doesn't make any sense.
The reason why according to SIA hypothesis A is more likely than hypothesis B is because on A more people like you exist than on B. If no people like you exist on A, then it's probability on SIA is zero and it's not more likely than B.
If God doesn't create any people than the ratio of people created by God vs atheism is definitely not in favor of God. It is literally the subject.
As a statistician, one of my main concerns with the Self-Indication Assumption (SIA) is that it treats ‘I exist’ as if it were a typical piece of evidence for updating our hypotheses, whereas from my own vantage point, my existence is guaranteed (probability 1). Hence, we do not truly have an independent observation. Let me try to be more clear:
Given universe A with billions of people and universe B with a gazillion of people the fact that "I exist" is not independent of the worlds being considered. The existence of observers is tied to the structure of each possible world, making "I exist" a given rather than an independent piece of evidence.
Again even more clear (hopefully):
Under SIA, we assign higher probability to World B because it has more observers, making our existence seem more likely in that world. However:
The observation that "I exist" isn't a random variable sampled from a distribution over observers. Instead, it is a given that applies equally in either world, conditional on the subject being able to make observations.
In other words it seems to me that the probability of "I exist" is 1 in both worlds, conditional on our own capacity to reason, so it cannot provide additional evidence to differentiate between them.
This undermines the usual machinery of Bayesian inference, which presumes we have evidence that can vary depending on which hypothesis is true. Here, the evidence ‘I exist’ does not really vary from my standpoint: it’s guaranteed if I’m around to observe it. Consequently, it seems like it does not provide additional, independent information to discriminate between Universe A and Universe B.
For this objection stated even more clearly see: https://mon0.substack.com/p/benthams-bulldog-ruins-my-weekend
Love your stuff btw!
Thanks! Love your stuff too! I think the stuff I say in section 3.4 about the Elga argument heads this off. See also https://benthams.substack.com/p/precisely-defining-the-self-indication
It sounds like the view you'd adopt would be compartmentalized conditionalization--your only evidence is that your experiences are had, the numbers don't matter. But CC is super crazy and violates Bayesian conditionalization https://benthams.substack.com/p/compartmentalized-conditionalization
Thank you kindly, I will have a nice evening checking your links out!
Interesting. Given that these anthropic arguments are partly based on statistical principles, I wonder if there have been any published works by people whose training was primarily in statistics, as opposed to people who are primarily philosophers. If so, was there any consensus from the statistical community?
Well, seeing as there are no published works on the anthropic argument, there are none by people who know about statistics. I know someone who thinks it works and has a degree in math. Many SIA boosters know a lot about math--most are philosophers, but that's just because SIA is a philosophical subject. Some technical areas of philosophy involve quite a lot of math.
>Thus, if naturalism is true, then if there are L people total, there are L people who are deceived, just as there are L people who aren’t deceived. Your credence in you being deceived should thus be undefined.
This doesn't follow. I'm not sure Bayesians even allow undefined probabilities, at least in the case of an ideal reasoner and non-super-mathematically-pathological propositions like "I am not being deceived" (as opposed to "this uniformly distributed random variable on the interval [0,1] belongs to this specific Vitali set I constructed via the Axiom of Choice"). But regardless of that technicality, just because the world is such that you can't meaningfully apply the principle of indifference or whatever anthropic principle to resolve a certain question, it doesn't automatically follow that you need to be skeptical in any sense about that question. Maybe you can fall back to other epistemic principles in cases like these, e.g., phenomenal conservatism.
It's also not obvious why the atheist can't get around all this by simply proposing some non-theistic axiological competitor that posits the same collection of worlds being created as you think God would create - i.e., the overall metaphysics of world creation is "just" that the best collection of worlds gets created full-stop, with no intermediary agent who's responsible for this. And so if you think that only induction-friendly hypotheses are in the running, and you think theism is induction-friendly due to the worlds that it would generate, this one should also be induction-friendly because it generates the same ones.
Finally, it's extraordinarily mysterious *how* God chooses which set of net-positive anti-inductive worlds he actualizes. Why would he choose one and not the other? Is it random? But we have no theory of probability that's going to work well to model this given the cardinalities involved, so it's "random" in the haziest possible sense (not to mention how weird it is to suggest an omniscient agent choosing something randomly, as if he doesn't know the outcome in advance, and as if there's some Metaphysical Random Number Generator/"MNRG" that is doing stuff outside of any universe and independently of his will and as if the same mystery doesn't adhere to the MNRG's process). In fact, if almost all worlds are inductive, shouldn't we have essentially 100% credence that the next induction I try to apply will succeed, instead of something appropriately lower like 99%? You might reply that we should go by the proportion of observer-moments within each universe where induction succeeds rather than across universes, but why? Putting aside that this sounds more like an SSA approach than SIA, if it's because the proportions are undefined like what you write about the atheistic multiverse hypothesis above, then you agree with my earlier point there - in cases where we can't reason this way because the math doesn't work out, we can just fall back to other principles. And indeed, even ignoring this weirdness, I should still be 100% certain that I'm not in an anti-inductive universe in general, which most would reject.
Always nice to hear from you Mark. Yes, I agree that the atheist can *in principle* have an explanation that mirrors the theist's explanation. However, it's hard to see what the plausible story is regarding how this will work out. The axiarchist explanation works, but I think axiarchism has other problems--I don't think, for instance, that there's a unique best collection of things.
I think if you adopt PC, then you get a defeater for your seemings if there are infinite deceived people. If the world is such that each galaxy has 1,000 deceived people and only 1 non-deceived people, it seems irrational to be highly confident that you're the non-deceived person in your galaxy.
This is how we treat other probabilities. If there are aleph null people both with red and green shirts, your credence in having a green shirt should be undefined. It seems that your credence regarding being deceived should work similarly--if there are some number of people both with and without some property, it seems that your credence in you having the property doesn't depend on the specific content of the property.
//Finally, it's extraordinarily mysterious *how* God chooses which set of net-positive anti-inductive worlds he actualizes.//
Well, God makes every *person* be in a world ideal for their flourishing. But for every particular person, it's unlikely the world ideal for their flourishing involves induction breaking. Thus, every person should think induction won't work.
There are some probabilistic hurdles here, but if there's a guy on our team who likes us having reliable cognitive faculties, and cares about us, the situation is considerably better.
Probably won't reply because I have too many commenters, but happy to discuss this more when we next chat.
>The axiarchist explanation works, but I think axiarchism has other problems--I don't think, for instance, that there's a unique best collection of things.
I would in fact agree, but you can still try to mirror whatever theism is doing. Instead of saying there's an optimal being psychologically choosing among collections of world to actualize, you can instead say there's an unintelligent axiological principle non-psychologically "choosing" among collections of world to actualize. You can ask how it's doing that, but as one of the things I tried to gesture at in my comment, God's process must also be also very mysterious indeed in order to make your thoughts about induction work out!
>I think if you adopt PC, then you get a defeater for your seemings if there are infinite deceived people. If the world is such that each galaxy has 1,000 deceived people and only 1 non-deceived people, it seems irrational to be highly confident that you're the non-deceived person in your galaxy.
You're offering a fallback principle: even if there are infinite observer-moments overall (i.e., across the totality of existence or the multiverse) such that X and infinite observer-moments such that ~X, so that we can't meaningfully compute any truly total proportions, we might still be able to reason about proportions within universes (or even galaxies, but I'll just stick with the descriptor "universes" for short to encompass anything like that) and go from there. But this won't apply to the mathematical multiverse hypothesis. Given any numerical proportion R of successful inductive inferences, there will be the same number/cardinality/whatever of universes where the proportion of successful inductive inferences in that universe is R. Worse, there will be just as many universes where *there is no well-defined proportion of inductive inferences*! So I don't think this strategy fits cleanly enough to constitute a defeater, and maybe we're allowed to use other fallback principles that don't rely on looking at proportions at all.
>Well, God makes every *person* be in a world ideal for their flourishing. But for every particular person, it's unlikely the world ideal for their flourishing involves induction breaking. Thus, every person should think induction won't work.
I thought you believed God has to do some very specific picking and choosing here -otherwise it seems there would be a uniquely optimal collection of worlds to actualize (namely, all the net positive ones, or all the ones where everyone is in their ideal flourishing situation, or something like that). Or am I misunderstanding what you wrote? And if you do think that, then the mystery of how to make sense of him doing this kicks in.
For example, if hypothetically you thought he chose some cardinality C of net-positive anti-inductive worlds and some larger cardinality D of net-positive inductive worlds, where D is larger than C (which is supposed to ensure all the people reasoning anthropically are justified in their reliance on induction), why would he choose C and D instead of C+1 and D+1? Wouldn't the latter be even better? So that's where I thought you might have to rely on some notion of random choice, which struck me as problematic in this context.
I'll just answer the last question: my view is God makes every possible person and gives them all the best sequence of lives.
What about past-future symmetry and the philosophy of time? I believe in B-theory and block universe and that the future is just as real as the past. A lot of the defenses of SIA are things like "wouldn't it be weird if we had very high credences about improbable future events". But that weirdness has to do with the weirdness of knowing what happens in the future and then how we can choose our actions based on that knowledge. This is something explored in the philosophy of time travel and maybe something you should look into.
Good question! The weirdness of knowing future events doesn't come from any fact about time. It comes more broadly from a principle about how evidence works. Your credence in some chancy event should equal its objective probability, unless you have evidence that it will turn out some way. That evidence takes the form of something that you've observed which is likelier to happen if the theory is true than if it's false.
Now, this rules out having your credence in an event depend on its future consequences. For you to have evidence now, there must be stuff you've observed which affects your judgment. If some event will happen in the future, and the present will look the same no matter how it turns out, then by definition you can't have future evidence about how it will turn out.
But the principle is broader! Consider:
A coin is flipped. If it is going to come up tails, a million years ago, a hundred faraway galaxies were destroyed. If it is going to come up heads, they weren't.
In this case, you should similarly have a credence of .5 in the coin coming up heads. Because you haven't observed whether the galaxies are destroyed, you have no evidence to nudge you away from your 50% credence in the coin coming up heads.
In short: the argument doesn't depend on anything about time. It depends on a principle about evidence. This broader principle entails the future oriented principle I gave in the article, but is broader, and it doesn't require treating the future and past differently.
I've read a lot of your work on this subject and I guess I still struggle to nail down exactly what is meant by "possible person" in general here. Are we talking about possible subjects of experience, or possible entities as described in a third-person sense, or something else? You say the SIA says you should think that there are more people who you currently might be - but isn't there just one person I currently might be, the particular entity I actually am? I guess if you believe in souls, then you could imagine being "slotted into" various different bodies with different contingent features, but if you think you just are this particular arrangement of psychophysical states in a necessary sense, then I guess I would see that as my "one red shirt" as opposed to everyone else's blue shirts (or infinitely many shirts of infinitely many different colors, I guess). If God said "I flipped a coin and either produced the particular arrangement of psychophysical states that comprise you, or that particular arrangement plus a million more," then obviously I wouldn't think I had any information one way or the other. But I guess that's how I see *all* of these thought experiments breaking down, so I must be missing something.
What matters is the number of people you might presently be. You know you are you, but you don't know which person (de re) you is (de se). Like, suppose that there are two identical copies of the mind behind Both Sides Brigade across the universe. Your current evidence doesn't tell you which of them you currently are.
I have no clue how this is supposed to solve the thought experiments. Like, take the Elga case I gave. One person is created, a coin is flipped, and if it comes up tails, 999 other people get created. You have to give up one of the following 4:
1) If you're created and know the coin comes up tails, the odds are 1/1000 that you're the first person.
2) You should follow Bayesian updating (even if you give this one up, the problems generally reappear).
3) After learning you're the first person, you shouldn't think at 1,000:1 odds that the coin will come up heads.
4) If you're created by this and don't know your birth rank, you should think tails is 1,000 times likelier than heads.
I don't know how your comments are supposed to inform which of these we're supposed to give up.
The question about duplicate minds is tricky for me because it seems to imply some sort of essential subjectivity that I'm not sure I accept - if there really were two collections of identical psychophysical states, then I guess I would doubt there's any particular answer to the question of "which one I am." Is the idea that many of these possible people are exact pyschophysical duplicates of other possible people?
Similarly, quoting you on this: "Suppose that we’re considering two theories—one of them says there’s one possible person who exists, the other says there are two possible people who both exist. Assume they’re equally externally credible. By Elga’s reasoning, the odds you’re the first person and only one person exists = the odds you’re the first person and two people exist = the odds you’re the second person and two people exist."
I just don't quite understand what it would be mean for me to exist "as the first person" versus exist "as the second person." Is the idea that there are just two "open slots" for personhood that each could be filled with any set of psychophysical states? Because then I don't see what's meaningful about saying I was in "the first slot" versus "the second slot." If I was created in a room with the other possible person, how could we figure out which one of us was the first person versus the second? Or are the two possible people two possible sets of psychophysical states, like Frank the Human and Glorbus the Alien? And I wake up, knowing I exist but not knowing whether I'm the alien or the human? That makes more sense to me, but then I don't see what the import is once I realize I *am* Frank the Human (or Glorbus the Alien) like I've realized that I am the person I am now. Shouldn't my credence return to 50/50 based on the two options left open?
Ultimately, I guess that's what I feel like I'm missing. If I know that I exist, then I also know that I am *necessarily* who I am - even if I can't "put a name" on who that person is in an external sense, it feels like I can still say "Well, I know that I am whoever this particular possible person is, so the likelihood of me being any other possible person is zero." I could even just give myself a sort of indexical name like THISMAN and then I don't see why all these cases don't reduce to the red shirt versus blue shirt example where the red shirt is THISMAN-ness. I'm sure I'm missing something, but that's always been my stumbling block!
The relevant kind of uncertainty is about epistemic probability. Thus, whether origin essentialism is true doesn't matter--even if it's metaphysically impossible that you're the person other than you are, you're not sure which person you are.
Suppose that the universe has 1,000 galaxies arranged from left to right. There's a copy of you in galaxy 3 and galaxy 955. It seems like there's a fact of the matter about whether *you* are in galaxy 3 or 955. I talked about this more here https://benthams.substack.com/p/debate-with-ape-in-the-coat-about?utm_source=publication-search
Probably can't reply to your reply, as I have many commenters, though happy to discuss this when we next chat.
No problem haha, I understand!
The part of your argument that seems to be doing the most work is the statement that "there’s no plausible atheistic account of reality on which Beth 2 people come to exist." But why is that? If that's the total number of possible people that could theoretically exist, why is theism necessary to instantiate it?
See section 2.
It seems to be too quick to go from "there are sizes of infinity greater than aleph nought" to "the set of people could have a cardinality greater than aleph nought."
I think it's pretty plausible that there couldn't be more than continuum-many spatial locations in a single space. Why? I think when we try to explain what it is for something to be a spatial location, it's natural to start saying stuff that presupposes that spatial locations--at least within a single "space"--have a structure that corresponds to the real numbers. While you can define bigger sets (eg, the power set of the reals) it's not at all clear they have the right internal structure to number the spatial locations.
I'm tempted to say similar stuff about people and their individuation conditions; I think we need to hear more about the metaphysics of persons before conceding that we're not talking nonsense in countenancing the possibility that the number of people is some large cardinal.
See section 4.3, titled "Maybe there are only aleph null possible people," (though commenting without reading the article isn't blameworthy as the article is quite long).
Sorry!
No worries.
Having read it, I think it basically presupposes a non naturalist conception of persons, even though I know you don't think you're doing that. The (or at least, an) alternative to souls is not arbitrary arrangements of points, but rather arrangements of points that play certain functional roles (they stick together, and their movements over time can be explained in terms of utility maximization...and certainly much more). The idea that for each truth there's a possible mind that thinks that truth is plausible if you think of minds as part of the irreducible furniture of the universe, but much less so if you think of them as emergent entities. I want to hear about how you'd have to arrange the basic stuff to get the functional profile of mind who only ever has the thought "cheese is tasty." I don't think it can be done.
What do you make of the Pruss argument and the USIA argument? Seems like you can just keep duplicating worlds. Even if you think you can't have identical copy worlds, just by varying a points/fields in the brain, you can get to Beth 2.
I mean, I don't know how exactly to make a brain of most configurations, but it seems possible to make one thinking only that cheese is tasty.
I don't see why I should think duplicating gets me from one cardinality of infinity to another. Take the natural numbers: 1, 2, 3...
Now duplicate them! 1,1, 2,2, 3,3...
We still have aleph nought items in our list.
I feel like I need to see a construction of the set of possible people that explains why if you try to put it into correspondence with the naturals, you're guaranteed to miss some possible people.
I see how that works if you think for each member of some set whose cardinality is already granted to be greater than the naturals, there's a possible person thinking about that member and only that member.
But as for the brain thing, if you think thinking "cheese is tasty" is an intrinsic property of a brain (eg, it instantiates certain qualia), then sure. This is Chalmers' view, I think. And plenty of non naturalists. But if you're more naturalistically inclined, you'll think you need to do a lot of work to tell a story about how the brain is casually embedded in its environment in a way that lets it have cheese thoughts at all. I tend to think that in telling that story, you'll be forced to attribute it a bunch more thoughts besides.
If you duplicate 1 Beth 1 times, you will, in fact, have Beth 1 numbers. You won't have Beth 1 *distinct* numbers, but the total number of numbers that you produce will be Beth 1. SIA favors theories on which there are more clones. The number of distinct people is irrelevant.
Do you think it would be possible for there to be, say, Beth 2 rocks in a giant multiverse? If not, why not? If so, why are people different?
The reason to think that the set of people can't be put in correspondence with the naturals is that there are more people than the naturals as shown by the arguments!
I think talking about the truths arguments won't be fruitful as it's the worst of the three.
You might think there could be worlds (maybe even this one!) where time and space and physics are better modeled with some hyperreal number system than the reals. And there are such systems with arbitrary cardinality, and these universes won't merely reduce to a union of a large number of utterly disconnected sub-universes.
Okay, so I'm going to do the thing you're probably quite bored of at this point... which is to express my reservations about SIA. Now I'm not a philosopher, just a guy with a science/computation background that's getting a bit rusty. But let's try!
> According to SIA, if a theory predicts 10 times as many people exist as another theory, so long as for all you know you might be any of the people, then it’s 10 times as likely you would come to exist.
Let's call this the Big Claim. First, my gut feeling from this is that SIA proves too much. The number of people in the universe is (in principle) measurable; if SIA means I can get a best estimate from my measures, then go into a quiet room, think hard for a while, repeat the process ten times, and then I should rationally hold that there are 10^10 times more people than I first measured (as long as I can think of a theory that allows it).... my gut feeling is that however convincing the arguments for SIA, something must have gone wrong somewhere. With all due respect to thought experiments, it's just too much concrete and unlikely information to be springing forth from just thinking about it.
Tentative thought: maybe I'd draw a line between strong and weak anthropics. Let's define anthropics as reasoning about probabilities while holding uncertain which observer in the system you are (let's call this indexicality). In some simpler cases, the question can be rephrased without reference to indexicality, by counting total observations among a given distribution of possible scenarios. In those cases I think it works out and you get a reasonable answer. But in more complicated cases, the question can't be rephrased without reference to "I am X" questions. In that case I'm not sure statistics are even possible, because as far as I know statistics are done over possible worlds, but whether I am John or Bob is not a fact of the world. John is John, Bob is Bob, and "I" is just a pronoun indicating the perspective of whoever is speaking right now, it's not a separate variable that can take either value. Mabye something like this could explain why simpler cases work out, without having to accept the stronger and weirder conclusions.
Let's look concretely at the "doomsday" scenario. In that case, the objective odds of the fair coin are by definition 50%; if you repeat the experiment 1000 times, you expect in average 500 heads and 500 tails. But the 500 tails will be observed 1000 times each, whereas each heads is observed only once. (We call an "observation" the moment a guy gets told the rules and wonders for the first time what the coin's value is in his timeline.) So from the perspective of a randomly chosen observation, the odds are 1 heads to 1000 tails, and the anthropic reasoning works out. Each observer was more likely to be observing from the branch that had more people in it. But note that we got there by rephrasing in a way that doesn't talk about "I am X", just by counting observations.
Now, maybe I haven't thought enough about it, but I don't see a way to get from conceding this, to the Big Claim above. In the Doomsday scenario, we know ahead of time distribution of probabilities according to which the two sub-scenarios happen, and the different participants are instantiated or not. This is then held constant throughout the thought experiment.
If we try to apply this to the actual universe, the strict equivalent would be: assume that the universe was created through some (possibly probabilistic) process, which is amenable to rational investigation. Now, whatever that process was, we don't get a choice; it's in the past, and we can't influence it (assuming no causal loops). So this process must have had a definite distribution of possible worlds with their probabilities, which is a given in the system, even if it's unknown to us. If we apply the "doomsday" reasoning to that scenario, what we learn is that, within that given distribution of possible created universes, we're more likely to be observing this from one of the more populated branches. As far as I can tell, that's all that the reasoning allows us to derive.
And that is a far cry from Big Claim above! It even directly contradicts it, because it says that whatever measure we can make of the number of people in the universe, *that* is likely to be within the upper range of possibilities, not only in this world, but also among all the worlds that could have been created by the same process.
In other words, we get the well-known weak anthropic principle back. Among all possible universes, we're likelier to be asking "why am I here" from one of the more populated ones. So even if we can think of theories where the universe would have 10 or 10^10 times more people than it appears to have, this actually gives us evidence *against* them.
Sorry for the long post, still trying to grapple with these reasonings. Not even sure if I've taken a well-known non-SIA position, or something else.
The proposal is that the people are in the multiverse, not that they're all on Earth. SIA doesn't have any preference regarding where the people are distributed.
Fine. Any thoughts on the Doomsday analysis?
SIA is the only way to avoid the doomsday argument consistent with Bayesian conditionalization https://philpapers.org/rec/ADEATT
Thanks, I'll have a read.
For now I tentatively side with Ape in the Coat, from the thread where you debated with him:
> Probability is a mathematical function and it's domain is event space. If your statement can not be interpreted as well-defined event of probability experiment, then you can't assign probability value to it.
But as I explain, you can have credences over event spaces which include de se evidence. E.g. the event space can be
the coin came up heads and I'm person 1
the coin came up tails and I'm person 1
the coin came up tails and I'm person 2
OK I guess that's where we disagree. I don't think "I am Bob" is an event, or functions like an event enough that you can assign probabilities to it, in the general case. Bob is just Bob, and Alice is Alice, and however much Bob thinks "I am Bob", there is no alternate world where he actually is Alice. So, if you can't assign sensible probabilities to something, then it's no wonder that Bayesian conditionalization fails.
On the other hand, in carefully designed thought experiments where people are pre-indexed according to some rules, even though "I am person #1" is not an event, questions like "in which modal branch am I likely to find myself" can be rephrased in objective terms by counting possible observations across the system. So in those cases you can get a cogent response to an anthropic-sounding question.
The same applies to the simple counter-example you gave in another thread, "I exist, therefore my parents had reproductive sex" sounds anthropic, but is not irreducibly so; if Bob thinks this, then it just amounts to the ordinary inference "Bob exists, therefore his parents had reproductive sex".
I'm sympathetic to your anthropic argument for God. I was a committed thirder on the Sleeping Beauty problem for years before I heard about the SIA, and I'm fond of technical quasi-mathematical arguments, and I am predisposed by disposition and upbringing to be theist.
I do, however, have at least a couple concerns.
(1) You broach in your post the possibility of infinitely many copies of the same person. It seems to me that the anthropic argument you make pushes us inevitably to believe in a God who created not just me, but very many copies of me. This clashes with my "Occam's razor" intuition that such profligate duplication (rather than diversification) is bizarre and unnatural to hypothesize. I could lean into Scott Alexander's "There is no cosmic unemployment rate" and say that haeccities don't exist so you can't actually make multiple copies of me... but I'm not sure that this works even if haeccities don't exist. Even if there's no such thing as "this" electron and "that" electron, after all, we can still have "two electrons".
(2) There are naturalistic accounts that would give us your unfathomably many people. They're unnatural and bizarre and I don't believe them, but I'd continue to disbelieve them even if I were persuaded that there is no God, so that provides (infinitely strong?) evidence against SIA. For example, on the Mathematical Universe Hypothesis, every mathematically possible universe exists with the same ontology as our physical reality, so every possible person exists. Moreover, by considering the direct sum of arbitrarily large numbers of copies of the same mathematical universe (a very common construction), we can end up with more copies of me than any cardinality of ZFC allows for. Does SIA provide infinitely strong evidence for the Mathematical Universe Hypothesis? Really?
(3) The mathematical formalism seems like it may be imposing more on reality than is actually there. Beth-2 really isn't that special of a cardinal. Why shouldn't we have more, or fewer, people? If people come into existence in sequence, should we index them by an ordinal instead of a cardinal? But there's something more fundamental than both of these issues, and that's that I don't think ZFC is the One True Model of mathematics. In NFU, for example, you can in fact describe the set of all people (or all groups, or all topological spaces, or...) regardless of its cardinality! The power set of a set might end up smaller than the original set, Cantor's paradox notwithstanding. I think you can even have a set of all true statements, though that might require some more delicacy. Even without such a radical step, nonstandard models of ZFC, or ZFC with large cardinal axioms, or ZFC with negations of large cardinal axioms, may land you with different beliefs about "how many people it's possible for there to be" and therefore "how many people there are". But the underlying nature of reality shouldn't depend on what math you use to model it, while your intuitions about how many people there are seem fairly model-dependent.
1) Even if you can't have exact duplicates, the Lewis argument shows there are at least Beth 2 people. So the argument still works. Regarding Ockham's razor, I think Ockham's razor only applies to fundamental entities (this has been discussed by Jonathan Schaffer a bit). If a coin got flipped a while ago, that created a lot of different kinds of things if tails, and a few kinds if heads, I don't think parsimony gives you reason to think it likely came up tails.
2) Well, it may be that if you came to think that there was no God you'd have to give up SIA. Nonetheless, SIA is the best view. Like, it can be that view A has strong arguments in its favor, but it works poorly with view B. The fact that accepting view B would make you give up view A wouldn't tell us if view A is plausible--its plausibility may give you a reason to reject view B. I think SIA updates you in favor of the Tegmark view, but it's independently implausible (for reasons I explain in the article, in the section about Tegmark's view).
3) As I say, I think that there are more than Beth 2 possible people. I think there's no set of all possible people, and I argue for that.
I'm afraid I don't know enough about set theory to comment very intelligently on some of what you say. Though I think Cantor's theorem is pretty well established purely by logic, and my comments in the section about why you shouldn't think there are aleph null people should be applicable.
(1) What do you mean by "fundamental entities"? I agree with you that if a fair coin would create more entities on one flip than the other, parsimony shouldn't commit me to the flip that ends up with fewer entities.
But to my mind, there's something of a clash between my intuition about Occam's razor and the anthropic principle. Occam's razor seems to want me to postulate the simplest explanation compatible with my experience, and SIA seems to want me to postulate the explanation-that-produces-the-most-people-like-me compatible with my experience. But the simplest explanation compatible with my experience is not that there are infinitely many duplicates or near-duplicates of me that I will never interact with or observe in any way.
(2) I don't think I expressed what I meant to clearly, probably because I am not yet clear on what I want to express. I first became exposed to the anthropic argument for God by your articles, and I'm still wrestling with my intuitions about them. SIA seems plausible to me. A cosmos with only finitely many (or only aleph null) people seems plausible to me. It seems, though, that if your syllogism doesn't have some hidden error, I should either give SIA probability 0 (by a Bayesian modus tollens) or a denumerable count of people probability 0 (by a Bayesian modus ponens). That seems sufficiently overconfident that it makes me want to revisit my thirder status, or else figure out why a limited SIA doesn't force me to grant a global one, or something.
(3) I read your argument, including its allusions to proper classes of people, and you can ignore my yammering about ordinals if you want. But I think you should be disturbed that you're making a set-theoretic argument that there's no set of all people (not for well-definedness reasons, but for cardinality reasons)! That means the theory you are using to make your argument isn't powerful enough to apprehend the state of the world that actually obtains!
Cantor's Theorem is indeed a well-established result, and I'm not disputing its correctness inside of ZFC. It does depend, though, on the restricted axiom (schema) of comprehension: given any set X and any formula phi(x), the set {x in X : phi(x)}. In NFU, though, this axiom requires further qualifications before it can be used, and thus Cantor's Theorem itself is a more qualified statement. (Intuitively, formulas like "x is not an element of x" have a suspicious sort of self-reference to them, and so we don't allow them to appear willy-nilly in our formulae.) If you're curious about why this is a sane perspective and what happens when you develop it, I'm happy to refer to you Randall Holmes's book https://randall-holmes.github.io/head.pdf.
But my general point isn't that Beth 2 doesn't exist, and it isn't that you should want a weakly stratified set-theoretic universe; I merely maintain that ZFC is a convenient rather than a canonical framework for reasoning, and you want to be careful with your infinities.
1) A fundamental entity is one that isn't explained by deeper entities.
Occam's razor is about priors, SIA is about updating from your existence. But as I think the coinflip case demonstrates, your priors shouldn't disfavor created entities.
2)
//It seems, though, that if your syllogism doesn't have some hidden error, I should either give SIA probability 0 (by a Bayesian modus tollens) or a denumerable count of people probability 0 (by a Bayesian modus ponens).//
I don't think this is right. You can have, say, credence in SIA of .9 and credence in finite people of .1. Your credence conditional on SIA (and you not being confused) of there being finite people should be 0, but you shouldn't be certain of SIA.
3) Yeah, I agree there are puzzles of how math works with things that are not sets. I'm not in a position to sort that out. Worst case scenario, I'd just accept that the collection of possible people was a set of some big size.
(1) Anyone in a position to update based on priors is also positioned to update based on existence. So both Occam's razor and SIA upweight and downweight various hypotheses before you've engaged meaningfully with the world at large, right?
(2) You are correct! I was being sloppy. All I demonstrated is that if your syllogism holds, then SIA and a denumerable population are almost disjoint possibilities.
...
What do you make of the following argument?
(a) God exists (because of SIA, and psychophysical harmony, and fine-tuning, and whatever else)
(b) From God's perspective, SIA affirms that He should expect as many beings like Him as are possible. Therefore, unless there's an ontological/necessity argument that God is unique, there should be infinitely many Gods.
(c) By Aumann's Theorem or something similar, we too should believe there are infinitely many Gods.
Regarding 1) yes, but this is totally normal. Even non-SIA views will do this--your existence will give you evidence for views on which you exist. But those are on average more complicated than views on which you don't. There's nothing probabilistically illicit about having priors that favor A and updating in favor of ~A.
Regarding 2) first of all, I think (c) would be false, as de se evidence can't be treated the same way as non-de-se evidence. Also, I don't think b) is right, as God is supposed to be omniscient, and directly acquainted with every truth. He doesn't figure things out by inference to the best explanation.
Probably can't reply to your response to this as I'm a bit busy.
(1) I mean, sure, if we take any brand of anthropic reasoning seriously then both Occam's razor and anthropic reasoning apply, and it's not illicit that it should be so. The a priori versus a posteriori distinction doesn't seem super meaningful to me when every reasoner can make the same posteriori arguments. My point is that the conclusion is reached with such confidence, despite seeming unnatural on other grounds, that I am forced to be suspicious of the method.
(2) A Christian or conventional monotheist does hold that God directly apprehends all truth in a de se sort of way, but I don't see why you should grant the same. Why should we expect God to have a kind (rather than degree) of knowledge so radically different from ours? Still, I agree that if God can directly apprehend His own uniqueness that He doesn't need to make reference to any SIA argument. Should He be surprised that He is unique?
I see that the distinction between de-se and non-de-se evidence exists, but I'm disquieted that I and God might both be sure that He exists, and yet draw different conclusions from that exact fact about whether other gods also exist.
Like, here's a toy example that doesn't have so much metaphysical nonsense. God flips a coin. If it comes up heads, He creates ten men in red shirts and one man in a blue shirt, and if it comes up tails He creates ten men in blue shirts and one man in a white shirt. Each white room has doors leading to each other white room. I wake up, and find that I have a red shirt. I now believe that heads is ten times as likely as tails by SIA. I then open one of the doors and see a man in a blue shirt on the other side. I should now (I claim) revert to even odds between heads and tails, since seeing this other man was ten times as likely if the coin came up tails as heads.
Right?
(I guess you can't respond because you are busy. Thanks for chatting! I expect I'll comment more on later posts)
Doesn't SIA prove too much? Since I'm American, wouldn't it be more likely that America is secretly 50x larger than it is purported to be, and the population similarly larger to inflate the probability that I am American - and that this is essentially a wide conspiracy?
So, it's a little complicated, but the basic answer is no.
What SIA tells you to think there are more of is people you might presently be. Now, you know you're an American, so it tells you to think there are infinite Americas throughout the multiverse. This is discussed a bit in section 4.7.
Thus, the theory tells you to think that there are many Americas in that sense through believing in a multiverse. For people other than those you might be, SIA gives no reason to think they're in America.
It could be that every possible person is created in America. This view will get an update in its favor, but will also have a similarly low prior--if all of reality is just one location repeated, given the infinite locations that could be repeated, it's infinitely unlikely that the location would be America.
Now, if you conclude that every possible person is created, SIA will hold that you should think a maximally large share of them are in America, though this just seems like the right result. And the math here gets messy as doing precise comparisons of infinities is a nightmare.
I'd like a highlight a theory I came upon recently that is consistent with both fine-tuning and the SIA, but which does not require a first mover.
Isn't it amazing how complicated humans are? They must have been designed by an intelligent creator. Actually, there's a known mechanism that complexity develops through gradual accumulation.
Isn't it interesting how the big bang came from a singularity, and that black holes are singularities? What would it imply if production of singularities created universes just slightly different from their parent universe?
It would imply that there are indeed infinite people, and actually infinite universes as well.
The theory is called cosmological natural selection, essentially that universes are optimized for black hole production (https://theeggandtherock.com/p/in-which-i-tell-you-about-my-next, audio version https://www.youtube.com/watch?v=rZ5inYnDWWA). This theory has made predictions about the early state of the universe which have been corroborated with data from the James Webb telescope (https://theeggandtherock.com/p/killer-new-evidence-that-supermassive).
One very interesting implication of the theory is that intelligent life is selected for because they have a tendency to create and harness black holes for energy production. Assuming the universe is positive utility, it seems like we have a moral duty to advance technological progress in order to create many more universes like our own.
That certainly won't get you a higher cardinality worth of people, so it won't avoid the anthropic argument. I don't think it solves fine-tuning--see the multiverse section https://benthams.substack.com/p/the-fine-tuning-argument-simply-works
First off, I don't really buy the arguments about cardinality because the relationship between mathematics and reality is rather fuzzy when we start talking about infinities.
But in any case, this theory certainly moots your point about deceived people because Boltzmann brains cannot develop black holes. In this theory, the universe selects for intelligent life that is capable of rationally interacting with the natural world, which Boltzmann brains and illogical minds are not.
Regarding the fine-tuning multiverse arguments:
> The process required for generating multiple universes is complex and requires fine-tuning of its own
I see this as the equivalent of the first-mover problem in that the theory explains how universes are created but can't explain how the process itself began. But theism also has this.
> Second, the multiverses have to be very improbable in a variety of ways! There’s fine-tuning of the laws, constants, and initial conditions—so it has to be able to vary all of them.
Also about how the process itself originated, so I view this as part of the first objection. Nevertheless, cosmological evolution does provide an mechanism for how these laws and constants are tuned - every child universe is a slight variation of the parent universe, perhaps affected by things like the mass of the black hole and what enters their event horizons.
> Third, a multiverse might lead to the proliferation of Boltzmann brains
Covered above, cosmological evolution does not select for Boltzmann brains
> Therefore, the multiverse can’t explain the most troubling kind of fine-tuning—fine-tuning for low entropy.
Black holes are hard to create when entropy is high, therefore universes select for low entropy.
> The multiverse is analogous to explaining why there’s a book like Shakespeare’s that exists somewhere by saying that there are an infinite number of monkeys typing on typewriters
Random selection wouldn't create Shakespeare, but a genetic algorithm would certainly be able to produce something like it.
> Fourth, even if a multiverse explains why we exist, it doesn’t explain fine-tuning for scientific discovery.
It does, because scientific discovery leads to the production of black-holes: https://phys.org/news/2023-12-ways-black-holes-energy-source.html. Isn't it weird that small black holes are theoretically the most efficient form of energy production in the universe?
> This is because God would be likely to create a multiverse.
The conditional probability is that if your god existed, he would be likely to create a multiverse, but this relies on that very particular type of god existing in the first place, which is unlikely.
> Similarly, for the multiverse to eliminate the force of fine-tuning, the odds of a multiverse has to be high on atheism.
The odds of the multiverse is high under atheism actually, because if universes are optimizing for universe creation, you naturally get a never-ending expansion of child universes.
Anyways, I think it's pretty ironic that your name references Thomas Huxley but you are arguing in favor of intelligent design over evolution.
The point about Boltzmann brains isn't that every universe will inevitably produce deceived people. It's that almost every universe with enough people to be supported anthropically will result in deception. It obviously doesn't do to dismiss a sound argument just by saying that math is fuzzy in its application to reality, when the right theory of anthropics tells you to be certain that theree are infinite people.
I obviously believe in evolution.
All the points about fine-tuning are confused, but I don't have the time to type out a detailed reply.
I agree that there are infinite numbers of people, what I disagree with is about whether the scope of that infinity matters. What I mean by the application of math to reality is fuzzy is specifically when speaking about different kinds of infinities.
The point I make about deceived people is in response to this particular point:
> But if there are infinite deceived people, and no more non-deceived people than deceived people, then you should have no confidence in the reliability of your cognitive faculties.
However, if reliable cognitive faculties are selected for then you should expect there to be many more non-deceived people than deceived people. Universes actually actively select against production of deceived people since that would require a different type of fine-tuning, but the result is totally useless for creation of singularities. Therefore you can be confident that you are actually non-deceived under cosmological evolution.
I talk about these things in the article. See section 2 and 4.
Yeah, we probably won't agree on this point. But I don't think it even matters because people are selected from a biased set, not a purely random one.
Doesn’t this lead to parody arguments though? Like someone coming up with a theory about a leprechaun making infinite people is now more likely cause you exist?
The theory that a leprechaun exists and makes infinite people gets an update from the fact that you exist. However, it's still not a good theory.
Isn't it still infinitely more likely than any theory that claims only one of you exists, though?
Yes. One consequence of SIA is that otherwise bad theories that predict many people beat good theories that predict few. But this is a general consequence whenever a view scores explains one kind of evidence poorly.
How comfortable are you with infinitesimal rather than zero probabilities for rare but not impossible events?
Thats my preferred view.
You're a brave man! I share your intuition that infinitesimal probabilities make sense, but to talk about probabilities like 1/Beth 2, you need the full machinery of the surreal numbers, not just petty infinitesimals like the hyperreals! Unfortunately, I'm not aware of a satisfactory development of surreal integration, much less of an exhaustive theory of surreal probability. I get nervous when my formalisms lag so far behind my intuition.
The SIA is easy not to buy. It applies probability to an event where probability doesn't make sense.
A coin flip being heads or tails might create Jack or Jill from the ether. The birth of a person, in reality, is not due to any such purely 'random' factors. The kind of conclusions that SIA draws are what are typically described as being "Not even wrong".
What event does SIA apply probability to that doesn't make sense? And can you tell me where any of the arguments for SIA go wrong?
SIA thought experiments refer to an abstract possibility for a human being created, often referencing thought experiments where people are created out of nothing in a room. But in the real world, people only exist through a natural cycle of reproduction that happens due to predictable events. Thought experiments about people being suddenly created or not created due to one singular decision do not offer appreciable insights for how the world works.
Well, for each of the thought experiments, you can imagine replacing the spontaneous creation with people being born through natural process. Also, thought experiments can be informative even if they're not realistic--the way to reason about creation of people doesn't depend on whether they were created through the childbirth process or spontaneously.
If you used the natural process of reproduction instead of spontaneous creation, then the conclusions normally drawn for SIA would seem obviously unsupported by the evidence. The person waking up in a room could reason that there are probably some number of humans that exist to avoid the problems of unavoidable incest from a very small (less than 500) population, assuming that they were healthy. But there would be no strong reason to think there must be a million, a billion, or infinitely more humans, because some tribe could continue having kids and then someone would possible wake up in a room one day.
It's weird how SIA people never respond to this. Everything is just magic and abstraction in their world. Nothing ever rooted in biology or physics.
I’m not sure I follow why any of this (or what I directly observe) necessarily suggests god is perfectly “good” versus any of the countless other ways god could be.
The argument gets you to a God who would create the most people that there could be. Other arguments (in particular, priors) get you to that God being perfect https://benthams.substack.com/p/god-best-explains-the-world
Thanks. I’ll re-read it and post my further questions about the perfect goodness of things there.
Edit: I guess my confusion was due to the following sentence, which makes it seems like your argument hinges to some extent on god being good:
> It’s good to create a person and give them a good life, so God would create, in his infinite power and goodness, some ungodly (Godly?) number of people.
Well, the argument raises the probability of a good God. If a good God, something that lots of people believe in, predicts some fact about the world better than most other theories, that fact is evidence for the theory.
I'm not convinced about SIA. I would think each coin toss creates a world of equal weight, so your weight in one room is 50% and in the other room 50%*N/N = 50%.
It depends on whether you are assigned to your room top down or bottom up.
If you follow the bottom up route, then you'd expect to end up in a universe derived from all possible multiverses.
(Thanks for writing this by the way - I'm nearing the end of Leslie's "Universes" and this is the next thing I wanted to explore.)
Thanks!
But that produces the result that if you find yourself as the first person, in a case where many people will be created if a coin that will be flipped comes up tails, you should be super confident that the coin will come up heads.
Didn't understand your reply. Is this what you meant?
"But that produces the result that if you find yourself IN the first ROOM, in a case where many people WOULD HAVE BEEN created if a coin that HAD BEEN flipped CAME up tails, you should be super confident that the coin HAD come up heads."
But that's trivially true: if you KNEW you were in the first room, then obviously it was heads.
No! Suppose that one person is created. Then a coin is flipped. If it comes up tails, a bunch of people get created. If you split your credence across the coinflips, then after updating on being the first person, you get near certainty that the fair coin will come up heads. See also section 3.1.
re Adam and Eve: they are not two random humans. They are by definition the first two, so DA doesn't apply.
re Lazy Adam: they've already defeated DA by being first (which is very unlikely for random people, so the rest is just fiction and proves nothing)
Just tell me what you think about the scenario I gave. What should your credences be after learning you're the first person?
Re Adam and Eve, the point is they don't know they're the first two people. After learning it, so long as they follow conditionalization, they get a massive update in favor of there being few people.
I think I was making too much of this.
If the example involves a human putting black and white balls in an urn it's obvious that normal combinatorial arithmetic applies.
An equivalent example using a god and people raises are all sorts of questions with unknowable answers like whether he's building rooms on Earth or creating worlds and how awareness finds its way into bodies.
If all universes/worlds were equal weight we'd all be quantum Boltzmann brains.
When you find out you're the first person you've already defeated the odds so it's reasonable to assume H is now 1,000 times likelier than ~H. (By selecting a person who's beaten 1000:1 odds we're in the realm of fiction - normal reality needn't apply in this artificial linked scenario.)
Do you think the King of England wakes up everyday and thinks: there are 8 billion people in the world, I can't possibly be King of England!
[Or Philip Goff thinks there are a gazillion self-aware particles in the universe, how come I'm human?]
PS: I'm perfectly happy with SIA within a single level in the multiverse, but not sure it can be automatically applied over multiple levels, but I'm still thinking about this. Artificial and Adam and Eve scenarios are questionably multi-level.
My main problem with this argument is that SIA / SSA is the wrong lens to use to determine the likelihood of initial causes and conditions.
You use a lot of coin flips as examples. That’s good for explaining SIA, but says nothing about the probability of theism being true. Mainly because the fact of whether or not god exists is nothing like a fair coin.
Imagine instead a cosmic lottery, picking balls randomly from a cosmic urn. Every time a red ball with the number “2” is picked, a million universes come into existence, but if any other ball comes up, only one universe comes into existence.
Given that you are a person who exists in a universe, which number do you think came up? The correct answer is that you have no way of knowing.
Without knowing the number of balls in the urn, how many are red, how many have the number “2”, how many drawings there are, etc. you simply don’t have enough information to calculate odds of anything. Maybe there are infinite drawings. Maybe all the balls in the urn are blue. Or maybe there’s just one ball in the urn, and it’s a red 2.
Before the coin flip metaphor is of any use, you need to know more about the likelihood of scenarios on offer in the first place, and you can’t use the anthropic argument to determine that.
As for all the evidence: You appear to conflate the chances of a scenario being true with the amount of evidence each scenario produces after the fact. But obviously, nothing that happens after the fact can change the initial chances of it happening.
We discussed/disagreed on The Sleeping Beauty problem a while back, in a discussion that sharpened my view on it. (Thanks.)
Basically, even if your chances of being right about a claim improves with tails, that’s not because the odds of tails being true have changed. It's because tails gives you more opportunities to be right. And, because the guess is about its own preconditions, you will be right more often if you choose the answer that, when true, allows you to be right more often.
This extrapolates to pretty much every thought experiment where you're supposed to deduce the outcome of a coin toss based on a single, non-conclusive observation.
I have other issues with the argument as well: I think you're unintentionally strawmanning modal realism and Tegmark; I suspect your play with infinities muddies the difference between cardinality and probability; I think even if you're right, a good god is not the only plausible explanation … but that's for another day.
If god creates only non-deluded people, then there are a lot of not created people. There are infinite ways to be deluded for every way you are not deluded, so the set of deluded people is the superset of non-deluded people and therefore has higher cordiality. Therefore by anthropic argument God doesn't exist and everyone is deluded.
> A world with God and other good stuff is better than a world with God alone because it has more good stuff. Now, if you count a world with God and other good stuff as a thing, then that thing is better than God alone, but God remains the best non-composite thing—the best single thing that doesn’t involve stitching together a bunch of different things.
That would require God be less than infinite good, otherwise ∞ + x = ∞.
> The anthropic argument claims that anthropic theory—specifically, SIA—raises the likelihood of theism. It’s not about whether God would create in the first place; it’s about how many people would be created by God vs. atheism. Thus, talking about whether God would create at all is changing the subject.
This doesn't make any sense.
The reason why according to SIA hypothesis A is more likely than hypothesis B is because on A more people like you exist than on B. If no people like you exist on A, then it's probability on SIA is zero and it's not more likely than B.
If God doesn't create any people than the ratio of people created by God vs atheism is definitely not in favor of God. It is literally the subject.