Suppose I notice I am a human on Earth in America. I consider two hypotheses. One is that everything is as it seems. The other is that there is a vast conspiracy to hide the fact that America is much bigger than I think - it actually contains one trillion trillion people. It seems like SIA should prefer the conspiracy theory (if the conspiracy is too implausible, just increase the posited number of people until it cancels out).
You can get around this by saying that infinity is too big for it to matter - since there are an infinite number of Americans (across all possible worlds), I'm no more likely to live in the conspiracy universe than the normal universe. But I think you can't do weird stuff with infinities like this. Consider 1000 rare classes of person (dictator, billionaire, dwarf, polar explorer, etc). I notice I'm not in most of these classes. But it seems like if there are an infinite number of Earths, then there are an infinite number of polar explorers and an infinite number of non-polar-explorers, and these aren't two different levels of infinity (there are about 1 million times more non-explorers than explorers). So I should be exactly as likely to be an explorer as a non-explorer. But the fact that I'm not in more than a handful of these rare classes proves that this isn't true. Therefore, you can't sweep the first problem under the rug by playing with infinities.
I accept that if the only possible theories were the conspiracy and the non-conspiracy theory, the conspiracy theory would win. This result is widely known and is the main objection to SIA--that it implies you should believe otherwise implausible things if they predict more observers. I'm not too worried for reasons given by Carlsmith https://joecarlsmith.com/2021/09/30/sia-ssa-part-4-in-defense-of-the-presumptuous-philosopher. To briefly summarize:
1) You shouldn't be that confident in the theory of anthropics, so any real person shouldn't use this reasoning. If you're 90% sure of SIA, this result won't follow.
2) Every view of anthropics can be shown--as I show in a forthcoming paper--to entail that there are some cases where you should reject well-established science based on anthropics. This isn't surprising--if anthropics says something about the world, it should be able to overturn otherwise confident judgments.
There's a lot more to say, and I think that SIA is so overwhelmingly attested that I don't really mind biting the bullet--also doesn't seem so bad when you realize that a billion times as many people makes it a billion times likelier that you'd exist.
As for the infinite stuff, it's not really clear how to do infinites with SIA. I think probably a lot of infinites are incomparable and as usual infinites ruin everything--especially ethics! I don't have a well-worked out theory of how to compare infinites in terms of SIA, but no one has a good theory of how to do infinite anthropics, so it's not uniquely a challenge for SIA (I elaborate on this more here https://benthams.substack.com/p/breaking-the-fourth-wall?utm_source=publication-search).
It may seem weird to have an argument involving infinite anthropics when it's not clear how to do infinite anthropic reasoning, but SIA clearly proscribes favoring bigger cardinalities of infinity. It's only messy when it's a bunch of infinites of the same cardinality.
EDIT: Possibly I'm an idiot in a great many ways. Read with caution. For one thing, I forgot that the concept of "expected value" is distinct from the most probable value.
UPDATE ON EDIT: After remembering the concept of expected value, I've seemingly determined that in my toy problem, as n approaches infinity, the expected chatroom number actually converges to 3 (the third chatroom?) I don't know how exactly to interpret this.
I don't believe increasing the posited number of people necessarily eventually cancels out the implausibility. For example, suppose there are n chatrooms for some n>2 such that the kth chatroom has k people (The first chatroom has 1 person, the second chatroom has 2 people, and so on until the nth chatroom which has n people) and suppose you've been uniformly randomly selected to be one of the people among all the chatrooms. Then the prior probability that you're in the chatroom with k people should be k/((n(n+1)/2), and given that information alone you should naturally suppose you're in the largest group, which has the highest probability.
But suppose also that everyone flips a coin, and if it comes up heads then they're required to send a message notifying the other members of the chatroom of their existence, while if it comes up tails they're never allowed to speak. In that situation, if you find yourself in a chatroom where no one else ever sends a message, then regardless of how big n is, once you've incorporated the evidence that you haven't gotten any messages using Bayes' theorem, the probability that you're alone and the probability that you're in the room with only one other person always remain the highest.
I could share the whole formula I worked out but it would be a bit of a mess, and I don't think it's necessary. The only insight you really need is that the probability of seeing no messages in a chatroom of size k diminishes as (1/2)^(k-1), while the prior probability that you're in a chatroom of size k to begin with only increases as k/(n(n+1)/2), and the former quickly overwhelms the latter.
So, in general, as long as you find an increasingly vast conspiracy increasingly implausible based on the evidence at a fast enough rate, you never have to concede.
(I can't promise that I haven't made several minor mistakes in my math here because I tend to do that, but I believe if anyone double-checks it my point will come through unscathed.)
Re: Infinities, you can't actually define a uniform probability distribution on a countably infinite set or unbounded set because either the probabilites would have to add up to zero or they would have to add up to infinity when they're supposed to add up to one. So e.g. although there are as many even natural numbers as there are square natural numbers, saying that a "randomly selected" natural number should be just as likely to be even as square doesn't actually make sense. The "randomly selected" part doesn't work.
You can define a uniform probability distribution on something like a finite closed interval using integration, but that only works because there's extra structure to the infinite set. So you could pick a random real number between 0 and 1. But then numbers with different properties aren't necessarily equally likely either even if they do make up infinite sets, like how getting a number whose decimal expansion begins 0.1... is only a ninth as likely as getting a number with some other first decimal digit.
If you assigned every natural number an infinitesimal probability ε = 1/ω where ω is supposed to be the "number" of natural numbers, then the total probability would be ε *ω = 1 which would be nice, but then you couldn't say that there are the same number of even numbers as square numbers without breaking arithmetic I don't think. I do like the idea of infinitesimals, but most formal ways of describing them are a bit complicated and the current math community consensus seems to be to avoid them unless you have a really good idea of what you're doing, which I don't. Another intuitive counterargument to the possibility of a uniform probability distribution over a countable set like the natural numbers is asking "How many digits would the typical randomly selected natural number have?" Any finite number of digits would seem to be far too few, but an infinite number of digits would make it not a natural number.
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As to why even the maximum number of people doesn't cancel out the improbability, if I understand your question correctly, as said it's because the probability of the evidence provided by there being no response gets much smaller much faster for larger groups than the prior probability that you're in a larger group increases.
This is evident in the small case of only four chatrooms:
If room one has 1 person, room two has 2 people, and so on up to room four, so that there are 10 people total, then your initial probability of winding up in the first room is 1/10, the second room is 2/10, the third room is 3/10, and the fourth room is 4/10. So to begin with, all else being equal, you should expect to have ended up in room four as expected.
But then if you add the coin-flip-response thing, and you notice that you've gotten no responses, the probability of that happening in the first room is 1 (guaranteed because you're the only person there), in the second room is 1/2, in the third room is 1/4, and in the fourth room is 1/8.
Bayes theorem tells us that P(H|E) = P(E|H)*P(H)/P(E) where H and E stand for hypothesis and evidence respectively. Using that, P(You're in the kth room given that you've observed no response) = P(You've observed no response given that you're in the kth room)*P(You're in the kth room)/P(You've observed no response).
Now, P(E) is the same for all k so it can be ignored if we're just making comparisons. And It's also tedious to write out so that's convenient.
But using what we've already established,
For the first room, k = 1 so P(E|H)*P(H) = (1)(1/10) = 1/10
While for the fourth room, k = 4 so P(E|H)*P(H) = (1/8)(4/10) = 1/20
And since as said the prior probability of the evidence is the same for both, that means the probability that you're in the first room given the evidence must be higher than the probability that you're in the fourth room given the evidence even though the fourth room has the most people.
Has that helped make sense of it? I hope I've done everything correctly and if I haven't I hope someone corrects me. I also recommend 3Blue1Brown's videos on Bayes' theorem if you haven't seen any of them: https://youtu.be/HZGCoVF3YvM
Hmm, interesting! Not sure what to think of what you said. Maybe when doing countable additivity with infintesimals you have to add up the infintesimals or something--or maybe something about hyperreals. I think that alternatives to SIA's approach will get even weirder results in cases of infinities https://benthams.substack.com/p/breaking-the-fourth-wall?utm_source=publication-search.
Re the conspiracy case, I don't worry too much about it as I basically bite the bullet. I think a conspiracy would be worth accepting if you were an ideal agent and could somehow rule out all the non-conspiracy ways of ruling out a bunch of people.
I think I agree with SIA too because it's better than the alternatives. I'm just saying that, as I understand it, you don't need to bite the bullet. Using SIA as your prior doesn't mean it can't be overruled by evidence in specific cases like supposing based on SIA that there are secretly a trillion people hiding in your pantry because it would make it more likely for you to live in your house if they were there too.
Wait, if there were two theories, one says there's just me, the other me and 1 trillion people with experiences like mine in my pantry, do you agree that SIA gives a trillion to one update in favor of the second?
>So, in general, as long as you find an increasingly vast conspiracy increasingly implausible based on the evidence at a fast enough rate, you never have to concede.
This is technically true, but I don't think this will help much, because realistically your prior can and will involve something along the lines of "X number of people exist according to some distribution with infinite mean." For example, if you think there's a *tiny* positive probability God has created n people in your epistemic situation, where God drew the number n randomly from the distribution with p(n) = 6/π^2 * 1/n^2 (which I picked because its expected value is infinite), then SIA completely prefers this to the "ordinary" hypothesis that there's only one copy of you, no matter how close to 1 the latter's prior. You need the hypothesis I mentioned, and all others like it (including ones where the minimum number of copies n that God creates is arbitrarily high, rather than 1), to have probability exactly 0, and even then you might run into additional troubles.
> So, in general, as long as you find an increasingly vast conspiracy increasingly implausible based on the evidence at a fast enough rate, you never have to concede.
You can design contrived priors to fit your prechosen posterior.
But if your priors are sensible occamian stuff, the conspiracies don't get implausible enough fast enough.
I'm not sure how you can be certain that sensible priors can't overcome most SIA-inspired conspiracies easily considering how fuzzy the idea of sensible priors is.
And anyway my example didn't have any contrived priors, so that's beside the point I was trying to make, which is that evidence may often be able to easily outweigh SIA as a prior. My prior in my example was equivalent to SIA, but it was a fairly simple piece of evidence that readily overcame it. And strong evidence is common: https://www.lesswrong.com/posts/JD7fwtRQ27yc8NoqS/strong-evidence-is-common
Evidence that moves a hypothesis from 1/10^100 to 0.5 is common. Evidence that moves from 0.5 to 1- 1/10^100 basically never happens.
Let H1= reality as normal.
Let H2 =gazillion people + flawless conspiracy to hide this.
Now on priors, both H1 and H2 are highly unlikely. H1 because anthropic reasoning. H2 because conspiracies of this kind are rare.
So when you look around you, you quickly gather strong evidence for (H1 or H2).
But the hypothesis predict identical observations, so all you have to tell between them is the priors. And if we are doing occam's razor, the prior likelihood of the conspiracy is determined by how many bits of information is needed to describe it. 2^-bits
So H1 gets more unlikely the more people you consider might exist. If you allow an unboundedly large (finite) number of people, then the maths kind of breaks and H1 becomes infinitely unlikely, but so does every other hypothesis.
I don't understand your reasoning with respect to Occam's razor. Are you saying that a flawless conspiracy is easy to describe just because it doesn't take very many bits to say "flawless conspiracy"?
I would think that the possible world with arbitrarily more people and a perfect conspiracy to hide them all would still require arbitrarily more information to describe accurately at a rapid rate. In my view, you don't just need to suppose the conspiracy, you also need to suppose all the hidden people with their own lives, thoughts, interactions, etc. that the conspiracy is covering up. Without settling on specific details, you can just consider how much information the additional hidden people would take to describe on average. And I suspect that, when that's accounted for, H2 should actually become infinitely unlikely relative to H1 on Occam's razor as well despite the prior based on SIA, just like happens in my coin-flipping example.
Maybe if tiny variations in physical constants at the beginning of the universe could lead to arbitrarily more people at the present time, then the possible worlds with arbitrarily more people would be just as easy to describe as our world on that level. But all of those worlds also having a flawless conspiracy to hide the extra people/whatever else is involved still seems like it would require considerable extra artificially-imposed info.
...Unless the tijy variations in physical constants lead to arbitrarily many people by creating overlapping "shadow earths" just like ours but which are all totally imperceptible to each other, and that counts as the flawless conspiracy. But if that could be demonstrated then I think I'd agree that we should suppose we're in the universe with a higher number of shadow earths and so more people.
No. I am saying that there exists some finite X such that it takes X bits to describe a flawless conspiracy.
This puts the conspiracy at a likelihood penalty of 2^-X.
But the larger the number of people hidden, the larger the anthropic bonus.
A conspiracy to hide more than 2^X * 8,000,000,000 people is hence more likely than normality. (according to this reasoning, which mostly gives me reason to doubt this reasoning)
Technically you also need to include the number of people being hidden. If you are writing a completely arbitrary number out in decimal, then each doubling of the number of people means 1 more bit used. But also means 2x as many hypothesis. So that kind of cancels out. (Or you could say your hypothesis in compact scientific notation) This doesn't really effect the picture much.
Occam's razor doesn't penalize the universe for being big.
There are at least 10^20 ish stars out there, each with their own composition and solar storms and whatever. Any hypothesis that lists all the details of every star is going to be VERY unlikely, by occam. But that is exactly compensated by the number of different theories that are all basically the same except a few sunspots in distant galaxies are rearranged.
The same goes for the "more people". Sure it takes a lot of info to describe any specific way those people could be. But that's compensated for by the number of ways those people could be. Leaving a very large number of very similar hypothesis, each with a very small individual probability.
I might be wrong about this, but I don't find this argument convincing. I have reservations about the SIA and theism's predictive ability, but I mostly disagree because I don't think atheism does such a bad job of predicting the existence of large numbers of people. To illustrate this, I've tried to list out some hypotheses that are alternatives to theism and still predict the existence of large numbers of people.
1. Tegmark's multiverse and modal realism
1.1. I don't think induction is a big problem for these worldviews, certainly relative to theism.
1.1.1. Suppose modal realism is true. The mere fact that there are infinitely many concretely existing possible worlds where induction fails does not imply that I am probably in such a world, or that induction fails in nearly all worlds. I'm not even sure it's possible to make such statements in a meaningful way - you would need to have a measure over all possible worlds, which is impossible because there is no set of all possible worlds.
1.1.2. Whatever the best way of thinking about uncertainty over possible worlds is, the idea that it would change if those possible worlds existed concretely is exceedingly strange.
1.1.3. Theism doesn't explain why induction works any better than atheism. The morally sufficient reasons God has for allowing the massive amount of evil that have existed throughout history are surely sufficient to allow him to create a world where induction doesn't work.
2. Alternative theisms: for any property that people existing can entail, just postulate a God who values that property rather than goodness. There are infinitely many of these, including
2.1. Evil God
2.2. God who just likes qualia, in general
2.3. God who mostly cares about aesthetic (but not necessarily moral) value
2.4. God who really likes Luxembourgers (maybe there's a reason they have such high GDP per capita)
2.5. and so on.
3. Generalized value selection hypotheses: take theism or any of the 'alternative theisms' and postulate a mindless force which tends to instantiate the corresponding values
4. Physical multiverse theories
4.1. I'm don't think it would be that hard to create mathematical models of multiverses containing Beth-2 or more people. It might be that those models wouldn't be well-motivated by empirical data in the conventional sense, but maybe we shouldn't expect them to be if most of the other universes are causally isolated from ours. And they would at least be motivated by anthropic considerations, which are empirical! (at least if SIA is correct).
4.2. Specifying the exact nature of this model shouldn't even be necessary! It seems *extremely* unfair to complain that physicists haven't proposed a mathematical multiverse model that would predict enough universes when philosophers and theologians haven't proposed a mathematical model of God and his act of creation.
5. Other multiverse theories: Suppose, for example, that there's a simple universe-generating monad which generates lots and lots of universes.
The problem is that almost all of these theories suck and occupy a tiny part of the hypothesis space. The only ones that are at all simple are modal and Tegmark realism, which I think undermine induction. Builes makes the point in more detail https://onlinelibrary.wiley.com/doi/10.1111/nous.12478?af=R.
There's no physical multiverse that produces enough people that anyone has ever proposed and if there is, I fear it would undermine induction. The others are monstrously complicated and arbitrary.
This reminds me of saying something like "okay, sure my having done the crime could explain my blood being all over the murder weapon but it could also be explained by (insert 27 half-baked theories).
Thanks for the link to the Builes paper! I'll give it a look.
I agree that most of these theories suck and are super ad hoc! I just think they're plausibly on par with theism because 'perfection' also seems gerrymandered to me. I can imagine changing my mind about that though.
Can you elaborate further on why you think God would allow factory farming but not failures of induction? The latter seems a lot easier to justify.
I'll agree that if your judgment prior to thinking about this argument is that theism is obviously totally crazy, akin to believe in ghosts, the argument won't move you. But probably most arguments are like that, even very good ones.
Well one reason is that if God allowed failures of induction--it would probably have failed by now. Another is that God would likely make predictable, stable physical laws where we can go wrong. That explains why we're allowed to do wrong things but also provides for induction. My theodicy explains why he'd do that.
To make it more concrete, let's take an ordinary inductive inference like "I have grown taller every day I've been alive, so I will keep growing taller every future day I'll be alive." This statement is clearly wrong, we observe that you will stop growing once you hit puberty. So here's another inductive law: "I have grown taller every day I've been alive and before puberty ended for me, so I will keep growing taller every day I've been alive and before puberty ends for me." But this also has counterexamples - you can take human growth hormone supplements, get shin extension surgery, position yourself so that major gravitational bodies like the Sun and moon are directly overhead, and these will all result in your height increasing after you've finished puberty.
Basically, you're acting like the truthmaker for statements like "I will keep growing taller until I finish puberty" already exists and is obviously induction, and it's not just a useful heuristic that is subject to all sorts of ceteris parabis contextual factors (that themselves are also subject to contextual factors). But the parts you're leaving out of your explanation 1) won't just resolve themselves and 2) directly contradict the putative inductive truth you're proposing once more accurately specified.
For the record, I think most if not all inductive laws have failed. You take physical laws as a paradigmaric example, but physics is notorious for paradigm changes. The laws of quantum field theory aren't the laws of quantum mechanics aren't the laws of relativity aren't the laws of Newtonian mechanics. In past posts you've also said you should believe the Sun will rise tomorrow based on inductive evidence, but eventually astronomical data tells us the Sun will expand to the point the Earth gets incinerated and so "the Sun will rise tomorrow" will be yet another failed inductive law.
>There's no physical multiverse that produces enough people that anyone has ever proposed and if there is, I fear it would undermine induction. The others are monstrously complicated and arbitrary.
I don't think there's an easy way to specify a God-creates-almost-every-possible-person scenario that avoids challenging induction given your commitments vis-a-vis SIA, but regardless: it's very easy to come up with a naturalistic hypothesis that doesn't do this, and which generates beth-2 possible people (if that's the cardinality you're focused on). Specifically: imagine a universe U exactly like ours, but there's a special particle X which pops in and out of existence at certain prescribed times, and which interacts with absolutely nothing else. For a given subset S of the interval [0,1], let U(S) be a universe in which X pops in at every time t in S (counted in seconds after the Big Bang), and vanishes for every other time. Then voila, consider the naturalistic hypothesis that each U(S) universe exists for every subset S of [0,1], and you have beth-2 distinct universes which play out exactly like ours, induction and all, aside from this harmless X-particle epiphenomenon.
This is extremely arbitrary, but it's still incredibly simple, and moreover I imagine it will be a lot less arbitrary/complex than the algorithm you suggest God might use to pick and choose universes to ensure inductive reliability of all agents.
Well, I think you probably need more than Beth 2 universes. I'm also having trouble understanding the picture of the universe. Finally, I think cloning our universe a bunch of times would probably undermine induction because there would be Beth 2 people for whom induction doesn't work.
>I'm also having trouble understanding the picture of the universe.
Beth 2 is the cardinality of the set of all subsets of the reals (or, equivalently, [0,1]). So I'm taking the universe and adding a completely epiphenomenal particle that does something slightly different for each subset of instants of time in the first second of the universe. Then I'm stipulating that all such universes exist (as a multiverse), for every such subset. That gets me beth-2 universes, all identical except for this particle which doesn't affect anything else.
>Finally, I think cloning our universe a bunch of times would probably undermine induction because there would be Beth 2 people for whom induction doesn't work.
It seems like SIA has little to say here, because you're going to get ∞/∞. But that's going to be true pretty much no matter what, to SIA's discredit. Moreover, all the universes are playing out exactly the same way aside from the epiphenomenal particle that doesn't influence any conscious agents or anything they interact with at all, so it's intuitive that you simply shouldn't reason anthropically across universes to begin with.
I should say that, given the way I've set this example up, it's actually hard (likely impossible) to do SIA mathematically because of a technical issue called "non-Lebesgue measurable sets." But again, I think that if you're trying to apply SIA on this scale of infinity, essentially all the mathematical machinery we've developed since the early 20th century to think about probability has to go out the window.
Ah, I see the picture. I think that picture of reality will have a super low prior and doesn't get enough universes, for I think Beth 2 isn't enough. I also think it undermines induction. I think that you should assign equal credence to being any actually existing observers with your evidence, so if there are the same number in inductive and non-inductive worlds, induction might go out the window, though I'm not that sure of that.
> I think that picture of reality will have a super low prior
Sure, I agree, it has a low prior. But it's still reasonably simple to describe, and part of my point was that it's not obviously lower than whichever divine hypothesis you're going with. Because even if God himself is simple (which, as you know, I'd like to deny), you think he has to have some decision procedure to pick and choose which universes to actualize in order to avoid inductive failure, and why think that any of these are more probable than my example?
You could say: well, even if any specific decision divine procedure is improbable, the hypothesis that God is using at least one of them (without saying which) is more probable than my example. My response is 1. that I imagine all of God's individual decision procedures will have something like infinite complexity and thus a plausibly zero prior, and so it's not clear how to add them all up much less what number they add up to; and, furthermore, 2. my example was also just one among infinitely many that would get me to the same sort of place, so you have to add all *those* up as well to keep things fair.
>and doesn't get enough universes, for I think Beth 2 isn't enough
I can probably modify it in a similar way for any other size (cardinal or not) you wish. Just add arbitrarily mathematically weird epiphenomena.
>I think that you should assign equal credence to being any actually existing observers with your evidence, so if there are the same number in inductive and non-inductive worlds, induction might go out the window, though I'm not that sure of that.
All of the worlds are very plausibly inductive, because the same thing is happening in each one of them at the same rhythm, all in parallel. (The only difference, again, is this one epiphenomenal particle that none of us ever notices.) Put another way, if God told you he made an infinite number of carbon copies of the actual world (and nothing else), would you really, truly disbelieve in induction? I wouldn't. I'd reason exactly as before and disregard the validity of any anthropic principle that said I shouldn't.
The analogy at the bottom is terrible. You’re attempting to twist the intuition that “one should have one consistent narrative when testifying in defense to a crime” into a broader claim about how many weak theories don’t work. But many weak theories in the abstract do in fact reduce the probability of a 28th theory when (like in a criminal case), one does not destroy one’s own credibility by asserting 27 inconsistent theories of innocence.
Hm. I wonder if these hypothesis all have a cumulative effect, too. Even if (a big if) bulldog is right that one perfectly good God is the “simplest” in some sense, the fact that there are endless very slightly less simple hypothesis must count for something.
The idea of a god being “simple” is quite difficult for me to swallow. If I told you I had a machine that could manufacture any cell phone currently on the market in an hour, would you expect that this machine would be simple? Why would supposing it could do more and more things until it was an omnipotent creator make it simpler? Far from simple, this seems like something impossibly complex. I would need to observe this machine in action to actually believe it exists because it sounds like it’s not even physically possible. Thankfully, under the typical god hypothesis, god has the ability to intervene in the world and could very easily prove to me (or anyone) that he/she exists. But as Christian theologians evince when they write books with titles like “The Hiddenness of God”, there is no omnipotent being out there trying to make us believe he/she exists.
"Why would supposing it could do more and more things until it was an omnipotent creator make it simpler?"
If the idea is that for every power a device/being has, it has some dedicated mechanism of effecting that power in place, I suppose your objection makes sense. That'd be a lot of mechanisms. But that isn't how God's supposed to work: dependent on subprocesses and assorted widgets to bring about X, Y, and Z. God really has one power, to bring about whatever it wants.
"How does it do that?" I'm unconvinced that an agent needs a mechanical explanation of how it brings about its goals. I don't see any contradiction in imagining an agent whose will is causally efficacious in itself. Might depend on your metaphysics of causation, I guess.
You make a good point. I agree that it is logically possible for such a thing to exist. It’s just highly unlikely in my view. We have zero precedent for such things. In the real world (as opposed to unfettered imaginings of otherworldly but logically possible things), creative abilities require complex mechanisms. “Is logically possible” is not an adequate substitute for “is probable”.
This is quite right I think. A priori, it seems like any of these theories are as good or better than “a perfect being did it”. And if we wanted to spend more time doing this, we could make up any number of logically consistent explanations. A priori we can’t just assume that one is better than another, so it comes down to how well each theory fits with the evidence. Then the problem of evil makes the idea of a morally perfect and omnipotent being existing very unlikely indeed.
Those theories aren't at all simple. Theism posits one core property--perfection--while almost all of those posit bizarre extra gerrymandered properties.
Perfection is only simple in the sense that you can name it with one word. Though to me that’s beside the point. I don’t think simple states of the universe are, a priori, more likely than complex ones.
How is "Perfection" a fundamental property, rather than being an ill defined and arbitrary english word that brings all sorts of complicated details along with it.
Could you give a short description of "perfection" to aliens? Could you write a short program to simulate what a perfect being would do?
Maximally good! You could write a program if you had the ability to include goodness as one of the fundamental operators. A perfect being would do whatever is the most good. Taking a fundamental thing without limits is simple.
Perfection sounds simple because it's a short word. But when you try to actually define perfection in detail, you will find it's actually rather complicated. Your mind was glossing over the complexity.
(The word smartphone is also one word and seems simple, but try describing one to someone from 1800 and you find it's not quite so simple)
Also, I still don't buy your arguments against the problem of evil.
If we have to suffer in order to develop our moral qualities, then why couldn't God just create us with the right moral qualities?
If we have to suffer in order to appreciate God more, then why couldn't God just create us with infinite appreciation?
If God created us because he ran out of unique perfect beings to create, then why couldn't he just duplicate the perfect beings instead of creating imperfect ones?
This reasoning is inherently unfalsifiable as it posits unknown reasons beyond our comprehension, making it impossible to critique or validate.
If someone justified every instance of suffering by saying it’s for unknown future benefits, this would be intellectually unsatisfying and could excuse any atrocity without accountability.
2. Strengthening Relationship with God
It is questionable whether an indifferent universe is necessary to strengthen relationships with God. An omnipotent God could presumably create bonds without inflicting suffering.
In human relationships, one doesn’t need to cause their loved ones to suffer to deepen their bond. Intentionally creating suffering to strengthen a relationship would be seen as abusive, not loving.
3. Soul-Building
The uneven distribution and overwhelming intensity of suffering suggest that not all suffering leads to soul-building. Many suffer without apparent growth, while some are broken by it.
Victims of extreme trauma, such as war or abuse, often suffer long-term psychological damage without any observable benefit, challenging the idea that all suffering is soul-building.
4. Building Connections with Others
Suggesting that an indifferent world enhances relationships undervalues the potential of positive experiences to build strong bonds without suffering.
Friendships and communities often thrive through shared positive experiences, not necessarily through shared suffering. The idea that suffering is needed for deep connections could justify neglect and harm.
5. Working with God
The existence of extreme moral and natural evils is hard to justify as necessary for cooperation with God. This implies a limitation on divine power.
Natural disasters causing widespread suffering (e.g., tsunamis, earthquakes) do not appear to foster meaningful cooperation with God but rather cause arbitrary harm, questioning the necessity of such events for divine-human collaboration.
6. Freely Choosing God
The argument that we need an indifferent universe to freely choose God does not account for the sincere seekers who struggle to find God due to perceived hiddenness.
Many individuals earnestly seeking spiritual truth may turn away from belief due to the overwhelming presence of suffering and indifference in the world, suggesting that divine hiddenness can hinder rather than facilitate free choice.
Theodicies that generalize suffering as necessary for greater goods risk insensitivity to individual suffering and the specific contexts of pain.
Telling a grieving parent that their child’s death serves a greater good can be deeply insensitive and dismissive of their personal tragedy.
There are instances of suffering that appear entirely gratuitous, serving no discernible purpose or benefit, challenging the notion that all suffering has a divine rationale.
The prolonged suffering and death of a child from a terminal illness often seem gratuitous and purposeless, raising serious questions about divine justice and benevolence.
Justifying an indifferent universe implies that a benevolent God permits or even causes suffering for higher purposes, which can conflict with our ethical intuitions about benevolence and justice.
A benevolent human being who allows preventable suffering to achieve a future good would be considered morally questionable, suggesting a similar issue when attributing such actions to God.
//5. HOW THE THEODICY DECIMATES THE CASE FOR ATHEISM//
1. The Existence of Physical Reality
The existence of a physical reality that operates under consistent natural laws is a strong point for naturalism, as it does not require an additional supernatural layer of explanation. Your theodicy suggests that God created an indifferent universe, but this posits an additional entity (God) without necessity.
Ockham’s Razor favors the simpler explanation, which is naturalism, as it does not posit an extra, undetectable creator to explain the physical universe.
2. The Success of Science Without Theistic Explanations
The success of science in explaining phenomena without invoking God highlights the predictive and explanatory power of naturalism. Your theodicy posits that an indifferent universe would look like a naturalistic one, but this does not add predictive power to theism; it simply adjusts theism to fit observed facts.
Naturalism predicts the success of methodological naturalism in science. Theism must be adapted (with the hypothesis of indifference) to align with this success, suggesting naturalism is inherently a better fit for the data.
3. Evolution
Evolution through natural selection is a robust and parsimonious explanation for the diversity of life, which does not require the hypothesis of a deity. Your theodicy incorporates evolution into theistic belief by suggesting an indifferent creation, but this adds complexity without necessity.
Naturalism explains evolution directly through natural processes. Theism, under your theodicy, again, must invoke an additional hypothesis (God creating an indifferent universe) to accommodate evolution.
4. The Biological Role of Pleasure and Pain
Naturalism directly accounts for the biological role of pleasure and pain through evolutionary pressures and the survival benefits of such mechanisms. Theism, as modified by your theodicy, suggests these are designed features of an indifferent universe, adding a layer of divine intention that naturalism does not require.
Pain as a mechanism to avoid harm and pleasure as a reinforcement for beneficial behaviors are directly explained by natural selection. Theism must posit that God intentionally included these features to mimic a godless universe.
5. Mind-Brain Dependence
Mind-brain dependence is empirically supported and directly predicted by naturalism, which posits that consciousness arises from physical processes. Your theodicy must argue that God created the brain to function independently, which is an added hypothesis.
Naturalism straightforwardly explains the correlation between brain states and mental states. Theism must invoke a reason why God would design the brain to operate as if there is no soul or divine influence.
6. Moral Handicaps
Naturalism explains moral handicaps through evolutionary psychology, where certain behaviors evolved because they were advantageous in ancestral environments. Your theodicy must suggest that God intended for these handicaps as part of an indifferent universe, complicating the explanation.
Selfish behaviors can be explained as remnants of survival strategies. Theism must posit why a benevolent God would create beings with these handicaps intentionally.
7. Nonresistant Nonbelief
Nonresistant nonbelief, where sincere seekers do not find belief in God, challenges the notion of a benevolent deity. Your theodicy must argue that this is part of creating an indifferent universe, but this seems counterintuitive for a God who desires relationships with His creation.
Many people seek God earnestly but do not find evidence or experience of Him. Naturalism predicts such experiences due to the lack of divine presence, whereas theism must reconcile this with a loving God’s intentions.
1. The SIA modifies our epistemic probability by factoring in the number of observers a theory predicts. It suggests that if more observers exist under a theory, it's more likely that the theory is true because you are one of those observers.
This approach conflates the number of observers with the probability of the theory being true. The fact that a theory predicts more observers doesn't necessarily make it more likely. Instead, it could be argued that each observer's perspective should be considered independently. The mere fact of your existence should not be more probable under a theory that predicts more people; rather, it should be considered under the initial conditions of the probability of heads or tails.
2. Also the SIA relies heavily on the definition of the reference class—the group of people you consider yourself part of. This can significantly affect the outcome.
The choice of reference class is arbitrary and can lead to different conclusions. In the coin toss example, considering all possible people versus just those in similar conditions (e.g., in white rooms) can yield vastly different probabilities. This arbitrary choice undermines the objectivity of the SIA and raises questions about its validity.
3. It also alters self-locating beliefs by suggesting that you are more likely to be in a scenario with more observers.
This reasoning can be problematic because it implies that the existence of other observers directly influences the probability of your own existence, which is a non-standard approach in probability theory. Traditional Bayesian probability does not factor in the existence of additional observers in this manner.
4. Human cognition is prone to biases, such as the availability heuristic, where individuals estimate probabilities based on how easily they can imagine instances.
The SIA may be influenced by such cognitive biases, leading people to overestimate the likelihood of scenarios with more observers simply because they can more easily imagine more people. This could distort rational probability assessment.
5. Intuitively, people may struggle with the implications of the SIA because it counteracts common sense and standard probabilistic reasoning.
The SIA's counterintuitive nature can lead to resistance and misunderstanding. People typically reason that the probability of an event (like a coin toss) should not be affected by unrelated outcomes (like the number of people created). This discrepancy between intuitive reasoning and SIA can make it psychologically unpalatable and difficult to accept.
6. Applying SIA can lead to extreme and impractical conclusions, such as radically altering beliefs based on hypothetical large populations.
This practical consequence makes the SIA less appealing. For instance, in the coin toss scenario, suggesting that tails is a million times more likely based solely on potential observer count can lead to impractical and unrealistic decision-making processes.
//This approach conflates the number of observers with the probability of the theory being true. The fact that a theory predicts more observers doesn't necessarily make it more likely. Instead, it could be argued that each observer's perspective should be considered independently. The mere fact of your existence should not be more probable under a theory that predicts more people; rather, it should be considered under the initial conditions of the probability of heads or tails.//
I didn't just assume that a theory that predicts more observers is more likely--I gave 4 arguments for it! You shouldn't just look at the objective probability of an event to see its propbability of producing you--for example, if my parents would only have sex if a coin came up heads, I should be very confident that it did.
//2. Also the SIA relies heavily on the definition of the reference class—the group of people you consider yourself part of. This can significantly affect the outcome.//
SIA just looks at the people you might currently be. Unlike SSA, it doesn't invoke a reference class.
//This reasoning can be problematic because it implies that the existence of other observers directly influences the probability of your own existence, which is a non-standard approach in probability theory. Traditional Bayesian probability does not factor in the existence of additional observers in this manner.//
SIA is just being a Bayesian about your existence. More observers makes it more likely I'd be one of them, for the reason given by Elga.
//4. Human cognition is prone to biases, such as the availability heuristic, where individuals estimate probabilities based on how easily they can imagine instances.
The SIA may be influenced by such cognitive biases, leading people to overestimate the likelihood of scenarios with more observers simply because they can more easily imagine more people. This could distort rational probability assessment.//
Why would a scenario be easier to imagine just by having more people? Huh? Also, I didn't just like assert SIA--I gave several arguments for it.
//The SIA's counterintuitive nature can lead to resistance and misunderstanding. People typically reason that the probability of an event (like a coin toss) should not be affected by unrelated outcomes (like the number of people created). This discrepancy between intuitive reasoning and SIA can make it psychologically unpalatable and difficult to accept.//
Well, SIA doesn't think that if a coin hasn't been flipped yet, but will create many observers if it comes up heads, that your credence in heads should be more than 1/2. After all, on SIA, what matters is the observers you might currently be. But I know I'm not one of the observers who will be created in the future. In contrast, SIA does judge past events by the number of observers, but this is totally reasonable. If I know a coin got flipped in the past and I would only come to exist if it came up heads, I should think it came up heads.
//This practical consequence makes the SIA less appealing. For instance, in the coin toss scenario, suggesting that tails is a million times more likely based solely on potential observer count can lead to impractical and unrealistic decision-making processes.//
Well that's why I gave an argument for the God's extreme coin toss result, as well as many other arguments for SIA. You're just assuming that your existence gives you no evidence for more people, which begs the question against SIA.
1. Again, the SIA relies on defining a reference class of observers, but there is no non-arbitrary way to determine this class. The selection of the reference class can drastically alter the probabilities, undermining the objectivity and reliability of the SIA.
In the God's coin toss scenario, if you consider the reference class to be all potential beings, the outcome differs from considering only those in a white room. This flexibility in choosing the reference class makes the SIA highly subjective.
2. SIA leads to inconsistencies when applied across different scenarios. It alters traditional Bayesian probability by incorporating the number of observers, which is not standard in probability theory.
In Bayesian reasoning, the probability of an event is updated based on evidence. The SIA, however, updates probabilities based on hypothetical additional observers, which can lead to paradoxical outcomes. For instance, it implies that more populous universes are inherently more likely, irrespective of other evidence.
3. The SIA can lead to counterintuitive and paradoxical implications. It can suggest absurd probabilities that defy common sense and practical reasoning.
If two universes exist, one with a million observers and one with a single observer, SIA implies you are almost certainly in the more populous universe, regardless of other factors. This could lead to absurd conclusions in cases where observational data clearly favors the less populous universe.
4. SIA de-emphasizes the importance of actual empirical evidence in favor of hypothetical population sizes. This undermines the empirical basis of probability and decision-making.
In scientific inquiry, theories are evaluated based on empirical evidence and predictive power, not on the number of potential observers they imply. SIA shifts focus away from evidence-based reasoning to speculative considerations about population sizes.
5. Also, SIA can involve circular reasoning by assuming what it sets out to prove—that a theory predicting more observers is more likely because it predicts more observers.
The argument that a universe with more observers is more likely because you are an observer presupposes that your existence is more probable in such a universe, which is the point under debate. This circularity weakens the logical foundation of the SIA.
6. SIA can lead to problematic ethical and existential conclusions by emphasizing the quantity of observers over the quality of their experiences.
If applied to moral philosophy, SIA might suggest that creating vast numbers of minimally conscious beings is preferable to fewer beings with richer experiences, simply because it increases the likelihood of being among the more numerous group. This clashes with ethical intuitions about the value of conscious experiences.
SIA seems solid. Consider actually playing god to recreate the coin flip scenario. You flip a coin two days in a row and give yourself this rule before starting: “If I flip heads, I will email 3 of my friends a message that says ‘hello.’ If I flip tails I’ll email 1 friend ‘hello’.” On day 1 you flip heads (just by chance) and email the 3. On day 2 you flip tails (again just coincidentally) and email the one. Now you tell all 4 friends what you did and ask them to guess what you flipped on the day they were emailed. If they all guess heads, 3 out of 4 will be correct. If they all guess tails 1 out of 4 will be correct. So heads is a better guess. That is, guessing that the more friends were emailed option (heads) has a higher probability of being the right guess.
- Tell all 4 friends about the coin flips and ask them to guess the outcome on the day they received the email.
The argument suggests that each friend, knowing the rules, should guess heads because, statistically, there are more emails sent out on heads days.
1. Sure, from the perspective of a friend who receives an email, the likelihood of having been emailed on a heads day is higher because more emails are sent on those days.
Hence, it makes sense for each friend to consider the probability of being emailed based on the number of emails sent. Since there are more emails sent on heads days, the base rate probability of being an emailed friend on a heads day is higher.
2. In this context, the friends are trying to guess the specific outcome of a coin flip that affected them directly. SIA suggests they are more likely to be one of the friends emailed on a heads day simply because more people are emailed on those days.
This is a valid application of SIA in a straightforward probability scenario where the number of observers (email recipients) directly correlates with the coin flip outcome. However, this simplistic scenario doesn’t address the broader philosophical and practical criticisms of SIA.
3. In real-world applications, defining the reference class (the set of all possible observers) is not as straightforward as counting email recipients. In the email scenario, the reference class is clear and well-defined, but in more complex scenarios, it can be highly subjective and arbitrary.
While SIA works neatly in the email example, its application to more complex and abstract philosophical problems (like the nature of the universe or anthropic reasoning) can lead to inconsistencies and paradoxical results, as previously discussed.
4. The simplicity of the email example allows SIA to function without encountering the deeper issues it faces in more complex and abstract contexts. In scenarios involving vast or unknown quantities of potential observers, the reference class problem, subjective interpretation, and potential circular reasoning make SIA less reliable.
I think I agree with you but do not know much about this. I do think, in general, it has some value as a heuristic. There are real-world cases where it works. The music a randomly selected person likes is more likely than not to be popular (in the literal sense) for this reason. Basically, you need extra evidence for thinking you are atypical in a particular way, because, by definition, there are more typical people than any particular type of atypical person. I think it’s also why you shouldn’t think you are the only conscious person while everyone else is a philosophical zombie (acts like a person but has no subjective experiences). However, I also don’t think the SIA can bear the weight B’sB puts on it with his argument.
1. You mention that SIA has some heuristic value, which is an excellent observation. As a heuristic, SIA suggests that we should consider ourselves as typical observers within the context we are analyzing. This means that in the absence of specific evidence to the contrary, it’s reasonable to assume that our experiences and preferences align with the majority. Your example of music preferences illustrates this well—most people’s musical tastes are aligned with popular trends because that's the majority's preference.
2. Indeed, there are real-world cases where SIA seems to apply effectively. For instance, if you were to randomly meet someone and guess their favorite type of music, betting on a popular genre increases your chances of being correct. This is because popular preferences reflect the majority, making it a safer assumption in the absence of specific knowledge about the individual.
3. You correctly note that thinking of oneself as atypical requires additional evidence. This stems from the basic statistical principle that typical cases are more frequent than atypical ones. In other words, by default, it's more likely that an individual falls within the majority unless there is significant evidence to suggest otherwise. This reasoning can be extended to numerous aspects of human behavior and characteristics.
4. Your point about not assuming you are the only conscious person while everyone else is a philosophical zombie is an interesting application of this reasoning. If we assume that consciousness is a typical trait among humans, then it's reasonable to believe that others are conscious as well, rather than the contrary. This aligns with the heuristic that unless there is substantial evidence suggesting that others are not conscious, the default assumption should be that they are.
5. However, you also rightly point out that SIA might not bear the weight placed on it by Bostrom's Simulation Argument (B'sB). Bostrom's argument suggests that if we assume we are typical observers, then it is statistically more likely that we are living in a simulation created by a posthuman civilization. This is because the number of simulated realities could vastly outnumber the one base reality.
Here, SIA's heuristic value may not suffice for such a profound conclusion. The leap from using SIA as a guideline for understanding everyday phenomena to concluding that we are probably living in a simulation requires a more robust foundation. The SIA in this context might oversimplify complex existential and epistemological questions, reducing them to mere statistical likelihoods without adequately addressing the deeper implications and the assumptions involved.
You are correct, the SIA cannot bear the weight BsB puts on it.
Suppose that the message on the wall says: “I, God, tossed a fair coin. If it came up heads, I created one person in a room like this. If it came up tails, I created one person, and a million apples, also in rooms like this.” Since I can't be an apple, my credence should be 50/50 about the coin.
Similarly, suppose that the message on the wall says: “I, God, tossed a fair coin. If it came up heads, I created one person in a room like this who has your DNA. If it came up tails, I created one person who has your DNA, and a million people who have different DNA." Since I can't be a person with different DNA, my credence should be 50/50 about the coin.
Doesn't the SIA rely on the claim that "I could be someone else"? But that's a meaningless statement. I can't be someone else, just like I can't be an apple, or an apple can't be a light bulb.
In the apple case, obviously the extra apples are irrelevant.
In the other case, the extra people who you are not are irrelevant. But this is not because SIA relies on the idea that you could be extra people. The notion relevant to SIA is "people you might currently be." Because there are a variety of people you might currently be, by Elga's reasoning, you should favor the theory on which there are more people you might currently be (if I might be Jon or Jack, then a theory that says there is Jon and Jack is superior because it makes it likelier that there'd be me).
It's not at all weird for there to be multiple people who you currently might be. Suppose that Jon and Jack go into a room and then get amnesia, unable to remember who they are. If I know the setup and I'm in the room, I should be undecided about whether I'm Jon or Jack.
Thanks. I think in general, your argument is mixing metaphysical modality and epistemic modality, but I'm not really sure.
Could I ask if either of the following situations are analogous to "God’s extreme coin toss"?
A: Your receive a letter in the mail saying "I tossed a coin. If it landed heads, I sent you (Bentham's Bulldog) a letter. If it landed tails, I sent you a letter and also sent a letter to 999,999 other people.
B: Your receive a letter in the mail saying "I made a list of 1 million people, and then tossed a coin. If it landed heads, I sent one letter to a random person on the list. If it landed tails, I sent a letter to everyone."
I assume you think B is analogous. If so, does that mean that in the heads scenario, God picked you out of a list of 1m people before you were created?
It's not mixing metaphysical modality and epistemic modality. The relevant bit is epistemic modality, for the argument.
I think those are not analogous. In the first case, I'm guaranteed to get a letter either way, in the second case, conditional on tails, I only have a 1 in a million chance of getting a letter.
In scenario B that I described, you are on the list of 1 million people. Before the coin toss (from the perspective of the letter-writer) if the coin is heads you have a 1 in a million chance of receiving a letter. If the coin is tails you have a 100% chance of getting the letter.
I suppose my point is that I understand the message on the wall to mean "I, God, tossed a fair coin. If it came up heads, I created YOU. If it came up tails, I created YOU and 999,999 other people."
To me, it seems that you understand the message to mean "I, God, tossed a fair coin. If it came up heads, I created one person (randomly selected from a set of 1 million people). If it came up tails, I created the entire set of 1 million people."
Sorry, typo, I meant conditional on heads you have a 1 in a million chance of getting the letter.
You misunderstand God's coin toss. It's about creating 1 person vs a million. There's then a question about how to reason about your existence if various different numbers of people were created. If you apply the Elga reasoning, and think that you're equally likely to be any of the million people created on tails as the one created on heads, if heads just creates one person, the odds of your existence is 1 in 1 million.
Here's an analogy: imagine that every person is in a room assigned a natural number. A coin is flipped. IF it comes up heads, every room gets a letter. If it comes up tails, just one room gets a letter. Upon getting a letter, I get huge evidence for heads. However, if tails entailed (pun intended) that my room in particular would get a letter, then I wouldn't get an update either way (of course, that theory would have a vanishingly low prior--what are the odds I'd be picked out out of the infinite people that could be).
I'm just not sure the propositions "I could exist" or "I could have not existed" have any meaning when interpreted as propositions involving epistemic modality. The proposition pertains to evidence which "I" hold, so my existence is "necessary" for the proposition to be meaningful. The "I" in the proposition must exist for there to be some evidence. So if the proposition refers to my existence as "possible", "probable", "contingent", etc. then it seems to be inconsistent with there being a necessary "I".
Anyway, we can leave it there. That's just my initial thoughts, and I'll have to think it through some more.
“You’re DNA” could mean the DNA of anyone. And this leaves SIA intact. If it had a particular genome sequence specified (not the words “your DNA”), and upon sequencing your genome you found that you matched, yes the odds would be only 50/50.
I think this argument is way stronger than almost any other argument for theism I have heard, even from professional philosophers (though who knows, maybe once I've thought about it more, I'll start thinking it's weak). But I still think it has some serious flaws.
First of all, even if there is a huge class of possible people, I known from my own subjective experience that the vast majority of them can't be me. Even if there is a possible mind that believes every possible truth, I already know that I am not one of those minds that believe infinitary truths, so SIA does not favor a world where those kinds of minds exist. SIA provides exactly zero evidence for a world where unsetly-many minds exist, one that believes every possible truth, over a world where only countably many minds exist who all believe finitary truths.
(This is similar to the SIA version of the doomsday argument. If I don't know my birth rank, then SIA says I should believe with a very high probability that a large number of humans will exist. But if I know my birth rank, SIA no longer gives me any evidence for the existence of a large number of future humans, it just cancels out the SSA argument that there will be fewer of them. Likewise, if I really could of been any of those possible minds, SIA would give me evidence that there are a lot of possible minds, but if I know that I'm one of a countable class of possible minds, SIA doesn't favor the hypothesis that Beth 2 minds exist over a hypothesis that says every possible mind from that countable class exists.)
Second, I'm not actually convinced that there are Beth-2 possible people. Not every "arrangement of stuff" is a person, and even for the arrangements of stuff that are people, personal identity is more coarse-grained then exact identity of physical arrangement (infinitely more coarse-grained, in fact). Any difference in the arrangement of stuff constituting a person that doesn't make a difference to that person's subjective experience doesn't make them a different person. And no, this doesn't mean I have to believe in a soul- that would be like saying that I must believe that computers have souls because there are only countably many possible computations even though there are Beth-2 possible arrangements of matter that could constitute a computer. (I think the soul argument is the worst argument made in this piece, on par with the really bad theistic arguments.)
I'm also not sure that for any truth, there's a possible mind that believes it. I can't even conceive of a mind that would be able to think about conjunctions of uncountably many statements. Maybe you can get me to believe that at least Beth 1 minds exist based on countable conjunctions, but anything higher than that just doesn't seem supported.
Third, RSIA does not favor necessitarianism. Say you have a pre-anthropic probability of 1% for necessitarianism. Necessitarianism, however, doesn't predict (pre-anthropically) that *you* are metaphysically necessary. It predicts that, whatever minds exist, they are necessary. Whatever your pre-anthropic prior probability that you exist is (based on SIA, it should be zero or some infinitesimal), you should have approximately the same pre-anthropic prior on your existence given necessitarianism. Once you learn that you exist, of course, you will use this anthropic evidence to update to a 100% chance that you are metaphysically necessary, given necessitarianism. But you can't then use this updated probability to update necessitarianism to be more likely - that would be double-counting the anthropic evidence.
(Basically, my pre-anthropic prior probability that necessitarianism is true would be split between all possible states of affairs that might be metaphysically necessary. Most of those states of affairs do not involve me existing, so necessitarianism does not imply that my existence would be likely.)
Fourth, any probability distribution you have on the number of possible people, or the pre-anthropic number of actual people, has to be 0 for all but countably many different cardinalities. It's not clear, then, that you can always use SIA to make hypotheses on which larger cardinalities exist infinitely more likely than any other hypothesis.
Fifth, I just don't see any strong reason why a large cardinality of people, if possible, couldn't exist on atheism. Sure, it would be less likely than on theism, but would it really be overwhelmingly less likely?
Sixth, the same inductive problems you pointed out for modal realism and Tegmark's multiverse would also apply to theism with Beth 2 people. If God creates every possible person, or even just a collection of people with the same cardinality as the set of all possible people, then the vast majority of them (100% of them, in fact) will not have anything we would describe as a coherent experience. There are only countably many experiences we could possibly have in a world where induction works.
There are possible minds whose thoughts are filled only with states of pain, but why would an infinitely good god create them? Shouldn't you believe in an evil god?
The argument doesn't need the idea God would make every possible person but just the idea that the number of people God would make would be very great. I also think that while there is a possible state one could be in where they'd be in pain, God would simply create that person not in pain.
Evil God would create more all possible people - both happy and unhappy. God can only create happy ones. It makes likelihood P(Evil God | all possible people exist) much more likely than P(Good God | all possible people exist). And whatever story explains Evil God creating happy people just lowers prior P(Evil God), even if it lowers proportionally to likelihood it's obvious we should favor likelihoods over priors.
If you think minds are classified by truths they think about, then there are minds whose thoughts are filled by truths of this type - "If I was subjected to M amount torture right now, I would experience N units of pain". I don't see how god can make these minds happy while preserving these thoughts.
>What, why would an evil God make happy people?
Maybe Evil God can't choose and can only create all possible people, it just lowers its prior probability.
This makes much more sense than that there is an all-benevolent god. That a being of maximal goodness is maximally simple is not true in any relevant sense I can think of, and even if it were, this is irrelevant. A priori, why would simple things be more likely to exist than complex ones? This is a groundless assumption.
Why do you think you’re not on an elaborate Truman show? There’s no relevant empirical evidence either way. The reason you think it’s less likely that you’re on an elaborate Truman show is because it’s less simple. You need to use non-empirical reasoning, and simplicity is a virtue for theories.
I’m agnostic as to whether or not I’m on a Truman Show. But I don’t hold my breath waiting for a crack in the sky because Truman Show is just one of countless logically possible explanations for all observed phenomena. I don’t play favorites with theories a priori and discount ones that have more moving parts. Hence, this explanation is as good as any other that fully fits the facts.* However, there are so many logically consistent, mutually exclusive such theories, that any one in particular has vanishingly low a priori probability of being correct.
One might mistakenly think otherwise because of Ockham’s Razor. The only relevant sense in which Ockham’s Razor is true is that theories that make more ambitious claims are less likely to be true on probabilistic grounds. For instance, if Theory A is that there is an ever-existing being that is all-powerful AND all-benevolent, and Theory B is that there exists an ever-existing being that is all-powerful but it’s level of benevolence is unspecified (that is, Theory B is agnostic as to this being’s level of benevolence; it may be maximally benevolent, minimally benevolent, or anything in between), then Theory A is necessarily less probable than Theory B.
*I actually don’t think this theory (Truman Show) predicts observed phenomena as well as metaphysical naturalism does, but let’s just suppose it does for the sake of argument. Here’s why I don’t think Truman Show is a good theory by the way:
Premise: There are no tell-tale signs that we are in a Truman Show reality.
Premise: The probabilty of having no tell-tale signs if we are actually in a Truman Show situation is greater than zero. (We cannot just assume that all logically possible Truman Show creating hypothetical entities would be perfect at hiding their tracks.)
Premise: Under metaphysical naturalism, the probability of having no tell-tale signs is zero.
Conclusion: Metaphysical Naturalism is more probably correct than a Truman Show situation.
I don't follow your reasoning in Premise (2): you don't need to assume that all logically possible Truman Show entities are perfect. Truman Show can equally predict the empirical evidence, if we can conceive of at least *one* logically (metaphysically) possible Truman-Show-creating entity that is perfect at hiding its tracks. As long as such a Truman Show entity is possible, call her X, the empirical evidence has equal probability on Truman-Show-X and ~Truman-Show-X.
I also don't follow your reasoning about Ockham's Razor. You claim that it "is true is that theories that make more ambitious claims are less likely to be true." But you also claim that "simple things be[ing] more likely to exist than complex ones" is "groundless" and that you "don't play favorites with theories a priori and discount ones that have more moving parts," and it would be a "mistake" to appeal to Ockham when evaluating theories *a priori*. But your explanation of why Ockham has force seemed reasonable to me! So which is it? I think you have a few options:
(1) There is no rational way to evaluate theories a priori, and Ockham can only be applied to a posteriori evidence. So we should be agnostic across all theories (skeptical or realist) that predict our experience with equal probability.
(2) Ockham does apply a priori. But an all-benevolent God is less simple than other theories that predict the evidence, so it is less likely to be true.
(3) Ockham does apply a priori, but there's a special way that "simplicity" is not the same as "ambition." Maybe "simplicity" is not well-defined. So an all-benevolent God might be simple, or not simple, but what matters is that it is more "ambitious" than other theories that predict the evidence, so it is less likely to be true.
In response to: “I don't follow your reasoning in Premise (2): you don't need to assume that all logically possible Truman Show entities are perfect. Truman Show can equally predict the empirical evidence, if we can conceive of at least *one* logically (metaphysically) possible Truman-Show-creating entity that is perfect at hiding its tracks. As long as such a Truman Show entity is possible, call her X, the empirical evidence has equal probability on Truman-Show-X and ~Truman-Show-X.”
Let me lay out my reasoning more clearly. A Truman Show scenario (as I meant it) is one where there are entities who have set up our universe, or some (most?) aspects of it so that they can watch us live our lives for their entertainment. Additionally, they attempt to deceive us into thinking they are not there and that our everyday lives are unfolding according to some natural course of events (i.e. not being manipulated by them). It is stacking the deck to assume they will be successful in all possible states of the universe qualifying as Truman Shows that populate the a priori probability space. (I understand now from reading more of your comments that you meant the Truman Show to mean a successful skeptical theory in the sense that, by definition, the deceiving entities succeed entirely in deceiving us. By the way, do you stipulate as part of the Truman Show theory that they will always be successful at deceiving us?) Let me define P(T) as the a priori probability that a Truman Show scenario of some kind is unfolding.
Now, by Metaphysical Naturalism I mean a state of affairs where all that exists are the things we’ve discovered to exist from direct observation and indirect-observation-plus-reasoning (science, roughly) plus possibly other things we have not discovered yet but that will be similar (enough) in nature to the things we have discovered so far. New types of particles are fine. New biological species are fine. New sorts of invisible but study-able and observable-with-instruments “waves” (like electro-magnetic waves but not yet discovered) are fine, too. Aliens are fine, too (if they aren’t magical–magical meaning “no mechanisms to do things that all human experience shows can’t be done without mechanisms to accomplish them”), but just to to make the comparison, I won’t allow super-technologically-advanced aliens who are perpetrating a Truman Show stunt on us. Let P(M) mean “the a priori probability that Metaphysical Naturalism” is true.
The tricky part is here. I speculate that P(T) = P(M). Why? I don’t really have a reason. I don’t even really know how to start assigning prior probabilities to such things so the only reasonable thing to do (it seems to me) is to assume P(T) = P(M). At this point, let’s introduce a bit of evidence: There have been no tell-tale signs of a Truman Show scenario unfolding. This is exactly what I expect under Metaphysical Naturalism. However, under Truman, at least sometimes, the deceiving entities are not successful (like in the actual Truman Show). So this evidence increases our credence in Metaphysical Naturalism and decreases our credence in the Truman Show theory. The posterior probability of Metaphysical Naturalism is greater than the posterior probability of Truman Show.
Was I right to assume P(T) = P(M)? I’m not really sure, but that’s kind of exactly why I did it. I can’t think of any good a priori arguments to favor one over the other so I set them equal. I’m not really satisfied with this though, so I’m open to ideas for how to better assign a priori probabilities. BUT I WILL NEVER ACCEPT SIMPLICITY AS A SIGN OF LIKELIHOOD TO OBTAIN! No, I’m kidding. I don’t think it works, but I’m not certain. I’ll explain more in further comments to your other question.
No, the reason you don't consider the hypothesis is because philosophical thinking isn't part of ordinary day to day living. The majority of what you do in any day is unratiocinated, trained behavior to a variety of stimuluses that exist in modern society.
>The reason you think it’s less likely that you’re on an elaborate Truman show is because it’s less simple.
...conditional on other evidence you've collected throughout your life that you falsly think applies in this case because you're underspecifying the skeptical scenario. There is no a priori reason to prefer being on the Truman show vs external world realism because both of these are stipulated to explain your experiences exactly. And it's not clear to me that there is any sort of agreed upon definition of a priori simplicity that could be used as a reliable measure to decide between the likelihood of various skeptical scenarios obtaining.
>There is no a priori reason to prefer being on the Truman show vs external world realism because both of these are stipulated to explain your experiences exactly.
I think you meant "there is no *a posteriori* reason to prefer...because both explain your experiences." Agreed. But my point was there does exist an *a priori* reason: simplicity (or something like that).
You can correct me if I'm misrepresenting you, but are you just biting the bullet here? You place equal credence on Truman show and external world realism?
There is no bullet to bite. If there were different consequences that hinged on whether one believed in external world realism vs being on the Truman show, then the skeptical scenario setup would have failed because the point of skeptical scenarios is to set up identical cases where the explanatory substrate varies. By stipulation you are ruling out any practical consequences to believing in either explanation, so there is no bullet to bite for either party ex hypothesi.
>But my point was there does exist an *a priori* reason: simplicity.
I don't think there's any metaphysical gap that simpler theories bridge versus less simple ones, and I also don't understand what you mean by a priori simplicity. It seems to me like simplicity is a human value that's subject to all sorts of contextual factors. If it's easier for people to work with simpler theories, then there will be an asymmetry between the Truman show and external world realism, in which case the skeptical scenario fails because there is a practical difference between the two - one of them is easier to work with than the other.
Furthermore, it seems to me that the Truman show posits just the Truman show whereas external world realism posits the Truman show plus everything else in the external world. What fact would I be getting wrong if I decided that the Truman show posits fewer variables and thus it's the simpler and truer hypothesis? Or why couldn't I invoke BB's conception of God as "absolutely simple perfection" to explain all my perceptions? Seems to me like that's simpler than both the Truman show and external world realism. And remember you can't appeal to any practical difference because you're stipulating those are equivalent between the theories.
Just to clarify, Truman show posits the Truman show + the creators + the viewers + the world the creators and viewers inhabit. But this is not really important. Consider:
(1) It is rational to assign low credence to being on the Truman show
(2) As we have agreed, (1) cannot depend on any empirical (a posteriori) evidence. So (1) must be a result of a priori reasoning.
(3) If simplicity is a virtue, then we have an a priori reason to support (1).
(4) Simplicity is a virtue.
One way to attack (4) is to posit some *other* a priori reason for (1). Another way to attack (4) is to deny (1): the intuition that it is rational to believe your are not in a skeptical scenario is confused. Since (forgive me if I'm wrong) you think that a priori reasoning is impermissible, (2) requires you to deny (1).
However, since (1) is prima facie extremely plausible to most people, I would characterize its denial as biting the bullet. It would be very weird if the rational position would be to be totally agnostic across realism and skeptical scenarios.
Already mentioned this to you in a DM, but thought I'd leave a comment here as well for posterity's sake. What do you think of the simple response that SIA entails the Tegmark mathematical universe hypothesis (MUH), and that SIA should therefore be revised, because MUH would undermine induction? Since MUH entails more than beth-2 observers (it entails all the observers modal realism does, plus various other kind of non-spatiotemporal or non-physical observers that are mathematically possible) then MUH is preferable to theism, since theism only entails beth-2 observers. So SIA would predict MUH over God. But MUH entails inductive failure, so logically SIA must be revised in cases of infinities; we shouldn't update our credences when based on reasoning about the infinite.
Now normally, as you yourself pointed out, we might reject theories which lead to inductive failure on the grounds that they are self-defeating. So for example, we might reject the multiverse hypothesis because it leads to too many Boltzmann brains, but if we are Boltzmann brains then we have no grounds to rely on our evidence that makes us think the multiverse is real in the first place. The problem with SIA reasoning though is that we don't rely on evidence of that kind to conclude that MUH is true. All we need to conclude that MUH is most probably true is the evidence of our existence, which we can get even if we lived in a world where induction was false, and where we have no basis for the future being like the past. If this is true, then we should abandon SIA or revise it in the case of infinities, since inductive failure would seem to be unacceptable. But if we have to revise SIA in cases of infinities, then it's not clear that the theism hypothesis is warranted.
I updated the argument from the DM to be about MUH (which entails more than beth-2 observers), so I think you will need a new response. :)
Anyways the idea is that we can't discard MUH just because of inductive failure, since the regular argument against inductive failure (it's self-defeating) doesn't apply here when we reason based on SIA.
Is this argument susceptible to the evil god challenge? It seems like evil god has equally strong reason to create as many people as possible as the traditional conception of god would. It naively seems to me that if this argument goes through, it’s equally good evidence for evil god?
This arguments relies on several premises and, as far as I can tell, basically all of them are wrong. At every reasoning step there is some crucial flaw. Even if we, for the sake of argument, assume that SIA is generally correct, then there are still all the other problems.
> Would God create all people?
> But even if you’re this confident, because the odds—as we’ll see—of your existence conditional on naturalism are so astronomically low—very near zero—even a 1% chance that God would create beings like us is enough for your existence to massively favor naturalism.
You probably meant "massively favor theism" instead of "massively favor naturalism" here.
You assume that 99% that God would not create us is overconfident on priors, but as a matter of fact, there is no lower boundary on probability that God would create any person. Under naturalism there at least some lower boundary - the one you calculate while assuming that all the fine-tuned constants of the universe just happened at random - even the stupidest naturalistic explanation provides at least some probability of our existence. But if we assume that some kind of God exists, without specifics - that would be a random sample from infinity, the chance that it just so happens that we got a God who would create us is literally zero. You keep equating the existence of God with the existence of a specific type of God who creates all possible life, for no particular reason, but this is an extra infinitely improbable assumption.
> I claim that thinking about SIA should make you into a theist, providing massively strong evidence for the existence of God. If God wouldn’t create you, then theism is already false, so this wouldn’t undermine the force of the argument—rather, it would just be a separate argument.
The reason why SIA provides an argument for theism is based on the assumption that existence of all possible people is more likely if God exists, than otherwise. If it's not the case, then SIA doesn't favor theism anymore. God who creates only one universe with only planet Earth filled with life is compatible with the observations, but not privileged by SIA in any way. On its own SIA is not in favor of theistic explanation of infinite people more than atheistic explanation of infinite people.
> Can atheism explain the anthropic data?
> Of all the theories ever proposed by atheists, there are, to the best of my knowledge, only two that naturally predict the existence of every possible person. They are modal realism, according to which every possible world exists, and Tegmark’s view according to which every possible mathematical structure is physically instantiated.
> The problem—and this is a more general problem for atheistic views—is that both of these views undermine induction.
This would be a problem for atheistic view only if we knew for a fact that induction is justified, which we do not know. Surely, we would like it to be true, but this is a completely separate question. From the perspective of SIA both atheistic and theistic explanation of infinite people are equal, and the appeal to our desire of induction to be justified is a different argument for the existence of God that has nothing to do with anthropics. But lets look at it anyway, does God help with induction?
> If there’s a God, our inductive processes are reliable—God would make sure there are stable laws and that everyone’s reasoning is mostly reliable over the course of their lives when they’re in a situation like ours.
Once again, you are simply assuming a specific type of God that would care about this kind of things, which is but a one possible type of God from infinity. What's more, such God would be penalized under SIA, as he would not create people with non-reliable reasoning, therefore creating less people, than counter-factually.
Also, as a tangent, notice that in our actual world, there are a lot of people with unreliable reasoning and lots of examples of induction not working.
> Other than these two, there’s no viable naturalistic explanation of why at least Beth 2 people would exist.
You can always come up with lazy atheistic model: there is some metaphysical law according to which Beth 2 people exist, which doesn't have any other properties of God - it's an inanimate force not a person. This model actually has an advantage over theism from the perspective of anthropics - we do not need to think about God applying SIA to his own existence - more on that below.
> Maybe there are only aleph null people
> I’ll argue, there are strong grounds for thinking that the number of possible people is not just aleph null or Beth 2 but unsetly many—too big to be a set. The infinites mathematicians talk about are infinite sets—but I think the number of possible people is a collection too large to be a set
If something is not a set than you can't coherently talk about it having cordinality and apply probability theory and therefore your argument is incoherent to begin with.
Now several meta-points. How could one notice problems with this argument even without engaging with it on object level.
First of all, SIA famously breaks down when reasoning about infinity and you are attempting to use it specifically in this case, so it's no surprise that it produces crazy results, which one shouldn't trust, even if they accept SIA for simple cases such as Sleeping Beauty or Doomsday Argument.
Secondly, you are talking about infinitely strong update in favor of theism just based on the fact of ones existence, regardless of any empirical evidence, and whether our minds were made corresponding to the universe by any optimization process. This is an incredible huge red flag and a contradiction of conservation of energy, never mind expected evidence.
//Under naturalism there at least some lower boundary - the one you calculate while assuming that all the fine-tuned constants of the universe just happened at random - even the stupidest naturalistic explanation provides at least some probability of our existence. But if we assume that some kind of God exists, without specifics - that would be a random sample from infinity, the chance that it just so happens that we got a God who would create us is literally zero.//
Well, if SIA is right, the odds of your existence on naturalism is either zero or infintesimal. In contrast, if a perfect being would make every possible person, then the creation of you is strongly predicted if a perfect being. Now, maybe your point is just that the odds of a perfect being are super low even if there's a creative being of some sort. I agree that if you start out thinking perfect being theism has a zero prior, this argument shouldn't move you, but you shouldn't do that because it's simple, elegant, and parsimonious.
You act surprised when I talk about God as a perfect being. Well that's what I mean when I say God. When I'm talking about limited beings that aren't perfect, I say gods. This is a terminological point, but it might clear up some confusion.
//This would be a problem for atheistic view only if we knew for a fact that induction is justified, which we do not know.//
I think we do know it. You shouldn't believe things that are crazy, and the idea that we have no basis for thinking the sun will rise tomorrow is crazy. Also, if induction doesn't work, it would probably have given out in the past--probably the laws of nature wouldn't have worked till this point.
//Once again, you are simply assuming a specific type of God that would care about this kind of things, which is but a one possible type of God from infinity.//
Well this one is simpler and more parsimonious. If you posit a god with random arbitrary desires, that's ad hoc and not simple or elegant.
//Also, as a tangent, notice that in our actual world, there are a lot of people with unreliable reasoning and lots of examples of induction not working.//
My claim is that everyone, on theism, who has mental states like mine currently will find they mostly work over the course of their life, counting what will happen in the next life. I also give a bunch of other reasons in the article why theism plus infinite people doesn't undermine induction.
//You can always come up with lazy atheistic model: there is some metaphysical law according to which Beth 2 people exist, which doesn't have any other properties of God - it's an inanimate force not a person. This model actually has an advantage over theism from the perspective of anthropics - we do not need to think about God applying SIA to his own existence - more on that below.//
Positing that there are just Beth 2 universes for no reason is not at all simple. You shouldn't posit an infinite number of things exist for no reason! Also, as I explain, this undermines induction.
//First of all, SIA famously breaks down when reasoning about infinity and you are attempting to use it specifically in this case, so it's no surprise that it produces crazy results, which one shouldn't trust, even if they accept SIA for simple cases such as Sleeping Beauty or Doomsday Argument.//
There are some cases where it's unclear how to apply SIA to infinites. But there are other much more obvious cases. This is one of them--SIA is only unclear when comparing infinites of the same cardinality, which we're not doing here.
//Secondly, you are talking about infinitely strong update in favor of theism just based on the fact of ones existence, regardless of any empirical evidence, and whether our minds were made corresponding to the universe by any optimization process. This is an incredible huge red flag and a contradiction of conservation of energy, never mind expected evidence.//
It doesn't violate expected evidence for reasons I've explained to you before. It takes your existence as evidence favoring theories where there are more people--no credence rises in expectation. God can violate conservation of energy in creating a multiverse, obviously, because he's omnipotent.
//Thirdly, the argument proves too much. Not just the existence of God, but infinite chain of more and more powerful Gods, where every n-th God creates all the possible n-1-th Gods. Just think about how God himself is supposed to reason under SIA.//
God has no uncertainty or need to reason because he's omniscient--directly aware of every fact. There needn't be an infinite chain of Gods--just one God who creates all possible people, which is what the arguments says there is.
Happy to chat about this over video call as we discussed doing at some point, I feel like we never get anywhere with our long text back and forths, and they get a bit tedious, sorry.
As for induction, sadly, we already had to abolish it in order to pass the first question anyway, so God involving theories do not have any advantage over non-God-involving ones. Also, as an induction related tangent:
> I think we do know it. You shouldn't believe things that are crazy, and the idea that we have no basis for thinking the sun will rise tomorrow is crazy.
Suppose I just told you that every reasoning step in your post is crazy and refused to ellaborate further. Would you consider it to be more substantial critique? Would you agree with someone who simply claims that we justifiably know that omnibenevalent god does not exist because it would be crazy otherwise? I don't think so. When you talk about anthropics and people simply dismiss it as some crazy nonsense, I think you are rightfully offended that they do not engage with the substance of your arguments. The appeal to craziness is just an appeal to intuition and intuitions may and often are wrong. If you have no justification for why something appears crazy to you it doesn't mean that you "just know it", it means that your intuition is baseless or you still didn't find the actual sourse for it. Don't get me wrong, common sense is a decent heuristic, especially when well callibrated. But you won't be able to grow as a philosopher without challenging it.
> Also, if induction doesn't work, it would probably have given out in the past--probably the laws of nature wouldn't have worked till this point.
Nope! That's inductive reasoning, and it wouldn't be valid in a world where induction doesn't work.
> My claim is that everyone, on theism, who has mental states like mine currently will find they mostly work over the course of their life, counting what will happen in the next life.
Have you just a priori proved that insanity is impossible under theism, therefore disproving theism? Or at least that it's impossible for *you in particular* to go insane, no matter what?
Okay, back to the track. If, despite everything, we, for the sake of argument, assume that indeed Omnibenevalent God is the simplest cause for the existence of all possible people, we still have to answer the last question: "Is the probability of Omnibenevalent God highter than comulative probability of other causes for the existence of all possible people?" His assumed simplicity may give him a boost in probability but it may be just having probability of several percents, while other alternatives have probability of tenth parts of a persent individually and yet together they absolutely truimpth over the Omnibenevalent God hypothesis.
So there is that, Three questions, without confidently answering "yes" to all of them your argument doesn't work.
> It doesn't violate expected evidence for reasons I've explained to you before. It takes your existence as evidence favoring theories where there are more people--no credence rises in expectation.
As another tangent, I may have a good example which can bring our disagreement about conservation of expected evidence closer to solution.
A coin is tossed. On Heads a red ball is placed in the room. On Tails a red and a blue ball are placed in the room. You come into the room, and immediately see a red ball. What is your confidence supposed to be that the coin came Heads?
> God can violate conservation of energy in creating a multiverse, obviously, because he's omnipotent.
That's an interesting question, actually. Being omnipotent can be perceived as having infinite energy to spare, therefore by creating stuff, he doesn't violate conservation of energy, so technically he can't violate it, unless he can make himself not omnipotent anymore and then still create stuff out of nothing.
But this is besides the point. Our brains can not violate conservation of energy. And it's our brains which make the inference from our existence to the existence of God - which would be a violation were it a reliable way to produce truth.
> SIA is only unclear when comparing infinites of the same cardinality, which we're not doing here.
Oh but we do! See the point about people who experience eternal torture and eternal bliss after leading regular lives like ours.
> God has no uncertainty or need to reason because he's omniscient--directly aware of every fact.
But surely, he can still reason right? If some way of reasoning systematically produces correct results, omnicient God should be able to arrive to the correct results using this method of reasoning - even though he doesn't really need it as he already knows the answers.
For example, God knows that 358794/3=119598. He still can apply long division to arrive to this result. It's not that long division suddenly breaks apart when God tries to use it.
And if SIA is true, that is, inference from ones existence to the existence of uncountable infinities of other creatures like you is correct, then God applying this method to his own existence would infer the existence of an infinity of other creators like him, and it has to be true inference. Of course, being omniscient while SIA is true, God would already know that infinite Gods like him exist - this is the only self-consistent possibility. Therefore from SIA we can deduce the existence of infinite Gods and infinite super-Gods who created the infinity of Gods and so on and so forth.
We can declare that SIA isn't applicable to God-like beings, but it will make the theory much less elegant as we will have to add an explicit exclusion case and on priors regular SIA should be assumed more probable.
> Well, if SIA is right, the odds of your existence on naturalism is either zero or infintesimal.
What exactly do you mean by naturalism here? Surely, there are possible explanations why infinite people exists without invoking a sentient creator and specifically Omnibenevelent one.
> Well that's what I mean when I say God.
I see a huge leap from "there is some reason why infinite people exist" to "there is this specific type of creator who created all of them". I feel that this jump to conclusion may be hidden behind the term "God" which can mean both specifically perfectly good creator and any type of extremely powerful demiurg. Anyway, with this out of our way lets look at three questions, all of which has to be answered "yes", so that implication from SIA to perfectly good God would work.
First question is "Would omnibenevalent God cretate all possible people". You present some case for it, but also later you claim that he would not create people for whom induction doesn't work. This is a huge problem because a set of people for whom induction doe not work seems to be a superset of people for whom it works reliably. Or at least we can be reasonably certain that omnibenevalent God would not create people who have regular lives like ours and then constantly experience eternal torture but the amount of such people is comparable to the amount of people who have regular lives and then experience eternal bliss. There is also an interesting in its own question whether living lives like ours and then experiencing eternal bliss/torture would be in defiance of induction or not and trying to correctly formalize what it even means that induction works/doesn't work. Anyway, it seems that God creates only some amount of possible people and therefore SIA doesn't imply it.
I really don't see a way out of this conundrum. Either we bite the bullet of not creating some considerable amount of people and the argument from SIA crumbles or we bite the bullet of creating literally every possible person, then there is no justification for induction and it's not even clear in what sense God in question is omnibenevalent.
Let's for the sake of argument bite the latter bullet. Second question is whether perfectly good God is the most likely creator of all possible people. You write:
> Well this one is simpler and more parsimonious. If you posit a god with random arbitrary desires, that's ad hoc and not simple or elegant.
Here you make an appeal to intuition that perfection is simple based on the fact that many human languages have one simple world for the concept. This is, of course, completely unpersuasive for anyone who understands up-to-date formalizations of complexity and reasons why we ended up embrasing them instead of appeals to natural language. But beyond that. How is perfection simple if we do not even understand what it entails? We can apply adjective "perfect" to opposite meaning nouns, like perfectly big and perfectly small. What size then is someone who is just "perfect"? Is perfection even a thing in itself? Does it have meaning without an additional noun? And so on and so forth. You need to properly formalize what is meant by "perfection" so that we can see that implications from it actually work instead of constantly redefining the term ad hoc. And, of course, there are many other, much simpler words is natural languages. Like "Red". Why not assume that the creator is someone whose essense is redness? You call such gods jerrymandered, but it's not clear by which principle you apply such description to them and not the perfectly good God, beyong basic wishful thinking. For me none of them appear parsimoniousin the slightest - you postulate infinities - the opposite thing to being parsimonious.
And of course there are explanations for the existence of all possible people that do not include sentient creators at all. To this you reply:
> Positing that there are just Beth 2 universes for no reason is not at all simple. You shouldn't posit an infinite number of things exist for no reason! Also, as I explain, this undermines induction.
But we are not just positing that there are Beth 2 universes for no reason! We claim that there is a reason - a methaphysical law according to which there has to exist every possible person. Surely, if you can just accept the existence of God as not needing any additional reason you can do the same courtesy to the existence of this metaphysical law? In a way it's simpler than any god - it doesn't require any sentience or will or other properties. It just does one thing.
100% this: “You assume that 99% that God would not create us is overconfident on priors, but as a matter of fact, there is no lower boundary on probability that God would create any person. Under naturalism there at least some lower boundary - the one you calculate while assuming that all the fine-tuned constants of the universe just happened at random - even the stupidest naturalistic explanation provides at least some probability of our existence. But if we assume that some kind of God exists, without specifics - that would be a random sample from infinity, the chance that it just so happens that we got a God who would create us is literally zero. You keep equating the existence of God with the existence of a specific type of God who creates all possible life, for no particular reason, but this is an extra infinitely improbable assumption.”
I had exactly this thought when reading a different Bentham’s Bulldog article. Basically, when he was explaining why fine-tuning was unlikely on naturalism, it occurred to me that exactly the same reasoning implies that a god that wants fine tuning is implausible. Here’s Bentham’s Bulldog followed by my slight rewording to employ the argument against a god that fine tunes:
Bentham’s Bulldog:
“To determine subjective chances, you should imagine a rational agent assigning probabilities to the possible outcomes before they know the actual outcomes. In the case of fine-tuning, for instance, a person who didn’t yet know what values the laws fell into would think there was a super small chance it would fall in the finely-tuned range because it could fall in any range. Because there are at least 10^120 values of the cosmological constant alone, and nothing special, conditional on naturalism, about the finely-tuned one that it happens to be, the odds of fine-tuning by chance of just the cosmological constant are 1/10^120.”
Bentham’s Bulldog’s argument slightly tweaked to argue against Theism:
“To determine subjective chances, you should imagine a rational agent assigning probabilities to the possible outcomes before they know the actual outcomes. In the case of a god that wants to finely tune physical constants to allow a universe exactly like ours to existence, for instance, a person who didn’t yet know what kind of god existed (or even if there was a god) would think there was a super small chance there would be a god with exactly that preference and the ability to produce such an outcome because this hypothesized being could have preferences of any sort whatsoever and also could have any conceivable level of ability and might even not exist at all. Because there are at least 10^120 values of the cosmological constant alone, and nothing special, conditional on “an omnipotent being exists”, about a god wanting to finely tune it to be what we observe it to be, the odds of there being a god with a preference for fine-tuning by chance of just the cosmological constant are 1/10^120.”
No, this is mistake. It violates conservation of expected evidence if you'll be around to observe all outcomes, and only some of them will raise your credence. But it's not violating COE to have you expect your credence to go up in the future. On average, tomorrow my credence will be higher in having not died tonight than it is today.
I’m afraid I don’t understand your response (what’s “conservation of expected evidence”?). But I’ll see if I can figure it out. Thank you for lively discussion!
Oh wait nvm I misread your point. Yeah, it's true that it's unlikely a perfect being would make exactly our constants, but it's also unlikely on atheism that there'd be exactly our constants. However, theism makes it more likely we'd have our constants, because it removes the most likely constants which would produce nothing of value.
I think most of my criticisms won’t seem to apply from your perspective given your definition of god as a perfect being, which differs from what I had thought you meant by god previously. But first pass, “there is some good and a lot of bad (a fact)” doesn’t follow with much likelihood from “there exists a being of maximal goodness”. Do I have to believe a theodicy for your argument to be sound and valid?
Yes, it makes no sense to make up entities with fantastical powers to “explain” things when there is no good independent evidence that such beings exist in the first place. Seriously, this argument is no better as an explanation than “the universe did it”. That is, it is the lack of an explanation dressed up as one.
It explains things in precisely the same empty way that “élan vital” explained biological evolution. How did god do it? I might ask. You’d have to say you don’t know. How do you know he/she could? Have you seen evidence of his/her ability to do such things? You’d have to say “no”. The truth is you merely stipulate as part of your theory that god has these abilities. But I can just stipulate as part of my atheistic theory of the universe that it would inevitably lead to life too. I know that probably won’t sway you because you believe that the existence of god is likely, a priori. I think that’s a grave mistake, though, and that god’s existence has as low of an a priori probability as the existence of a spaghetti monster in the outer reaches of space (to use Dawkin’s metaphor for a being that is logically possible but whose existence can’t be empirically verified or falsified).
Observation is definitely very important. But how about people in another country that you have never seen video footage of or audio recordings of? You haven’t observed them but do believe in their existence. Isn’t it that their existence “explains” why a lot of other people who are in a position to observe them in some way say they are there?
> size of the collection if there's no cardinality
Isn’t there a pretty compelling argument that this entire section of your argument is backwards. I.E. that the conclusion one should draw from “there is no set of all truths” is not “wow there are so many truths”, but that “all truths” is a meaningless phrase.
You’re doing that thing where you confuse colloquialisms with formal. If you said that in a conversation, I would get what you’re saying, but “truths” in the context of what you’re saying is not a number which you can just plug into a comparator function. Would it not be like saying that 0! >>> anything?
I guess a more productive thing for me to say is this: What’s your answer to the Patrick Grim 1984 note on the failure to apply this “all truths” business to possible worlds. (and the sources cited in that as to why any non-set construction similarly fails)
I don't think I'm confusing anything. The sentence "there are more truths than marbles in my room," is true. It's not just a colloquial shorthand--if it is, I fail to see what thing it expresses other than the plain meaning. What's the alternative to there being all truths? There just being some truths?
I haven't read the Grim piece that carefully--can you elaborate on the point?
I would say the alternative is that you can only ever create a partial set of truths, which you can always expand on by creating its power set, such that there can never be a set of all truths that’s amenable to comparison in the way you want it to be.
Grim’s point is very short. He says that a conception of worlds is that a world represents a set of propositions or a correlate to a set of propositions to which no further propositions can be added without precipitating inconsistency. (Citing Robert Merrihaw Adams in *Theories of Actuality*, and one other person).
We would thus define what “actually” exists as the set of propositions which deliver, which are actually true. Such a world would be the set of all true propositions. However, because we can infinitely power set and paradox a set of all truths, any “actual” world of all truths would leave out come truths and be non-actual. We can thus never produce any actual set of affairs that contains all truths. (Citing “Some neglected problems of omniscience”)
He then goes on to say it’s highly dubious that any alternate construction, like calling all truths a “class” will work. At least not if we want to still be able to do math with it, which I think you need in order to derive and apply Bayes.
Yes, this is correct. You can not use arguments about number of all possible people if "all possible people" isn't even a coherent mathematical concept.
Well, then what it is? What is this "collection" thing you are talking about and how it evades the reasons why a set of all possible people is not possible?
It seems you treat the situation as a semantic game where it turns out you can't use the word "set" anymore so you need to replace it with some other word, for example "collection", and now you are good to go. But this isn't how math works. What name you use is irrelevant, you need to logically pinpoint an entity with its properties, and formally prove that it exists, and that there can be collections of things that can't be sets of, define the concept of cordinality for this new entity and rewrite probability theory so that it could be used with collections, instead of sets. Till then your reasoning is invalid.
I'm sorry if someone already pointed that out, but I think that there's a flaw in that argument: sometimes things are just impossible and no anthropic arguments can change that. While your reasoning implicitly assume that existence of God is not just possible but relatively equiprobable with an atheist world, and that God can in fact create vast infinities of people (and again, not just can but it doesn't incur any significant probability penalties compared to a mere infinite physical universe).
What if none of this is possible? There is not, in fact, a writing on the wall of your room telling you that God flipped a coin to decide between creating Aleph-0 and Beth-2 humans. The physical world exists and can support humans, anything beyond that is speculation that begs the question. **If** God exists and is omnipotent to that ridiculous degree, then all right, you're more likely to find yourself in one of His infinite gardens. Is he though?
I aim to give an argument that dramatically increases the probability of God existing. If you start out extremely, overwhelmingly confident that God doesn't exist then you probably won't be moved but that is not, as you suggest, a flaw in the argument, any more than it would be a flaw in an argument for evolution that, were one to already be certain of creationism, they wouldn't be moved by it.
Sometimes you come to conclude something is possible because you find that it is actual. You might not realize that consciousness can split, but finding that it actually does should rid you of that presupposition. Similarly, if this overwhelmingly raises the probability of God existing, so too should it lower the probability that God is genuinely impossible.
I guess what makes me feel iffy is that you seem to implicitly presuppose weird metaphysics, where there's a meta-universe in which universes with or without God and various infinities of people are not only logically possible but actually exist.
For example, in https://benthams.substack.com/p/all-theories-of-anthropics-are-presumptuous not only it's entirely possible that the "larger" theory has a subtle implication making it logically impossible, but also that both are viable but the smaller universe is simply the one that physically exists.
The sleeping beauty thought experiment also sneaks in a bunch of assumptions: you are told the rules of the game and that the coin is fair and there's a suggestion that the experiment is run multiple times so you can use your frequentist intuitions about why maximizing the expected value makes sense.
But in your argument all this stuff makes much less sense. You can't have God both exist and not-exist. And if God doesn't exist then those uncountable infinities of people don't exist, so you can't find yourself among them. I guess I don't think that you can use anthropic reasoning in a one-shot problem.
I mean one naturalistic theory with big infinities of people is just infinitely many identical copies of our exact universe. Is there any particular reason to think this exists beyond dubious anthropic arguments. No. Is it a simple theory that fits our observations and doesn't break induction. Yes.
Another alternative is to look very closely at the tegmark multiverse.
So there is 1 universe that's just quantum mechanics as usual. And then oodles of universes where random junk appears in front of you. But for every universe where a giraffe spontaneously appears in front of you, there is a corresponding universe where the giraffe appears in a pocket dimension while you continue living as normal.
This gets into subtleties of measure theory. There are ways to say that everything exists, but some things exist more than others.
Imagine randomly generating an infinitely long computer program. The version of physics without magic giraffes appearing is shorter, so is more likely to appear (and will appear more times) in the infinite program.
So if all possible infinite computer programs exist, we can still have some form of induction. Shorter programs have more copies.
Your argument depends a lot on details of set theory you don't seem to understand. Uncountable cardinalities are confusing in ways you don't grapple with.
You have to be very careful to define things in axiomatic set theory before you can talk about their cardinality or whether they constitute a set. You don't do this; you never define "truth", and the way "true statement" is usually defined in mathematics the true statements are a countably infinite set.
The set of all configurations of matter is only beth-2 if you think each real-number-valued point can have a different state. This does not make sense; the universe appears to be discrete at the Planck scale, suggesting only finitely many possible positions that can have a particle, and even if not, the particles cannot be spaced in weird configurations like arbitrary sets of real numbers (which can get really, *really* weird, including unmeasurable sets, the Cantor set, sets that cannot be described by any mathematical statement, etc.). I would say the number of possible minds seems not merely countable to me, but actually finite, just because I can only imagine finitely many possible experiences (for instance, my eyes only have so many "pixels", each observing finitely many colors and intensities since they must be represented by neurons sending finitely many electrons across their channels; my memory is also finite and I will not remember more than a few million years of experience at a time, probably. Put it together and you have finitely many possible experiences.)
There are, by the way, countable models of ZFC set theory: models in which all the usual axioms hold but, viewed from outside the model, there are only countably many sets (and each set is countable). Such models can still prove that a power set is of larger cardinality than the original set -- this statement would be true *when cardinality is measured within the model*, but not when it is viewed from the outside. This should give us pause regarding how to interpret uncountable cardinalities.
A truth is something that's true--something that corresponds to reality. I didn't precisely define it because I'm not writing a mathematics paper but am instead speaking normal English. I agree infinites get really weird, but I think that they won't be weird in ways that threaten the argument. An analogy would be: imagine that there were unsetly many people put to sleep and then some number were woken. SIA thinks that being created is analogous to being woken--more is more likely, and while there might be cases where it's unclear exactly how to make comparisons, everyone getting woken up is infinitely more likely, obviously, than just finite people being woken up.
You'd have to think that on such a picture, it's metaphysically impossible to have reality composed of points--but that would be really weird! There might be only finitely many different possible minds, but on SIA what matters is the number of minds, not the number of distinct minds (as the arguments for it show). The view on which the thing that matters is the number of distinct minds is called compartmentalized conditionalization and it egregiously violates conservation of evidence.
To see this, suppose that I’m considering two hypotheses. Both predict that there are two people in a room. One of them predicts that both of them will, when they look under a table see a red strip of tape, while the other theory predicts that one of the two people will see a red strip and the other a blue strip.
On this view, suppose the people in the room haven’t looked at the strip of tape yet. They should expect their credence in the second hypothesis to go up. If they see a blue strip, then the second hypothesis is confirmed. If they see a red strip then their credence won’t change, because both theories predict someone seeing a red strip. So therefore they should expect their credence to rise.
Also, the argument I give in 2.4 provides a huge problem for compartmenalized conditionalization. It also gives a huge update in favor of modal realism.
The number of minds makes no sense, since I can index minds by anything (eg label each mine by a set). The argument for beth2 minds isn't coherent if we are not counting distinct minds (indeed, what even is there to count?)
By distinct minds I mean distinct life histories and/or observed universes. Your conservation of evidence isn't relevant.
By truth you say you mean "something that is true", but logicians worked very hard to formalize the subtleties and came up with a theory that has countably many truths. You are not writing a math paper because it cannot be written: your definition of truth is not a coherent concept.
Finally, no matter how you slice it none of it implies God: it could be a law of the universe that all minds exist, to the extent that's a coherent statement (which it doesn't seem to be). "God exists" and "all minds exist" seem equally unexplained.
What are you talking about? You can have two minds that are physically identical but are different--for example, if a copy of my brain were 10 galaxies over, it would be physically the same while being somewhere else.
Asserting that "Your conservation of evidence isn't relevant," does not, in fact, show that my argument showing it violates conservation of evidence is wrong! If there are Beth 2 possible distinct universes, then there are at least Beth 2 possible brains--because Beth 2 of the universes have brains--and more if universes are duplicable.
Logicians have worked hard to come up with a theory that has countably many truths? What? I'm not aware of any logician who has done this because it's flatly absurd. For every real number N, it's true that it's between N+1 and N-1, so there are at least Beth 1 truths (and more because every subset of a truth is a truth). My definition of truth is the standard one agreed upon by most philosophers--correspondence to reality https://survey2020.philpeople.org/survey/results/4926, though, of course, it's amenable to any of the standard theories of truth.
Finally, you suggest that it could just be a brute law that all possible minds exist. Sure it's possible, but possible doesn't equal probable. In order not to undermine induction, one must think that most minds are in inductive worlds so it can't be that simply every possible experience is had infinite times over (for most of them are non-inductive). That theory is also less parsimonious because it posits an infinite number of things with no explanation, rather than just one God.
We all will have to invoke some unexplained things. An atheist will have to think that whatever is fundamental--laws, perhaps, or initial conditions--don't have a cause. God not having a cause is on similar ground--perhaps more viable, in fact, because God might be necessary. Additionally, unlike the every minds exists view, theism is independently motivated because it explains a lot about the world and is parsimonious rather than being a joke theory that no one had ever thought of prior to hearing this argument.
You claim that I'm ignorant of set theory and then proceed to get everything wrong!
In mathematics, a statement is a finite string. The statement "every real number n is between n-1 and n+1" is one true statement. There are, additionally, infinitely many statements of the form "3.5 is between 2.5 and 4.5", "pi is between pi-1 and pi+1", etc.
However, there are only countably many such statements, because all but countably many real numbers cannot be named, so cannot appear in a statement. There's subtlety here that you're ignoring. "Real numbers" are less real than you think; basic questions about them, like whether certain sets of them exist, cannot be determined within ZFC. Experts in set theory routinely say things like "there are many possible set theories, some with more sets than others, with no way to choose between them".
Just saying "correspondence to reality" doesn't save you because real numbers aren't real -- you've never seen most of them, they cannot be named even in principle.
There are countably many true statements in any formal system. If you're going to appeal to mathematical concepts you should get them right.
You assert that real numbers aren't real because I've never seen them. Well, this is a wildly contentious view in philosophy of math that I reject--I'm a platonist--and, in fact, there are some things that exist that I haven't seen. Whether some version of set theory is right will depend on questions in the philosophy of math.
But anyways, even if numbers don't really exist, there might still be true statements about them. Nominalists about math still generally think that it's true that, say, 32.438957238493278932 is less than 35--perhaps they're fictionalists, for instance, and think it's only true within the fiction.
You're just assuming without argument that any truth must be expressable in finite characters. But that's obviously false!
"You're just assuming without argument that any truth must be expressable in finite characters. But that's obviously false!"
Oh yeah? Give me one example of a truth not expressible in finite characters :P
If you're a platonist who believes the reals are real, can you tell me whether there's a platonically correct answer to the continuum hypothesis? It's just a question about the existence of a set of reals. I assume you think it's either true or false? Not clear that mathematicians agree with you.
You posit the universe is made of real numbers, a true continuum, but making the continuum real really does bring up questions like the continuum hypothesis and whether it has a truth value. Luckily the universe is discrete at the Planck scale (and finite to boot). Even if it wasn't, the universe certainly cannot be tiled arbitrarily with particles at every real number-- that's arbitrary sets of reals, literal continuum hypothesis territory. Yet the beth2 argument relies on this.
> Given this, if L is the biggest number of people that there could be, whichever theory best predicts L people existing infinitely outperforms alternative theories. Theism best predicts L people existing, because God would create all possible people who he could give good lives. So, therefore, theism gets a big probabilistic boost.
This seems to imply theism predicts L minus bad lives.
Some version of multiversal atheism implies L (good lives + bad lives). Therefore, multiversal atheism seems more likely?
Help me understand this.
Suppose I notice I am a human on Earth in America. I consider two hypotheses. One is that everything is as it seems. The other is that there is a vast conspiracy to hide the fact that America is much bigger than I think - it actually contains one trillion trillion people. It seems like SIA should prefer the conspiracy theory (if the conspiracy is too implausible, just increase the posited number of people until it cancels out).
You can get around this by saying that infinity is too big for it to matter - since there are an infinite number of Americans (across all possible worlds), I'm no more likely to live in the conspiracy universe than the normal universe. But I think you can't do weird stuff with infinities like this. Consider 1000 rare classes of person (dictator, billionaire, dwarf, polar explorer, etc). I notice I'm not in most of these classes. But it seems like if there are an infinite number of Earths, then there are an infinite number of polar explorers and an infinite number of non-polar-explorers, and these aren't two different levels of infinity (there are about 1 million times more non-explorers than explorers). So I should be exactly as likely to be an explorer as a non-explorer. But the fact that I'm not in more than a handful of these rare classes proves that this isn't true. Therefore, you can't sweep the first problem under the rug by playing with infinities.
What am I missing?
I accept that if the only possible theories were the conspiracy and the non-conspiracy theory, the conspiracy theory would win. This result is widely known and is the main objection to SIA--that it implies you should believe otherwise implausible things if they predict more observers. I'm not too worried for reasons given by Carlsmith https://joecarlsmith.com/2021/09/30/sia-ssa-part-4-in-defense-of-the-presumptuous-philosopher. To briefly summarize:
1) You shouldn't be that confident in the theory of anthropics, so any real person shouldn't use this reasoning. If you're 90% sure of SIA, this result won't follow.
2) Every view of anthropics can be shown--as I show in a forthcoming paper--to entail that there are some cases where you should reject well-established science based on anthropics. This isn't surprising--if anthropics says something about the world, it should be able to overturn otherwise confident judgments.
There's a lot more to say, and I think that SIA is so overwhelmingly attested that I don't really mind biting the bullet--also doesn't seem so bad when you realize that a billion times as many people makes it a billion times likelier that you'd exist.
As for the infinite stuff, it's not really clear how to do infinites with SIA. I think probably a lot of infinites are incomparable and as usual infinites ruin everything--especially ethics! I don't have a well-worked out theory of how to compare infinites in terms of SIA, but no one has a good theory of how to do infinite anthropics, so it's not uniquely a challenge for SIA (I elaborate on this more here https://benthams.substack.com/p/breaking-the-fourth-wall?utm_source=publication-search).
It may seem weird to have an argument involving infinite anthropics when it's not clear how to do infinite anthropic reasoning, but SIA clearly proscribes favoring bigger cardinalities of infinity. It's only messy when it's a bunch of infinites of the same cardinality.
In summary, then, Christ is king.
EDIT: Possibly I'm an idiot in a great many ways. Read with caution. For one thing, I forgot that the concept of "expected value" is distinct from the most probable value.
UPDATE ON EDIT: After remembering the concept of expected value, I've seemingly determined that in my toy problem, as n approaches infinity, the expected chatroom number actually converges to 3 (the third chatroom?) I don't know how exactly to interpret this.
I don't believe increasing the posited number of people necessarily eventually cancels out the implausibility. For example, suppose there are n chatrooms for some n>2 such that the kth chatroom has k people (The first chatroom has 1 person, the second chatroom has 2 people, and so on until the nth chatroom which has n people) and suppose you've been uniformly randomly selected to be one of the people among all the chatrooms. Then the prior probability that you're in the chatroom with k people should be k/((n(n+1)/2), and given that information alone you should naturally suppose you're in the largest group, which has the highest probability.
But suppose also that everyone flips a coin, and if it comes up heads then they're required to send a message notifying the other members of the chatroom of their existence, while if it comes up tails they're never allowed to speak. In that situation, if you find yourself in a chatroom where no one else ever sends a message, then regardless of how big n is, once you've incorporated the evidence that you haven't gotten any messages using Bayes' theorem, the probability that you're alone and the probability that you're in the room with only one other person always remain the highest.
I could share the whole formula I worked out but it would be a bit of a mess, and I don't think it's necessary. The only insight you really need is that the probability of seeing no messages in a chatroom of size k diminishes as (1/2)^(k-1), while the prior probability that you're in a chatroom of size k to begin with only increases as k/(n(n+1)/2), and the former quickly overwhelms the latter.
So, in general, as long as you find an increasingly vast conspiracy increasingly implausible based on the evidence at a fast enough rate, you never have to concede.
(I can't promise that I haven't made several minor mistakes in my math here because I tend to do that, but I believe if anyone double-checks it my point will come through unscathed.)
Re: Infinities, you can't actually define a uniform probability distribution on a countably infinite set or unbounded set because either the probabilites would have to add up to zero or they would have to add up to infinity when they're supposed to add up to one. So e.g. although there are as many even natural numbers as there are square natural numbers, saying that a "randomly selected" natural number should be just as likely to be even as square doesn't actually make sense. The "randomly selected" part doesn't work.
You can define a uniform probability distribution on something like a finite closed interval using integration, but that only works because there's extra structure to the infinite set. So you could pick a random real number between 0 and 1. But then numbers with different properties aren't necessarily equally likely either even if they do make up infinite sets, like how getting a number whose decimal expansion begins 0.1... is only a ninth as likely as getting a number with some other first decimal digit.
I think you could if you do tricky things with infintesimals.
Why doesn't it cancel out the improbability if we think there is the maximum number of possible people?
Public service announcement to disregard much of what I've said. See my edit above and my conversation with Donald below for details.
If you assigned every natural number an infinitesimal probability ε = 1/ω where ω is supposed to be the "number" of natural numbers, then the total probability would be ε *ω = 1 which would be nice, but then you couldn't say that there are the same number of even numbers as square numbers without breaking arithmetic I don't think. I do like the idea of infinitesimals, but most formal ways of describing them are a bit complicated and the current math community consensus seems to be to avoid them unless you have a really good idea of what you're doing, which I don't. Another intuitive counterargument to the possibility of a uniform probability distribution over a countable set like the natural numbers is asking "How many digits would the typical randomly selected natural number have?" Any finite number of digits would seem to be far too few, but an infinite number of digits would make it not a natural number.
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As to why even the maximum number of people doesn't cancel out the improbability, if I understand your question correctly, as said it's because the probability of the evidence provided by there being no response gets much smaller much faster for larger groups than the prior probability that you're in a larger group increases.
This is evident in the small case of only four chatrooms:
If room one has 1 person, room two has 2 people, and so on up to room four, so that there are 10 people total, then your initial probability of winding up in the first room is 1/10, the second room is 2/10, the third room is 3/10, and the fourth room is 4/10. So to begin with, all else being equal, you should expect to have ended up in room four as expected.
But then if you add the coin-flip-response thing, and you notice that you've gotten no responses, the probability of that happening in the first room is 1 (guaranteed because you're the only person there), in the second room is 1/2, in the third room is 1/4, and in the fourth room is 1/8.
Bayes theorem tells us that P(H|E) = P(E|H)*P(H)/P(E) where H and E stand for hypothesis and evidence respectively. Using that, P(You're in the kth room given that you've observed no response) = P(You've observed no response given that you're in the kth room)*P(You're in the kth room)/P(You've observed no response).
Now, P(E) is the same for all k so it can be ignored if we're just making comparisons. And It's also tedious to write out so that's convenient.
But using what we've already established,
For the first room, k = 1 so P(E|H)*P(H) = (1)(1/10) = 1/10
While for the fourth room, k = 4 so P(E|H)*P(H) = (1/8)(4/10) = 1/20
And since as said the prior probability of the evidence is the same for both, that means the probability that you're in the first room given the evidence must be higher than the probability that you're in the fourth room given the evidence even though the fourth room has the most people.
Has that helped make sense of it? I hope I've done everything correctly and if I haven't I hope someone corrects me. I also recommend 3Blue1Brown's videos on Bayes' theorem if you haven't seen any of them: https://youtu.be/HZGCoVF3YvM
Hmm, interesting! Not sure what to think of what you said. Maybe when doing countable additivity with infintesimals you have to add up the infintesimals or something--or maybe something about hyperreals. I think that alternatives to SIA's approach will get even weirder results in cases of infinities https://benthams.substack.com/p/breaking-the-fourth-wall?utm_source=publication-search.
Re the conspiracy case, I don't worry too much about it as I basically bite the bullet. I think a conspiracy would be worth accepting if you were an ideal agent and could somehow rule out all the non-conspiracy ways of ruling out a bunch of people.
I think I agree with SIA too because it's better than the alternatives. I'm just saying that, as I understand it, you don't need to bite the bullet. Using SIA as your prior doesn't mean it can't be overruled by evidence in specific cases like supposing based on SIA that there are secretly a trillion people hiding in your pantry because it would make it more likely for you to live in your house if they were there too.
Wait, if there were two theories, one says there's just me, the other me and 1 trillion people with experiences like mine in my pantry, do you agree that SIA gives a trillion to one update in favor of the second?
>So, in general, as long as you find an increasingly vast conspiracy increasingly implausible based on the evidence at a fast enough rate, you never have to concede.
This is technically true, but I don't think this will help much, because realistically your prior can and will involve something along the lines of "X number of people exist according to some distribution with infinite mean." For example, if you think there's a *tiny* positive probability God has created n people in your epistemic situation, where God drew the number n randomly from the distribution with p(n) = 6/π^2 * 1/n^2 (which I picked because its expected value is infinite), then SIA completely prefers this to the "ordinary" hypothesis that there's only one copy of you, no matter how close to 1 the latter's prior. You need the hypothesis I mentioned, and all others like it (including ones where the minimum number of copies n that God creates is arbitrarily high, rather than 1), to have probability exactly 0, and even then you might run into additional troubles.
> So, in general, as long as you find an increasingly vast conspiracy increasingly implausible based on the evidence at a fast enough rate, you never have to concede.
You can design contrived priors to fit your prechosen posterior.
But if your priors are sensible occamian stuff, the conspiracies don't get implausible enough fast enough.
I'm not sure how you can be certain that sensible priors can't overcome most SIA-inspired conspiracies easily considering how fuzzy the idea of sensible priors is.
And anyway my example didn't have any contrived priors, so that's beside the point I was trying to make, which is that evidence may often be able to easily outweigh SIA as a prior. My prior in my example was equivalent to SIA, but it was a fairly simple piece of evidence that readily overcame it. And strong evidence is common: https://www.lesswrong.com/posts/JD7fwtRQ27yc8NoqS/strong-evidence-is-common
Did you see my comment on that lesswrong post.
Evidence that moves a hypothesis from 1/10^100 to 0.5 is common. Evidence that moves from 0.5 to 1- 1/10^100 basically never happens.
Let H1= reality as normal.
Let H2 =gazillion people + flawless conspiracy to hide this.
Now on priors, both H1 and H2 are highly unlikely. H1 because anthropic reasoning. H2 because conspiracies of this kind are rare.
So when you look around you, you quickly gather strong evidence for (H1 or H2).
But the hypothesis predict identical observations, so all you have to tell between them is the priors. And if we are doing occam's razor, the prior likelihood of the conspiracy is determined by how many bits of information is needed to describe it. 2^-bits
So H1 gets more unlikely the more people you consider might exist. If you allow an unboundedly large (finite) number of people, then the maths kind of breaks and H1 becomes infinitely unlikely, but so does every other hypothesis.
I don't understand your reasoning with respect to Occam's razor. Are you saying that a flawless conspiracy is easy to describe just because it doesn't take very many bits to say "flawless conspiracy"?
I would think that the possible world with arbitrarily more people and a perfect conspiracy to hide them all would still require arbitrarily more information to describe accurately at a rapid rate. In my view, you don't just need to suppose the conspiracy, you also need to suppose all the hidden people with their own lives, thoughts, interactions, etc. that the conspiracy is covering up. Without settling on specific details, you can just consider how much information the additional hidden people would take to describe on average. And I suspect that, when that's accounted for, H2 should actually become infinitely unlikely relative to H1 on Occam's razor as well despite the prior based on SIA, just like happens in my coin-flipping example.
Maybe if tiny variations in physical constants at the beginning of the universe could lead to arbitrarily more people at the present time, then the possible worlds with arbitrarily more people would be just as easy to describe as our world on that level. But all of those worlds also having a flawless conspiracy to hide the extra people/whatever else is involved still seems like it would require considerable extra artificially-imposed info.
...Unless the tijy variations in physical constants lead to arbitrarily many people by creating overlapping "shadow earths" just like ours but which are all totally imperceptible to each other, and that counts as the flawless conspiracy. But if that could be demonstrated then I think I'd agree that we should suppose we're in the universe with a higher number of shadow earths and so more people.
No. I am saying that there exists some finite X such that it takes X bits to describe a flawless conspiracy.
This puts the conspiracy at a likelihood penalty of 2^-X.
But the larger the number of people hidden, the larger the anthropic bonus.
A conspiracy to hide more than 2^X * 8,000,000,000 people is hence more likely than normality. (according to this reasoning, which mostly gives me reason to doubt this reasoning)
Technically you also need to include the number of people being hidden. If you are writing a completely arbitrary number out in decimal, then each doubling of the number of people means 1 more bit used. But also means 2x as many hypothesis. So that kind of cancels out. (Or you could say your hypothesis in compact scientific notation) This doesn't really effect the picture much.
Occam's razor doesn't penalize the universe for being big.
There are at least 10^20 ish stars out there, each with their own composition and solar storms and whatever. Any hypothesis that lists all the details of every star is going to be VERY unlikely, by occam. But that is exactly compensated by the number of different theories that are all basically the same except a few sunspots in distant galaxies are rearranged.
The same goes for the "more people". Sure it takes a lot of info to describe any specific way those people could be. But that's compensated for by the number of ways those people could be. Leaving a very large number of very similar hypothesis, each with a very small individual probability.
I might be wrong about this, but I don't find this argument convincing. I have reservations about the SIA and theism's predictive ability, but I mostly disagree because I don't think atheism does such a bad job of predicting the existence of large numbers of people. To illustrate this, I've tried to list out some hypotheses that are alternatives to theism and still predict the existence of large numbers of people.
1. Tegmark's multiverse and modal realism
1.1. I don't think induction is a big problem for these worldviews, certainly relative to theism.
1.1.1. Suppose modal realism is true. The mere fact that there are infinitely many concretely existing possible worlds where induction fails does not imply that I am probably in such a world, or that induction fails in nearly all worlds. I'm not even sure it's possible to make such statements in a meaningful way - you would need to have a measure over all possible worlds, which is impossible because there is no set of all possible worlds.
1.1.2. Whatever the best way of thinking about uncertainty over possible worlds is, the idea that it would change if those possible worlds existed concretely is exceedingly strange.
1.1.3. Theism doesn't explain why induction works any better than atheism. The morally sufficient reasons God has for allowing the massive amount of evil that have existed throughout history are surely sufficient to allow him to create a world where induction doesn't work.
2. Alternative theisms: for any property that people existing can entail, just postulate a God who values that property rather than goodness. There are infinitely many of these, including
2.1. Evil God
2.2. God who just likes qualia, in general
2.3. God who mostly cares about aesthetic (but not necessarily moral) value
2.4. God who really likes Luxembourgers (maybe there's a reason they have such high GDP per capita)
2.5. and so on.
3. Generalized value selection hypotheses: take theism or any of the 'alternative theisms' and postulate a mindless force which tends to instantiate the corresponding values
4. Physical multiverse theories
4.1. I'm don't think it would be that hard to create mathematical models of multiverses containing Beth-2 or more people. It might be that those models wouldn't be well-motivated by empirical data in the conventional sense, but maybe we shouldn't expect them to be if most of the other universes are causally isolated from ours. And they would at least be motivated by anthropic considerations, which are empirical! (at least if SIA is correct).
4.2. Specifying the exact nature of this model shouldn't even be necessary! It seems *extremely* unfair to complain that physicists haven't proposed a mathematical multiverse model that would predict enough universes when philosophers and theologians haven't proposed a mathematical model of God and his act of creation.
5. Other multiverse theories: Suppose, for example, that there's a simple universe-generating monad which generates lots and lots of universes.
The problem is that almost all of these theories suck and occupy a tiny part of the hypothesis space. The only ones that are at all simple are modal and Tegmark realism, which I think undermine induction. Builes makes the point in more detail https://onlinelibrary.wiley.com/doi/10.1111/nous.12478?af=R.
The evil God is a challenge, but I think I addressed it decisively here https://benthams.substack.com/p/the-evil-god-challenge?utm_source=publication-search
There's no physical multiverse that produces enough people that anyone has ever proposed and if there is, I fear it would undermine induction. The others are monstrously complicated and arbitrary.
This reminds me of saying something like "okay, sure my having done the crime could explain my blood being all over the murder weapon but it could also be explained by (insert 27 half-baked theories).
Thanks for the link to the Builes paper! I'll give it a look.
I agree that most of these theories suck and are super ad hoc! I just think they're plausibly on par with theism because 'perfection' also seems gerrymandered to me. I can imagine changing my mind about that though.
Can you elaborate further on why you think God would allow factory farming but not failures of induction? The latter seems a lot easier to justify.
I'll agree that if your judgment prior to thinking about this argument is that theism is obviously totally crazy, akin to believe in ghosts, the argument won't move you. But probably most arguments are like that, even very good ones.
Well one reason is that if God allowed failures of induction--it would probably have failed by now. Another is that God would likely make predictable, stable physical laws where we can go wrong. That explains why we're allowed to do wrong things but also provides for induction. My theodicy explains why he'd do that.
To make it more concrete, let's take an ordinary inductive inference like "I have grown taller every day I've been alive, so I will keep growing taller every future day I'll be alive." This statement is clearly wrong, we observe that you will stop growing once you hit puberty. So here's another inductive law: "I have grown taller every day I've been alive and before puberty ended for me, so I will keep growing taller every day I've been alive and before puberty ends for me." But this also has counterexamples - you can take human growth hormone supplements, get shin extension surgery, position yourself so that major gravitational bodies like the Sun and moon are directly overhead, and these will all result in your height increasing after you've finished puberty.
Basically, you're acting like the truthmaker for statements like "I will keep growing taller until I finish puberty" already exists and is obviously induction, and it's not just a useful heuristic that is subject to all sorts of ceteris parabis contextual factors (that themselves are also subject to contextual factors). But the parts you're leaving out of your explanation 1) won't just resolve themselves and 2) directly contradict the putative inductive truth you're proposing once more accurately specified.
For the record, I think most if not all inductive laws have failed. You take physical laws as a paradigmaric example, but physics is notorious for paradigm changes. The laws of quantum field theory aren't the laws of quantum mechanics aren't the laws of relativity aren't the laws of Newtonian mechanics. In past posts you've also said you should believe the Sun will rise tomorrow based on inductive evidence, but eventually astronomical data tells us the Sun will expand to the point the Earth gets incinerated and so "the Sun will rise tomorrow" will be yet another failed inductive law.
>There's no physical multiverse that produces enough people that anyone has ever proposed and if there is, I fear it would undermine induction. The others are monstrously complicated and arbitrary.
I don't think there's an easy way to specify a God-creates-almost-every-possible-person scenario that avoids challenging induction given your commitments vis-a-vis SIA, but regardless: it's very easy to come up with a naturalistic hypothesis that doesn't do this, and which generates beth-2 possible people (if that's the cardinality you're focused on). Specifically: imagine a universe U exactly like ours, but there's a special particle X which pops in and out of existence at certain prescribed times, and which interacts with absolutely nothing else. For a given subset S of the interval [0,1], let U(S) be a universe in which X pops in at every time t in S (counted in seconds after the Big Bang), and vanishes for every other time. Then voila, consider the naturalistic hypothesis that each U(S) universe exists for every subset S of [0,1], and you have beth-2 distinct universes which play out exactly like ours, induction and all, aside from this harmless X-particle epiphenomenon.
This is extremely arbitrary, but it's still incredibly simple, and moreover I imagine it will be a lot less arbitrary/complex than the algorithm you suggest God might use to pick and choose universes to ensure inductive reliability of all agents.
Well, I think you probably need more than Beth 2 universes. I'm also having trouble understanding the picture of the universe. Finally, I think cloning our universe a bunch of times would probably undermine induction because there would be Beth 2 people for whom induction doesn't work.
>I'm also having trouble understanding the picture of the universe.
Beth 2 is the cardinality of the set of all subsets of the reals (or, equivalently, [0,1]). So I'm taking the universe and adding a completely epiphenomenal particle that does something slightly different for each subset of instants of time in the first second of the universe. Then I'm stipulating that all such universes exist (as a multiverse), for every such subset. That gets me beth-2 universes, all identical except for this particle which doesn't affect anything else.
>Finally, I think cloning our universe a bunch of times would probably undermine induction because there would be Beth 2 people for whom induction doesn't work.
It seems like SIA has little to say here, because you're going to get ∞/∞. But that's going to be true pretty much no matter what, to SIA's discredit. Moreover, all the universes are playing out exactly the same way aside from the epiphenomenal particle that doesn't influence any conscious agents or anything they interact with at all, so it's intuitive that you simply shouldn't reason anthropically across universes to begin with.
I should say that, given the way I've set this example up, it's actually hard (likely impossible) to do SIA mathematically because of a technical issue called "non-Lebesgue measurable sets." But again, I think that if you're trying to apply SIA on this scale of infinity, essentially all the mathematical machinery we've developed since the early 20th century to think about probability has to go out the window.
Ah, I see the picture. I think that picture of reality will have a super low prior and doesn't get enough universes, for I think Beth 2 isn't enough. I also think it undermines induction. I think that you should assign equal credence to being any actually existing observers with your evidence, so if there are the same number in inductive and non-inductive worlds, induction might go out the window, though I'm not that sure of that.
> I think that picture of reality will have a super low prior
Sure, I agree, it has a low prior. But it's still reasonably simple to describe, and part of my point was that it's not obviously lower than whichever divine hypothesis you're going with. Because even if God himself is simple (which, as you know, I'd like to deny), you think he has to have some decision procedure to pick and choose which universes to actualize in order to avoid inductive failure, and why think that any of these are more probable than my example?
You could say: well, even if any specific decision divine procedure is improbable, the hypothesis that God is using at least one of them (without saying which) is more probable than my example. My response is 1. that I imagine all of God's individual decision procedures will have something like infinite complexity and thus a plausibly zero prior, and so it's not clear how to add them all up much less what number they add up to; and, furthermore, 2. my example was also just one among infinitely many that would get me to the same sort of place, so you have to add all *those* up as well to keep things fair.
>and doesn't get enough universes, for I think Beth 2 isn't enough
I can probably modify it in a similar way for any other size (cardinal or not) you wish. Just add arbitrarily mathematically weird epiphenomena.
>I think that you should assign equal credence to being any actually existing observers with your evidence, so if there are the same number in inductive and non-inductive worlds, induction might go out the window, though I'm not that sure of that.
All of the worlds are very plausibly inductive, because the same thing is happening in each one of them at the same rhythm, all in parallel. (The only difference, again, is this one epiphenomenal particle that none of us ever notices.) Put another way, if God told you he made an infinite number of carbon copies of the actual world (and nothing else), would you really, truly disbelieve in induction? I wouldn't. I'd reason exactly as before and disregard the validity of any anthropic principle that said I shouldn't.
The analogy at the bottom is terrible. You’re attempting to twist the intuition that “one should have one consistent narrative when testifying in defense to a crime” into a broader claim about how many weak theories don’t work. But many weak theories in the abstract do in fact reduce the probability of a 28th theory when (like in a criminal case), one does not destroy one’s own credibility by asserting 27 inconsistent theories of innocence.
Hm. I wonder if these hypothesis all have a cumulative effect, too. Even if (a big if) bulldog is right that one perfectly good God is the “simplest” in some sense, the fact that there are endless very slightly less simple hypothesis must count for something.
The idea of a god being “simple” is quite difficult for me to swallow. If I told you I had a machine that could manufacture any cell phone currently on the market in an hour, would you expect that this machine would be simple? Why would supposing it could do more and more things until it was an omnipotent creator make it simpler? Far from simple, this seems like something impossibly complex. I would need to observe this machine in action to actually believe it exists because it sounds like it’s not even physically possible. Thankfully, under the typical god hypothesis, god has the ability to intervene in the world and could very easily prove to me (or anyone) that he/she exists. But as Christian theologians evince when they write books with titles like “The Hiddenness of God”, there is no omnipotent being out there trying to make us believe he/she exists.
"Why would supposing it could do more and more things until it was an omnipotent creator make it simpler?"
If the idea is that for every power a device/being has, it has some dedicated mechanism of effecting that power in place, I suppose your objection makes sense. That'd be a lot of mechanisms. But that isn't how God's supposed to work: dependent on subprocesses and assorted widgets to bring about X, Y, and Z. God really has one power, to bring about whatever it wants.
"How does it do that?" I'm unconvinced that an agent needs a mechanical explanation of how it brings about its goals. I don't see any contradiction in imagining an agent whose will is causally efficacious in itself. Might depend on your metaphysics of causation, I guess.
Why should there be an agent in the first place?
The universe could just be.
You make a good point. I agree that it is logically possible for such a thing to exist. It’s just highly unlikely in my view. We have zero precedent for such things. In the real world (as opposed to unfettered imaginings of otherworldly but logically possible things), creative abilities require complex mechanisms. “Is logically possible” is not an adequate substitute for “is probable”.
Here's my hypothesis: things just are the way they are. There's no need for an "external" unmoved mover - the universe itself is the unmoved mover.
This is quite right I think. A priori, it seems like any of these theories are as good or better than “a perfect being did it”. And if we wanted to spend more time doing this, we could make up any number of logically consistent explanations. A priori we can’t just assume that one is better than another, so it comes down to how well each theory fits with the evidence. Then the problem of evil makes the idea of a morally perfect and omnipotent being existing very unlikely indeed.
Those theories aren't at all simple. Theism posits one core property--perfection--while almost all of those posit bizarre extra gerrymandered properties.
Perfection is only simple in the sense that you can name it with one word. Though to me that’s beside the point. I don’t think simple states of the universe are, a priori, more likely than complex ones.
No, it's simple in that it invokes one fundamental property without limit.
How are the properties of being able to do anything logically possible, being maximally good, and knowing all things one property?
There's one property that's fundamental--perfection or in other words, unlimited goodness.
How is "Perfection" a fundamental property, rather than being an ill defined and arbitrary english word that brings all sorts of complicated details along with it.
Could you give a short description of "perfection" to aliens? Could you write a short program to simulate what a perfect being would do?
Maximally good! You could write a program if you had the ability to include goodness as one of the fundamental operators. A perfect being would do whatever is the most good. Taking a fundamental thing without limits is simple.
Perfection sounds simple because it's a short word. But when you try to actually define perfection in detail, you will find it's actually rather complicated. Your mind was glossing over the complexity.
(The word smartphone is also one word and seems simple, but try describing one to someone from 1800 and you find it's not quite so simple)
Also, I still don't buy your arguments against the problem of evil.
If we have to suffer in order to develop our moral qualities, then why couldn't God just create us with the right moral qualities?
If we have to suffer in order to appreciate God more, then why couldn't God just create us with infinite appreciation?
If God created us because he ran out of unique perfect beings to create, then why couldn't he just duplicate the perfect beings instead of creating imperfect ones?
That is not my theodicy! https://benthams.substack.com/p/why-theres-evil
1. Unknown Reasons and Afterlife Goods
This reasoning is inherently unfalsifiable as it posits unknown reasons beyond our comprehension, making it impossible to critique or validate.
If someone justified every instance of suffering by saying it’s for unknown future benefits, this would be intellectually unsatisfying and could excuse any atrocity without accountability.
2. Strengthening Relationship with God
It is questionable whether an indifferent universe is necessary to strengthen relationships with God. An omnipotent God could presumably create bonds without inflicting suffering.
In human relationships, one doesn’t need to cause their loved ones to suffer to deepen their bond. Intentionally creating suffering to strengthen a relationship would be seen as abusive, not loving.
3. Soul-Building
The uneven distribution and overwhelming intensity of suffering suggest that not all suffering leads to soul-building. Many suffer without apparent growth, while some are broken by it.
Victims of extreme trauma, such as war or abuse, often suffer long-term psychological damage without any observable benefit, challenging the idea that all suffering is soul-building.
4. Building Connections with Others
Suggesting that an indifferent world enhances relationships undervalues the potential of positive experiences to build strong bonds without suffering.
Friendships and communities often thrive through shared positive experiences, not necessarily through shared suffering. The idea that suffering is needed for deep connections could justify neglect and harm.
5. Working with God
The existence of extreme moral and natural evils is hard to justify as necessary for cooperation with God. This implies a limitation on divine power.
Natural disasters causing widespread suffering (e.g., tsunamis, earthquakes) do not appear to foster meaningful cooperation with God but rather cause arbitrary harm, questioning the necessity of such events for divine-human collaboration.
6. Freely Choosing God
The argument that we need an indifferent universe to freely choose God does not account for the sincere seekers who struggle to find God due to perceived hiddenness.
Many individuals earnestly seeking spiritual truth may turn away from belief due to the overwhelming presence of suffering and indifference in the world, suggesting that divine hiddenness can hinder rather than facilitate free choice.
Theodicies that generalize suffering as necessary for greater goods risk insensitivity to individual suffering and the specific contexts of pain.
Telling a grieving parent that their child’s death serves a greater good can be deeply insensitive and dismissive of their personal tragedy.
There are instances of suffering that appear entirely gratuitous, serving no discernible purpose or benefit, challenging the notion that all suffering has a divine rationale.
The prolonged suffering and death of a child from a terminal illness often seem gratuitous and purposeless, raising serious questions about divine justice and benevolence.
Justifying an indifferent universe implies that a benevolent God permits or even causes suffering for higher purposes, which can conflict with our ethical intuitions about benevolence and justice.
A benevolent human being who allows preventable suffering to achieve a future good would be considered morally questionable, suggesting a similar issue when attributing such actions to God.
//5. HOW THE THEODICY DECIMATES THE CASE FOR ATHEISM//
1. The Existence of Physical Reality
The existence of a physical reality that operates under consistent natural laws is a strong point for naturalism, as it does not require an additional supernatural layer of explanation. Your theodicy suggests that God created an indifferent universe, but this posits an additional entity (God) without necessity.
Ockham’s Razor favors the simpler explanation, which is naturalism, as it does not posit an extra, undetectable creator to explain the physical universe.
2. The Success of Science Without Theistic Explanations
The success of science in explaining phenomena without invoking God highlights the predictive and explanatory power of naturalism. Your theodicy posits that an indifferent universe would look like a naturalistic one, but this does not add predictive power to theism; it simply adjusts theism to fit observed facts.
Naturalism predicts the success of methodological naturalism in science. Theism must be adapted (with the hypothesis of indifference) to align with this success, suggesting naturalism is inherently a better fit for the data.
3. Evolution
Evolution through natural selection is a robust and parsimonious explanation for the diversity of life, which does not require the hypothesis of a deity. Your theodicy incorporates evolution into theistic belief by suggesting an indifferent creation, but this adds complexity without necessity.
Naturalism explains evolution directly through natural processes. Theism, under your theodicy, again, must invoke an additional hypothesis (God creating an indifferent universe) to accommodate evolution.
4. The Biological Role of Pleasure and Pain
Naturalism directly accounts for the biological role of pleasure and pain through evolutionary pressures and the survival benefits of such mechanisms. Theism, as modified by your theodicy, suggests these are designed features of an indifferent universe, adding a layer of divine intention that naturalism does not require.
Pain as a mechanism to avoid harm and pleasure as a reinforcement for beneficial behaviors are directly explained by natural selection. Theism must posit that God intentionally included these features to mimic a godless universe.
5. Mind-Brain Dependence
Mind-brain dependence is empirically supported and directly predicted by naturalism, which posits that consciousness arises from physical processes. Your theodicy must argue that God created the brain to function independently, which is an added hypothesis.
Naturalism straightforwardly explains the correlation between brain states and mental states. Theism must invoke a reason why God would design the brain to operate as if there is no soul or divine influence.
6. Moral Handicaps
Naturalism explains moral handicaps through evolutionary psychology, where certain behaviors evolved because they were advantageous in ancestral environments. Your theodicy must suggest that God intended for these handicaps as part of an indifferent universe, complicating the explanation.
Selfish behaviors can be explained as remnants of survival strategies. Theism must posit why a benevolent God would create beings with these handicaps intentionally.
7. Nonresistant Nonbelief
Nonresistant nonbelief, where sincere seekers do not find belief in God, challenges the notion of a benevolent deity. Your theodicy must argue that this is part of creating an indifferent universe, but this seems counterintuitive for a God who desires relationships with His creation.
Many people seek God earnestly but do not find evidence or experience of Him. Naturalism predicts such experiences due to the lack of divine presence, whereas theism must reconcile this with a loving God’s intentions.
1. The SIA modifies our epistemic probability by factoring in the number of observers a theory predicts. It suggests that if more observers exist under a theory, it's more likely that the theory is true because you are one of those observers.
This approach conflates the number of observers with the probability of the theory being true. The fact that a theory predicts more observers doesn't necessarily make it more likely. Instead, it could be argued that each observer's perspective should be considered independently. The mere fact of your existence should not be more probable under a theory that predicts more people; rather, it should be considered under the initial conditions of the probability of heads or tails.
2. Also the SIA relies heavily on the definition of the reference class—the group of people you consider yourself part of. This can significantly affect the outcome.
The choice of reference class is arbitrary and can lead to different conclusions. In the coin toss example, considering all possible people versus just those in similar conditions (e.g., in white rooms) can yield vastly different probabilities. This arbitrary choice undermines the objectivity of the SIA and raises questions about its validity.
3. It also alters self-locating beliefs by suggesting that you are more likely to be in a scenario with more observers.
This reasoning can be problematic because it implies that the existence of other observers directly influences the probability of your own existence, which is a non-standard approach in probability theory. Traditional Bayesian probability does not factor in the existence of additional observers in this manner.
4. Human cognition is prone to biases, such as the availability heuristic, where individuals estimate probabilities based on how easily they can imagine instances.
The SIA may be influenced by such cognitive biases, leading people to overestimate the likelihood of scenarios with more observers simply because they can more easily imagine more people. This could distort rational probability assessment.
5. Intuitively, people may struggle with the implications of the SIA because it counteracts common sense and standard probabilistic reasoning.
The SIA's counterintuitive nature can lead to resistance and misunderstanding. People typically reason that the probability of an event (like a coin toss) should not be affected by unrelated outcomes (like the number of people created). This discrepancy between intuitive reasoning and SIA can make it psychologically unpalatable and difficult to accept.
6. Applying SIA can lead to extreme and impractical conclusions, such as radically altering beliefs based on hypothetical large populations.
This practical consequence makes the SIA less appealing. For instance, in the coin toss scenario, suggesting that tails is a million times more likely based solely on potential observer count can lead to impractical and unrealistic decision-making processes.
//This approach conflates the number of observers with the probability of the theory being true. The fact that a theory predicts more observers doesn't necessarily make it more likely. Instead, it could be argued that each observer's perspective should be considered independently. The mere fact of your existence should not be more probable under a theory that predicts more people; rather, it should be considered under the initial conditions of the probability of heads or tails.//
I didn't just assume that a theory that predicts more observers is more likely--I gave 4 arguments for it! You shouldn't just look at the objective probability of an event to see its propbability of producing you--for example, if my parents would only have sex if a coin came up heads, I should be very confident that it did.
//2. Also the SIA relies heavily on the definition of the reference class—the group of people you consider yourself part of. This can significantly affect the outcome.//
SIA just looks at the people you might currently be. Unlike SSA, it doesn't invoke a reference class.
//This reasoning can be problematic because it implies that the existence of other observers directly influences the probability of your own existence, which is a non-standard approach in probability theory. Traditional Bayesian probability does not factor in the existence of additional observers in this manner.//
SIA is just being a Bayesian about your existence. More observers makes it more likely I'd be one of them, for the reason given by Elga.
//4. Human cognition is prone to biases, such as the availability heuristic, where individuals estimate probabilities based on how easily they can imagine instances.
The SIA may be influenced by such cognitive biases, leading people to overestimate the likelihood of scenarios with more observers simply because they can more easily imagine more people. This could distort rational probability assessment.//
Why would a scenario be easier to imagine just by having more people? Huh? Also, I didn't just like assert SIA--I gave several arguments for it.
//The SIA's counterintuitive nature can lead to resistance and misunderstanding. People typically reason that the probability of an event (like a coin toss) should not be affected by unrelated outcomes (like the number of people created). This discrepancy between intuitive reasoning and SIA can make it psychologically unpalatable and difficult to accept.//
Well, SIA doesn't think that if a coin hasn't been flipped yet, but will create many observers if it comes up heads, that your credence in heads should be more than 1/2. After all, on SIA, what matters is the observers you might currently be. But I know I'm not one of the observers who will be created in the future. In contrast, SIA does judge past events by the number of observers, but this is totally reasonable. If I know a coin got flipped in the past and I would only come to exist if it came up heads, I should think it came up heads.
//This practical consequence makes the SIA less appealing. For instance, in the coin toss scenario, suggesting that tails is a million times more likely based solely on potential observer count can lead to impractical and unrealistic decision-making processes.//
Well that's why I gave an argument for the God's extreme coin toss result, as well as many other arguments for SIA. You're just assuming that your existence gives you no evidence for more people, which begs the question against SIA.
1. Again, the SIA relies on defining a reference class of observers, but there is no non-arbitrary way to determine this class. The selection of the reference class can drastically alter the probabilities, undermining the objectivity and reliability of the SIA.
In the God's coin toss scenario, if you consider the reference class to be all potential beings, the outcome differs from considering only those in a white room. This flexibility in choosing the reference class makes the SIA highly subjective.
2. SIA leads to inconsistencies when applied across different scenarios. It alters traditional Bayesian probability by incorporating the number of observers, which is not standard in probability theory.
In Bayesian reasoning, the probability of an event is updated based on evidence. The SIA, however, updates probabilities based on hypothetical additional observers, which can lead to paradoxical outcomes. For instance, it implies that more populous universes are inherently more likely, irrespective of other evidence.
3. The SIA can lead to counterintuitive and paradoxical implications. It can suggest absurd probabilities that defy common sense and practical reasoning.
If two universes exist, one with a million observers and one with a single observer, SIA implies you are almost certainly in the more populous universe, regardless of other factors. This could lead to absurd conclusions in cases where observational data clearly favors the less populous universe.
4. SIA de-emphasizes the importance of actual empirical evidence in favor of hypothetical population sizes. This undermines the empirical basis of probability and decision-making.
In scientific inquiry, theories are evaluated based on empirical evidence and predictive power, not on the number of potential observers they imply. SIA shifts focus away from evidence-based reasoning to speculative considerations about population sizes.
5. Also, SIA can involve circular reasoning by assuming what it sets out to prove—that a theory predicting more observers is more likely because it predicts more observers.
The argument that a universe with more observers is more likely because you are an observer presupposes that your existence is more probable in such a universe, which is the point under debate. This circularity weakens the logical foundation of the SIA.
6. SIA can lead to problematic ethical and existential conclusions by emphasizing the quantity of observers over the quality of their experiences.
If applied to moral philosophy, SIA might suggest that creating vast numbers of minimally conscious beings is preferable to fewer beings with richer experiences, simply because it increases the likelihood of being among the more numerous group. This clashes with ethical intuitions about the value of conscious experiences.
You are massively confused!
I do not think being "massively confused" works that way.
SIA seems solid. Consider actually playing god to recreate the coin flip scenario. You flip a coin two days in a row and give yourself this rule before starting: “If I flip heads, I will email 3 of my friends a message that says ‘hello.’ If I flip tails I’ll email 1 friend ‘hello’.” On day 1 you flip heads (just by chance) and email the 3. On day 2 you flip tails (again just coincidentally) and email the one. Now you tell all 4 friends what you did and ask them to guess what you flipped on the day they were emailed. If they all guess heads, 3 out of 4 will be correct. If they all guess tails 1 out of 4 will be correct. So heads is a better guess. That is, guessing that the more friends were emailed option (heads) has a higher probability of being the right guess.
1. Coin Flip Rules:
- Flip a coin each day.
- If heads, email 3 friends.
- If tails, email 1 friend.
2. Results:
- Day 1: Flip heads, email 3 friends.
- Day 2: Flip tails, email 1 friend.
3. Query to Friends:
- Tell all 4 friends about the coin flips and ask them to guess the outcome on the day they received the email.
The argument suggests that each friend, knowing the rules, should guess heads because, statistically, there are more emails sent out on heads days.
1. Sure, from the perspective of a friend who receives an email, the likelihood of having been emailed on a heads day is higher because more emails are sent on those days.
Hence, it makes sense for each friend to consider the probability of being emailed based on the number of emails sent. Since there are more emails sent on heads days, the base rate probability of being an emailed friend on a heads day is higher.
2. In this context, the friends are trying to guess the specific outcome of a coin flip that affected them directly. SIA suggests they are more likely to be one of the friends emailed on a heads day simply because more people are emailed on those days.
This is a valid application of SIA in a straightforward probability scenario where the number of observers (email recipients) directly correlates with the coin flip outcome. However, this simplistic scenario doesn’t address the broader philosophical and practical criticisms of SIA.
3. In real-world applications, defining the reference class (the set of all possible observers) is not as straightforward as counting email recipients. In the email scenario, the reference class is clear and well-defined, but in more complex scenarios, it can be highly subjective and arbitrary.
While SIA works neatly in the email example, its application to more complex and abstract philosophical problems (like the nature of the universe or anthropic reasoning) can lead to inconsistencies and paradoxical results, as previously discussed.
4. The simplicity of the email example allows SIA to function without encountering the deeper issues it faces in more complex and abstract contexts. In scenarios involving vast or unknown quantities of potential observers, the reference class problem, subjective interpretation, and potential circular reasoning make SIA less reliable.
I think I agree with you but do not know much about this. I do think, in general, it has some value as a heuristic. There are real-world cases where it works. The music a randomly selected person likes is more likely than not to be popular (in the literal sense) for this reason. Basically, you need extra evidence for thinking you are atypical in a particular way, because, by definition, there are more typical people than any particular type of atypical person. I think it’s also why you shouldn’t think you are the only conscious person while everyone else is a philosophical zombie (acts like a person but has no subjective experiences). However, I also don’t think the SIA can bear the weight B’sB puts on it with his argument.
1. You mention that SIA has some heuristic value, which is an excellent observation. As a heuristic, SIA suggests that we should consider ourselves as typical observers within the context we are analyzing. This means that in the absence of specific evidence to the contrary, it’s reasonable to assume that our experiences and preferences align with the majority. Your example of music preferences illustrates this well—most people’s musical tastes are aligned with popular trends because that's the majority's preference.
2. Indeed, there are real-world cases where SIA seems to apply effectively. For instance, if you were to randomly meet someone and guess their favorite type of music, betting on a popular genre increases your chances of being correct. This is because popular preferences reflect the majority, making it a safer assumption in the absence of specific knowledge about the individual.
3. You correctly note that thinking of oneself as atypical requires additional evidence. This stems from the basic statistical principle that typical cases are more frequent than atypical ones. In other words, by default, it's more likely that an individual falls within the majority unless there is significant evidence to suggest otherwise. This reasoning can be extended to numerous aspects of human behavior and characteristics.
4. Your point about not assuming you are the only conscious person while everyone else is a philosophical zombie is an interesting application of this reasoning. If we assume that consciousness is a typical trait among humans, then it's reasonable to believe that others are conscious as well, rather than the contrary. This aligns with the heuristic that unless there is substantial evidence suggesting that others are not conscious, the default assumption should be that they are.
5. However, you also rightly point out that SIA might not bear the weight placed on it by Bostrom's Simulation Argument (B'sB). Bostrom's argument suggests that if we assume we are typical observers, then it is statistically more likely that we are living in a simulation created by a posthuman civilization. This is because the number of simulated realities could vastly outnumber the one base reality.
Here, SIA's heuristic value may not suffice for such a profound conclusion. The leap from using SIA as a guideline for understanding everyday phenomena to concluding that we are probably living in a simulation requires a more robust foundation. The SIA in this context might oversimplify complex existential and epistemological questions, reducing them to mere statistical likelihoods without adequately addressing the deeper implications and the assumptions involved.
You are correct, the SIA cannot bear the weight BsB puts on it.
Could I ask about "God’s extreme coin toss"?
Suppose that the message on the wall says: “I, God, tossed a fair coin. If it came up heads, I created one person in a room like this. If it came up tails, I created one person, and a million apples, also in rooms like this.” Since I can't be an apple, my credence should be 50/50 about the coin.
Similarly, suppose that the message on the wall says: “I, God, tossed a fair coin. If it came up heads, I created one person in a room like this who has your DNA. If it came up tails, I created one person who has your DNA, and a million people who have different DNA." Since I can't be a person with different DNA, my credence should be 50/50 about the coin.
Doesn't the SIA rely on the claim that "I could be someone else"? But that's a meaningless statement. I can't be someone else, just like I can't be an apple, or an apple can't be a light bulb.
What am I missing?
In the apple case, obviously the extra apples are irrelevant.
In the other case, the extra people who you are not are irrelevant. But this is not because SIA relies on the idea that you could be extra people. The notion relevant to SIA is "people you might currently be." Because there are a variety of people you might currently be, by Elga's reasoning, you should favor the theory on which there are more people you might currently be (if I might be Jon or Jack, then a theory that says there is Jon and Jack is superior because it makes it likelier that there'd be me).
It's not at all weird for there to be multiple people who you currently might be. Suppose that Jon and Jack go into a room and then get amnesia, unable to remember who they are. If I know the setup and I'm in the room, I should be undecided about whether I'm Jon or Jack.
Thanks. I think in general, your argument is mixing metaphysical modality and epistemic modality, but I'm not really sure.
Could I ask if either of the following situations are analogous to "God’s extreme coin toss"?
A: Your receive a letter in the mail saying "I tossed a coin. If it landed heads, I sent you (Bentham's Bulldog) a letter. If it landed tails, I sent you a letter and also sent a letter to 999,999 other people.
B: Your receive a letter in the mail saying "I made a list of 1 million people, and then tossed a coin. If it landed heads, I sent one letter to a random person on the list. If it landed tails, I sent a letter to everyone."
I assume you think B is analogous. If so, does that mean that in the heads scenario, God picked you out of a list of 1m people before you were created?
It's not mixing metaphysical modality and epistemic modality. The relevant bit is epistemic modality, for the argument.
I think those are not analogous. In the first case, I'm guaranteed to get a letter either way, in the second case, conditional on tails, I only have a 1 in a million chance of getting a letter.
In scenario B that I described, you are on the list of 1 million people. Before the coin toss (from the perspective of the letter-writer) if the coin is heads you have a 1 in a million chance of receiving a letter. If the coin is tails you have a 100% chance of getting the letter.
I suppose my point is that I understand the message on the wall to mean "I, God, tossed a fair coin. If it came up heads, I created YOU. If it came up tails, I created YOU and 999,999 other people."
To me, it seems that you understand the message to mean "I, God, tossed a fair coin. If it came up heads, I created one person (randomly selected from a set of 1 million people). If it came up tails, I created the entire set of 1 million people."
Sorry, typo, I meant conditional on heads you have a 1 in a million chance of getting the letter.
You misunderstand God's coin toss. It's about creating 1 person vs a million. There's then a question about how to reason about your existence if various different numbers of people were created. If you apply the Elga reasoning, and think that you're equally likely to be any of the million people created on tails as the one created on heads, if heads just creates one person, the odds of your existence is 1 in 1 million.
Here's an analogy: imagine that every person is in a room assigned a natural number. A coin is flipped. IF it comes up heads, every room gets a letter. If it comes up tails, just one room gets a letter. Upon getting a letter, I get huge evidence for heads. However, if tails entailed (pun intended) that my room in particular would get a letter, then I wouldn't get an update either way (of course, that theory would have a vanishingly low prior--what are the odds I'd be picked out out of the infinite people that could be).
Thanks for the responses.
I'm just not sure the propositions "I could exist" or "I could have not existed" have any meaning when interpreted as propositions involving epistemic modality. The proposition pertains to evidence which "I" hold, so my existence is "necessary" for the proposition to be meaningful. The "I" in the proposition must exist for there to be some evidence. So if the proposition refers to my existence as "possible", "probable", "contingent", etc. then it seems to be inconsistent with there being a necessary "I".
Anyway, we can leave it there. That's just my initial thoughts, and I'll have to think it through some more.
“You’re DNA” could mean the DNA of anyone. And this leaves SIA intact. If it had a particular genome sequence specified (not the words “your DNA”), and upon sequencing your genome you found that you matched, yes the odds would be only 50/50.
I think this argument is way stronger than almost any other argument for theism I have heard, even from professional philosophers (though who knows, maybe once I've thought about it more, I'll start thinking it's weak). But I still think it has some serious flaws.
First of all, even if there is a huge class of possible people, I known from my own subjective experience that the vast majority of them can't be me. Even if there is a possible mind that believes every possible truth, I already know that I am not one of those minds that believe infinitary truths, so SIA does not favor a world where those kinds of minds exist. SIA provides exactly zero evidence for a world where unsetly-many minds exist, one that believes every possible truth, over a world where only countably many minds exist who all believe finitary truths.
(This is similar to the SIA version of the doomsday argument. If I don't know my birth rank, then SIA says I should believe with a very high probability that a large number of humans will exist. But if I know my birth rank, SIA no longer gives me any evidence for the existence of a large number of future humans, it just cancels out the SSA argument that there will be fewer of them. Likewise, if I really could of been any of those possible minds, SIA would give me evidence that there are a lot of possible minds, but if I know that I'm one of a countable class of possible minds, SIA doesn't favor the hypothesis that Beth 2 minds exist over a hypothesis that says every possible mind from that countable class exists.)
Second, I'm not actually convinced that there are Beth-2 possible people. Not every "arrangement of stuff" is a person, and even for the arrangements of stuff that are people, personal identity is more coarse-grained then exact identity of physical arrangement (infinitely more coarse-grained, in fact). Any difference in the arrangement of stuff constituting a person that doesn't make a difference to that person's subjective experience doesn't make them a different person. And no, this doesn't mean I have to believe in a soul- that would be like saying that I must believe that computers have souls because there are only countably many possible computations even though there are Beth-2 possible arrangements of matter that could constitute a computer. (I think the soul argument is the worst argument made in this piece, on par with the really bad theistic arguments.)
I'm also not sure that for any truth, there's a possible mind that believes it. I can't even conceive of a mind that would be able to think about conjunctions of uncountably many statements. Maybe you can get me to believe that at least Beth 1 minds exist based on countable conjunctions, but anything higher than that just doesn't seem supported.
Third, RSIA does not favor necessitarianism. Say you have a pre-anthropic probability of 1% for necessitarianism. Necessitarianism, however, doesn't predict (pre-anthropically) that *you* are metaphysically necessary. It predicts that, whatever minds exist, they are necessary. Whatever your pre-anthropic prior probability that you exist is (based on SIA, it should be zero or some infinitesimal), you should have approximately the same pre-anthropic prior on your existence given necessitarianism. Once you learn that you exist, of course, you will use this anthropic evidence to update to a 100% chance that you are metaphysically necessary, given necessitarianism. But you can't then use this updated probability to update necessitarianism to be more likely - that would be double-counting the anthropic evidence.
(Basically, my pre-anthropic prior probability that necessitarianism is true would be split between all possible states of affairs that might be metaphysically necessary. Most of those states of affairs do not involve me existing, so necessitarianism does not imply that my existence would be likely.)
Fourth, any probability distribution you have on the number of possible people, or the pre-anthropic number of actual people, has to be 0 for all but countably many different cardinalities. It's not clear, then, that you can always use SIA to make hypotheses on which larger cardinalities exist infinitely more likely than any other hypothesis.
Fifth, I just don't see any strong reason why a large cardinality of people, if possible, couldn't exist on atheism. Sure, it would be less likely than on theism, but would it really be overwhelmingly less likely?
Sixth, the same inductive problems you pointed out for modal realism and Tegmark's multiverse would also apply to theism with Beth 2 people. If God creates every possible person, or even just a collection of people with the same cardinality as the set of all possible people, then the vast majority of them (100% of them, in fact) will not have anything we would describe as a coherent experience. There are only countably many experiences we could possibly have in a world where induction works.
There are possible minds whose thoughts are filled only with states of pain, but why would an infinitely good god create them? Shouldn't you believe in an evil god?
The argument doesn't need the idea God would make every possible person but just the idea that the number of people God would make would be very great. I also think that while there is a possible state one could be in where they'd be in pain, God would simply create that person not in pain.
Evil god would create infinitely more people, so under SIA evil god is infinitely more likely
Evil God and good God would create the same number! On my view, that number would be every possible person--and then they'd give them a good life. Evil God is also false for other reasons https://benthams.substack.com/p/the-evil-god-challenge?utm_source=publication-search
Evil God would create more all possible people - both happy and unhappy. God can only create happy ones. It makes likelihood P(Evil God | all possible people exist) much more likely than P(Good God | all possible people exist). And whatever story explains Evil God creating happy people just lowers prior P(Evil God), even if it lowers proportionally to likelihood it's obvious we should favor likelihoods over priors.
What, why would an evil God make happy people?
Also, if I'm right God would make all possible people and then just make them all happy.
If you think minds are classified by truths they think about, then there are minds whose thoughts are filled by truths of this type - "If I was subjected to M amount torture right now, I would experience N units of pain". I don't see how god can make these minds happy while preserving these thoughts.
>What, why would an evil God make happy people?
Maybe Evil God can't choose and can only create all possible people, it just lowers its prior probability.
This makes much more sense than that there is an all-benevolent god. That a being of maximal goodness is maximally simple is not true in any relevant sense I can think of, and even if it were, this is irrelevant. A priori, why would simple things be more likely to exist than complex ones? This is a groundless assumption.
Why do you think you’re not on an elaborate Truman show? There’s no relevant empirical evidence either way. The reason you think it’s less likely that you’re on an elaborate Truman show is because it’s less simple. You need to use non-empirical reasoning, and simplicity is a virtue for theories.
I’m agnostic as to whether or not I’m on a Truman Show. But I don’t hold my breath waiting for a crack in the sky because Truman Show is just one of countless logically possible explanations for all observed phenomena. I don’t play favorites with theories a priori and discount ones that have more moving parts. Hence, this explanation is as good as any other that fully fits the facts.* However, there are so many logically consistent, mutually exclusive such theories, that any one in particular has vanishingly low a priori probability of being correct.
One might mistakenly think otherwise because of Ockham’s Razor. The only relevant sense in which Ockham’s Razor is true is that theories that make more ambitious claims are less likely to be true on probabilistic grounds. For instance, if Theory A is that there is an ever-existing being that is all-powerful AND all-benevolent, and Theory B is that there exists an ever-existing being that is all-powerful but it’s level of benevolence is unspecified (that is, Theory B is agnostic as to this being’s level of benevolence; it may be maximally benevolent, minimally benevolent, or anything in between), then Theory A is necessarily less probable than Theory B.
*I actually don’t think this theory (Truman Show) predicts observed phenomena as well as metaphysical naturalism does, but let’s just suppose it does for the sake of argument. Here’s why I don’t think Truman Show is a good theory by the way:
Premise: There are no tell-tale signs that we are in a Truman Show reality.
Premise: The probabilty of having no tell-tale signs if we are actually in a Truman Show situation is greater than zero. (We cannot just assume that all logically possible Truman Show creating hypothetical entities would be perfect at hiding their tracks.)
Premise: Under metaphysical naturalism, the probability of having no tell-tale signs is zero.
Conclusion: Metaphysical Naturalism is more probably correct than a Truman Show situation.
I don't follow your reasoning in Premise (2): you don't need to assume that all logically possible Truman Show entities are perfect. Truman Show can equally predict the empirical evidence, if we can conceive of at least *one* logically (metaphysically) possible Truman-Show-creating entity that is perfect at hiding its tracks. As long as such a Truman Show entity is possible, call her X, the empirical evidence has equal probability on Truman-Show-X and ~Truman-Show-X.
I also don't follow your reasoning about Ockham's Razor. You claim that it "is true is that theories that make more ambitious claims are less likely to be true." But you also claim that "simple things be[ing] more likely to exist than complex ones" is "groundless" and that you "don't play favorites with theories a priori and discount ones that have more moving parts," and it would be a "mistake" to appeal to Ockham when evaluating theories *a priori*. But your explanation of why Ockham has force seemed reasonable to me! So which is it? I think you have a few options:
(1) There is no rational way to evaluate theories a priori, and Ockham can only be applied to a posteriori evidence. So we should be agnostic across all theories (skeptical or realist) that predict our experience with equal probability.
(2) Ockham does apply a priori. But an all-benevolent God is less simple than other theories that predict the evidence, so it is less likely to be true.
(3) Ockham does apply a priori, but there's a special way that "simplicity" is not the same as "ambition." Maybe "simplicity" is not well-defined. So an all-benevolent God might be simple, or not simple, but what matters is that it is more "ambitious" than other theories that predict the evidence, so it is less likely to be true.
In response to: “I don't follow your reasoning in Premise (2): you don't need to assume that all logically possible Truman Show entities are perfect. Truman Show can equally predict the empirical evidence, if we can conceive of at least *one* logically (metaphysically) possible Truman-Show-creating entity that is perfect at hiding its tracks. As long as such a Truman Show entity is possible, call her X, the empirical evidence has equal probability on Truman-Show-X and ~Truman-Show-X.”
Let me lay out my reasoning more clearly. A Truman Show scenario (as I meant it) is one where there are entities who have set up our universe, or some (most?) aspects of it so that they can watch us live our lives for their entertainment. Additionally, they attempt to deceive us into thinking they are not there and that our everyday lives are unfolding according to some natural course of events (i.e. not being manipulated by them). It is stacking the deck to assume they will be successful in all possible states of the universe qualifying as Truman Shows that populate the a priori probability space. (I understand now from reading more of your comments that you meant the Truman Show to mean a successful skeptical theory in the sense that, by definition, the deceiving entities succeed entirely in deceiving us. By the way, do you stipulate as part of the Truman Show theory that they will always be successful at deceiving us?) Let me define P(T) as the a priori probability that a Truman Show scenario of some kind is unfolding.
Now, by Metaphysical Naturalism I mean a state of affairs where all that exists are the things we’ve discovered to exist from direct observation and indirect-observation-plus-reasoning (science, roughly) plus possibly other things we have not discovered yet but that will be similar (enough) in nature to the things we have discovered so far. New types of particles are fine. New biological species are fine. New sorts of invisible but study-able and observable-with-instruments “waves” (like electro-magnetic waves but not yet discovered) are fine, too. Aliens are fine, too (if they aren’t magical–magical meaning “no mechanisms to do things that all human experience shows can’t be done without mechanisms to accomplish them”), but just to to make the comparison, I won’t allow super-technologically-advanced aliens who are perpetrating a Truman Show stunt on us. Let P(M) mean “the a priori probability that Metaphysical Naturalism” is true.
The tricky part is here. I speculate that P(T) = P(M). Why? I don’t really have a reason. I don’t even really know how to start assigning prior probabilities to such things so the only reasonable thing to do (it seems to me) is to assume P(T) = P(M). At this point, let’s introduce a bit of evidence: There have been no tell-tale signs of a Truman Show scenario unfolding. This is exactly what I expect under Metaphysical Naturalism. However, under Truman, at least sometimes, the deceiving entities are not successful (like in the actual Truman Show). So this evidence increases our credence in Metaphysical Naturalism and decreases our credence in the Truman Show theory. The posterior probability of Metaphysical Naturalism is greater than the posterior probability of Truman Show.
Was I right to assume P(T) = P(M)? I’m not really sure, but that’s kind of exactly why I did it. I can’t think of any good a priori arguments to favor one over the other so I set them equal. I’m not really satisfied with this though, so I’m open to ideas for how to better assign a priori probabilities. BUT I WILL NEVER ACCEPT SIMPLICITY AS A SIGN OF LIKELIHOOD TO OBTAIN! No, I’m kidding. I don’t think it works, but I’m not certain. I’ll explain more in further comments to your other question.
No, the reason you don't consider the hypothesis is because philosophical thinking isn't part of ordinary day to day living. The majority of what you do in any day is unratiocinated, trained behavior to a variety of stimuluses that exist in modern society.
>The reason you think it’s less likely that you’re on an elaborate Truman show is because it’s less simple.
...conditional on other evidence you've collected throughout your life that you falsly think applies in this case because you're underspecifying the skeptical scenario. There is no a priori reason to prefer being on the Truman show vs external world realism because both of these are stipulated to explain your experiences exactly. And it's not clear to me that there is any sort of agreed upon definition of a priori simplicity that could be used as a reliable measure to decide between the likelihood of various skeptical scenarios obtaining.
>There is no a priori reason to prefer being on the Truman show vs external world realism because both of these are stipulated to explain your experiences exactly.
I think you meant "there is no *a posteriori* reason to prefer...because both explain your experiences." Agreed. But my point was there does exist an *a priori* reason: simplicity (or something like that).
You can correct me if I'm misrepresenting you, but are you just biting the bullet here? You place equal credence on Truman show and external world realism?
There is no bullet to bite. If there were different consequences that hinged on whether one believed in external world realism vs being on the Truman show, then the skeptical scenario setup would have failed because the point of skeptical scenarios is to set up identical cases where the explanatory substrate varies. By stipulation you are ruling out any practical consequences to believing in either explanation, so there is no bullet to bite for either party ex hypothesi.
>But my point was there does exist an *a priori* reason: simplicity.
I don't think there's any metaphysical gap that simpler theories bridge versus less simple ones, and I also don't understand what you mean by a priori simplicity. It seems to me like simplicity is a human value that's subject to all sorts of contextual factors. If it's easier for people to work with simpler theories, then there will be an asymmetry between the Truman show and external world realism, in which case the skeptical scenario fails because there is a practical difference between the two - one of them is easier to work with than the other.
Furthermore, it seems to me that the Truman show posits just the Truman show whereas external world realism posits the Truman show plus everything else in the external world. What fact would I be getting wrong if I decided that the Truman show posits fewer variables and thus it's the simpler and truer hypothesis? Or why couldn't I invoke BB's conception of God as "absolutely simple perfection" to explain all my perceptions? Seems to me like that's simpler than both the Truman show and external world realism. And remember you can't appeal to any practical difference because you're stipulating those are equivalent between the theories.
Just to clarify, Truman show posits the Truman show + the creators + the viewers + the world the creators and viewers inhabit. But this is not really important. Consider:
(1) It is rational to assign low credence to being on the Truman show
(2) As we have agreed, (1) cannot depend on any empirical (a posteriori) evidence. So (1) must be a result of a priori reasoning.
(3) If simplicity is a virtue, then we have an a priori reason to support (1).
(4) Simplicity is a virtue.
One way to attack (4) is to posit some *other* a priori reason for (1). Another way to attack (4) is to deny (1): the intuition that it is rational to believe your are not in a skeptical scenario is confused. Since (forgive me if I'm wrong) you think that a priori reasoning is impermissible, (2) requires you to deny (1).
However, since (1) is prima facie extremely plausible to most people, I would characterize its denial as biting the bullet. It would be very weird if the rational position would be to be totally agnostic across realism and skeptical scenarios.
Already mentioned this to you in a DM, but thought I'd leave a comment here as well for posterity's sake. What do you think of the simple response that SIA entails the Tegmark mathematical universe hypothesis (MUH), and that SIA should therefore be revised, because MUH would undermine induction? Since MUH entails more than beth-2 observers (it entails all the observers modal realism does, plus various other kind of non-spatiotemporal or non-physical observers that are mathematically possible) then MUH is preferable to theism, since theism only entails beth-2 observers. So SIA would predict MUH over God. But MUH entails inductive failure, so logically SIA must be revised in cases of infinities; we shouldn't update our credences when based on reasoning about the infinite.
Now normally, as you yourself pointed out, we might reject theories which lead to inductive failure on the grounds that they are self-defeating. So for example, we might reject the multiverse hypothesis because it leads to too many Boltzmann brains, but if we are Boltzmann brains then we have no grounds to rely on our evidence that makes us think the multiverse is real in the first place. The problem with SIA reasoning though is that we don't rely on evidence of that kind to conclude that MUH is true. All we need to conclude that MUH is most probably true is the evidence of our existence, which we can get even if we lived in a world where induction was false, and where we have no basis for the future being like the past. If this is true, then we should abandon SIA or revise it in the case of infinities, since inductive failure would seem to be unacceptable. But if we have to revise SIA in cases of infinities, then it's not clear that the theism hypothesis is warranted.
I think it entails not that but theism!
I updated the argument from the DM to be about MUH (which entails more than beth-2 observers), so I think you will need a new response. :)
Anyways the idea is that we can't discard MUH just because of inductive failure, since the regular argument against inductive failure (it's self-defeating) doesn't apply here when we reason based on SIA.
I think theism entails more than Beth 2 people.
Is this argument susceptible to the evil god challenge? It seems like evil god has equally strong reason to create as many people as possible as the traditional conception of god would. It naively seems to me that if this argument goes through, it’s equally good evidence for evil god?
Yes, but I think evil god is false for other reasons https://benthams.substack.com/p/the-evil-god-challenge?utm_source=publication-search
This arguments relies on several premises and, as far as I can tell, basically all of them are wrong. At every reasoning step there is some crucial flaw. Even if we, for the sake of argument, assume that SIA is generally correct, then there are still all the other problems.
> Would God create all people?
> But even if you’re this confident, because the odds—as we’ll see—of your existence conditional on naturalism are so astronomically low—very near zero—even a 1% chance that God would create beings like us is enough for your existence to massively favor naturalism.
You probably meant "massively favor theism" instead of "massively favor naturalism" here.
You assume that 99% that God would not create us is overconfident on priors, but as a matter of fact, there is no lower boundary on probability that God would create any person. Under naturalism there at least some lower boundary - the one you calculate while assuming that all the fine-tuned constants of the universe just happened at random - even the stupidest naturalistic explanation provides at least some probability of our existence. But if we assume that some kind of God exists, without specifics - that would be a random sample from infinity, the chance that it just so happens that we got a God who would create us is literally zero. You keep equating the existence of God with the existence of a specific type of God who creates all possible life, for no particular reason, but this is an extra infinitely improbable assumption.
> I claim that thinking about SIA should make you into a theist, providing massively strong evidence for the existence of God. If God wouldn’t create you, then theism is already false, so this wouldn’t undermine the force of the argument—rather, it would just be a separate argument.
The reason why SIA provides an argument for theism is based on the assumption that existence of all possible people is more likely if God exists, than otherwise. If it's not the case, then SIA doesn't favor theism anymore. God who creates only one universe with only planet Earth filled with life is compatible with the observations, but not privileged by SIA in any way. On its own SIA is not in favor of theistic explanation of infinite people more than atheistic explanation of infinite people.
> Can atheism explain the anthropic data?
> Of all the theories ever proposed by atheists, there are, to the best of my knowledge, only two that naturally predict the existence of every possible person. They are modal realism, according to which every possible world exists, and Tegmark’s view according to which every possible mathematical structure is physically instantiated.
> The problem—and this is a more general problem for atheistic views—is that both of these views undermine induction.
This would be a problem for atheistic view only if we knew for a fact that induction is justified, which we do not know. Surely, we would like it to be true, but this is a completely separate question. From the perspective of SIA both atheistic and theistic explanation of infinite people are equal, and the appeal to our desire of induction to be justified is a different argument for the existence of God that has nothing to do with anthropics. But lets look at it anyway, does God help with induction?
> If there’s a God, our inductive processes are reliable—God would make sure there are stable laws and that everyone’s reasoning is mostly reliable over the course of their lives when they’re in a situation like ours.
Once again, you are simply assuming a specific type of God that would care about this kind of things, which is but a one possible type of God from infinity. What's more, such God would be penalized under SIA, as he would not create people with non-reliable reasoning, therefore creating less people, than counter-factually.
Also, as a tangent, notice that in our actual world, there are a lot of people with unreliable reasoning and lots of examples of induction not working.
> Other than these two, there’s no viable naturalistic explanation of why at least Beth 2 people would exist.
You can always come up with lazy atheistic model: there is some metaphysical law according to which Beth 2 people exist, which doesn't have any other properties of God - it's an inanimate force not a person. This model actually has an advantage over theism from the perspective of anthropics - we do not need to think about God applying SIA to his own existence - more on that below.
> Maybe there are only aleph null people
> I’ll argue, there are strong grounds for thinking that the number of possible people is not just aleph null or Beth 2 but unsetly many—too big to be a set. The infinites mathematicians talk about are infinite sets—but I think the number of possible people is a collection too large to be a set
If something is not a set than you can't coherently talk about it having cordinality and apply probability theory and therefore your argument is incoherent to begin with.
Now several meta-points. How could one notice problems with this argument even without engaging with it on object level.
First of all, SIA famously breaks down when reasoning about infinity and you are attempting to use it specifically in this case, so it's no surprise that it produces crazy results, which one shouldn't trust, even if they accept SIA for simple cases such as Sleeping Beauty or Doomsday Argument.
Secondly, you are talking about infinitely strong update in favor of theism just based on the fact of ones existence, regardless of any empirical evidence, and whether our minds were made corresponding to the universe by any optimization process. This is an incredible huge red flag and a contradiction of conservation of energy, never mind expected evidence.
Thirdly, the argument proves too much. Not just the existence of God, but infinite chain of more and more powerful Gods, where every n-th God creates all the possible n-1-th Gods. Just think about how God himself is supposed to reason under SIA. Also see this comment: https://open.substack.com/pub/benthams/p/science-and-religion?r=j14r1&utm_campaign=comment-list-share-cta&utm_medium=web&comments=true&commentId=58325007
Thanks for the typo!
//Under naturalism there at least some lower boundary - the one you calculate while assuming that all the fine-tuned constants of the universe just happened at random - even the stupidest naturalistic explanation provides at least some probability of our existence. But if we assume that some kind of God exists, without specifics - that would be a random sample from infinity, the chance that it just so happens that we got a God who would create us is literally zero.//
Well, if SIA is right, the odds of your existence on naturalism is either zero or infintesimal. In contrast, if a perfect being would make every possible person, then the creation of you is strongly predicted if a perfect being. Now, maybe your point is just that the odds of a perfect being are super low even if there's a creative being of some sort. I agree that if you start out thinking perfect being theism has a zero prior, this argument shouldn't move you, but you shouldn't do that because it's simple, elegant, and parsimonious.
You act surprised when I talk about God as a perfect being. Well that's what I mean when I say God. When I'm talking about limited beings that aren't perfect, I say gods. This is a terminological point, but it might clear up some confusion.
//This would be a problem for atheistic view only if we knew for a fact that induction is justified, which we do not know.//
I think we do know it. You shouldn't believe things that are crazy, and the idea that we have no basis for thinking the sun will rise tomorrow is crazy. Also, if induction doesn't work, it would probably have given out in the past--probably the laws of nature wouldn't have worked till this point.
//Once again, you are simply assuming a specific type of God that would care about this kind of things, which is but a one possible type of God from infinity.//
Well this one is simpler and more parsimonious. If you posit a god with random arbitrary desires, that's ad hoc and not simple or elegant.
//Also, as a tangent, notice that in our actual world, there are a lot of people with unreliable reasoning and lots of examples of induction not working.//
My claim is that everyone, on theism, who has mental states like mine currently will find they mostly work over the course of their life, counting what will happen in the next life. I also give a bunch of other reasons in the article why theism plus infinite people doesn't undermine induction.
//You can always come up with lazy atheistic model: there is some metaphysical law according to which Beth 2 people exist, which doesn't have any other properties of God - it's an inanimate force not a person. This model actually has an advantage over theism from the perspective of anthropics - we do not need to think about God applying SIA to his own existence - more on that below.//
Positing that there are just Beth 2 universes for no reason is not at all simple. You shouldn't posit an infinite number of things exist for no reason! Also, as I explain, this undermines induction.
//First of all, SIA famously breaks down when reasoning about infinity and you are attempting to use it specifically in this case, so it's no surprise that it produces crazy results, which one shouldn't trust, even if they accept SIA for simple cases such as Sleeping Beauty or Doomsday Argument.//
There are some cases where it's unclear how to apply SIA to infinites. But there are other much more obvious cases. This is one of them--SIA is only unclear when comparing infinites of the same cardinality, which we're not doing here.
//Secondly, you are talking about infinitely strong update in favor of theism just based on the fact of ones existence, regardless of any empirical evidence, and whether our minds were made corresponding to the universe by any optimization process. This is an incredible huge red flag and a contradiction of conservation of energy, never mind expected evidence.//
It doesn't violate expected evidence for reasons I've explained to you before. It takes your existence as evidence favoring theories where there are more people--no credence rises in expectation. God can violate conservation of energy in creating a multiverse, obviously, because he's omnipotent.
//Thirdly, the argument proves too much. Not just the existence of God, but infinite chain of more and more powerful Gods, where every n-th God creates all the possible n-1-th Gods. Just think about how God himself is supposed to reason under SIA.//
God has no uncertainty or need to reason because he's omniscient--directly aware of every fact. There needn't be an infinite chain of Gods--just one God who creates all possible people, which is what the arguments says there is.
Happy to chat about this over video call as we discussed doing at some point, I feel like we never get anywhere with our long text back and forths, and they get a bit tedious, sorry.
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As for induction, sadly, we already had to abolish it in order to pass the first question anyway, so God involving theories do not have any advantage over non-God-involving ones. Also, as an induction related tangent:
> I think we do know it. You shouldn't believe things that are crazy, and the idea that we have no basis for thinking the sun will rise tomorrow is crazy.
Suppose I just told you that every reasoning step in your post is crazy and refused to ellaborate further. Would you consider it to be more substantial critique? Would you agree with someone who simply claims that we justifiably know that omnibenevalent god does not exist because it would be crazy otherwise? I don't think so. When you talk about anthropics and people simply dismiss it as some crazy nonsense, I think you are rightfully offended that they do not engage with the substance of your arguments. The appeal to craziness is just an appeal to intuition and intuitions may and often are wrong. If you have no justification for why something appears crazy to you it doesn't mean that you "just know it", it means that your intuition is baseless or you still didn't find the actual sourse for it. Don't get me wrong, common sense is a decent heuristic, especially when well callibrated. But you won't be able to grow as a philosopher without challenging it.
> Also, if induction doesn't work, it would probably have given out in the past--probably the laws of nature wouldn't have worked till this point.
Nope! That's inductive reasoning, and it wouldn't be valid in a world where induction doesn't work.
> My claim is that everyone, on theism, who has mental states like mine currently will find they mostly work over the course of their life, counting what will happen in the next life.
Have you just a priori proved that insanity is impossible under theism, therefore disproving theism? Or at least that it's impossible for *you in particular* to go insane, no matter what?
Okay, back to the track. If, despite everything, we, for the sake of argument, assume that indeed Omnibenevalent God is the simplest cause for the existence of all possible people, we still have to answer the last question: "Is the probability of Omnibenevalent God highter than comulative probability of other causes for the existence of all possible people?" His assumed simplicity may give him a boost in probability but it may be just having probability of several percents, while other alternatives have probability of tenth parts of a persent individually and yet together they absolutely truimpth over the Omnibenevalent God hypothesis.
So there is that, Three questions, without confidently answering "yes" to all of them your argument doesn't work.
> It doesn't violate expected evidence for reasons I've explained to you before. It takes your existence as evidence favoring theories where there are more people--no credence rises in expectation.
As another tangent, I may have a good example which can bring our disagreement about conservation of expected evidence closer to solution.
A coin is tossed. On Heads a red ball is placed in the room. On Tails a red and a blue ball are placed in the room. You come into the room, and immediately see a red ball. What is your confidence supposed to be that the coin came Heads?
> God can violate conservation of energy in creating a multiverse, obviously, because he's omnipotent.
That's an interesting question, actually. Being omnipotent can be perceived as having infinite energy to spare, therefore by creating stuff, he doesn't violate conservation of energy, so technically he can't violate it, unless he can make himself not omnipotent anymore and then still create stuff out of nothing.
But this is besides the point. Our brains can not violate conservation of energy. And it's our brains which make the inference from our existence to the existence of God - which would be a violation were it a reliable way to produce truth.
> SIA is only unclear when comparing infinites of the same cardinality, which we're not doing here.
Oh but we do! See the point about people who experience eternal torture and eternal bliss after leading regular lives like ours.
> God has no uncertainty or need to reason because he's omniscient--directly aware of every fact.
But surely, he can still reason right? If some way of reasoning systematically produces correct results, omnicient God should be able to arrive to the correct results using this method of reasoning - even though he doesn't really need it as he already knows the answers.
For example, God knows that 358794/3=119598. He still can apply long division to arrive to this result. It's not that long division suddenly breaks apart when God tries to use it.
And if SIA is true, that is, inference from ones existence to the existence of uncountable infinities of other creatures like you is correct, then God applying this method to his own existence would infer the existence of an infinity of other creators like him, and it has to be true inference. Of course, being omniscient while SIA is true, God would already know that infinite Gods like him exist - this is the only self-consistent possibility. Therefore from SIA we can deduce the existence of infinite Gods and infinite super-Gods who created the infinity of Gods and so on and so forth.
We can declare that SIA isn't applicable to God-like beings, but it will make the theory much less elegant as we will have to add an explicit exclusion case and on priors regular SIA should be assumed more probable.
> Happy to chat about this over video call
Looking forward to it!
> Well, if SIA is right, the odds of your existence on naturalism is either zero or infintesimal.
What exactly do you mean by naturalism here? Surely, there are possible explanations why infinite people exists without invoking a sentient creator and specifically Omnibenevelent one.
> Well that's what I mean when I say God.
I see a huge leap from "there is some reason why infinite people exist" to "there is this specific type of creator who created all of them". I feel that this jump to conclusion may be hidden behind the term "God" which can mean both specifically perfectly good creator and any type of extremely powerful demiurg. Anyway, with this out of our way lets look at three questions, all of which has to be answered "yes", so that implication from SIA to perfectly good God would work.
First question is "Would omnibenevalent God cretate all possible people". You present some case for it, but also later you claim that he would not create people for whom induction doesn't work. This is a huge problem because a set of people for whom induction doe not work seems to be a superset of people for whom it works reliably. Or at least we can be reasonably certain that omnibenevalent God would not create people who have regular lives like ours and then constantly experience eternal torture but the amount of such people is comparable to the amount of people who have regular lives and then experience eternal bliss. There is also an interesting in its own question whether living lives like ours and then experiencing eternal bliss/torture would be in defiance of induction or not and trying to correctly formalize what it even means that induction works/doesn't work. Anyway, it seems that God creates only some amount of possible people and therefore SIA doesn't imply it.
I really don't see a way out of this conundrum. Either we bite the bullet of not creating some considerable amount of people and the argument from SIA crumbles or we bite the bullet of creating literally every possible person, then there is no justification for induction and it's not even clear in what sense God in question is omnibenevalent.
Let's for the sake of argument bite the latter bullet. Second question is whether perfectly good God is the most likely creator of all possible people. You write:
> Well this one is simpler and more parsimonious. If you posit a god with random arbitrary desires, that's ad hoc and not simple or elegant.
Here you make an appeal to intuition that perfection is simple based on the fact that many human languages have one simple world for the concept. This is, of course, completely unpersuasive for anyone who understands up-to-date formalizations of complexity and reasons why we ended up embrasing them instead of appeals to natural language. But beyond that. How is perfection simple if we do not even understand what it entails? We can apply adjective "perfect" to opposite meaning nouns, like perfectly big and perfectly small. What size then is someone who is just "perfect"? Is perfection even a thing in itself? Does it have meaning without an additional noun? And so on and so forth. You need to properly formalize what is meant by "perfection" so that we can see that implications from it actually work instead of constantly redefining the term ad hoc. And, of course, there are many other, much simpler words is natural languages. Like "Red". Why not assume that the creator is someone whose essense is redness? You call such gods jerrymandered, but it's not clear by which principle you apply such description to them and not the perfectly good God, beyong basic wishful thinking. For me none of them appear parsimoniousin the slightest - you postulate infinities - the opposite thing to being parsimonious.
And of course there are explanations for the existence of all possible people that do not include sentient creators at all. To this you reply:
> Positing that there are just Beth 2 universes for no reason is not at all simple. You shouldn't posit an infinite number of things exist for no reason! Also, as I explain, this undermines induction.
But we are not just positing that there are Beth 2 universes for no reason! We claim that there is a reason - a methaphysical law according to which there has to exist every possible person. Surely, if you can just accept the existence of God as not needing any additional reason you can do the same courtesy to the existence of this metaphysical law? In a way it's simpler than any god - it doesn't require any sentience or will or other properties. It just does one thing.
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100% this: “You assume that 99% that God would not create us is overconfident on priors, but as a matter of fact, there is no lower boundary on probability that God would create any person. Under naturalism there at least some lower boundary - the one you calculate while assuming that all the fine-tuned constants of the universe just happened at random - even the stupidest naturalistic explanation provides at least some probability of our existence. But if we assume that some kind of God exists, without specifics - that would be a random sample from infinity, the chance that it just so happens that we got a God who would create us is literally zero. You keep equating the existence of God with the existence of a specific type of God who creates all possible life, for no particular reason, but this is an extra infinitely improbable assumption.”
I had exactly this thought when reading a different Bentham’s Bulldog article. Basically, when he was explaining why fine-tuning was unlikely on naturalism, it occurred to me that exactly the same reasoning implies that a god that wants fine tuning is implausible. Here’s Bentham’s Bulldog followed by my slight rewording to employ the argument against a god that fine tunes:
Bentham’s Bulldog:
“To determine subjective chances, you should imagine a rational agent assigning probabilities to the possible outcomes before they know the actual outcomes. In the case of fine-tuning, for instance, a person who didn’t yet know what values the laws fell into would think there was a super small chance it would fall in the finely-tuned range because it could fall in any range. Because there are at least 10^120 values of the cosmological constant alone, and nothing special, conditional on naturalism, about the finely-tuned one that it happens to be, the odds of fine-tuning by chance of just the cosmological constant are 1/10^120.”
Bentham’s Bulldog’s argument slightly tweaked to argue against Theism:
“To determine subjective chances, you should imagine a rational agent assigning probabilities to the possible outcomes before they know the actual outcomes. In the case of a god that wants to finely tune physical constants to allow a universe exactly like ours to existence, for instance, a person who didn’t yet know what kind of god existed (or even if there was a god) would think there was a super small chance there would be a god with exactly that preference and the ability to produce such an outcome because this hypothesized being could have preferences of any sort whatsoever and also could have any conceivable level of ability and might even not exist at all. Because there are at least 10^120 values of the cosmological constant alone, and nothing special, conditional on “an omnipotent being exists”, about a god wanting to finely tune it to be what we observe it to be, the odds of there being a god with a preference for fine-tuning by chance of just the cosmological constant are 1/10^120.”
No, this is mistake. It violates conservation of expected evidence if you'll be around to observe all outcomes, and only some of them will raise your credence. But it's not violating COE to have you expect your credence to go up in the future. On average, tomorrow my credence will be higher in having not died tonight than it is today.
I’m afraid I don’t understand your response (what’s “conservation of expected evidence”?). But I’ll see if I can figure it out. Thank you for lively discussion!
Oh wait nvm I misread your point. Yeah, it's true that it's unlikely a perfect being would make exactly our constants, but it's also unlikely on atheism that there'd be exactly our constants. However, theism makes it more likely we'd have our constants, because it removes the most likely constants which would produce nothing of value.
I think most of my criticisms won’t seem to apply from your perspective given your definition of god as a perfect being, which differs from what I had thought you meant by god previously. But first pass, “there is some good and a lot of bad (a fact)” doesn’t follow with much likelihood from “there exists a being of maximal goodness”. Do I have to believe a theodicy for your argument to be sound and valid?
Bulldog’s Theodicy can be found here: https://benthams.substack.com/p/why-theres-evil
I personally think that animal suffering demolishes it, but you can come to your own conclusions.
I think it's far more likely that the cosmos has always existed. And there is no need for a god to create anything, much less people.
No part of my argument depends on how long the cosmos has been around ofr.
Yes, it makes no sense to make up entities with fantastical powers to “explain” things when there is no good independent evidence that such beings exist in the first place. Seriously, this argument is no better as an explanation than “the universe did it”. That is, it is the lack of an explanation dressed up as one.
The evidence for any being is that it explains things!
It explains things in precisely the same empty way that “élan vital” explained biological evolution. How did god do it? I might ask. You’d have to say you don’t know. How do you know he/she could? Have you seen evidence of his/her ability to do such things? You’d have to say “no”. The truth is you merely stipulate as part of your theory that god has these abilities. But I can just stipulate as part of my atheistic theory of the universe that it would inevitably lead to life too. I know that probably won’t sway you because you believe that the existence of god is likely, a priori. I think that’s a grave mistake, though, and that god’s existence has as low of an a priori probability as the existence of a spaghetti monster in the outer reaches of space (to use Dawkin’s metaphor for a being that is logically possible but whose existence can’t be empirically verified or falsified).
That's not how I see it. The evidence for any being is that I can observe it in some way.
But I'm obviously out of my depth here. Should probably have kept my mouth shut rather than revealing my ignorance.
Observation is definitely very important. But how about people in another country that you have never seen video footage of or audio recordings of? You haven’t observed them but do believe in their existence. Isn’t it that their existence “explains” why a lot of other people who are in a position to observe them in some way say they are there?
> size of the collection if there's no cardinality
Isn’t there a pretty compelling argument that this entire section of your argument is backwards. I.E. that the conclusion one should draw from “there is no set of all truths” is not “wow there are so many truths”, but that “all truths” is a meaningless phrase.
No, what? There are lots of true statements about all truths such as "there are more truths than marbles in my room."
Value Error. Attempted to compare finite value with undefined.
You’re doing that thing where you confuse colloquialisms with formal. If you said that in a conversation, I would get what you’re saying, but “truths” in the context of what you’re saying is not a number which you can just plug into a comparator function. Would it not be like saying that 0! >>> anything?
I guess a more productive thing for me to say is this: What’s your answer to the Patrick Grim 1984 note on the failure to apply this “all truths” business to possible worlds. (and the sources cited in that as to why any non-set construction similarly fails)
I don't think I'm confusing anything. The sentence "there are more truths than marbles in my room," is true. It's not just a colloquial shorthand--if it is, I fail to see what thing it expresses other than the plain meaning. What's the alternative to there being all truths? There just being some truths?
I haven't read the Grim piece that carefully--can you elaborate on the point?
I would say the alternative is that you can only ever create a partial set of truths, which you can always expand on by creating its power set, such that there can never be a set of all truths that’s amenable to comparison in the way you want it to be.
Grim’s point is very short. He says that a conception of worlds is that a world represents a set of propositions or a correlate to a set of propositions to which no further propositions can be added without precipitating inconsistency. (Citing Robert Merrihaw Adams in *Theories of Actuality*, and one other person).
We would thus define what “actually” exists as the set of propositions which deliver, which are actually true. Such a world would be the set of all true propositions. However, because we can infinitely power set and paradox a set of all truths, any “actual” world of all truths would leave out come truths and be non-actual. We can thus never produce any actual set of affairs that contains all truths. (Citing “Some neglected problems of omniscience”)
He then goes on to say it’s highly dubious that any alternate construction, like calling all truths a “class” will work. At least not if we want to still be able to do math with it, which I think you need in order to derive and apply Bayes.
I agree it's not a set or a class but instead a collection. I don't think you can powerset the truths https://www.youtube.com/watch?v=CFx4hg9fRbA&t=1s
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Yes, this is correct. You can not use arguments about number of all possible people if "all possible people" isn't even a coherent mathematical concept.
It's not incoherent! It's just not a set!
Well, then what it is? What is this "collection" thing you are talking about and how it evades the reasons why a set of all possible people is not possible?
It seems you treat the situation as a semantic game where it turns out you can't use the word "set" anymore so you need to replace it with some other word, for example "collection", and now you are good to go. But this isn't how math works. What name you use is irrelevant, you need to logically pinpoint an entity with its properties, and formally prove that it exists, and that there can be collections of things that can't be sets of, define the concept of cordinality for this new entity and rewrite probability theory so that it could be used with collections, instead of sets. Till then your reasoning is invalid.
I'm sorry if someone already pointed that out, but I think that there's a flaw in that argument: sometimes things are just impossible and no anthropic arguments can change that. While your reasoning implicitly assume that existence of God is not just possible but relatively equiprobable with an atheist world, and that God can in fact create vast infinities of people (and again, not just can but it doesn't incur any significant probability penalties compared to a mere infinite physical universe).
What if none of this is possible? There is not, in fact, a writing on the wall of your room telling you that God flipped a coin to decide between creating Aleph-0 and Beth-2 humans. The physical world exists and can support humans, anything beyond that is speculation that begs the question. **If** God exists and is omnipotent to that ridiculous degree, then all right, you're more likely to find yourself in one of His infinite gardens. Is he though?
I aim to give an argument that dramatically increases the probability of God existing. If you start out extremely, overwhelmingly confident that God doesn't exist then you probably won't be moved but that is not, as you suggest, a flaw in the argument, any more than it would be a flaw in an argument for evolution that, were one to already be certain of creationism, they wouldn't be moved by it.
Sometimes you come to conclude something is possible because you find that it is actual. You might not realize that consciousness can split, but finding that it actually does should rid you of that presupposition. Similarly, if this overwhelmingly raises the probability of God existing, so too should it lower the probability that God is genuinely impossible.
I guess what makes me feel iffy is that you seem to implicitly presuppose weird metaphysics, where there's a meta-universe in which universes with or without God and various infinities of people are not only logically possible but actually exist.
For example, in https://benthams.substack.com/p/all-theories-of-anthropics-are-presumptuous not only it's entirely possible that the "larger" theory has a subtle implication making it logically impossible, but also that both are viable but the smaller universe is simply the one that physically exists.
The sleeping beauty thought experiment also sneaks in a bunch of assumptions: you are told the rules of the game and that the coin is fair and there's a suggestion that the experiment is run multiple times so you can use your frequentist intuitions about why maximizing the expected value makes sense.
But in your argument all this stuff makes much less sense. You can't have God both exist and not-exist. And if God doesn't exist then those uncountable infinities of people don't exist, so you can't find yourself among them. I guess I don't think that you can use anthropic reasoning in a one-shot problem.
I mean one naturalistic theory with big infinities of people is just infinitely many identical copies of our exact universe. Is there any particular reason to think this exists beyond dubious anthropic arguments. No. Is it a simple theory that fits our observations and doesn't break induction. Yes.
Another alternative is to look very closely at the tegmark multiverse.
So there is 1 universe that's just quantum mechanics as usual. And then oodles of universes where random junk appears in front of you. But for every universe where a giraffe spontaneously appears in front of you, there is a corresponding universe where the giraffe appears in a pocket dimension while you continue living as normal.
This gets into subtleties of measure theory. There are ways to say that everything exists, but some things exist more than others.
Imagine randomly generating an infinitely long computer program. The version of physics without magic giraffes appearing is shorter, so is more likely to appear (and will appear more times) in the infinite program.
So if all possible infinite computer programs exist, we can still have some form of induction. Shorter programs have more copies.
Your argument depends a lot on details of set theory you don't seem to understand. Uncountable cardinalities are confusing in ways you don't grapple with.
You have to be very careful to define things in axiomatic set theory before you can talk about their cardinality or whether they constitute a set. You don't do this; you never define "truth", and the way "true statement" is usually defined in mathematics the true statements are a countably infinite set.
The set of all configurations of matter is only beth-2 if you think each real-number-valued point can have a different state. This does not make sense; the universe appears to be discrete at the Planck scale, suggesting only finitely many possible positions that can have a particle, and even if not, the particles cannot be spaced in weird configurations like arbitrary sets of real numbers (which can get really, *really* weird, including unmeasurable sets, the Cantor set, sets that cannot be described by any mathematical statement, etc.). I would say the number of possible minds seems not merely countable to me, but actually finite, just because I can only imagine finitely many possible experiences (for instance, my eyes only have so many "pixels", each observing finitely many colors and intensities since they must be represented by neurons sending finitely many electrons across their channels; my memory is also finite and I will not remember more than a few million years of experience at a time, probably. Put it together and you have finitely many possible experiences.)
There are, by the way, countable models of ZFC set theory: models in which all the usual axioms hold but, viewed from outside the model, there are only countably many sets (and each set is countable). Such models can still prove that a power set is of larger cardinality than the original set -- this statement would be true *when cardinality is measured within the model*, but not when it is viewed from the outside. This should give us pause regarding how to interpret uncountable cardinalities.
A truth is something that's true--something that corresponds to reality. I didn't precisely define it because I'm not writing a mathematics paper but am instead speaking normal English. I agree infinites get really weird, but I think that they won't be weird in ways that threaten the argument. An analogy would be: imagine that there were unsetly many people put to sleep and then some number were woken. SIA thinks that being created is analogous to being woken--more is more likely, and while there might be cases where it's unclear exactly how to make comparisons, everyone getting woken up is infinitely more likely, obviously, than just finite people being woken up.
You'd have to think that on such a picture, it's metaphysically impossible to have reality composed of points--but that would be really weird! There might be only finitely many different possible minds, but on SIA what matters is the number of minds, not the number of distinct minds (as the arguments for it show). The view on which the thing that matters is the number of distinct minds is called compartmentalized conditionalization and it egregiously violates conservation of evidence.
To see this, suppose that I’m considering two hypotheses. Both predict that there are two people in a room. One of them predicts that both of them will, when they look under a table see a red strip of tape, while the other theory predicts that one of the two people will see a red strip and the other a blue strip.
On this view, suppose the people in the room haven’t looked at the strip of tape yet. They should expect their credence in the second hypothesis to go up. If they see a blue strip, then the second hypothesis is confirmed. If they see a red strip then their credence won’t change, because both theories predict someone seeing a red strip. So therefore they should expect their credence to rise.
Also, the argument I give in 2.4 provides a huge problem for compartmenalized conditionalization. It also gives a huge update in favor of modal realism.
The number of minds makes no sense, since I can index minds by anything (eg label each mine by a set). The argument for beth2 minds isn't coherent if we are not counting distinct minds (indeed, what even is there to count?)
By distinct minds I mean distinct life histories and/or observed universes. Your conservation of evidence isn't relevant.
By truth you say you mean "something that is true", but logicians worked very hard to formalize the subtleties and came up with a theory that has countably many truths. You are not writing a math paper because it cannot be written: your definition of truth is not a coherent concept.
Finally, no matter how you slice it none of it implies God: it could be a law of the universe that all minds exist, to the extent that's a coherent statement (which it doesn't seem to be). "God exists" and "all minds exist" seem equally unexplained.
What are you talking about? You can have two minds that are physically identical but are different--for example, if a copy of my brain were 10 galaxies over, it would be physically the same while being somewhere else.
Asserting that "Your conservation of evidence isn't relevant," does not, in fact, show that my argument showing it violates conservation of evidence is wrong! If there are Beth 2 possible distinct universes, then there are at least Beth 2 possible brains--because Beth 2 of the universes have brains--and more if universes are duplicable.
Logicians have worked hard to come up with a theory that has countably many truths? What? I'm not aware of any logician who has done this because it's flatly absurd. For every real number N, it's true that it's between N+1 and N-1, so there are at least Beth 1 truths (and more because every subset of a truth is a truth). My definition of truth is the standard one agreed upon by most philosophers--correspondence to reality https://survey2020.philpeople.org/survey/results/4926, though, of course, it's amenable to any of the standard theories of truth.
Finally, you suggest that it could just be a brute law that all possible minds exist. Sure it's possible, but possible doesn't equal probable. In order not to undermine induction, one must think that most minds are in inductive worlds so it can't be that simply every possible experience is had infinite times over (for most of them are non-inductive). That theory is also less parsimonious because it posits an infinite number of things with no explanation, rather than just one God.
We all will have to invoke some unexplained things. An atheist will have to think that whatever is fundamental--laws, perhaps, or initial conditions--don't have a cause. God not having a cause is on similar ground--perhaps more viable, in fact, because God might be necessary. Additionally, unlike the every minds exists view, theism is independently motivated because it explains a lot about the world and is parsimonious rather than being a joke theory that no one had ever thought of prior to hearing this argument.
You claim that I'm ignorant of set theory and then proceed to get everything wrong!
In mathematics, a statement is a finite string. The statement "every real number n is between n-1 and n+1" is one true statement. There are, additionally, infinitely many statements of the form "3.5 is between 2.5 and 4.5", "pi is between pi-1 and pi+1", etc.
However, there are only countably many such statements, because all but countably many real numbers cannot be named, so cannot appear in a statement. There's subtlety here that you're ignoring. "Real numbers" are less real than you think; basic questions about them, like whether certain sets of them exist, cannot be determined within ZFC. Experts in set theory routinely say things like "there are many possible set theories, some with more sets than others, with no way to choose between them".
Just saying "correspondence to reality" doesn't save you because real numbers aren't real -- you've never seen most of them, they cannot be named even in principle.
There are countably many true statements in any formal system. If you're going to appeal to mathematical concepts you should get them right.
You assert that real numbers aren't real because I've never seen them. Well, this is a wildly contentious view in philosophy of math that I reject--I'm a platonist--and, in fact, there are some things that exist that I haven't seen. Whether some version of set theory is right will depend on questions in the philosophy of math.
But anyways, even if numbers don't really exist, there might still be true statements about them. Nominalists about math still generally think that it's true that, say, 32.438957238493278932 is less than 35--perhaps they're fictionalists, for instance, and think it's only true within the fiction.
You're just assuming without argument that any truth must be expressable in finite characters. But that's obviously false!
"You're just assuming without argument that any truth must be expressable in finite characters. But that's obviously false!"
Oh yeah? Give me one example of a truth not expressible in finite characters :P
If you're a platonist who believes the reals are real, can you tell me whether there's a platonically correct answer to the continuum hypothesis? It's just a question about the existence of a set of reals. I assume you think it's either true or false? Not clear that mathematicians agree with you.
You posit the universe is made of real numbers, a true continuum, but making the continuum real really does bring up questions like the continuum hypothesis and whether it has a truth value. Luckily the universe is discrete at the Planck scale (and finite to boot). Even if it wasn't, the universe certainly cannot be tiled arbitrarily with particles at every real number-- that's arbitrary sets of reals, literal continuum hypothesis territory. Yet the beth2 argument relies on this.
> Given this, if L is the biggest number of people that there could be, whichever theory best predicts L people existing infinitely outperforms alternative theories. Theism best predicts L people existing, because God would create all possible people who he could give good lives. So, therefore, theism gets a big probabilistic boost.
This seems to imply theism predicts L minus bad lives.
Some version of multiversal atheism implies L (good lives + bad lives). Therefore, multiversal atheism seems more likely?