In order to do probability theory you first need to define a probability space. A probability space has 1) a sample space, 2) an event space, and 3) a probability function defined on the event space. The probability space needs to satisfy the Kolmogorov axioms which are 1) non-negativity of events, 2) one of the events has unit measure, and 3) sigma-addivity, or basically you need a sigma algebra.
When you define your sample space you need to use set theory by definition (unless you want to invent a new probability theory which is broader than what is currently meant by probability theory). But this is impossible, because "all logically possible worlds" is too large for set theory to handle, and its not clear if naive-modal-logic is similar to naive-unrestricted-set-theory (which is known to be inconsistent). Are you using ZFC set theory when you define your sample space?
Until you can show that the model you have created can satisfy the axioms or probability theory there is no need to consider your arguments. This is *not* a pedantic objection, the issues in trying to apply probability theory to the space of all logically possible worlds are so incredibly fraught that I doubt it can ever be done consistently.
Now to be clear, when you first say:
"Your existence is more likely if there are more people" you have now introduced the concept of likelihood and an implicit probability space. There is a lot of work that needs to be done before you can make this statement.
Consider, for example, a dice which has the number 1, 1, 2, 3, 4, 5. Is it necessarily the case that "a dice roll is more likely if there are more numbers?" In other words, is "1" more likely?
Not necessarily! It could be a weighted die which almost never lands on the two 1s. So you also need to define the probability function. You have implicitly assumed without stating that the uniform distribution is the correct one to use here without ever justifying that assumption.
You don't really need these things to do probability, or at least to construct an informal probabilistic argument that has *some* intuitive force. Some people have in fact proposed dropping this or that Kolmogorov axiom - e.g., going with a finitely additive probability measure, or having hyperreal-valued probabilities, at least in certain circumstances. But even these alternative-but-still formal approaches may not be necessary to motivate certain philosophical views, as long as our informal arguments rely on certain structural features we would expect any reasonable formalization of probability to possess.
I specifically doubt sticking to strict ZFC is truly necessary to do something akin to probability. I wouldn't be surprised if you can do (non-standard) probabilities with NBG-style class-sized hyperreal probabilities, for example, although I doubt this approach will help all that much with BB's project, for various separate reasons. Still, he doesn't need to go this far. The sample space could just be the set of all universes whose physical (or whatever) laws can be described in a finite number of equations or words/symbols, maybe weighed by the minimum description length of the laws themselves, and then those universes whose laws involve numerical parameters could be given some appropriately natural-seeming prior over those parameters if available. Something like that, I'd guess, although some important questions about priors would remain. I doubt there will be unsetly many universes left anymore on this approach, but he doesn't really need that.
"You don't really need these things to do probability, or at least to construct an informal probabilistic argument that has *some* intuitive force."
I agree that for the typical case you don't need to do that much work. But when you are considering every logical possible world I am quite convinced that you won't be able to coherently apply a probability theory. When you say, "But even these alternative-but-still formal approaches may not be necessary to motivate certain philosophical views, as long as our informal arguments rely on certain structural features we would expect any reasonable formalization of probability to possess" I would object that in fact intuitive and informal arguments which are probability-ish are already known to fail because of simple paradoxes.
" I specifically doubt sticking to strict ZFC is truly necessary to do something akin to probability. I wouldn't be surprised if you can do (non-standard) probabilities with NBG-style class-sized hyperreal probabilities, for example, although I doubt this approach will help all that much with BB's project, for various separate reasons."
I agree you could probably expand probability theory, and you don't need to stick to ZFC, but again, I do think that all logically possible worlds is far too large.
"Still, he doesn't need to go this far. The sample space could just be the set of all universes whose physical (or whatever) laws can be described in a finite number of equations or words/symbols, maybe weighed by the minimum description length of the laws themselves, and then those universes whose laws involve numerical parameters could be given some appropriately natural-seeming prior over those parameters if available... I doubt there will be unsetly many universes left anymore on this approach"
Indeed, I agree. This would be a vaild approach to take. But you need to make this explicit, and you can't handwave over the details here.
>When you say, "But even these alternative-but-still formal approaches may not be necessary to motivate certain philosophical views, as long as our informal arguments rely on certain structural features we would expect any reasonable formalization of probability to possess" I would object that in fact intuitive and informal arguments which are probability-ish are already known to fail because of simple paradoxes.
There are paradoxes applying to some informal principles in some circumstances, most famously the principle of indifference, but that doesn't automatically mean every informal principle is off the table.
For example, suppose God tells you he chose a natural number at random using some uncomputable distribution. There's famously no such thing as a fair lottery over the naturals, so it's really not clear how to model this, or if it's even possible to model this. Infinitesimals won't work; complexity-based priors on God's secret distribution also won't work, given my stipulation on uncomputability. Still, it's perfectly intuitive to argue that the "probability" of God choosing an odd number, whatever it is, ought to be greater than or equal to the "probability" that he chose an odd prime number.
I'm not sure if God could do such a thing. Just because we imagine that it should be intuitively do-able doesn't mean that it is. I understand what you are saying, and share your intuitition, and maybe God could do this for the natural numbers. It feels like a God should be able to pick a random natural number such that every one is equally likely? But maybe not! And once you start getting as large as 'every logically possible world' my credence shrinks down to near zero.
I wasn't supposing God was picking a natural number uniformly at random, but was instead picking it via some uncomputable but well-defined probability distribution which is completely unknown to us. It's our own credences which we'd want to be uniform if it were possible, not God's actual distribution.
Great comment. You hit a lot of things I wanted to say. I would add, though that the “important questions about priors” are quite a conundrum.
For example, you went with finite number of equations but there could a universe with an infinite number of equations that’s still consistent with beings like us.
Even in Universes with finite equations, do we do a normal or uniform distribution on the constants? What about on identical laws and parameters but different initial conditions? How is that weighted?
It’s quite a big subject to get around.
However, I do agree with the general sentiment that, for an informal-intuitive argument, there’s no need to go that far. The gist of it is simply that, assuming all these possible worlds are kinda equally valid, the ones with more people are more likely. I don’t know that you can stretch that reasoning to infinite people though. That’s where the work needs to happen in my opinion.
BB probably answered this somewhere but what if there’s a maximum in the distribution where if you keep adding people in the universe, that universe becomes less likely, eventually converging on 0?
Okay, suppose I said the following: it's more likely that OJ did the crime if his blood was at the scene of the crime. Does that require using set theory by definition or a probability function on event space or the like? No! How is this different?
Let me try to be clearer: the OJ sample space would be all worlds consistent with the laws of physics as we know them, the event space would be all Borel sets of these grouped by their indistinguishability to us, and we would have some type of probability function weighted by what we think people typically do with their time. We group the event space like this because it does not matter to us if atom 914273 was at position 5235.4 or position 5235.6, because we don't have knowledge of that nor would we be able to distinguish the two.
Very crucially, the laws of physics seem uncountably infinite, and continuous. I know that probability theory works on sets like those, so I can reasonably apply it!
But you might object: surely you haven't considered every possible event! God could have done something to OJ which would violate the laws of physics as we know them, and even if this is unlikely it is still possible.
Except that I would reply that if we open the door to those possibilities it is not clear to me now if we have an uncountable infinity, and so I don't think we could apply probability theory. This is not breaking any metaphysicals laws, a mathematical model is just a model, and there is no reason to expect that the (metaphysics of?) the universe needs to be such that probability theory can be applied to it.
That's the first issue: the inability to reasonably define a sample space.
The second issue, assuming you can get over the first, would be the probability function itself. For something like the existence of the universe it is not clear if a uniform probability distribution makes sense. In fact, maybe you would argue that the correct distribution is just to apply a probability of "1" to the universe as it currently exists and a probability of "0" to every other universe. Or something like that. There is a lot to say here.
And here's a third issue, related to the first: it is not clear if you can make your event space satisfy the axiom of sigma-additivity. Consider a world where you exist, and assume it has a probability of x. Now consider a world where 2 people (like you) exist, and it must have a probability of 2x. So, okay, you quickly see that allowing this to go to infinity would result in a probability that doesn't add up to 1 if x is greater than 0. So we have to say that any individual world where someone like you exists has probability 0.
Normally, when dealing with infinite sets we get around this by considering indistinguishable Borel sets. So, if you wanted to consider the height of something in a range [2,3] you can say that any individual value between 2 and 3 has a probability of 0, but that a value in the range [x,y] has probability (y-x)/(3-2) for a uniform distribution. So you measure somebody's height, and find it is 2.8, but really its more like 2.8 +/- 0.001, so you could say this had a probability of .002 if you were using the uniform distribution.
It does not seem possible to define any meaningful Borel sets when any universe is fair game.
I would say that yes, it does, but it is just that most of the time these things are implicit. The sample space would be the things which OJ could plausibly have been doing. The event space would be the Borel sets of these. The probability function would be weighted by priors you had on the various likelihoods of each of those events. (There are a lot of outlandish things which could explain why there was blood at the scene of the crime, but he wasn't there, but these would be assigned a low probability). Notably, we wouldn't assume a uniform probability distribution, it would be weighted by what a typical person (or more precisely OJ himself) is likely to do.
You don't need to explicitly spell out every single event that could happen, because that would take forever. We are saved here because extremely unlikely things which are physically possible for OJ to have been doing can be assigned very small probabilities and neglected. Instead of dealing with logical possibility we could also assume something like physical possibility (which is a much much much smaller event space).
Anyway, the point here is that specifying the event space here is impractical because of how long it would take to do, but there is nothing objectionable about it per se, and it wouldn't be hard to give a rough sketch in that direction. Meanwhile, when you are dealing with every logical possible world it is not even going to be possible to define a sample space: logical possibility is bigger than set theory. So, we cannot apply the axioms of probability theory to that.
Beth numbers describe infinite sets, which transcend any physical instantiation. While some infinities can loosely model processes or entities in the natural world, higher infinities are more conceptual.
I don't think that this is an agreed upon consequence of MWI. It's quite complicated to actually count the number of possible worlds in MWI because of the way decoherence works and when exactly branches stop being causally connected to be viewed as "separate worlds". Some people do estimate a huge but finite number of worlds and other something like continuous infinity.
But more to the point: it's not that clear that this implies infinite people as well as there could be only finite branches with finite people in it (and infinitely many more but without humans).
Yeah, good point, it's not exactly clear. My understanding is that the general agreement is that there are at least continuum many people and that they're largely uniform, in that they have continuum many have people. Then again, I don't really know physics, and this understanding is just based on brief convos with people who do, so I could be wrong.
It needn't be that there are Beth 1 *people* as nelson said infinites of Beth or above aren't actually instantiated.
Here's the point: suppose that MWI did, in fact, predict that many people. It would be odd to reject MWI based on the impossibility of rejecting that many people.
Yes, agreed with the general reasoning that you cannot reject it on that basis. And to be clear about MWI, I think most physicists would probably bet that it does predict infinite worlds with potentially infinite people in total. No one views this eventuality as a weak point of MWI.
Just want to express how grateful I am to you for leaving a very perceptive and reasonable comment. The other comments on this post were deeply confused, and it was driving me sort of insane.
>My understanding is that the general agreement is that there are at least continuum many people and that they're largely uniform, in that they have continuum many have people.
If that is your understanding why did you arbitrarily choose beth 2? As a "naturalist" (I'm not, but let's say for argument it's a reasonable approximation) I would be much more interested in your argumentation if you chose aleph 1, the more common number used to represent the cardinality of the continuum, a not unreasonable cardinality of "infinite" people.
I am not misunderstanding, at the very least you are being imprecise with your mathematical language. In multiple places you have made the claim that there are "Beth 2 people". The paper you link references other work talking about the size of the configuration space of 4D spacetime, not the number of people. Though it seems that Gómez-Torrente also has a limited understanding of the math he is talking about.
There is no fact of the matter because we don't know whether or not time will ever end or if entropy will ever reverse course. If time never ends and entropy becomes reversible then we can potentially have infinite observers, but e.g. every observer dying in every world is also something that's possible. As always BB makes spurious metaphysical claims about (enpirical, studyable, easily learnable) topics he has barely engaged with, bah humbug.
> (7) [...] on theism, it’s likely that the number of people that would exist would be the maximum number it could be.
But this does not seem to match our experience of the world. There's only eight billion people or so on Earth and we're not at a population limit. There are seven other planets in our solar system completely devoid of people - indeed, we haven't found any other people at all in the parts of the universe we have observed so far. If God wants to maximise the number of people, why is our area so lacking in them?
You might argue God has made universes with a wide variety of densities of people and we just happen to be in a lower-density universe. But, given we exist, shouldn't we expect to find ourselves in a higher-density universe, since there are proportionally more observers in higher-density universes?
The SIA argument makes sense in the Sleeping Beauty case because every person that gets woken up is the same person. There are three cases in which that person gets woken up, and two of them are in the tails condition. From having been wakened (and knowledge of the SB setup) the waker can conclude that tails is twice as likely as heads.
But my understanding of the situation described in this post is that there are Beta_2 **distinct individuals** who **all** get created. Each one gets created exactly once. In such a case you can't reason from you having been wakened (or born) that tails is more likely. Compare this story:
A) One ball is put into an urn. Let's call this ball "John".
B) A coin is flipped, and if tails comes up, another ball ("Jack") is put into the urn.
C) One ball is removed from the urn.
What are the chances that the ball removed from the urn is John?
The answer, assuming a fair coin, is 75%. If heads came up (50% chance) then the ball removed must (100%) have been the first (and only) one put into the urn: John. If tails came up (50%), then there's a 50% chance the one that came out was the first in (John), and likewise 50% chance that it was the second (Jack).
The argument doesn't change if we add an infinite number of balls in step (B). It just reduces the chance that the ball is John from 75% to 50%.
If all you know is that a ball came out of the urn (and the original rules for this game), then you must conclude that it is twice as likely that the ball that came out is John and the coin came up heads as that the ball is John and the coin came up tails.
And that is **exactly** the way the ball should reason if it could. Thus this premise:
> It’s just as likely that you’re John and that the coin will come up heads as that you’re John and the coin will come up tails. <
is wrong. Thus your argument that tails is twice as likely as heads fails (in this context), and thus premise 2 of the anthropic argument is undermined.
Yes, I have read the further arguments provided in (two of) the other papers you cite. They don't help, because the situation is not parallel to what we see in Sleeping Beauty. The people in the anthropic argument only get "wakened" once. Consider the version of Sleeping Beauty in which you are the main sleeper, but instead of waking you a second time on tails, a **different** person will get woken up on Tuesday.
When you are wakened, what credence should you give to heads having been rolled? The answer is 50% **because** you only get woken up once either way, so the number of wakings for you is the same either way.
Now if you happen to be the **secondary** sleeper in that game and you get woken up, the credence you should give to heads is 0%. There is **no chance** that the secondary sleeper will be wakened (during game play) if heads gets rolled. So you might object "What if I don't know whether I'm the primary or secondary sleeper? Then the logic goes back to the original Sleeping Beauty, doesn't it?"
Yes, it does. But in the anthropic argument you **do** know that you are the primary sleeper. You are awake whether God created infinitely many people or evolution created a finite number of people. Head or tails, you wake up. Once.
Belief in premise (2) of the anthropic argument is not justified. Thus belief in its conclusion on its basis is likewise unjustified.
Now I am wondering what exactly you mean by God, perhaps you have written on this elsewhere. Presumably it's the traditional theistic God that is omnibenevolent, omnipotent, and omniscient. And that given that God is all good, and that the existence of people is good, theism predicts that an infinite number of people exist.
But God is also traditionally defined to be a person or being, that is not just some force but an actual nonphysical mind which has experiences, qualia, self awareness, etc.
But I don't see how you get from the existence of infinite people to the existence of a nonphysical mind. The hypothesis that explains the data of infinite people existing would be the presence of a some powerful force that does good, but it would be merely a force like gravity, not a mind like God.
Frankly, this sounds like nonsense. Here’s a better counter argument: math is a spherical cow. There are many possible logical constructs to explain the reality. So why do you think your spherical cow represents reality? When you can’t perform an experiment any crack pot theory is valid.
What the hell? I gave an argument, which, if put into premises, comes out as the following:
1) There are at least Beth 2 people.
2) If there are at least Beth 2 people that favors theism over atheism.
3) Therefore, the fact that there are at least Beth 2 people favors theism over atheism.
Which premise do you disagree with? How is anything about spherical cows supposed to be relevant.
There are *some* things we believe based on experiment. Other things we believe based on philosophical argument. For example, the way we know that the world wasn't made five minutes ago looking old can't be through experiment. The principle "everything is known through experiment," is self-defeating, because it's not known through experiment.
Well, if the crickets lived good lives, given that a cricket farm making more crickets than could fit in any spatiotemporally-connected region of space would be a miracle, it would be quite a bit of evidence.
What my comment was supposed to highlight is that the connection between probabilities, numbers, and God is usually a non sequitur.
Probabilities aren't really real. They are just words on screens or thoughts in our heads. Probabilities might predict the motion or sequence of real events, like the Monty Hall Goat quiz show. The existence (or lack thereof) of multiple universes and God aren't observable events to predict. At best, they are part of models and theories made up on blackboards to try and make other models and theories look more consistent. Making a long chain of probabilities to say "And therefore God" could be swapped in with any other absurd conclusion.
2, or maybe it is disagreeing with the idea of there being a Beth number at all. Rereading the original chain of arguments:
"Your existence is more likely if there are more people. E.g., if a coin gets flipped that creates one person if heads and ten people if tails, you should think it’s ten times likelier that it came up tails than that it came up heads."
The number of people that exist does not seem like it would have any bearing on "your" existence. "Your" existence is a product of exactly how many people and things also existed in proximity to you. The only coin being flipped is the physical process that creates the genes and womb environment for a baby, but any hypothetical baby born similarly still won't be "you".
Is any of what’s being argued here grounded in reality or just an intellectual exercise? Why are you so confident of your untestable model or reality when even Newton’s failed?
The Anthropic Argument is vapid precisely because it can’t be tested. In fact, it’s so easy to create purely logical constructions to explain reality, you’d need to argue why you can have any confidence in any construction. There is no evidence to back any metaphysical claim. Zero.
To press further on the idea that the spherical cows of math have little bearing on the real world, consider the concept of infinity.
I am not aware of any “real” infinity. In fact, it’s a hypothesis.
So yes, I can be both Beth numbers. Let’s name one Alpha and the other Omega. I am God, this is my reality.
You can’t prove me wrong. I also can’t prove that we are the result of some complicated stochastic process.
Yes, it's all grounded in reality. As I explained, there are reasons to think the premises are true. In fact, you'll even notice that the argument I give in this article provide reason to think that there are infinite people.
The difference between good arguments and non-sensical strings of words isn't that good argument have testable premises, but that they have defensible premises. As I explained, if you reject that, you can't even justify the premise that there are truths and your view is self-defeating, as the premise that good arguments can only have testable premises is itself untestable.
2. If there are at least Beth 3 people then the theory of the army of multidimensional fairies is favored over atheism. The multidimensional fairies obviously have an interest in creating at least Beth 3 people.
3. Therefore, the fact that there are at least Beth 3 people favors multidimensional fairies over atheism.
4. Since Beth 3 is greater than Beth 2, clearly multidimensional fairies are favored over theism.
This argumentation is arbitrary and unjustified. Your usage of math is too weak to support the heavy claims you are trying to make. Your source is a non-mathematical philosopher writing in a paper about what another non-mathematical philosopher wrote in a paper about what Quine wrote on worlds. Which, by the way, I followed the sources and I can't find Quine making this argument, would love to read it.
* Mathematically speaking if you consider the multi-verse hypothesis in a multi-dimensional hyper inflation at the quantum level in a Einstein-Rosen bridge it is clear that there are Beth 3 people.
Well, I don't know why the army of fairies would be likelier to make Beth 3 people than atheism. But if they would, while this would then, by definition, be evidence, for fairies over atheism, fairies have a low prior, so it wouldn't be decisive evidence.
I don't get what you're saying about Einstein-Rosen bridges.
First of all, the proof is from Lewis not Quine. Second, you don't have to take it on authority, it's pretty straightforward. People are made of points. But there are Beth 1 points in a line, so Beth 2 (the powerset of Beth 1) ways of arranging points.
The "Mathematically speaking..." part at the end of my comment was intentional gibberish, I had hoped it was obvious. I was just showing how if you use enough complex language taken from usually poorly understood sciences you can justify anything you want. I am not actually arguing the Beth 3 hypothesis.
I would love to see a proper mathematical formulation for what you're saying because it doesn't seem to jive to me. The leap you make from people being made of points to Beth 1 points on a line that is arbitrary. Then your conclusion is saying the number of configurations of points == number of people, this also is not clear.
The way I see it is in a single universe there are countable infinite objects (aleph 0). We can say particles, or atoms, or chairs, or even bipedal organisms living on wet, rocky planets orbiting 3rd generation main sequence stars. In all cases the cardinality of the set is countably infinite for one universe.
If we choose to hypothesize the multiverse than we invoke the cardinality Aleph 1 (or Beth 1 if you prefer) for the number of objects in the infinity of universes. This is the same whether we say in "this moment" or across all time.
Counting objects is not the same as counting configurations. If you count the number of configurations in any one universe that gives you Aleph 1 cardinality, but that is in essence just compressing the same information content into one universe. Consider that a slightly different configuration of this universe is the same as an alternate universe that is slightly different.
Now I'll admit I am not a mathematician, just a software developer/IT professional that reads a lot of this stuff in his free time. If you have a real mathematical proof that shows this Beth 2 claim it would be interesting to see and I would gladly accept any real formalization contradicting what I am saying.
I am really just trying to point out that the main aspects of your argument are poorly justified and arguably unknowable. It's a moot point though, in some sense, as nothing in your argument says that your definition of "God" is anymore likely than my definition of "multidimensional fairies", so it continues to be unconvincing.
Also, I don't see why it's not possible to believe there are Aleph 1 people in universe as an atheist. I think plenty of atheists believe complex life is emergent and in an infinite universe there are infinite people, add the multifverse and we're good, no conflict there. I personally am not a fan of multiverse theory but I have no problem putting it in the background as you say.
I will respond, but let me note that it's fairly ridiculous for you to call me a charlatan when you don't have the faintest clue what you're talking about on some subject. I don't go around calling people charlatans when I don't understand subjects.
Okay, now on to the serious matters.
First, I have now explained why there are Beth 2 people at least AND linked a paper explaining it. I don't know how many more times I can explain it. In short, the world is made up of points. You can rearrange them. There are Beth 1 points in a line, and Beth 2 ways to rearrange Beth 2 points.
However, there could be a multiverse containing many objects. Even if per universe there are only aleph null objects, that's no limit on the number of *possible objects*.
//Counting objects is not the same as counting configurations. If you count the number of configurations in any one universe that gives you Aleph 1 cardinality, but that is in essence just compressing the same information content into one universe.//
Well, if they're composed of points, you get Beth 2. But anyways, insofar as each configuration is a possible world--ie, every sequence *could* exist--then there are Beth 2 (if points) or Beth 1 (if not) particles.
//Also, I don't see why it's not possible to believe there are Aleph 1 people in universe as an atheist.//
Well, it's not clear if aleph 1 equals beth 1--you're assuming the continuum hypothesis it seems. But yes, an atheist could think there are beth 1 people. This gets dicier with Beth 2 though. No plausible multiverse model gets you Beth 2, and virtually none get you Beth 1 people. (MWI might get you enough, but then if MWI is true there will be more possible people because you can take subsets of the wave function. Also if, as I've argued, there are too many people to be a set https://benthams.substack.com/p/the-best-argument-for-god then MWI--and every plausible naturalistic view--is obviously woefully insufficient).
Again you are conflating points and particles and your explanations of this cardinality argument seem strange. I've read through the paper you provided and it doesn't appear to provide a justification for your argument. I wish you could understand that I don't need you to repeat your explanation, I get what you are saying I just don't buy it and you haven't presented any rigorous mathematical formulation.
"No plausible multiverse model gets you Beth 2..."
This seems to be you making my point. On the one hand you are presenting Beth 2 as the cardinality of people as if it is a fact and then on the other you admit that the accepted scientific perspective says otherwise. I would have less of a problem with your argument if it at least had the humility to acknowledge that this is a _hypothesis_ and not an established fact. People unfamiliar with these concepts take what you say at face value and you should be more careful not to generate unnecessary confusion.
On a side note, I think this is the last time for a while I interact with you, I was hopeful that my impression of you from other comment threads or posts was mistaken but it seems clear that you have a certain resistance to listening to criticism and hold an almost authoritarian stance on your ideas.
Have you ever considered the fact that you are not perfect? That you have beliefs and ideas right now that you hold dearly that are false? I think any philosopher needs to hold tight to a sense of Socratic Humility and avoid dogmatism as it prevents growth and discovering situations where you may be wrong.
1. You could be wrong about anything and are definitely wrong about some things.
2. If you are wrong about things, you are unable to notice the fault on your own.
3. Therefore you should be skeptical of your own ideas and seek to root out falsehoods, especially those that receive frequent criticism.
I did no such name calling and if you feel ofended by my response I am sorry, it was not my intention. Your acusation though, of me "not having the faintest clue" reeks of arrogance and is unfounded as you don't know what I do or do not know. If you'd like to contest any of my points or provide a formal backing for your logic I would love to hear it otherwise I have no interest in reducing the conversation to agression and insults.
>The number of people that there could be is at least a very large infinity called Beth 2. I think it’s more, but let’s be generous to the naturalist, and say it’s Beth 2.
The philosopher John Leslie used to critique "social" models of the trinity by suggesting that, by Leibniz's assertion that a good God must create the best of all possible worlds, and that N+1 perfect minds is entails more good experience than N perfect minds, the Godhead must include infinite persons. I don't know if he ever wrote about this being agreeable to Christian accounts of cosmic creation, theosis, and apokatastasis.
The elephant in the room appears to be the multiverse of the universal wavefunction? This is a perfectly atheistic explanation for uncountably infinite observers.
It can’t be right because it proves too much. The argument still works if you replace “people” with any other good thing, such as “original manuscripts of Shakespeare plays”. The argument still works if you replace “god” with any other being or computer capable of simulating a lot of that. And even if the argument worked it wouldn’t prefer the Christian god to any other flavor of god.
>The argument still works if you replace “people” with any other good thing, such as “original manuscripts of Shakespeare plays”.
Anthropic reasoning only applies to subjects capable of observation, not goods generally.
>The argument still works if you replace “god” with any other being or computer capable of simulating a lot of that.
The argument takes the form:
1. A particular person, such as the one reading this, exist
2. (1) is infinitely more likely if the maximal number of persons exist rather than any countable number
3. The maximal number of persons existing is best explained by the existence of an agent with the power and will to create the maximum number of persons
i.e. your existence is infinitely more predicted by the existence of something productive of uncountable infinities of persons rather than optimistic naturalism's steady-state cosmos of boundless space.
This is not true of Bostrom's formulation of the simulation argument, which merely concludes that a particular person/civilization is more likely simulated than not - in fact the conclusions do not contradict. A simulated person, if such a person is possible, could rationally conclude that her simulated existence is most probable if God exists *even if she correctly believed she was simulated*. Much like the blogger (presumably) also believes his personhood is explained in a proximate sense by the actions of his parents.
>And even if the argument worked it wouldn’t prefer the Christian god to any other flavor of god.
Yes, as long as the god in question has the properties traditionally ascribed to the monotheist's Creator-God, such as maximal power, knowledge, moral perfection, and modal necessity. Philosophical arguments in this area are about Ho Theos, not theoi.
I have another objection to the anthropic argument. It applies probabilistic reasoning to a domain that is more fundamental and prior to probability (existence itself), and therefore draws its unusual conclusions merely as a result of applying probability theory to a domain where it is undefined.
Does your existence give you evidence that your parents didn't use highly effective contraception with a failure rate of .00000000000000001%? Does that argument "apply probabilistic reasoning to a domain that is more fundamental...(Existence itself)?" How is that argument any different?
My main objection to the existence of God is that I hold purely hedonic utilitarianism to be true, and this world does not appear to be one created by a God that, by necessity of hedonic utilitarianism's truth, would hold likewise. The reason I think the only valuable good is positive emotional valence is because it is the only thing that can be subjectively experienced as good in itself. All other values are mediated by positive emotional valence, in that it feels good to fulfill or contemplate the fulfillment of that value. I like to point out that even asceticism has a self-satisfied contemplation that motivates it. So, if the only value is pleasure, and an omnibenevolent God would seek to maximize value in his creation, we can expect that the only thing God would create would be an infinite number of minds experiencing an infinite amount of pleasure for an infinite amount of time. Since we are not currently exalting in the Beatific Vision, we can conclude that we were not created by an omnibenevolent God. I know you like to say that we were put in an imperfect world because it produces afterlife goods that might have value in our infinite lifespans, but this relies on non-hedonic utilitarianism which holds that there are ultimate values other than pleasure, which I think is simply false. Pleasure is so self-evident as the only final good that we can conclude we are not in a God-created universe because we can observe that pleasure is not being currently maximized.
I don't agree with this argument. I mean, I don't quite know what it means to subjectively experience as good in itself, but it can have two meanings:
1) Have and see as good. In this case, the premise is false.
2) Have as a subjective experience and perceive as good. In this case, the premise is question-begging. No person who thinks that things other than subjective experiences can be good or bad will grant that for something to be good it must be subjectively perceived as good.
Additionally, hedonic utilitarianism is extremely philosophically controversial. Almost every philosopher thinks that it's false. Thus, you shouldn't be more than, say, 90% confident in it. But then the argument won't give you more than a Bayes factor of 9 in favor of atheism.
There might also be various necessary connections between goods, so that experiences in this life are in some way needed for the best sorts of afterlife experiences.
What does your anthropic argument say about the conventional, scientific explanation for the existence of people on earth (i.e., from the first simple cells that emerged roughly 3.5 billion years ago, life evolved through increasingly complex forms, ultimately leading to the emergence of Homo sapiens approximately 300,000 years ago in Africa)? Is that all a big myth?
So each universe in the overall multiverse has its own unique scientifically valid explanation for how humans arose? That doesn't sound like a parsimonious explanation, and it's not empirically testable.
Well, first of all, we do have empirical evidence for it: namely, that you exist. As I explain in the post, when we're precise, your existence gives you massive evidence for it.
Parsimony has to do with *fundamental* things, not just the number of total things that exist. It doesn't violate Ockham's razor to think the universe is very big!
I'll be honest with you. A lot of the posts on your blog seem sensible and well-reasoned. And even if I don't necessarily agree with everything you write in one of those "conventional" posts, I at least understand your arguments. But this anthropics stuff seems extraordinarily irrational and difficult to comprehend. It's like you have a split personality, with one "alter" being a normal smart dude, and the other one being totally bonkers.
I have an alternative theory, and unfortunately there is no way to describe it without sounding mean. The theory: you don't know anything about anthropics.
This shouldn't be that surprising. Most people don't. Your comments so far have evinced based--and rather extreme--misunderstandings of the argument. Furthermore, anthropics is very complicated--it's genuinely difficult to really get it! Philosophers often remark that it's the trickiest area of philosophy. It's also quite alien from our ordinary experience, and thus prone to misunderstanding.
I think this theory is supported by two facts (and I suspect a third):
1) I've published on the area of anthropics, written obsessively about it for about a year, and spent hundreds of hours reflecting on it. You've likely done no such thing, nor anything in the vicinity of that. Thus, it's probably likelier that you're confused than that I am.
2) The anthropic argument tends to get a much better reception from philosophers. Many think it's a good argument. Many of those who don't say that they don't know if it works because they haven't written about anthropics.
3) Probably you don't have a background that would give you special anthropics expertise. Given that, it wouldn't be that surprising if you were confused about it.
Analogy: suppose that you didn't know anything about physics. Some undergraduate blogger with a publication about some specific physics topic, many blog posts about that topic, and two other publications about physics more broadly. This undergraduate writes extensively in favor of some thesis about black holes. You, likely having no background in physics, and certainly no in black holes, think their arguments sound silly and are confusing. Should you think they're simply full of shit?
Again, I apologize if this comment comes off as mean. Sadly, there isn't a way to write a comment extensively justifying the thesis that "actually, you're the one who's confused about this subject," without sounding a bit mean.
I don't think you're being mean, certainly no meaner than I was.
Are there any smart non-philosophers—people like mathematicians, physicists, cosmologists, or statisticians—who have studied anthropics and have an opinion about it? I'd feel better about spending time researching this area if I thought that the theory has some traction outside of just a small subset of philosophers.
Hm. The anthropics arguments I know so far are easy to follow even for non-experts. (Cool World's about Simulation, Grabby Aliens, and cosmological fine-tuning.)
Yours is not, it feels very rushed. Sorry.
One recommendation is to phrase it more as an iterative game with bets (like the sleeping beauty setup), but of course that's a considerable difficulty, since we only have one life (or at least currently only have access to this one). And of course arguments about Simulation all run into this problem too. (Hence why it ends up 50% +/- 1 based on one's biases ... assumptions!)
Observation selection requires a plausible mechanism first, we need a list of the counterfactuals. The "the more people more chance for me" is too vague. It would make sense to rephrase it in terms of third-party individuals. (Cognitively juggling alternate selves is pretty hard.) So a random observer looks around and sees *gestures wildly* and due to the assumption that if there are more people it's more likely for them to observe whatever they are currently observing. Okay, so were there fewer people this random observer wouldn't exist. Sure, but this does not let the observer conclude anything about causation, because this mechanism is basically tautological.
The model proposed in step 2 does not differentiate based on number of individuals. That's your assumption. We don't have data for this mechanism. (For example we can say that the more people the faster we burn through all of our resources. So it's entirely possible that if the number of people crosses a threshold we start an all out war and a great filter event says hello. It's consistent with us not seeing huge alien bonanzas. [but of course we barely scanned any planets for biosignatures, so I think the only thing we know is we can rule out late-Kardashev civilizations]) ... but I got a bit sidetracked, sorry!
Fundamentally to do model selection we need data that's connected to the mechanism. Ie. we need something observable that would not be in the counterfactuals. (Or would be lower probability.)
And ... so ... based on my (naive) understanding the problem is that we are discussing a well-known zero-data phenomenon (ie. Mr. Cosmic T. Pot).
I sort of feel like this too. Maybe I'm not smart enough to understand it, maybe it doesn't make sense, or maybe I could understand it if I really spent time thinking about it but I don't care to.
There must be an infinity of people who don't exist and never will relative to those who do or ever have. Therefore the best that can be said about the existence of any of us who do exist uses the word "fluke" if even that word adds understanding.
Well as I say, probably you are one of the people in the multiverse. In fact, that's how the probabilistic reasoning behind the argument works.
I don't understand why people leave snarky comments on articles when they obviously neither have read the argument nor have any clue what they're talking about. I don't go to Terrence Tao's blog and snark!
In order to do probability theory you first need to define a probability space. A probability space has 1) a sample space, 2) an event space, and 3) a probability function defined on the event space. The probability space needs to satisfy the Kolmogorov axioms which are 1) non-negativity of events, 2) one of the events has unit measure, and 3) sigma-addivity, or basically you need a sigma algebra.
When you define your sample space you need to use set theory by definition (unless you want to invent a new probability theory which is broader than what is currently meant by probability theory). But this is impossible, because "all logically possible worlds" is too large for set theory to handle, and its not clear if naive-modal-logic is similar to naive-unrestricted-set-theory (which is known to be inconsistent). Are you using ZFC set theory when you define your sample space?
Until you can show that the model you have created can satisfy the axioms or probability theory there is no need to consider your arguments. This is *not* a pedantic objection, the issues in trying to apply probability theory to the space of all logically possible worlds are so incredibly fraught that I doubt it can ever be done consistently.
Now to be clear, when you first say:
"Your existence is more likely if there are more people" you have now introduced the concept of likelihood and an implicit probability space. There is a lot of work that needs to be done before you can make this statement.
Consider, for example, a dice which has the number 1, 1, 2, 3, 4, 5. Is it necessarily the case that "a dice roll is more likely if there are more numbers?" In other words, is "1" more likely?
Not necessarily! It could be a weighted die which almost never lands on the two 1s. So you also need to define the probability function. You have implicitly assumed without stating that the uniform distribution is the correct one to use here without ever justifying that assumption.
There is a lot of work to do!
You don't really need these things to do probability, or at least to construct an informal probabilistic argument that has *some* intuitive force. Some people have in fact proposed dropping this or that Kolmogorov axiom - e.g., going with a finitely additive probability measure, or having hyperreal-valued probabilities, at least in certain circumstances. But even these alternative-but-still formal approaches may not be necessary to motivate certain philosophical views, as long as our informal arguments rely on certain structural features we would expect any reasonable formalization of probability to possess.
I specifically doubt sticking to strict ZFC is truly necessary to do something akin to probability. I wouldn't be surprised if you can do (non-standard) probabilities with NBG-style class-sized hyperreal probabilities, for example, although I doubt this approach will help all that much with BB's project, for various separate reasons. Still, he doesn't need to go this far. The sample space could just be the set of all universes whose physical (or whatever) laws can be described in a finite number of equations or words/symbols, maybe weighed by the minimum description length of the laws themselves, and then those universes whose laws involve numerical parameters could be given some appropriately natural-seeming prior over those parameters if available. Something like that, I'd guess, although some important questions about priors would remain. I doubt there will be unsetly many universes left anymore on this approach, but he doesn't really need that.
"You don't really need these things to do probability, or at least to construct an informal probabilistic argument that has *some* intuitive force."
I agree that for the typical case you don't need to do that much work. But when you are considering every logical possible world I am quite convinced that you won't be able to coherently apply a probability theory. When you say, "But even these alternative-but-still formal approaches may not be necessary to motivate certain philosophical views, as long as our informal arguments rely on certain structural features we would expect any reasonable formalization of probability to possess" I would object that in fact intuitive and informal arguments which are probability-ish are already known to fail because of simple paradoxes.
" I specifically doubt sticking to strict ZFC is truly necessary to do something akin to probability. I wouldn't be surprised if you can do (non-standard) probabilities with NBG-style class-sized hyperreal probabilities, for example, although I doubt this approach will help all that much with BB's project, for various separate reasons."
I agree you could probably expand probability theory, and you don't need to stick to ZFC, but again, I do think that all logically possible worlds is far too large.
"Still, he doesn't need to go this far. The sample space could just be the set of all universes whose physical (or whatever) laws can be described in a finite number of equations or words/symbols, maybe weighed by the minimum description length of the laws themselves, and then those universes whose laws involve numerical parameters could be given some appropriately natural-seeming prior over those parameters if available... I doubt there will be unsetly many universes left anymore on this approach"
Indeed, I agree. This would be a vaild approach to take. But you need to make this explicit, and you can't handwave over the details here.
>When you say, "But even these alternative-but-still formal approaches may not be necessary to motivate certain philosophical views, as long as our informal arguments rely on certain structural features we would expect any reasonable formalization of probability to possess" I would object that in fact intuitive and informal arguments which are probability-ish are already known to fail because of simple paradoxes.
There are paradoxes applying to some informal principles in some circumstances, most famously the principle of indifference, but that doesn't automatically mean every informal principle is off the table.
For example, suppose God tells you he chose a natural number at random using some uncomputable distribution. There's famously no such thing as a fair lottery over the naturals, so it's really not clear how to model this, or if it's even possible to model this. Infinitesimals won't work; complexity-based priors on God's secret distribution also won't work, given my stipulation on uncomputability. Still, it's perfectly intuitive to argue that the "probability" of God choosing an odd number, whatever it is, ought to be greater than or equal to the "probability" that he chose an odd prime number.
I'm not sure if God could do such a thing. Just because we imagine that it should be intuitively do-able doesn't mean that it is. I understand what you are saying, and share your intuitition, and maybe God could do this for the natural numbers. It feels like a God should be able to pick a random natural number such that every one is equally likely? But maybe not! And once you start getting as large as 'every logically possible world' my credence shrinks down to near zero.
I wasn't supposing God was picking a natural number uniformly at random, but was instead picking it via some uncomputable but well-defined probability distribution which is completely unknown to us. It's our own credences which we'd want to be uniform if it were possible, not God's actual distribution.
Great comment. You hit a lot of things I wanted to say. I would add, though that the “important questions about priors” are quite a conundrum.
For example, you went with finite number of equations but there could a universe with an infinite number of equations that’s still consistent with beings like us.
Even in Universes with finite equations, do we do a normal or uniform distribution on the constants? What about on identical laws and parameters but different initial conditions? How is that weighted?
It’s quite a big subject to get around.
However, I do agree with the general sentiment that, for an informal-intuitive argument, there’s no need to go that far. The gist of it is simply that, assuming all these possible worlds are kinda equally valid, the ones with more people are more likely. I don’t know that you can stretch that reasoning to infinite people though. That’s where the work needs to happen in my opinion.
BB probably answered this somewhere but what if there’s a maximum in the distribution where if you keep adding people in the universe, that universe becomes less likely, eventually converging on 0?
Okay, suppose I said the following: it's more likely that OJ did the crime if his blood was at the scene of the crime. Does that require using set theory by definition or a probability function on event space or the like? No! How is this different?
Let me try to be clearer: the OJ sample space would be all worlds consistent with the laws of physics as we know them, the event space would be all Borel sets of these grouped by their indistinguishability to us, and we would have some type of probability function weighted by what we think people typically do with their time. We group the event space like this because it does not matter to us if atom 914273 was at position 5235.4 or position 5235.6, because we don't have knowledge of that nor would we be able to distinguish the two.
Very crucially, the laws of physics seem uncountably infinite, and continuous. I know that probability theory works on sets like those, so I can reasonably apply it!
But you might object: surely you haven't considered every possible event! God could have done something to OJ which would violate the laws of physics as we know them, and even if this is unlikely it is still possible.
Except that I would reply that if we open the door to those possibilities it is not clear to me now if we have an uncountable infinity, and so I don't think we could apply probability theory. This is not breaking any metaphysicals laws, a mathematical model is just a model, and there is no reason to expect that the (metaphysics of?) the universe needs to be such that probability theory can be applied to it.
That's the first issue: the inability to reasonably define a sample space.
The second issue, assuming you can get over the first, would be the probability function itself. For something like the existence of the universe it is not clear if a uniform probability distribution makes sense. In fact, maybe you would argue that the correct distribution is just to apply a probability of "1" to the universe as it currently exists and a probability of "0" to every other universe. Or something like that. There is a lot to say here.
And here's a third issue, related to the first: it is not clear if you can make your event space satisfy the axiom of sigma-additivity. Consider a world where you exist, and assume it has a probability of x. Now consider a world where 2 people (like you) exist, and it must have a probability of 2x. So, okay, you quickly see that allowing this to go to infinity would result in a probability that doesn't add up to 1 if x is greater than 0. So we have to say that any individual world where someone like you exists has probability 0.
Normally, when dealing with infinite sets we get around this by considering indistinguishable Borel sets. So, if you wanted to consider the height of something in a range [2,3] you can say that any individual value between 2 and 3 has a probability of 0, but that a value in the range [x,y] has probability (y-x)/(3-2) for a uniform distribution. So you measure somebody's height, and find it is 2.8, but really its more like 2.8 +/- 0.001, so you could say this had a probability of .002 if you were using the uniform distribution.
It does not seem possible to define any meaningful Borel sets when any universe is fair game.
I would say that yes, it does, but it is just that most of the time these things are implicit. The sample space would be the things which OJ could plausibly have been doing. The event space would be the Borel sets of these. The probability function would be weighted by priors you had on the various likelihoods of each of those events. (There are a lot of outlandish things which could explain why there was blood at the scene of the crime, but he wasn't there, but these would be assigned a low probability). Notably, we wouldn't assume a uniform probability distribution, it would be weighted by what a typical person (or more precisely OJ himself) is likely to do.
You don't need to explicitly spell out every single event that could happen, because that would take forever. We are saved here because extremely unlikely things which are physically possible for OJ to have been doing can be assigned very small probabilities and neglected. Instead of dealing with logical possibility we could also assume something like physical possibility (which is a much much much smaller event space).
Anyway, the point here is that specifying the event space here is impractical because of how long it would take to do, but there is nothing objectionable about it per se, and it wouldn't be hard to give a rough sketch in that direction. Meanwhile, when you are dealing with every logical possible world it is not even going to be possible to define a sample space: logical possibility is bigger than set theory. So, we cannot apply the axioms of probability theory to that.
No real instantiation of any Beth number.
Beth numbers describe infinite sets, which transcend any physical instantiation. While some infinities can loosely model processes or entities in the natural world, higher infinities are more conceptual.
So you think you can rule out a priori MWI, as it entails Beth numbers of people existing.
I don't think that this is an agreed upon consequence of MWI. It's quite complicated to actually count the number of possible worlds in MWI because of the way decoherence works and when exactly branches stop being causally connected to be viewed as "separate worlds". Some people do estimate a huge but finite number of worlds and other something like continuous infinity.
But more to the point: it's not that clear that this implies infinite people as well as there could be only finite branches with finite people in it (and infinitely many more but without humans).
Yeah, good point, it's not exactly clear. My understanding is that the general agreement is that there are at least continuum many people and that they're largely uniform, in that they have continuum many have people. Then again, I don't really know physics, and this understanding is just based on brief convos with people who do, so I could be wrong.
It needn't be that there are Beth 1 *people* as nelson said infinites of Beth or above aren't actually instantiated.
Here's the point: suppose that MWI did, in fact, predict that many people. It would be odd to reject MWI based on the impossibility of rejecting that many people.
Yes, agreed with the general reasoning that you cannot reject it on that basis. And to be clear about MWI, I think most physicists would probably bet that it does predict infinite worlds with potentially infinite people in total. No one views this eventuality as a weak point of MWI.
Just want to express how grateful I am to you for leaving a very perceptive and reasonable comment. The other comments on this post were deeply confused, and it was driving me sort of insane.
>My understanding is that the general agreement is that there are at least continuum many people and that they're largely uniform, in that they have continuum many have people.
If that is your understanding why did you arbitrarily choose beth 2? As a "naturalist" (I'm not, but let's say for argument it's a reasonable approximation) I would be much more interested in your argumentation if you chose aleph 1, the more common number used to represent the cardinality of the continuum, a not unreasonable cardinality of "infinite" people.
You misunderstand! I was saying I think at least continuum many people actually exist *if MWI is true*. The number of possible worlds is at least Beth 2, as shown here https://philarchive.org/archive/GOMMRA#:~:text=Anthropic%20reasoning%20for%20modal%20realists.&text=typicality%20assumption%20or%20a%20randomness,2021)%2C%20109ff.).
I am not misunderstanding, at the very least you are being imprecise with your mathematical language. In multiple places you have made the claim that there are "Beth 2 people". The paper you link references other work talking about the size of the configuration space of 4D spacetime, not the number of people. Though it seems that Gómez-Torrente also has a limited understanding of the math he is talking about.
There is no fact of the matter because we don't know whether or not time will ever end or if entropy will ever reverse course. If time never ends and entropy becomes reversible then we can potentially have infinite observers, but e.g. every observer dying in every world is also something that's possible. As always BB makes spurious metaphysical claims about (enpirical, studyable, easily learnable) topics he has barely engaged with, bah humbug.
> (7) [...] on theism, it’s likely that the number of people that would exist would be the maximum number it could be.
But this does not seem to match our experience of the world. There's only eight billion people or so on Earth and we're not at a population limit. There are seven other planets in our solar system completely devoid of people - indeed, we haven't found any other people at all in the parts of the universe we have observed so far. If God wants to maximise the number of people, why is our area so lacking in them?
You might argue God has made universes with a wide variety of densities of people and we just happen to be in a lower-density universe. But, given we exist, shouldn't we expect to find ourselves in a higher-density universe, since there are proportionally more observers in higher-density universes?
The SIA argument makes sense in the Sleeping Beauty case because every person that gets woken up is the same person. There are three cases in which that person gets woken up, and two of them are in the tails condition. From having been wakened (and knowledge of the SB setup) the waker can conclude that tails is twice as likely as heads.
But my understanding of the situation described in this post is that there are Beta_2 **distinct individuals** who **all** get created. Each one gets created exactly once. In such a case you can't reason from you having been wakened (or born) that tails is more likely. Compare this story:
A) One ball is put into an urn. Let's call this ball "John".
B) A coin is flipped, and if tails comes up, another ball ("Jack") is put into the urn.
C) One ball is removed from the urn.
What are the chances that the ball removed from the urn is John?
The answer, assuming a fair coin, is 75%. If heads came up (50% chance) then the ball removed must (100%) have been the first (and only) one put into the urn: John. If tails came up (50%), then there's a 50% chance the one that came out was the first in (John), and likewise 50% chance that it was the second (Jack).
The argument doesn't change if we add an infinite number of balls in step (B). It just reduces the chance that the ball is John from 75% to 50%.
If all you know is that a ball came out of the urn (and the original rules for this game), then you must conclude that it is twice as likely that the ball that came out is John and the coin came up heads as that the ball is John and the coin came up tails.
And that is **exactly** the way the ball should reason if it could. Thus this premise:
> It’s just as likely that you’re John and that the coin will come up heads as that you’re John and the coin will come up tails. <
is wrong. Thus your argument that tails is twice as likely as heads fails (in this context), and thus premise 2 of the anthropic argument is undermined.
Yes, I have read the further arguments provided in (two of) the other papers you cite. They don't help, because the situation is not parallel to what we see in Sleeping Beauty. The people in the anthropic argument only get "wakened" once. Consider the version of Sleeping Beauty in which you are the main sleeper, but instead of waking you a second time on tails, a **different** person will get woken up on Tuesday.
When you are wakened, what credence should you give to heads having been rolled? The answer is 50% **because** you only get woken up once either way, so the number of wakings for you is the same either way.
Now if you happen to be the **secondary** sleeper in that game and you get woken up, the credence you should give to heads is 0%. There is **no chance** that the secondary sleeper will be wakened (during game play) if heads gets rolled. So you might object "What if I don't know whether I'm the primary or secondary sleeper? Then the logic goes back to the original Sleeping Beauty, doesn't it?"
Yes, it does. But in the anthropic argument you **do** know that you are the primary sleeper. You are awake whether God created infinitely many people or evolution created a finite number of people. Head or tails, you wake up. Once.
Belief in premise (2) of the anthropic argument is not justified. Thus belief in its conclusion on its basis is likewise unjustified.
Now I am wondering what exactly you mean by God, perhaps you have written on this elsewhere. Presumably it's the traditional theistic God that is omnibenevolent, omnipotent, and omniscient. And that given that God is all good, and that the existence of people is good, theism predicts that an infinite number of people exist.
But God is also traditionally defined to be a person or being, that is not just some force but an actual nonphysical mind which has experiences, qualia, self awareness, etc.
But I don't see how you get from the existence of infinite people to the existence of a nonphysical mind. The hypothesis that explains the data of infinite people existing would be the presence of a some powerful force that does good, but it would be merely a force like gravity, not a mind like God.
I mean an all-knowing, powerful, etc being. I explained here why I believe in God. https://benthams.substack.com/p/god-best-explains-the-world
Interesting, thank you. Would this also imply that there exists at least Beth-2 Gods?
No, SIA only gives you reason to think that there are Beth 2 people with your exact experiences.
Frankly, this sounds like nonsense. Here’s a better counter argument: math is a spherical cow. There are many possible logical constructs to explain the reality. So why do you think your spherical cow represents reality? When you can’t perform an experiment any crack pot theory is valid.
1. I exist.
2. You don’t.
Care to debate?
What the hell? I gave an argument, which, if put into premises, comes out as the following:
1) There are at least Beth 2 people.
2) If there are at least Beth 2 people that favors theism over atheism.
3) Therefore, the fact that there are at least Beth 2 people favors theism over atheism.
Which premise do you disagree with? How is anything about spherical cows supposed to be relevant.
There are *some* things we believe based on experiment. Other things we believe based on philosophical argument. For example, the way we know that the world wasn't made five minutes ago looking old can't be through experiment. The principle "everything is known through experiment," is self-defeating, because it's not known through experiment.
How many crickets does a cricket farm need to make before God becomes real? If they make Beth 3 crickets, do they make two Gods?
Well, if the crickets lived good lives, given that a cricket farm making more crickets than could fit in any spatiotemporally-connected region of space would be a miracle, it would be quite a bit of evidence.
What my comment was supposed to highlight is that the connection between probabilities, numbers, and God is usually a non sequitur.
Probabilities aren't really real. They are just words on screens or thoughts in our heads. Probabilities might predict the motion or sequence of real events, like the Monty Hall Goat quiz show. The existence (or lack thereof) of multiple universes and God aren't observable events to predict. At best, they are part of models and theories made up on blackboards to try and make other models and theories look more consistent. Making a long chain of probabilities to say "And therefore God" could be swapped in with any other absurd conclusion.
Okay, so which step in the argument do you disagree with. Put formally, the argument is:
1) There are at least Beth 2 people.
2) If there are at least Beth 2 people that raises the likelihood of theism.
2, or maybe it is disagreeing with the idea of there being a Beth number at all. Rereading the original chain of arguments:
"Your existence is more likely if there are more people. E.g., if a coin gets flipped that creates one person if heads and ten people if tails, you should think it’s ten times likelier that it came up tails than that it came up heads."
The number of people that exist does not seem like it would have any bearing on "your" existence. "Your" existence is a product of exactly how many people and things also existed in proximity to you. The only coin being flipped is the physical process that creates the genes and womb environment for a baby, but any hypothetical baby born similarly still won't be "you".
Is any of what’s being argued here grounded in reality or just an intellectual exercise? Why are you so confident of your untestable model or reality when even Newton’s failed?
The Anthropic Argument is vapid precisely because it can’t be tested. In fact, it’s so easy to create purely logical constructions to explain reality, you’d need to argue why you can have any confidence in any construction. There is no evidence to back any metaphysical claim. Zero.
To press further on the idea that the spherical cows of math have little bearing on the real world, consider the concept of infinity.
I am not aware of any “real” infinity. In fact, it’s a hypothesis.
So yes, I can be both Beth numbers. Let’s name one Alpha and the other Omega. I am God, this is my reality.
You can’t prove me wrong. I also can’t prove that we are the result of some complicated stochastic process.
Yes, it's all grounded in reality. As I explained, there are reasons to think the premises are true. In fact, you'll even notice that the argument I give in this article provide reason to think that there are infinite people.
The difference between good arguments and non-sensical strings of words isn't that good argument have testable premises, but that they have defensible premises. As I explained, if you reject that, you can't even justify the premise that there are truths and your view is self-defeating, as the premise that good arguments can only have testable premises is itself untestable.
Here is a counter argument to show the absurdity:
1. There are at least Beth 3 people*
2. If there are at least Beth 3 people then the theory of the army of multidimensional fairies is favored over atheism. The multidimensional fairies obviously have an interest in creating at least Beth 3 people.
3. Therefore, the fact that there are at least Beth 3 people favors multidimensional fairies over atheism.
4. Since Beth 3 is greater than Beth 2, clearly multidimensional fairies are favored over theism.
This argumentation is arbitrary and unjustified. Your usage of math is too weak to support the heavy claims you are trying to make. Your source is a non-mathematical philosopher writing in a paper about what another non-mathematical philosopher wrote in a paper about what Quine wrote on worlds. Which, by the way, I followed the sources and I can't find Quine making this argument, would love to read it.
* Mathematically speaking if you consider the multi-verse hypothesis in a multi-dimensional hyper inflation at the quantum level in a Einstein-Rosen bridge it is clear that there are Beth 3 people.
Well, I don't know why the army of fairies would be likelier to make Beth 3 people than atheism. But if they would, while this would then, by definition, be evidence, for fairies over atheism, fairies have a low prior, so it wouldn't be decisive evidence.
I don't get what you're saying about Einstein-Rosen bridges.
First of all, the proof is from Lewis not Quine. Second, you don't have to take it on authority, it's pretty straightforward. People are made of points. But there are Beth 1 points in a line, so Beth 2 (the powerset of Beth 1) ways of arranging points.
The "Mathematically speaking..." part at the end of my comment was intentional gibberish, I had hoped it was obvious. I was just showing how if you use enough complex language taken from usually poorly understood sciences you can justify anything you want. I am not actually arguing the Beth 3 hypothesis.
I would love to see a proper mathematical formulation for what you're saying because it doesn't seem to jive to me. The leap you make from people being made of points to Beth 1 points on a line that is arbitrary. Then your conclusion is saying the number of configurations of points == number of people, this also is not clear.
The way I see it is in a single universe there are countable infinite objects (aleph 0). We can say particles, or atoms, or chairs, or even bipedal organisms living on wet, rocky planets orbiting 3rd generation main sequence stars. In all cases the cardinality of the set is countably infinite for one universe.
If we choose to hypothesize the multiverse than we invoke the cardinality Aleph 1 (or Beth 1 if you prefer) for the number of objects in the infinity of universes. This is the same whether we say in "this moment" or across all time.
Counting objects is not the same as counting configurations. If you count the number of configurations in any one universe that gives you Aleph 1 cardinality, but that is in essence just compressing the same information content into one universe. Consider that a slightly different configuration of this universe is the same as an alternate universe that is slightly different.
Now I'll admit I am not a mathematician, just a software developer/IT professional that reads a lot of this stuff in his free time. If you have a real mathematical proof that shows this Beth 2 claim it would be interesting to see and I would gladly accept any real formalization contradicting what I am saying.
I am really just trying to point out that the main aspects of your argument are poorly justified and arguably unknowable. It's a moot point though, in some sense, as nothing in your argument says that your definition of "God" is anymore likely than my definition of "multidimensional fairies", so it continues to be unconvincing.
Also, I don't see why it's not possible to believe there are Aleph 1 people in universe as an atheist. I think plenty of atheists believe complex life is emergent and in an infinite universe there are infinite people, add the multifverse and we're good, no conflict there. I personally am not a fan of multiverse theory but I have no problem putting it in the background as you say.
I will respond, but let me note that it's fairly ridiculous for you to call me a charlatan when you don't have the faintest clue what you're talking about on some subject. I don't go around calling people charlatans when I don't understand subjects.
Okay, now on to the serious matters.
First, I have now explained why there are Beth 2 people at least AND linked a paper explaining it. I don't know how many more times I can explain it. In short, the world is made up of points. You can rearrange them. There are Beth 1 points in a line, and Beth 2 ways to rearrange Beth 2 points.
Yes, there are aleph null particles, trees, etc in an infinite universe. But there are Beth 1 points. This is wikipedia knowledge https://en.wikipedia.org/wiki/Beth_number#Beth_one
However, there could be a multiverse containing many objects. Even if per universe there are only aleph null objects, that's no limit on the number of *possible objects*.
//Counting objects is not the same as counting configurations. If you count the number of configurations in any one universe that gives you Aleph 1 cardinality, but that is in essence just compressing the same information content into one universe.//
Well, if they're composed of points, you get Beth 2. But anyways, insofar as each configuration is a possible world--ie, every sequence *could* exist--then there are Beth 2 (if points) or Beth 1 (if not) particles.
//Also, I don't see why it's not possible to believe there are Aleph 1 people in universe as an atheist.//
Well, it's not clear if aleph 1 equals beth 1--you're assuming the continuum hypothesis it seems. But yes, an atheist could think there are beth 1 people. This gets dicier with Beth 2 though. No plausible multiverse model gets you Beth 2, and virtually none get you Beth 1 people. (MWI might get you enough, but then if MWI is true there will be more possible people because you can take subsets of the wave function. Also if, as I've argued, there are too many people to be a set https://benthams.substack.com/p/the-best-argument-for-god then MWI--and every plausible naturalistic view--is obviously woefully insufficient).
Again you are conflating points and particles and your explanations of this cardinality argument seem strange. I've read through the paper you provided and it doesn't appear to provide a justification for your argument. I wish you could understand that I don't need you to repeat your explanation, I get what you are saying I just don't buy it and you haven't presented any rigorous mathematical formulation.
"No plausible multiverse model gets you Beth 2..."
This seems to be you making my point. On the one hand you are presenting Beth 2 as the cardinality of people as if it is a fact and then on the other you admit that the accepted scientific perspective says otherwise. I would have less of a problem with your argument if it at least had the humility to acknowledge that this is a _hypothesis_ and not an established fact. People unfamiliar with these concepts take what you say at face value and you should be more careful not to generate unnecessary confusion.
On a side note, I think this is the last time for a while I interact with you, I was hopeful that my impression of you from other comment threads or posts was mistaken but it seems clear that you have a certain resistance to listening to criticism and hold an almost authoritarian stance on your ideas.
Have you ever considered the fact that you are not perfect? That you have beliefs and ideas right now that you hold dearly that are false? I think any philosopher needs to hold tight to a sense of Socratic Humility and avoid dogmatism as it prevents growth and discovering situations where you may be wrong.
1. You could be wrong about anything and are definitely wrong about some things.
2. If you are wrong about things, you are unable to notice the fault on your own.
3. Therefore you should be skeptical of your own ideas and seek to root out falsehoods, especially those that receive frequent criticism.
I did no such name calling and if you feel ofended by my response I am sorry, it was not my intention. Your acusation though, of me "not having the faintest clue" reeks of arrogance and is unfounded as you don't know what I do or do not know. If you'd like to contest any of my points or provide a formal backing for your logic I would love to hear it otherwise I have no interest in reducing the conversation to agression and insults.
>The number of people that there could be is at least a very large infinity called Beth 2. I think it’s more, but let’s be generous to the naturalist, and say it’s Beth 2.
The philosopher John Leslie used to critique "social" models of the trinity by suggesting that, by Leibniz's assertion that a good God must create the best of all possible worlds, and that N+1 perfect minds is entails more good experience than N perfect minds, the Godhead must include infinite persons. I don't know if he ever wrote about this being agreeable to Christian accounts of cosmic creation, theosis, and apokatastasis.
The elephant in the room appears to be the multiverse of the universal wavefunction? This is a perfectly atheistic explanation for uncountably infinite observers.
The book of the Flying Spaghetti Monster says he created aleph(BB(BB(69420) people, so he is infinitely more likely than your god
It can’t be right because it proves too much. The argument still works if you replace “people” with any other good thing, such as “original manuscripts of Shakespeare plays”. The argument still works if you replace “god” with any other being or computer capable of simulating a lot of that. And even if the argument worked it wouldn’t prefer the Christian god to any other flavor of god.
>The argument still works if you replace “people” with any other good thing, such as “original manuscripts of Shakespeare plays”.
Anthropic reasoning only applies to subjects capable of observation, not goods generally.
>The argument still works if you replace “god” with any other being or computer capable of simulating a lot of that.
The argument takes the form:
1. A particular person, such as the one reading this, exist
2. (1) is infinitely more likely if the maximal number of persons exist rather than any countable number
3. The maximal number of persons existing is best explained by the existence of an agent with the power and will to create the maximum number of persons
i.e. your existence is infinitely more predicted by the existence of something productive of uncountable infinities of persons rather than optimistic naturalism's steady-state cosmos of boundless space.
This is not true of Bostrom's formulation of the simulation argument, which merely concludes that a particular person/civilization is more likely simulated than not - in fact the conclusions do not contradict. A simulated person, if such a person is possible, could rationally conclude that her simulated existence is most probable if God exists *even if she correctly believed she was simulated*. Much like the blogger (presumably) also believes his personhood is explained in a proximate sense by the actions of his parents.
>And even if the argument worked it wouldn’t prefer the Christian god to any other flavor of god.
Yes, as long as the god in question has the properties traditionally ascribed to the monotheist's Creator-God, such as maximal power, knowledge, moral perfection, and modal necessity. Philosophical arguments in this area are about Ho Theos, not theoi.
This is a fun thread!
I have another objection to the anthropic argument. It applies probabilistic reasoning to a domain that is more fundamental and prior to probability (existence itself), and therefore draws its unusual conclusions merely as a result of applying probability theory to a domain where it is undefined.
Does your existence give you evidence that your parents didn't use highly effective contraception with a failure rate of .00000000000000001%? Does that argument "apply probabilistic reasoning to a domain that is more fundamental...(Existence itself)?" How is that argument any different?
My main objection to the existence of God is that I hold purely hedonic utilitarianism to be true, and this world does not appear to be one created by a God that, by necessity of hedonic utilitarianism's truth, would hold likewise. The reason I think the only valuable good is positive emotional valence is because it is the only thing that can be subjectively experienced as good in itself. All other values are mediated by positive emotional valence, in that it feels good to fulfill or contemplate the fulfillment of that value. I like to point out that even asceticism has a self-satisfied contemplation that motivates it. So, if the only value is pleasure, and an omnibenevolent God would seek to maximize value in his creation, we can expect that the only thing God would create would be an infinite number of minds experiencing an infinite amount of pleasure for an infinite amount of time. Since we are not currently exalting in the Beatific Vision, we can conclude that we were not created by an omnibenevolent God. I know you like to say that we were put in an imperfect world because it produces afterlife goods that might have value in our infinite lifespans, but this relies on non-hedonic utilitarianism which holds that there are ultimate values other than pleasure, which I think is simply false. Pleasure is so self-evident as the only final good that we can conclude we are not in a God-created universe because we can observe that pleasure is not being currently maximized.
I don't agree with this argument. I mean, I don't quite know what it means to subjectively experience as good in itself, but it can have two meanings:
1) Have and see as good. In this case, the premise is false.
2) Have as a subjective experience and perceive as good. In this case, the premise is question-begging. No person who thinks that things other than subjective experiences can be good or bad will grant that for something to be good it must be subjectively perceived as good.
Additionally, hedonic utilitarianism is extremely philosophically controversial. Almost every philosopher thinks that it's false. Thus, you shouldn't be more than, say, 90% confident in it. But then the argument won't give you more than a Bayes factor of 9 in favor of atheism.
There might also be various necessary connections between goods, so that experiences in this life are in some way needed for the best sorts of afterlife experiences.
What does your anthropic argument say about the conventional, scientific explanation for the existence of people on earth (i.e., from the first simple cells that emerged roughly 3.5 billion years ago, life evolved through increasingly complex forms, ultimately leading to the emergence of Homo sapiens approximately 300,000 years ago in Africa)? Is that all a big myth?
Lol, I obviously agree with that! I just think there's a big multiverse with many myths.
So each universe in the overall multiverse has its own unique scientifically valid explanation for how humans arose? That doesn't sound like a parsimonious explanation, and it's not empirically testable.
Well, first of all, we do have empirical evidence for it: namely, that you exist. As I explain in the post, when we're precise, your existence gives you massive evidence for it.
Parsimony has to do with *fundamental* things, not just the number of total things that exist. It doesn't violate Ockham's razor to think the universe is very big!
I'll be honest with you. A lot of the posts on your blog seem sensible and well-reasoned. And even if I don't necessarily agree with everything you write in one of those "conventional" posts, I at least understand your arguments. But this anthropics stuff seems extraordinarily irrational and difficult to comprehend. It's like you have a split personality, with one "alter" being a normal smart dude, and the other one being totally bonkers.
I have an alternative theory, and unfortunately there is no way to describe it without sounding mean. The theory: you don't know anything about anthropics.
This shouldn't be that surprising. Most people don't. Your comments so far have evinced based--and rather extreme--misunderstandings of the argument. Furthermore, anthropics is very complicated--it's genuinely difficult to really get it! Philosophers often remark that it's the trickiest area of philosophy. It's also quite alien from our ordinary experience, and thus prone to misunderstanding.
I think this theory is supported by two facts (and I suspect a third):
1) I've published on the area of anthropics, written obsessively about it for about a year, and spent hundreds of hours reflecting on it. You've likely done no such thing, nor anything in the vicinity of that. Thus, it's probably likelier that you're confused than that I am.
2) The anthropic argument tends to get a much better reception from philosophers. Many think it's a good argument. Many of those who don't say that they don't know if it works because they haven't written about anthropics.
3) Probably you don't have a background that would give you special anthropics expertise. Given that, it wouldn't be that surprising if you were confused about it.
Analogy: suppose that you didn't know anything about physics. Some undergraduate blogger with a publication about some specific physics topic, many blog posts about that topic, and two other publications about physics more broadly. This undergraduate writes extensively in favor of some thesis about black holes. You, likely having no background in physics, and certainly no in black holes, think their arguments sound silly and are confusing. Should you think they're simply full of shit?
Again, I apologize if this comment comes off as mean. Sadly, there isn't a way to write a comment extensively justifying the thesis that "actually, you're the one who's confused about this subject," without sounding a bit mean.
I don't think you're being mean, certainly no meaner than I was.
Are there any smart non-philosophers—people like mathematicians, physicists, cosmologists, or statisticians—who have studied anthropics and have an opinion about it? I'd feel better about spending time researching this area if I thought that the theory has some traction outside of just a small subset of philosophers.
Hm. The anthropics arguments I know so far are easy to follow even for non-experts. (Cool World's about Simulation, Grabby Aliens, and cosmological fine-tuning.)
Yours is not, it feels very rushed. Sorry.
One recommendation is to phrase it more as an iterative game with bets (like the sleeping beauty setup), but of course that's a considerable difficulty, since we only have one life (or at least currently only have access to this one). And of course arguments about Simulation all run into this problem too. (Hence why it ends up 50% +/- 1 based on one's biases ... assumptions!)
https://www.lesswrong.com/posts/Y5nCyLBy9B6cJPsZN/is-grabby-aliens-built-on-good-anthropic-reasoning?commentId=gFy7AYuydsyZfvPx8
Observation selection requires a plausible mechanism first, we need a list of the counterfactuals. The "the more people more chance for me" is too vague. It would make sense to rephrase it in terms of third-party individuals. (Cognitively juggling alternate selves is pretty hard.) So a random observer looks around and sees *gestures wildly* and due to the assumption that if there are more people it's more likely for them to observe whatever they are currently observing. Okay, so were there fewer people this random observer wouldn't exist. Sure, but this does not let the observer conclude anything about causation, because this mechanism is basically tautological.
The model proposed in step 2 does not differentiate based on number of individuals. That's your assumption. We don't have data for this mechanism. (For example we can say that the more people the faster we burn through all of our resources. So it's entirely possible that if the number of people crosses a threshold we start an all out war and a great filter event says hello. It's consistent with us not seeing huge alien bonanzas. [but of course we barely scanned any planets for biosignatures, so I think the only thing we know is we can rule out late-Kardashev civilizations]) ... but I got a bit sidetracked, sorry!
Fundamentally to do model selection we need data that's connected to the mechanism. Ie. we need something observable that would not be in the counterfactuals. (Or would be lower probability.)
And ... so ... based on my (naive) understanding the problem is that we are discussing a well-known zero-data phenomenon (ie. Mr. Cosmic T. Pot).
I sort of feel like this too. Maybe I'm not smart enough to understand it, maybe it doesn't make sense, or maybe I could understand it if I really spent time thinking about it but I don't care to.
See my response to Alex.
There must be an infinity of people who don't exist and never will relative to those who do or ever have. Therefore the best that can be said about the existence of any of us who do exist uses the word "fluke" if even that word adds understanding.
Well as I say, probably you are one of the people in the multiverse. In fact, that's how the probabilistic reasoning behind the argument works.
I don't understand why people leave snarky comments on articles when they obviously neither have read the argument nor have any clue what they're talking about. I don't go to Terrence Tao's blog and snark!