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I think this argument gets some crucial stuff about probability and infinities wrong.

"if fewer than Beth 2 people exist, then 0% of possible people exist, which would make the odds of my existence in particular zero"

Having a measure of zero doesn't imply non-existence, impossibility, or anything meaningful at all about the probability of your existence. A measure of zero simply means the size of the set of actually existing people is negligible in comparison to the set of all possible people. Your argument is kind of like saying the probability of selecting .2523 from [0, 1] is 0 because "0% of numbers exist" - it's 0 because its measure is 0. Or you could consider the subset of rational numbers within the set of all reals - same issue. I'm actually not sure if you're suggesting you randomly select a person from the set of all possible people and integrate over the subset of actually existing people, or if you're suggesting you integrate over the entire range. But either way, it doesn't make much sense. To get meaningful probabilities, you have to look at ranges. Given this sample space, you have to use PDF, not simple division. And, if you want to integrate over the entire space, we need to use a nonuniform distribution, otherwise you violate normalization. This means not every person has the same probability of existing.

Since the sample space you're using is uncountably infinite, you're suggesting humans are not discrete objects. I'm not really sure how that works. But even if humans weren't discrete, I still have no idea what it would mean to say a powerset of an infinity of people exist. Power sets of infinities are abstractions - it's not sensible to say that Beth 2 people actually exist.

If God can somehow make cardinal infinities of persons, then why would this ever stop? If even making countably infinite persons isn't a limit on him, and he can make powersets of infinities of people, then he can take the power set ad infinitum. This seems to lead to a contradiction - he's going to make the maximum number of people, but there is no maximum number of people.

This raises the question as to where all these people are. The number of people has clearly varied over time - it hasn't been constant at some maximum. The universe is mostly devoid of life. So, where are all these Beth 2 people? Is God keeping some infinite vat of souls? If so, then you run into exactly the same problem as before. If God selects some soul from the vat to exist at any given time, you again have measure zero.

I think you rightly point out God would maximize life. But then anthropic reasoning points in exactly the opposite direction you're claiming - the universe is hostile to life. We certainly don't observe Beth 2 people. Your claims go against empirical observation. And, as I mentioned before, the very existence of humans suggests God isn't real: https://link.springer.com/article/10.1007/s11841-009-0137-0

Regardless, and I think most crucially, these probabilities simply aren't meaningful. Your existence is determined by initial conditions in conjunction with nomological laws, not someone selecting a random person out of a set of Beth 2 possible people. Your existence is not a random event, so all of this probabilistic reasoning is irrelevant.

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May 21Liked by Bentham's Bulldog

Sure, I'll give anthropics a try. What's the worst that could happen? :v

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I call this the “Platonic fallacy”. Your whole line of reasoning is based in the idea that your mind can impose its reasons to reality. The Aristotelian revolution in Philosophy was the inversion of Platonism: ideas are abstracted from reality, they are not true archetypes. All you reasoning about what exist beyond reality is abusive extrapolation.

Your mind belongs to reality, its ideas can at most represent reality and never ever can transcend it.

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My mind doesn't impose any reasons. My mind figures out things about reality.

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And only about reality. Beyond reality, there is no reason to think that reason works at all.

You can know at most as much as a Laplace demon. Beyond the Laplace demon, why shall you trust reason itself?

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I totally respect intra universe anthropic argument, but when you use for multiverse extrapolation, the whole thing collapse into “anything goes”.

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Thanks for the post Bulldog. I think you should make the meme dogs older as you become more philosophically competent. Perhaps 10% for every time you change your mind on an issue of significance.

I think this argument isn't taken as seriously as it could be because arguments in the form of "you can reason, therefore 100% chance of God" are abundent and usually quite unconvincing. It makes sense that people would slot this argument into the bucket where it belongs and not consider it further. Now I think that people should talk about it more because it is quite interesting, but the reaction is understandable.

A few more argumentative points:

The argument does not only admit that things get weird with infinities, but affirmative relies on the dubious notion that bayesian reasoning can apply between and within various classes of infinities. I think even you have to give some credence to the counterargument that infinities cannot be compared in this manner. If that's true, then the SIA anthropic argument falls flat.

I suppose I would also say that the God's coin toss example doesn't quite prove your argument. One could say "Yes, I would agree that God creating 1,000,000 people in this white room is 1,000,000 times more likely, even if I don't update on the fact of my existence, because it increases my chances of being *in this room*, as opposed to somewhere else".

Now you have two reasonable responses that I have heard so far. Firstly, you say that *sometimes* we have to update on the fact of our own existence. Our mothers did not use perfectly effective contraception. Secondly, you will say that we can modify the hypothetical to say that the *only* people in existence are either the one person in the white room on heads, or the 1,000,000 people in the white room on tails.

As to point one, I don't think contraception works. That is updating through our knowledge that we were born from our mother and that humans must be born to be alive. We wouldn't need to update on our "own existence". (For example, an outside observer would also reach the same conclusion, even if they were informed that I was a p-zombie).

I don't think there is a cost to denying the second hypothetical. Intitutively, I think that in order for me to reason about the process of my creation, I must exist. So my existence necessarily precedes logic, and doesn't require any updating. I think this is partially because in a deep sense the world exists only inside the mind, so there is no existence outside of consciousness. But also, just in terms of the coin flip, there is a 100% chance that someone like you will emerge as conscious post-flip. So your existence in an identical room provides no evidence for anything.

Is this just SSA? I would say its neither; the refusal to update on existence. It just seems exceptionally odd that there is a metaphysical first priniple that either the maximum possible number of people exist, or the minimum possible number of people exist.

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"So far, the number of people who have written rebuttals is precisely one."

Forgot Joe Schmid?

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I think anthropics worth caring for. It's a sphere where a lot of smart people are severly confused and resolving this confusion is important. I do not hope that it will reveal some deep secrets about the universe, and I believe that anyone who does will be dissapointed a lot in the end. Getting an accurate map requires actually exploring the territory, instead of obsessing over the fact that you are a map maker. In the end I expect everything to simply add up to normality, but hey, it's about the journey not the destination, am I right?

And oh boy, do I empathize with having to listen to people saying completely crazy things about the topic. The irony of course, is that both of us consider the other one to be one of these crazies, while himself to be one of the surprisingly few reasonable people. But, I think, this shouldn't prevent us from empathy to each other from across the divide.

I think SIA appears to you so obvious because you have some blind spot regarding its troubling consequenses of SIA, for example:

Being arbitrary sure that your biological parents were absolutely incapable to conceive you

Being mostly certain that if you are one of two first people in the universe you do not need to procreate in order to keep humanity from extinction

Being able to win a lottery by creating copies of your mind

Thinking that you can retro-causally move boulders with your mind

Thinking that awakening in a room gives you more evidence than being brought into the room while awake

Thinking that experiencing memory loss can make you more confident in an event about which you could previously only reason on priors.

And so on and so forth. It's not even hard to come up with them. For every case of SSA presumptiosness, there is a similar case of SIA presumptiosness. And while SSA at least has the plausible deniability of shifting reference classes, SIA allows to only eat the loss. You are aware of it, you keep saying that all anthropic theories are presumptious, but somehow treat it in favor of SIA, instead of treating it as a reason to construct new, non-presumptious anthropic theory.

Likewise, the troubling SIA results that you mention are much more troubling together, then you give them credit. They basically make SIA self-defying. SIA is simultaneously extremely sure that there are infinite people and completely unable to reason about this particular case that it assumes to be most probable. You can rescue other theories that mess up infinite cases by assuming that actual infinities are impossible, but you can't do it with SIA.

And some of the cases that you frame as troubling for non-SIA reasoning, appear to be so only for people who have already accepted SIA. The most obvious case here is SIA assumption that reasoning about death and non-existence has to be the same. If we do not reason about death and non-existence being the same in ethics why should we do it in anthropics? It's at least not obvious that SIA's version is correct, or even this is actually a troubling case for SIA. See this: https://www.lesswrong.com/posts/LnearFbA4thE646tR/dead-men-tell-tales-falling-out-of-love-with-sia

When you make arguments for SIA, from my perspective, you leave obvious holes in them. Like with the doomsday argument. You yourself notice the possibility to evade doomsday conclusion without SIA by assuming that I couldn't possibly be born in the future in the first place. But then you dismis it because "it seems like I could have existed in the future instead of now" without investigating it further. Like why does it seem this way to you? What is the justification for such intuition? Maybe it's wrong? What's the paradoxical consequences if we assume that it is? You do not really explore this alternative just declare it a priori absurd, which is quite unpersuasive. As a matter of fact, there is a very good reason to think that I couldn't be born in the future or in the past, based on our knowledge about the way universe works: my causal history depends on a specific sexual interaction between my parents, which would be impossible any other time than the exact moment of my conception. Probabilistic models that assume otherwise simply ignore scientific evidence.

SIA is a huge bullet to bite unless you've already done it. It does not appear true from the outside, unless you happen to have corresponding intuitions and majority of people does not have them. So, when you make a new exciting proof of God via SIA, even theists are cautious. They know that psychophysical harmony is true, so of course they would like a proof of God that is based on it. But this SIA business... may work for those who already accept it, I guess. And for atheists, well, it's just another reason to discard SIA, because the non-existence of God appears to be a much more lopsided issue than theories of anthropics.

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My problem with anthropics is one of relevance. The arguments I have seen are either utterly fantastic or otherwise self-evident. Also, I'm not sure if we are reaching the point where the conclusions drawn simply make the premises too remote to consider.

Here's a tangible example for me: It is safe to assume that if I take a million draws from a sample of 500 trillion options, it's a million times more likely that you get the one specific draw you are looking for than if you only took one draw from that sample. But in a sample size of infinity, it doesn't matter how many finite draws you take from it; the probability is still zero. So the difference in the cardinality of the sample size makes a difference in the result.

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"If you reject SIA, you get horrendous paradoxes including..." I'm not sure if this, and similar formulations throughout your post, are exactly the right way to frame it. A lot of the paradoxes you mention are not inevitable results of rejecting the SIA, but rather results of accepting one of the existing major alternatives to the SIA in the literature. I think this is a pretty meaningful distinction, because anthropic reasoning is a very new field of philosophy which there's been very little work on (as you acknowledge) and there's very little reason to think that the spectrum of views currently available in the literature exhausts the scope of plausible options.

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Which ones do you think are not inevitable results of rejecting SIA? I think they all are and argue for that in the linked post.

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The first one I clicked on was the boulder example, which was presented in your original article as a reductio against the SSA. But maybe you think that it also applies to any conceivable anthropic view (at least any such view that passes some minimal threshold of plausibility) that isn't the SIA- I'd be sort of initially skeptical of such claims given how little of logical space has been explored wrt anthropic views, but perhaps you are right.

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That section was about why that problem applied to all views other than SIA.

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Do you think these reductios would apply to the anthropic decision theory view that you talked with Nora Belrose about?

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I don't think she has an anthropic theory because she doesn't think that there are facts about the odds of various scenarios. She just thinks there are what one should bet at, and that depends on their values. Suffice it to say, I think this is a crazy view.

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I see, I think we are talking past each other. I meant to just talk about views one could hold that say something relevant to these kinds of cases about anthropic reasoning. Not necessarily anthropic theories given what you seem to mean.

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I think her view is just not a view of anthropoids in any real sense. It doesn’t tell you what credence to have in anthropoid propositions.

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I must be too dim to follow the argument for god. It seems based on a lottery conception. If you happen to win the lottery, does that mean everyone else does too? It’s almost metaphysically certain that I will not win a lottery drawing, but it’s even more certain that *someone* will.

We happen to be in the one tiny rock in an area millions of light years wide that otherwise contains no life. We won the lottery and our (evolved) solipsism leads some of us to think there must be lots of lottery winners. I think there are vanishingly few other winners and lean toward none at all, at least none that are coincident with our time frame.

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I think the general reason for the blank “sounds interesting” reaction (from my famously expert reading of social cues) is probably one of or a mix of these:

1. Most people haven’t studied anthropics in the way that they might have studied philosophy of mind (relating to psychophysical harmony - non-philosophers tend to have a similar reaction to psychophysical harmony) and they know that it is a notoriously difficult and complex subject area, so they do not feel comfortable making a judgement between SIA vs SSA. A personal thing for me that apply for others too is that, while your arguments for SIA sound convincing, I can’t help but not fully commit myself to it because I haven’t encountered any arguments from others vigorously defending SSA, or a debate between you and someone who defends SSA. Having heard only one perspective, it often feels intellectually irresponsible to form an opinion on whether it is right, especially if you are hearing a Substack blogger’s opinion that conflicts with many academic philosophers’ (not to devalue your work obviously, but for someone who hasn’t read all your work it is reasonable to be sceptical because philosophy bloggers are wrong more often than philosophers).

2. It proves so much. Because of this, I imagine many people react to it similar to someone hearing Anselm’s ontological argument, in that they may not be able to pinpoint why they think it’s wrong but it sounds too good to be true, so they are rightfully sceptical.

3. At least in comparison to psychophysical harmony, there isn’t an equivalent to how many philosophers saw already in the literature that pph was a significant problem that could be solved by theism.

4. Maybe some of the theists are committed to the impossibility of actual infinites because they accept the Kalam cosmological argument.

I hope that once you publish the paper, it gets more serious academic attention.

Also, do you think you’ll ever be able to get Bostrom on to talk about SSA vs SIA?

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