# The Lottery Fallacy, Fine-Tuning, and the Multiverse

Our best current science suggests that our universe is fine-tuned for life. That is to say, certain numbers in basic physics – e.g. the strength of gravity, the mass of electrons, etc. – are, against improbable odds, exactly as they need to be for life to be possible. Many scientists and philosophers think this is evidence for a multiverse, but I disagree. What we have evidence for us that our universe is fine-tuned and postulating a huge number of other universes doesn’t explain this.

I recently wrote a Scientific American article on this, and there have been two blog posts from Skeptics Guide to the Universe in response. Earlier this week, host Steve Novella and I got together to discuss the issue, and an edited version of our discussion will be going up on their podcast tomorrow. The discussion prompted me to clarify my argument in my own mind, and I’d like to share here how I’m thinking about it now.

Steve accuses me of committing the lottery fallacy. But what is the lottery fallacy? Suppose against improbable odds my lottery numbers come up. Clearly there’s something going wrong if I think there needs to be some special explanation of the fact that I won. Steve suggests that the error consists in focusing on the particular person who won – Philip Goff – rather than merely the fact that someone won. Similarly, by focusing on the fact that our universe – rather than just some universe – is fine-tuned, he thinks I’m committing the same fallacy.

I don’t think this is the right explanation of the lottery fallacy. Sometimes a focus on the particular person is appropriate. Suppose, for example, that the partner of the person who picked the numbers wins on a billion to one odds. Then it does seem we want to focus on the particular person who won.

What’s the difference between the two cases? The fact that Philip Goff won the lottery is improbable, but it’s not improbable that it happened by chance. Why is that? Because there’s no (non-ad hoc) non-chance hypothesis that would render it much more probable. Whereas when it comes to the fact that the partner of the person who picked the numbers won, this is just as improbable as Philip Goff winning, but in this case it’s not only improbable but improbable that it happened by chance. Why? Because there is a (non-ad hoc) non-chance hypothesis that would render it more probable, namely the hypothesis that there was collusion between the person who chose the numbers and her partner. Assuming that hypothesis, it’s much more likely that the partner would win that it is on the hypothesis that the numbers were picked randomly.

What about the fine-tuning case? I think we’re struck by the fine-tuning not because it’s improbable – whatever numbers had come up would be equally improbable – but because it’s improbable that it happened by chance. And, again, this is because there’s a non-chance hypothesis that would render it much more probable, namely the hypothesis that considerations of value were involved in determining the values of the constants. If the process that determined the constants was sensitive to the value of the resulting universe, then it wouldn’t be surprising that the constants would end up fine-tuned, much less surprising that it would be if they were selected at random.

So I don’t think the lottery fallacy is anything to do with focusing on the particular individual rather than the general fact; rather it’s a matter of fallaciously inferring from the fact that something is improbable to the fact it’s improbable that it happened by chance. But the fact that our universe in fine-tuned is not only improbable, it’s also improbable that it happened by chance. Therefore, focusing on the fact that our universe is fine-tuned – rather than that some universe is fine-tuned – does not commit the lottery fallacy.

So that’s why I don’t agree with Steve’s argument against my position. Let me try a different way of making the case for my position (this is a modified form of the argument White defends in the postscript to a reprint of this article). We can only gain support for a hypothesis with the evidence we in fact have. We can either think of evidence as our actual observations, or as the concrete, physical states of affairs we know about through observation. Whether you think of the fine-tuning evidence as our actual observations, or you think of it as the concrete fine-tuned physical universe we live in, in either case our evidence is not made more probable by the multiverse hypothesis. Yes, the existence of some fine-tuned universe is made more probable by that hypothesis. But we have to work with the evidence we in fact have, and the evidence we in fact have is constituted by the properties of this concrete, physical universe (or our observations of it), and this is not made more probable by the multiverse hypothesis

Many people have worried about the Joker analogy I make in my Scientific American article, on the grounds that, in this thought experiment, you pre-exist the flukey event. In the discussion I had with Steve, I got around this with a different thought experiment. Suppose your conception came about through IVF. And suppose you discover as an adult that when the doctor fertilised the egg, she rolled twenty dice to see whether she’d do it, committing only to fertilise the egg if they all came up sixes. Does your discovery that your birth was dependent on this improbable event provide you with evidence that the doctor did the same in many other IVF cases, rolling dice to decide whether to fertilise the egg? I don’t think so; all you have evidence for is that your conception was decided in this way, and whether or not the doctor did this in other cases has no bearing on how likely it was that the right numbers would come up with your conception. By analogy, all we have evidence for is that the right numbers came up for our universe, and whether or not there are other universes has no bearing on how likely it was that the right numbers came up for our universe.

In correspondence after our discussion, Steve proposed tweaking the thought experiment: suppose I’m considering whether the doctor rolled dice many times or only once to decide whether to fertilise the egg that made me. I agree in that case you would have evidence for that hypothesis, as that hypothesis makes *your* existence more likely, and your existence constitutes your evidence. But that modified IVF hypothesis corresponds to a sci fi scenario in which our universe had a number of shots at fixing its constants (i.e. random processes reset them numerous times) and the Guardian of the Universe only allowed it to proceed if they came up fine-tuned. That hypothesis would make our evidence (our fine-tuned universe) more likely. But that’s not the multiverse hypothesis. According to the standard multiverse hypothesis (eternal inflation + string theory) our universe had only one shot at fixing its constants. That corresponds to a scenario in which there is only one dice roll to determine whether the egg that produced you gets fertilised.

In our discussion, Steve came up with another thought experiment. Suppose the mischievous god Loki has just brought you into existence, and he tells you that he rolled twenty dice to decide whether or not to create a person, committing only to create a person if they all came up six (I’ve modified the example a little to make it similar to mine, but the substance is the same). Do you have grounds to think Loki has done this many times, on the assumption that each time he creates a person it’s a distinct person? I admit I did have to think about this one, and my intuitions are less firm that in the IVF case. So we need an explanation of why intuitions are different in these two cases. I suggest it’s because in the IVF case, it’s totally clear that the hypothesis I’m considering is one in which other babies would be born who aren’t me, whereas in the Loki case, it’s easy to slip into thinking he’s been having lots of shots at creating me. If I’m considering the scenario in which Locki had numerous shots at creating me, then I do find evidential support. But this is analogous to the tweaked IVF thought experiment in which the doctor rolled dice numerous times to decide whether to create me, and, as I argued above, this does not mirror the real-world fine-tuning case.

In summary: the fine-tuning is very puzzling, but it’s not evidence that we live in a multiverse.

The Author

I am a philosopher and consciousness researcher at Durham University, UK. My research focuses on how to integrate consciousness into our scientific worldview.

1. johnkaczm says

The most interesting place for consciousness to exist in the universe is the integrated information interface between spacetime and the most complex structure in the known universe……the human brain. It took 13.8 billion years of cosmological and astrobiological evolution, in order to evolve this structure as fast as possible! Ever since the big bang, quantum tunnelling has been the key process in enabling this to happen. It continues to provide different sources of constant energy flux, making highly advanced complexification in molecular and biological evolution possible. It opens prebiotic astrochemical pathways and enables and influences the biomolecular nanomachines that maintain the processes of life. If consciousness does exist within the fabric of spacetime, it will continue to have it’s most direct influence the future evolution of our universe, through its interface with human brains.

On Fri, Feb 26, 2021, 10:19 AM Conscience and Consciousness wrote:

> Philip Goff posted: ” Our best current science suggests that our universe > is fine-tuned for life. That is to say, certain numbers in basic physics – > e.g. the strength of gravity, the mass of electrons, etc. – are, against > improbable odds, exactly as they need to be for life t” >

2. johnkaczm says

Regarding the evolution of the human brain-You can not have the tip of the leaf at the top of the tallest tree, without the rest of the forest.

Life has not been trudging up the slopes of mount improbable, it is now enjoying the view from the summit of mount certain!

On Fri, Feb 26, 2021, 10:19 AM Conscience and Consciousness wrote:

> Philip Goff posted: ” Our best current science suggests that our universe > is fine-tuned for life. That is to say, certain numbers in basic physics – > e.g. the strength of gravity, the mass of electrons, etc. – are, against > improbable odds, exactly as they need to be for life t” >

• Thanks John, although I’m not sure how this impacts the argument?

3. Alex Popescu says

I think this constant bringing up of the analogies and talk of the lottery fallacy beats about the bush somewhat. Of course it is important to defend oneself against Steven’s critique (i.e. lottery fallacy), and it is no doubt interesting to explore why our intuitions may go astray with certain analogies. However, the actual fact of the matter regarding whether fine tuning should increase our credence in the multiverse is easily, demonstrably false. And simply pointing this out early would, I think, have been quite helpful to Steven. Granted, I did not see the interview; although I read his after-the-fact blog post.

To see this, let’s take your IVF example. In the fine tuned scenario we find that rolling 20 sixes in a row amounts to a chance of roughly 1 in 2.73 x10^16. If we postulate 10^20 IVF trials; we would then expect something like ~4000 trials to have resulted in a successful fertilization. Imagine now that there are an infinite number of parallels universes wherein either the doctor implements 10^20 IVF trials or just a single trial. Accounting for the selection effect, the odds that you will end up being born a multi IVF baby versus a single IVF baby are (~4000)(~2.73 x 10^16):1, or in other words for every ~2.73 x 10^16 universes, on average you have 1 single IVF baby and 10^20 multi IVF babies.

But notice this ratio holds constant no matter the degree of fine tuning. If the doctor had instead rolled a single dice, so that the odds were 1/6; we would then get on average 1.66 x 10^20 babies in the multi IVF scenario. So that for every 6 universes, on average you would have 10^20 multi IVF babies and 1 single IVF baby. Hence, Steven is wrong to say that the selection effect makes inferring a multiverse on the basis of fine tuning more credible. Fine tuning alone doesn’t increase our credence in the multiverse; it doesn’t increase the likelihood of our potentially ending up in a multiverse. You can find a similar explanation here: https://www.reasonmethis.com/2021/02/fine-tuning-and-multiverse-much-shorter.html

I owe this explanation to that blogger who introduced me to this simple method of expressing the ratios (using an ensemble technique). It was his original idea.

Notice that it also doesn’t matter what proportion you assign to the number of universes (if for example, you wish to stipulate that for every 1000 universes with a multi IVF trial, there are 12 universes with a single IVF trial). We would simply add a coefficient to our probability calculations; the actual ratio always remains constant throughout (before and after fine tuning).

• I tried to analyse the problem along those lines but I think it doesn’t really work for a subtle reason.

As soon as you envision having a multi-universe scenarios (of say n universes) as well as a single-universe scenario, you are positing a composite scenario which is just the multi-universe scenario of n+1 universes. This way of thinking of the problem therefore begs the question by assuming that the multi-universe scenario is correct. I think this invalidates any attempts to analyse it this way, which is probably why you’re finding that fine-tuning doesn’t matter.

• Alex Popescu says

@Disagreeble Me
I don’t think that follows at all. We don’t have to envision a multi-universe scenario which hosts both multiverses and single universes side by side (nor was I imagining such a scenario). Rather, we simply have to believe that it is possible that that we could have been born in either a multiverse or a single universe cosmology. Further, epistemic possibility is enough; one doesn’t have to go as far as granting physical possibility. As long as we assign equal value to all fine tuned universes, such that we are equally likely to be born in any one of them ceteris paribus, we are properly taking into account the selection effect.

Notice that granting that a multiverse is possible doesn’t entail that we have to believe the multiverse exists, nor does it “beg the question by assuming that the multi-universe scenario is correct” as you put it. We can talk about possibility without having to invoke ontology; just as we can use modal logic without having to accept modal realism.

• Hi Alex,

I claim that I’m not misinterpreting you, and that your argument has a fallacy at its heart that you don’t recognise. I feel confident in saying so because I spent a lot of time thinking through arguments like these, and comparing with lotteries and other real-world scenarios where I could test them. Your line of thinking echoes my own. But I’ve realised it doesn’t work.

In your argument, you have two scenarios — multi-universe and single universe. You try to consider them separately, but I claim you cannot, because they are both invoked at the same time in the same argument. I’m aware that you don’t realise you’re considering them side by side, but I claim that this is nevertheless effectively what you are doing. As soon as you try to ask what are your odds of being born in the multi-universe condition rather than the single-universe condition, you’re lumping them together into one super-scenario whether you like it or not.

For instance this red flag: “As long as we assign equal value to all fine tuned universes”. In this sentence, as far as I can make out, you’re talking about all fine tuned universes, whether in the single-universe condition or the multi-universe condition. So you are considering them as an ensemble. I claim that this is illegitimate. Such an ensemble just is the multi-universe condition, because you are treating all observers in that ensemble as equivalent. This is a thought experiment, after all. Nothing here is physically instantiated. All observers are just as real as each other, which is to say not at all. Whether the single-universe condition or multiverse condition is chosen is meaningless. It’s just a label we’ve attached to the scenario ignoring the fact that we’ve presupposed the multiverse condition in the set up of the experiment.

Here’s one issue that might illustrate the kinds of problems we get into. Why, for instance, are you only considering one single-universe scenario? There are as many different single-universe scenarios as there are possible worlds. Assuming there are a bajillion possible worlds, you might be better off considering a bajillion single-universe scenarios and a single multi-universe scenario with a bajillion worlds realised all at once. On this analysis, the number of observers finding themselves in single-universe scenarios is exactly equal to the number finding themselves in multi-universe scenarios, which is a radically different conclusion to the one you reached originally.

I can see some possible objections.

Why assume the multiverse has all possible worlds rather than a subset? If we had a subset, then there are many more multiverse scenarios, if we counted each possible subset. But this again just shows that we can get all kinds of different results based on what assumptions we want to make about how to model the possibilities.

Why assume there are a bajillion possible worlds rather than an infinite number? OK, but that doesn’t help, because we can’t really reason very well about probabilities in infinite ensembles. Intuition suggests that there are as half as many even integers as integers, but its generally accepted by mathematicians that there are the same number, because you can match every integer uniquely with an even integer just by multiplying it by two.

While this kind of ensemble reasoning does work for most statistical questions of this sort, I’m convinced it doesn’t work for this specific question. We need other tools.

• Alex Popescu says

Hey Disagreeable Me,

You brought up a second objection in addition to your last. I attempted to anticipate such an objection by writing in my first post “Notice that it also doesn’t matter what proportion you assign to the number of universes…We would simply add a coefficient to our probability calculations; the actual ratio always remains constant throughout (before and after fine tuning)”

So I agree the ensemble technique is an inadequate measure, by itself, of how much we should privilege the multiverse versus the single universe hypotheses. That is because the sampling procedures are arbitrary, we could choose to say that there are a “bajillion single-universe scenarios and a single multi-universe scenario with a bajillion worlds realised all at once” as you put it. Or we could just as arbitrarily choose an opposite ratio to the favour of the multiverses. But I never actually claimed to solve the problem of whether we should pick the multiverse or the single universe, rather I (and the blogger that I referenced) merely attempted to show that fine tuning plays no role in such probabilistic inference.

So it doesn’t matter what ratio you pick, as long as your sampling procedure remains fixed both before and after fine tuning. The whole point is that we want to know how fine tuning modifies the odds ceteris paribus, so we have to keep the sampling method fixed (even though our sampling is of course arbitrary). Unless you have an argument which shows that fine tuning itself should modify the proportion of multiverses relative to single universes that we assume are possible; it doesn’t follow that the sampling procedure being arbitrary is fatal. So your potential objections to your own objection are not needed.

This leads us back full circle to your first objection; which I admit I did not completely understand. I think I inadvertently misled you by claiming that I personally wasn’t envisioning such a multi-universe scenario. My point was that this was irrelevant, because our envisioning such a scenario doesn’t entail that we are begging the question. Again, all we are doing in speculating that we could have been born in either multiverse or single universe, and then envisioning/imagining an ensemble technique to mentally calculate the odds; is stipulating that the multiverse is possibly realizable.

Yes, such an ensemble scenario is itself a multi-universe scenario, but again we are just taking it to be the case that such a scenario represents the possibilities and not that such a scenario is actual. Therefore, because the conclusion is not “the multiverse is possible” there is no begging the question.

Perhaps you meant to say that it begs the question in that it presupposes the odds it means to conclude, but that would be a line of critique similar to your second objection which I addressed above. Let me know if I have still misinterpreted you.

• Hi Alex,

My claim is that because this kind of ensemble calculation is fatally flawed, we can conclude nothing from it. As such, the fact that fine-tuning plays no role in our fatally flawed calculations does not indicate that fine-tuning has no role to play in a correct assessment.

The reason it is fatally flawed is because you’re effectively building a model multiverse and then trying to assess the probability that observers within it are in a multiverse (this is why I say you’re begging the question). It’s no wonder that fine-tuning plays no role. Granted, you’re not getting 100% of observers in a multiverse as you should, but I think that’s only because you’re incorrectly labelling some observers as denizens of a single-universe when in fact they are all in a multiverse due to how the thought experiment is set up.

• Alex Popescu says

With all due respect, I think you have still not understood me correctly because I am not doing this: “you’re effectively building a model multiverse and then trying to assess the probability that observers within it are in a multiverse”

I’m NOT actually trying to calculate the odds of how likely it would be that we ended up in a multiverse. The entire point of my last post was that this was irrelevant. It doesn’t matter what the odds are, and it doesn’t matter that you are correct that the assignment of such odds is arbitrary (which I of course recognized). My point was that for any such odds, no matter what they are on a scale from zero to infinity; it holds true that fine tuning plays no role in the modification of the odds.

So I’m not constructing a particular multiverse model and then saying, here are the odds that we live in a multiverse. That would indeed be begging the question. Instead, I wrote that out of all the possible infinite multiverse models one can construct (take your pick) it holds true that fine tuning plays no role in the calculation regarding the likelihood of the multiverse existing, even though the likelihood changes from model to model.

• Hi Alex,

I see what you mean, and I apologise for not being clearer. I understand that you personally are trying to show that fine-tuning doesn’t enter it and not calculate the odds that we are in a multiverse. I’m speaking loosely, informally, and I mean “you”, as in “one”, as in “one who conducts such ensemble analyses”.

One who conducts such ensemble analyses is trying to calculate the odds of being in a multiverse for observers who are all effectively in a multiverse. This approach does not work as it begs the question. The fact that fine-tuning doesn’t enter into this flawed approach is therefore no blow against the idea of taking fine-tuning into account in other approaches.

• Alex Popescu says

Hey Disagreeable Me,

So as I see it there are two different objections here. The first you brought up says that we can’t use the ensemble technique because the entirety of such analysis begs the question, no matter the multiverse model being used. The second objection you brought up has to do with the arbitrariness involved in picking one multiverse model over another. If I understood you correctly, it seems like we agree that the second objection isn’t fatal on the grounds that the fine tuning reasoning is equally applicable to all such multiverse models. Rather, you object to invoking the ensemble technique on general grounds ala the first objection.

So I feel that this brings us back to a difference of interpretation regarding how we should think about the relationship between possibility and ontology. I argue that postulating such a multi(multi/single universe) scenario doesn’t beg the question. Since, in my view, saying that it is possible that we could have been born in a multiverse just is to say that we can conduct such ensemble analysis.

I argue that you are in fact invoking an ontological burden on the past of the reasoner; it’s just that you are kicking the can down the road so to speak. It seems that you are equating the “possibility space” in which the multiverse/single-universe lie side by side in our imaginations, as itself being some kind of multiverse (that holds the subset multiverse along with the “single” universe). You say that you realize that nothing is being actualized here as we are discussing possibilities only, but you argue that postulating such a scenario nevertheless necessitates we believe in the multi-multiverse scenario.

But I am denying this; I don’t accept that to postulate that we can imagine a multiverse and single universe side by side (what we do when we say we could have been born in either) means that we must believe in a multiverse encapsulating both things. That is because I take “accepting the multiverse hypothesis” to mean believing it is actually realized. Or at least believing that it is physically possible, which I don’t accept either because I don’t equate epistemic possibility with physically possibility.

So it doesn’t follow in the end that we aren’t capturing observers in the single universes (since you argue there would be no single universes). Because granting that there are odds ratios between the multiverse and single universe doesn’t entail believing that the multi-multiverse hypothesis is true, only that it is epistemically possible. And if you don’t maintain the former, you aren’t begging the question.

• Hi Disagreeable Me, I am the blogger Alex was referring to. Your objection seems to be based on a bit of linguistic confusion. The ensemble consists of G (gazillion) worlds. Each world consists of either an S scenario (single universe/single room/IVF doctor who chose to do only a single try/etc.) or an M scenario (multi-verse/room/etc.). What is the proportion of S vs M worlds? That’s your prior. For example, if, as far as you know, Loki had no preference between S and M, you effectively assume he flipped a coin. If that whole situation happened in G independent worlds, then you’ll have 0.5G S-worlds and 0.5G M-worlds.

• Hi Disagreeable Me, I got a little confused about how comments work on this platform. My previous post, where I described members of the ensemble as “worlds”, which can be either an S-world (for single) or an M-world (for multi), is still “awaiting moderation”. I wanted to clarify what my actual response to your objection then is:

You talk about effectively having just multiverses with n+1 universes instead of n. Using the “world” terminology, you’re then saying that every S world is a part of some M world, but that contradicts the actual ensemble setup I and Alex described.

• Hi Alex,

Just to explain how my two objections relate to your point, my thesis is that ensemble analysis doesn’t work for this question because it unknowingly begs the question, and that this leads to crazy outcomes like being able to get any result you want and that fine tuning does not much affect the result. Garbage in, garbage out. So, the point about the arbitrariness of the model is just to show that you get garbage out. Your conclusion about fine tuning is in my view similarly garbage (no offense intended).

You don’t think it’s begging the question.

Here’s an analogy with another thought experiment. Suppose we want to explore whether we are real or whether we exist only in a thought experiment, and suppose we deem each to be equally likely, so we model this with an ensemble consisting of an observer who we stipulate to be real and an observer who we stipulate to only exist in a thought experiment. I’m not going to continue the analysis any further, but something seems fishy to me here, because in fact both observers exist only in thought experiments, and by stipulating that one is real we are making a mistake. But of course this doesn’t mean that since both observers are actually in thought experiments, the odds for any observer (i.e. you and me) being in a thought experiment is 100%. Rather I say this kind of analysis is useless.

Similarly, by stipulating that any of our observers are in a single universe scenario, we are stipulating that their universe is somehow realer than the others, which is not true. I just don’t think you can make stipulations about what exists or doesn’t exist in this way. The ontological argument for the existence of God is a similar mistake.

> but you argue that postulating such a scenario nevertheless necessitates we believe in the multi-multiverse scenario.

I’m not talking about what you believe. I’m saying the analysis doesn’t work because it’s subtly circular. This has nothing to do with psychology or epistemology. It’s strictly a claim that this form of argument doesn’t work for this question.

I mean, we both seem to agree that this form of analysis is useless (as we agree that the model is arbitrary). So why draw any conclusions at all from it?

• One more stab at this.

As soon as you entertain the possibility that there is a multiverse, with the intention of counting observers in multiverses versus single universes, you’re making a mistake because you’re biasing the result in favour of the multiverse, which has vastly more observers.

The question is instead how seriously we should take that possibility in the first place, before we begin counting observers at all. That’s where fine-tuning comes in.

• Or another way to put it — you can’t analyse things in an ensemble this way because it is incoherent to consider at the same time observers in a single-universe scenario as well as observers in a multi-universe scenario, because these states of affairs are mutually contradictory. These are not observers with blue eyes versus observers with green eyes. The conditions we are setting up are supposed to be maximally global, like mathematical truths. Either there is a multiverse or there isn’t. We can’t have a population of observers some of whom are in a multiverse and some of whom are not. They belong in two different thought experiments, not in one, and it is not legitimate to calculate probabilities drawn from a mix of both conditions taken together because such a population is incoherent.

• Alex Popescu says

Disagreeable Me,

Let me begin with your begging the question/circularity objection.

Firstly, there are two claims here:
A) There is a problem with the multiverse ensemble analysis technique
B) This problem, if only partly, is due to the fact that the technique begs the question

So, we definitely agree with A, or as you phrased it “if garbage in, garbage out”. You brought up the problem of arbitrariness and I definitely agree with it. But notice that this is a problem of soundness; that is, if we lack the correct inputs (we don’t know which odds ratios to use) then we get a garbage output. This is entirely different from saying that the technique is invalid however, which is what your circularity objection would amount to.

So, I contend that you are right that it would be absurd to use such an ensemble technique for both the multiverse and the “are we real” thought experiment. But the problems related to both have to do with lack of soundness, in this case we don’t know enough in either case to warrant a good input. In the “are we real” thought experiment, we have no evidence/reason to prefer either outcome, and so the inputs are totally arbitrary. But that isn’t the same thing as saying that we are begging the question. The reason this distinction is important, is because the analysis that fine tuning plays no role in the multiverse calculations is correct as long as the ensemble technique is valid. So the ensemble analysis doesn’t have to be sound for us to correctly use it.

In reply to my reasoning that we are not begging the question on account of the fact that we don’t need to invoke actuality when we speak of possibility, you merely pointed out that the technique has a lot of problems. But that only goes as far as demonstrating A (which I agreed to) when you need to show B. I don’t deny these problems, I just think they’re owed to the problem of arbitrariness (a problem of soundness) and not to the technique’s invalidity.

As for the ontological argument, I don’t think it’s remotely similar. We aren’t imagining or thinking something into being. The point is that you shouldn’t grant a favorable odds ratio (or prior) to the multiverse unless you have good reason for it. I’m not disputing that at all; I’m saying that assuming that we had good grounds to believe in the multiverse and then wanted to calculate the odds ratio using the ensemble technique, no matter the multiverse model we picked, or the prior odds we assigned (which, as mentioned, should be based on evidence); fine tuning will make no difference.

Secondly, you wrote: “As soon as you entertain the possibility that there is a multiverse, with the intention of counting observers in multiverses versus single universes, you’re making a mistake because you’re biasing the result in favour of the multiverse, which has vastly more observers.”

But this is a question of whether we should assume the multiverse is possible, but notice that I’m just speaking of epistemic possibility, which is very open-ended (basically any logically possible scenario is epistemically possible). At best this objection would entail that we should start by privileging the single universe cosmology heavily in the absence of evidence (which I agree with); it doesn’t entail that we can’t invoke possibility or that the argument/ technique is circular. It might mean that the right thing to do is to be agnostic, but that just conveys that we shouldn’t ask whether we ought to prefer the multiverse vs. single universe (I also sympathize with this); it doesn’t mean that we can’t infer that fine tuning would play no role (since that only depends on validity).

Thirdly, you wrote:
” you can’t analyse things in an ensemble this way because it is incoherent to consider at the same time observers in a single-universe scenario as well as observers in a multi-universe scenario, because these states of affairs are mutually contradictory”

I’m not quite sure what to say here. I don’t think there’s any problem with considering mutually exclusive possibilities, because we do such things all the time. For example, I might ask, what is the probability that I will end up in prison x or prison y if incarcerated? Either option is mutually exclusive to the other, but it’s still perfectly legitimate to construct an ensemble analysis and reason that prison y is more likely on the grounds that it hosts ten times more inmates than x. Perhaps I have misunderstood you, but your last objection if true would basically prevent us from engaging in almost all probabilistic calculations.

Best,

Alex

• Alex Popescu says

Previously I wrote: “So the ensemble analysis doesn’t have to be sound for us to correctly use it.” When I meant to say: “So the ensemble analysis doesn’t have to be sound for us to correctly infer that fine tuning would play no role regarding the probabilities of the multiverse being true”‘

Best,

Alex

• Alex Popescu says

So, the bottom line is, what is your argument regarding my claim being circular? You write: “I’m not talking about what you believe. I’m saying the analysis doesn’t work because it’s subtly circular”

But my argument only begs the question if I would have to believe or depend on something in my premises that ends up in my conclusion. You abandoned your claim that I have to believe the multi-multiverse is true. The only other way I would be begging the question is if the multi-multiverse scenario only works on account of the multiverse being true. But that’s an even steeper claim; we would have to presuppose a certain ontology to begin our ensemble reasoning, which I assume you don’t hold to.

So this point of yours, “ It’s strictly a claim that this form of argument doesn’t work for this question.” which you subsequently wrote; doesn’t prove that the ensemble analysis begs the question. That’s because pointing out problems with the analysis doesn’t show the analysis is invalid, and as I said, the actual problems you mentioned are due to lack of soundness (if we put in bad inputs, we get garbage outputs).

So how then can we still conclude that the ensemble technique is invalid/circular?

• Hi Alex,

When I say garbage in/garbage out, I don’t just mean that we need to get the specific inputs to the model right to get the right answer. I’m trying to make a more general point that the very structure of the model is flawed and so we can’t trust any conclusions we draw from it, including the irrelevance of fine-tuning.

We can drop the arbitrariness point I think as we seem to be on the same page. I’ll semi-concede the point that this may be irrelevant. Your argument that validity matters more than soundness seems plausible, so without thinking about it too deeply let’s say that’s correct. I am arguing that it is invalid after all.

I’m not very committed to arguing that there’s a lot of similarity to the ontological argument. It just reminds me of it a little. Both arguments involve stipulating existence or non-existence in arguments about whether something exists, and I think that leads to mistakes. But it’s an aside and I suggest we drop it.

On begging the question (and circularity), I don’t mean that your argument against the relevance of fine-tuning begs the question. I mean that ensemble thought experiments about the probability of being in a multiverse beg the question by effectively positing a multiverse. But I now want to retreat from this way of putting it because it doesn’t seem to be getting us anywhere due to disagreements about whether it is fair to call the union of S-worlds and M-worlds a multiverse. Instead I want to emphasize that such arguments are quantifying over an incoherent population, as I outlined in my comment to Reason Me This down the page.

You address this point of course.

> I don’t think there’s any problem with considering mutually exclusive possibilities, because we do such things all the time. For example, I might ask, what is the probability that I will end up in prison x or prison y if incarcerated? Either option is mutually exclusive to the other, but it’s still perfectly legitimate to construct an ensemble analysis and reason that prison y is more likely on the grounds that it hosts ten times more inmates than x.

I agree that there’s nothing wrong with this analysis, because the conditions are not universal predicates. A population of inmates some of whom are in prison x and some of whom are in prison y is perfectly coherent. A population of observers some of whom are in multiverses and some of whom are in solitary universes is not. Even in an abstract thought experiments, where none of the observers actually exist, I maintain you can’t quantify over an incoherent population like this.

• Alex Popescu says

Hey Disagreeable Me,

I must say that I don’t think the two objections of the “sneaking in the multiverse” and the universal predicate are the same (but just linguistically disguised). Nevertheless, I did read over your post to ReasonMeThis, and I still didn’t quite understand why you think we can’t quantify over universal predicates in mutually exclusive scenarios (except to reiterate that we can’t).

There’s nothing inherently invalid about making such quantification. There’s no problems of self reference etc… at hand that could cause issues. Notice that the predicate isn’t truly universal (all x), some restriction is placed on x in that x has to be an observer. So we’re not potentially making a self referential statement here (and even if we were, that doesn’t have to be contradictory by fiat). Again, why can’t we quantify over all observers in a hypothetical thought experiment involving people existing on either Mars or Earth for example?

You wrote: “ quantifying over such a population…is tantamount to hypothesizing about population A and population B and G being true and G being false.”

But of course this doesn’t follow, we aren’t hypothesizing an and condition; the two scenarios are meant to be exclusive. And again mutually exclusive thoughts scenarios are perfectly acceptable. It would be helpful, if you could point out why you think such quantification over the universal observer is bad; or why you think it’s bad to quantify over the entirety of a class (e.g. could we not talk about “all peanuts” in some ensemble analysis either?).

Best,

Alex

• Hi Alex,

In the interests of pruning digressions, I won’t attempt to explain why I think my two phrasings of this objection are substantially the same unless you’re very interested. I’ll stick with discussing the “incoherent population” phrasing.

> There’s nothing inherently invalid about making such quantification.

The problem is not with the quantification step so much as that you’re quantifying over an incoherent object — a population composed of observers for some of which a universal predicate is true and for some of which it is false. This population amounts to an inconsistent mathematical object. We can draw contradictions from it, because S and M are not really independent.

Let me do so in detail with a formal logical analysis.

Assume x is some observer in the single universe condition (S) and y is some observer in the multiple-universe condition (M).

The set up of the experiment treats these as if they are predicates taking one variable as a parameter, e.g. S(x) or M(x) where x is some observer. If that were so, then we could have S(x) and M(y) at the same time. But as I think they are universal predicates, I think this is wrong. I think these predicates take no parameters, because whether S is true or M is true does not depend on who is asking or for whom we are evaluating the question. So they should be modelled as just S or M, i.e. zeroth-order predicates. Furthermore, S and M are simply opposites, so we can do away with M and have S and ¬S. So saying that x is in our population (let’s call our population the set P), and S is true for x is just saying x ∈ P ∧ S, while saying y is in our population and M is true for y is just saying y ∈ P ∧ ¬S. Having both x and y in our population is therefore to say x ∈ P ∧ S ∧ y ∈ P ∧ ¬S. Which is a contradiction, because we can’t have S ∧ ¬S.

We could perhaps do away with mentioning P at all and just say ∃x: S and ∃y: ¬S, but then I worry that you’ll take me to task for interpreting you as asserting that these observers actually exist when they don’t. Whether you want to say they exist or not, you must put them into a set P in order to do statistics on that population, and this set is incoherent.

I don’t think restricting x to be an observer makes any difference to this analysis. It’s just adding O(x) ∧ O(y) to the contradiction, where O means the parameter is an observer.

> Again, why can’t we quantify over all observers in a hypothetical thought experiment involving people existing on either Mars or Earth for example?

But of course we can. Because the existence of someone on Earth is compatible with the existence of someone on Mars. But anyone at all being in a single universe is not compatible with anyone at all being in a multiverse. If the number of universes in existence is N, S is just the proposition that N = 1, while M is just the proposition that N > 1. The number of universes in existence is the same no matter who is asking.

> But of course this doesn’t follow, we aren’t hypothesizing an and condition; the two scenarios are meant to be exclusive. And again mutually exclusive thoughts scenarios are perfectly acceptable.

I don’t think that’s what this thought experiment is doing though. It’s assembling a single population which requires two mutually incompatible scenarios to be true at the same time. It’s not presenting a dichotomy where if S, then such and such, and if M then such and such.

> or why you think it’s bad to quantify over the entirety of a class (e.g. could we not talk about “all peanuts” in some ensemble analysis either?).

Nothing wrong about quantifying over a class, as long as the class is coherent. Peanuts are a coherent class. The union of the set of observers for which S is true and the set of observers for which ¬S is true is not a coherent class unless we suppose that one of these sets is empty. But the setup of the thought experiment assumes both sets are non-empty.

• Alex Popescu says

Hey Disagreeable Me,

To clarify, I think you are now stipulating your original claim of begging the question, but I still believe that is different from the general claim that we can’t quantify with universal predicates over mutually exclusive scenarios. Of course it follows that if you’re correct about the ensemble technique begging the question, then such quantification is incoherent. But that is different from the general claim. To demonstrate this with the mars and earth example; I didn’t actually mean that we should quantify over some observers. I was envisioning a case wherein we had two mutually exclusive scenarios of all observers existing on either mars or the earth.

Similarly, your point about the “all peanuts” case being fine seems to suggest that the problem is not with your original claim that universally quantifying over mutually exclusive scenarios is bad, but just that the population is incoherent on the grounds that we are begging the question. But notice that one can stipulate something like “all peanuts are salty” and “all peanuts lack salt” in one possible ensemble scenario with no problems. In any case, this is a side discussion; let’s now get into the meat of the issue.

Firstly, I wish to demonstrate that it is possible to construct such an ensemble analysis using the existential quantifier (without having to take on an existential burden); that’s important because even if you are right that there are issues with universal quantification here, we can still save the technique in that way. Secondly, I’ll critique your points because I don’t think they are actually true.

So, regarding this; “We could perhaps do away with mentioning P at all and just say ∃x: S and ∃y: ¬S, but then I worry that you’ll take me to task for interpreting you as asserting that these observers actually exist when they don’t.”

That’s precisely what modal logic exists for; to quantify over possible entities without incurring an existential burden. It would be perfectly legitimate to set up our ensemble analysis with the following conditions:

Let ◇∃x:S
and ◇∃y: ¬S

There is no contradiction here unless you believe:
□∃x:S & □∃y: ¬S

Of course it would be nice if we didn’t have to translate it in such a way (since we want to pick out all observers), but the conclusions of the ensemble analysis are still valid if we only pick out a subset of all hypothetical, imaginary observers. As long as the sampling procedure (i.e. ratio) that we used in picking out this subset was fixed both before and after the fine tuning analysis, then we would be fine. So the only way that I can see that one can challenge the statements: (◇∃x:S) & (◇∃y: ¬S) is if you adopted a kind of modal realism, and argued that accepting that there was were such possible universes entails their reality.

Secondly, going back to the universal quantification method, I have no idea how you derived this: “x ∈ P ∧ S ∧ y ∈ P ∧ ¬S”
when surely the actual translation is this no?
“(x ∈ P ∧ S) v (y ∈ P ∧ ¬S)”

You just stipulated that we are saying that x has to be in both S and ~S, when of course the ensemble analysis concedes nothing of the kind. The only way it would follow that the ensemble analysis entails (x ∈ S) & (x ∈ ¬S) is if somehow the ensemble technique necessarily imposed an ontological burden (going back to our first discussion); such that (◇(x):S) & (◇(y): ¬S) entails that both possible universes exist in a multi-multiverse; which in turn means that (x):S entails (x): ¬S.

I hope I’ve demonstrated that you do in fact have the burden to prove either,
1) that we incur an ontological burden and the multi-multiverse has to exist
2) that we incur an epistemic burden and have to believe that the multi-multiverse exists

If you don’t believe in 1 v 2, then how can you keep maintaining that this “(x):S entails (x): ¬S” is itself entailed from our utilizing the ensemble technique?

In any case, I hope that I have at least demonstrated that we don’t have to translate the analysis in the way you wanted it to be translated. Ultimately, I think your contention that such analysis demonstrating that fine tuning plays no role is an “absurd result”, is rather unfair and uncharitable. That is the whole point of what we are trying to argue; at the end of the day we are attempting to show that taking into account the selection effect makes no difference. One can show this through such simple analysis (per the above), or one can do it as Goff did, by challenging the impact of the selection effect via philosophical argumentation (i.e. invoking TER or special identity conditions).

Thanks for the interesting discussion.

• Alex Popescu says

To briefly sum up:

If we used the existential quantifier to quantify over a subset of hypothetical observers; we wouldn’t have to assign the observers captured by the x predicate and the y predicate to the same population class. We would just have one subgroup living in the possible single universe and another living in the possible multiverse. Whatever ratios one decided to pick to represent the number of such observers, as long as this ratio remained fixed both before and after fine tuning (which of course we are stipulating by default); the consequences hold.

Secondly, regarding universal quantification, it’s not contradictory to stipulate that the same population is possibly both A and ~A. We do this all the time (see: my prisoners example). The only way we get a contradiction is if you go from possibility to actuality, but like I said that brings us back full circle.

In other words, this: “ a population composed of observers for some of which a universal predicate is true and for some of which it is false”

Doesn’t follow, unless you think that invoking two contradictory possible setups entails two contradictory actual setups.

• Yes, although I disagree with Disagreeable Me ultimately, I think I agree with him on this one.

4. Andrew says

Hi, I’ve been following the multiverse & fine-tuning discussion for some time, and I’m drawn to your statement “What we have evidence for [is] that our universe is fine-tuned…”. I’m unaware of anything that could genuinely be called *evidence*.
What we do have, and what is confused with evidence, is the *concept* of fine tuning. To your analogy, that you can conceive that your parents’ doctor rolled a dice to decide on your conception (no pun intended) is in no way evidence of the doctor doing that. The doctor’s notes or a contemporary witness would be evidence – but even a large collection of dice amongst the (now deceased) doctors’ estate is not evidence. Science is better than speculation.
The “we’re living in a simulation” proponents have fallen for a similar fallacy … that they can conceive of something is in no way related to the fact, possibility, or likelihood of that something being true.

• This debate just takes fine-tuning as a given for the sake of argument. Whether there actually is evidence of fine-tuning is a separate issue.

On that point, a lot of scientists certainly seem to think there is such evidence. Whether they are right or wrong on this, they are not merely impressed by the concept of fine tuning. There are arguments to show that had constants been slightly different, then life would have been impossible.

I think you miss the point of the analogy to the doctor rolling a dice. We are not trying to infer whether the doctor rolled the dice for our conception. Instead, it’s a given (so perhaps there is a contemporary witness). What we are trying to infer is whether this happened many times or once.

• Yes, I agree with disagreeable me. Many, many high profile physicists think there is very strong evidence for fine-tuning. The book ‘A fortunate universe’ is a great account of the evidence.

5. High Mass Particle says

Any universe that can reproduce would quickly make insignificant any universe that pops up by random in both quantity and quality because natural selection improves quality. Such universes would rightly be called life. Universes that reproduce would have a genetic code that is copied into smaller offspring (high mass particles).

6. Bindo says

There was question was how come my statement that life is same in living beings and inert objects like stone etc.
Ans: What we call as life and lifelessness are based on the exhibition of certain qualities by individual objects. We call objects like humanity animals etc having life and objects like stone table chair etc are lifeless. This difference between the two is based on the exhibition of movement and reaction to senses.
The confusion arose from identifying life as Atma. Life and Atma are not the same.

While Life is an expression of certain qualities, Atma is the swaroopa of anything. There’s nothing that is without swaroopa is what my statement implied.
Just as light’s reflection happens from all surfaces but some reflect some do not. Does that mean light is not reflecting? The reflection depends on the quality of the surface. In some it will be cent-percent while it varies in varying degrees in others. But the very reason we are able to see them itself is the proof of the reflection.

Same way Satchitananda, or Existence-Awareness-Bliss is the swaroopa or the substratum on which we become aware of the existance of anything. We cannot separate existance from awareness, just as light and heat, there for if the objects demonstrate awareness or not, the very fact of existance declares that, through existance it makes itself qualified for awareness.
Depending on the Upadi or the instrument the quality to show awareness or not varies similar to reflection.

7. Chris G. says

If something that MIGHT be true (multiverse) makes it more likely that something we KNOW to be true (fine-tuning) more likely to have happened in the first place, we CANNOT infer from this that the first thing (multiverse) must (or even probably) is the case.

It’s one possible explanation. It is no more or less likely to be true.

Isn’t this confusing an hypothesis for an inference/conclusion on Steve’s part?

• > “It is no more or less likely to be true.”

While there may be circumstances where your reasoning applies, I’m not sure this is correct in general.

For example:

We know to be true: (1) Mike has been murdered. (2) Joe claims he saw Alice murder Mike.
Might be true: (3) Alice murdered Mike.

(3) makes (2) more likely, even though there might be other explanations for (2) (e.g. Joe murdered Mike and is framing Alice). I think we can infer that (2) should increase our credence in (3).

I think the circumstances where your reasoning would apply would be where we have independent reasons to reject the possible explanation (e.g. footage of Joe murdering Mike).

• Yes, I agree with disagreeable me. Evidence you know to be true can make highly probable a hypothesis that would otherwise not be known.

8. Hi Philip,

Didn’t realise you had blogged on this when I emailed you yesterday.

(
To anyone else interested, the gist of it was
1. IVF scenario and the Loki scenario are equivalent, but the Loki scenario is fairer because it doesn’t rely on common sense pushing us towards Philip’s conclusion. I thought we both accepted these as acceptable analogies for fine tuning.
2. I accept the multiverse analogue in both Loki and IVF.
3. The crux of the issue here is how we conceive of identity and in particular how we interpret phrases like “our world” and “this universe”. I hold that it is incoherent to think of the possibility that “our world” might have had constants other than it has — then it wouldn’t be “our world”. But you appear to hold to a stronger notion of identity, such that “this universe” picks out a universe that we can imagine might have turned out radically different while still being this universe.
)

On reading this blog post, I’ve updated on a couple of things. First you reject the Loki analogy for much the same reason that I reject the IVF analogy — that it unfairly nudges our intuitions by playing on implicit assumptions we may not realise we are making. For me, the problem was the practical impossibility of any IVF doctor conducting gajillions of dice-rolling trials. For you the problem was that we may imagine Loki to have had multiple opportunities to create the same person.

Could we patch the Loki analogy by saying that Loki composes the person’s genome at random (within the constraints of a viable human genome)? Or would you worry that the same person could have had a different genome, just as you think that the same universe could have had different constants? Either way, I’m intrigued. If you could have been the same person even having been born with a radically different genome, then the way you think of identity is quite strange to me and I’d like to inquire further. If you couldn’t be the same person having been born with a radically different genome, then I wonder why it makes sense to talk of the possibility that our universe could have had radically different constants.

In any case, if you now accept the patched analogy, then we have an analogy we are both happy with but where I still think the correct conclusion supports a multiverse and you think the reverse. We would appear to be at an impasse. The identity issue is key to making further progress, I think.

• Thanks Disagreeable me. Yes, I think the identity of conditions of a universe is a crucial issue that Steve and I didn’t get onto. In the academic version of the paper, I respond to this by arguing that in the standard scientific conception of the multiverse (eternal inflation + string theory) our universe could have had different constants: https://www.philipgoffphilosophy.com/uploads/1/4/4/4/14443634/is_the_fine-tuning_evidence_for_a_multiverse_.pdf I’m currently re-working this to take into account more of the literature.

Interesting objection to my IVF analogy. I think we could get around this by just imagining the doctor rolling fewer dice. The scale of the improbability shouldn’t make a different to whether we have some evidential support.

Nice re-working of the Loki analogy. I do think I’m defined by my genome, and I now don’t have the intuition that I have evidence that Loki did this many times. One challenge for your view is as follows: Couldn’t one equally interpret this as evidence that Loki has been rolling the dice to see whether to do something, and this is the first time the thing he decided to do was make a person? I can’t see a principled way in which one would rule out that interpretation of the evidence.

Here’s a more theoretical argument I made in a recent email to Steve:

Let’s contrast the fine-tuning case with a less controversial example of a selection effect:

“A classic example of selection bias is the election poll taken by the Literary Digest in 1936. On the basis of a large survey, the Digest predicted that Alf Langdon, the Republican presidential candidate, would win by a large margin. But the actual election resulted in a landslide for the incumbent, Franklin D. Roosevelt. How could such a large sample yield such a wayward prediction? The Digest, it turned out, had harvested the addresses for its survey mainly from telephone books and motor vehicle registries. This introduced a strong selection effect. The poor of the depression era, a group that disproportionally supported Roosevelt, often did not have phones or cars.

The Literary Digest suffered a major reputation loss and soon went out of business. It was superseded by a new generation of pollsters, including George Gallup, who not only got the 1936 election right but also managed to predict what the Digest’s prediction would be to within 1%, using a sample that was only one thousandth as large. The key to Gallup’s success lay in his accounting for known selection effects. Statistical techniques are now routinely used to correct for many kinds of selection bias.”

In this case, before we took the selection effect into account, it seems that it would be improbable to have the data we have on the hypothesis that FDR had huge support in the country. Once we take into account the selection effect, we see that the data is highly improbable on the hypothesis that FRD has huge support among the wealthy​ but actually is not highly improbable on the hypothesis that FDR has huge support among the country more generally. So how probable the evidence is relative to the two hypotheses changes (or rather we correct our understanding of how probable the evidence is relative to the two hypotheses).

This is just not what’s happening in the fine-tuning case. We start off struck by how improbable it is that I should be here observing a fine-tuned universe, relative to the hypothesis that the constants were determined by chance. Once I take into account the selection effect, it’s just as improbable that I should be here observing a fine-tuned universe if the constants were determined by chance. It changes nothing. Of course, relative to the hypothesis that there’s a multiverse, it’s not so improbable that someone should be observing a fine-tuned universe. But that’s just because pretty much any event is probable in a multiverse; it’s nothing to do with the presence of a selection effect. If there were a multiverse, it’s not so improbable that someone should be observing highly improbable events like their grandma coming back from the dead by natural but ludicrously improbable quantum fluctuations. In contrast to the first case, in the fine-tuning case, taking into account the selection effect changes nothing regarding the probability of the evidence​ relative to each hypothesis. And that’s all that matters for Bayesian inference (apart from priors, and nothing is changed there either). It feels intuitive to say ‘Because of the selection effect, we don’t need an explanation of why our​ universe is fine-tuned’. But once you actually write out the Bayesian calculation, the selection effect in this case is irrelevant.

• Thanks Philip.

I read the paper a few months ago, has the discussion of identity changed since then? I guess my point is that by identifying this universe with a point in pre-inflation space, you’re making assumptions about identity conditions that are not going to be accepted by all. While you do make explicit and argue for many of your assumptions, what you seem to take for granted is that that there is a metaphysical fact of the matter about identity conditions in the first place, rather than adopting the pragmatic attitude that if it quacks like a duck and walks like a duck then it’s a duck. By talking about the possibility that our bubble universe could have turned out differently while still being the particular universe it is, you seem to me to be talking about a duck which might have developed into a goose while still being the same duck, and I don’t think that’s correct.

You mention Leibniz’s law to argue against the idea that a universe with all the same properties as ours but at a different location could be the same universe, but I think that cuts two ways. If our universe cannot be identical with another (otherwise identical) universe at another location, then our universe with the fine-tuned constants it has cannot be identical with an alternate history version where it turns out with very different constants. I would say that the former case are much more alike than the latter case, especially as the locations of the universes within the larger inflationary space is a property which is unobservable within the universe itself, and arguably hidden from any conceivable non-omniscient observer. As such, I would say it’s not even a real property of the universe. From the God’s eye point of view, I would say these are two instances of the same universe. From our point of view, I would just say they are the same universe. I would even say it makes no difference to us if either one of these universes suddenly vanishes as we will continue to live in the other one. This view of identity is not common but again the point is just that you may want to make explicit your assumption that there is actually a metaphysical fact of the matter on identity. But maybe this assumption is so widespread it doesn’t warrant addressing?

On to Loki: you do think you are defined by your genome. First, just a minor nitpick. I think you mean that had your genome been different you wouldn’t have been you. I suspect we agree that identical twins are not the same person even if they have the same genome. But then I don’t get why things are different for universes. I would say that had the constants been different this universe wouldn’t have been this universe. Can you distinguish the two cases for me?

> Couldn’t one equally interpret this as evidence that Loki has been rolling the dice to see whether to do something, and this is the first time the thing he decided to do was make a person?

I thought the experiment was set up such that we are told that Loki is rolling dice to decide whether to make a person or not. We don’t know how many times he has done this. By opening up the possibility that he’s rolling the dice to do anything at all, you seem to be weakening the
analogy to the multiverse, because I’m not sure what his decision to make a rock instead of a person would correspond to. The outcome of a dud, lifeless universe is already catered for by just rolling the wrong dice. I suspect that all you’re doing here is making the creation of a person more improbable, effectively just adding more dice, because now he has to roll all the right dice as well as randomly decide to make a person. If Loki’s decision is arbitrary, that only makes the fine-tuning all the more delicate, strengthening the case for a multiverse on my view, so I would assume he has conducted even more bajillions of dice trials before creating me.

> We start off struck by how improbable it is that I should be here observing a fine-tuned universe, relative to the hypothesis that the constants were determined by chance

Relative to the hypothesis that the constants were determined by chance and that there is only one universe. If there is no multiverse, it is surprising that the one possible world which happens to exist also happens to be one of the few that supports life.

> Once I take into account the selection effect, it’s just as improbable that I should be here observing a fine-tuned universe if the constants were determined by chance.

That doesn’t seem entirely right to me. The selection effect only comes into play once we assume a multiverse. Once we assume a multiverse, it’s not so improbable that you should be here observing a fine tuned-universe. The assumption of the multiverse is doing the heavy lifting here, explaining your existence. The selection effect explains what you should expect to observe, because you could not possibly be observing a universe inhospitable to life.

> But that’s just because pretty much any event is probable in a multiverse; it’s nothing to do with the presence of a selection effect.

The selection effect is that most or all observers will see a fine-tuned multiverse. No observers should be observing a universe incompatible with life. So a universe that is observed is not a typical universe, just as a person polled by The Literary Digest is not a typical person.

So, given that there is a multiverse, it is not surprising that we see a fine-tuned universe. But given that there was a multiverse, I would neverthless be very surprised to see my Grandma reanimated by quantum fluctuations. The multiverse helps explain the former but not the latter.

9. My previous post, where I described members of the ensemble as “worlds”, which can be either an S-world (for single) or an M-world (for multi), is still “awaiting moderation”. I wanted to clarify what my actual response to your objection then is:

You talk about effectively having just multiverses with n+1 universes instead of n. Using the “world” terminology, you’re then saying that every S world is a part of some M world, but that contradicts the actual ensemble setup I and Alex described.

• Alex Popescu says

Hey ReasonMeThis,

Glad to see you here. I think he is saying that merely imagining the possibility of a multiverse or single universe side by side is itself to construct a multiverse. In other words, the “possibility space” in which our ensemble analysis takes place is itself a multiverse which hosts multiverses side by side with single universe. Hence, we are begging the question, but this only follows if we believe that invoking possibility somehow necessitates that we first have to accept a certain ontology. And of course I (we) don’t believe that.

10. Hey Alex,
do you also agree that it’s at least in part linguistic confusion, since the word multiverse is being used in two completely different senses, its normal meaning and as a very non-standard synonim for “ensemble”? These two “multiverses” have nothing really to do with each other, right?

• Hi Reason Me (and Alex),

I don’t think it’s a linguistic confusion. I’ve tried to put the argument a few different ways now, but let me emphasize the following way.

Trying to calculate probabilities by considering a population of observers some of which are in condition S (in single universes) and some of which are in condition M (in multiverses) is a fallacy for these particular conditions because these are universal predicates and contradict each other.

By universal predicates I mean that if either S or M is true for any observer then it must be true for all observers. if anyone is in a single universe then everyone is. If anyone is in a multiverse then everyone is. This follows easily enough from what it means to be in a single universe or multiverse.

Other universal predicates include mathematical truths. So, even though we don’t know whether Goldbach’s conjecture (G) is true or false, it is true or it is false nevertheless. We can hypothesise about a population for which G is true. We can hypothesise about a population for which G is false. In either case we are just hypothesising about a population and separately about a truth value for G. What we cannot do is hypothesise about a population for which it is true for some and not for others, or make statistical arguments by quantifying over such a population, because to do so is tantamount to hypothesizing about population A and population B and G being true and G being false.

Whatever about my phrasing about the observers collectively inhabiting a super-multiverse, the fact remains that the population the argument quantifies over is incoherent.

• Alex Popescu says

Yes I agree. I only put forward my statement to point out that I thought the conflation (no pejorative intended) was intentional. And that it wasn’t the case, for example, that Disagreeable Me thought that I was actually stipulating that there must be such a multi-multiverse.

11. Hi Disagreeable Me,
thanks for clarifying, I feel I understand your objection much better now. Do you agree that the objection then is inapplicable to the IVF case, Loki, the Joker analogy, the aliens creating planets analogy from Steven? That’s because in these cases it is not contradictory for an ensemble of such experiments to exist. Are you then saying that the multiverse question is radically disanalogous in this regard from all these analogies Steven and Philip have been employing?

• No, I think the objection is still applicable, if construed correctly.

First, to cleanly break these analogies from the multiverse issue, let’s stipulate that there is only one world in the context of these analogies. The random trials in these thought experiments correspond to the creation of a world in S vs M. The whole of the world in these thought experiments corresponds to the whole of existence in S vs M.

On the IVF case, M = the hypothesis that this particular doctor (or alternatively, that any doctor in the world, but let’s for simplicity say this same doctor, Dr X) has conducted bajillions of dice trials. Either this is true or it is false. You can’t have a population of people drawn from the same world where the hypothesis that Dr X has conducted bajillions of dice trials is true for some and false for others. Eiither Dr X has conducted bajillions of dice trials or she hasn’t. You certainly could have a population some of which were produced as a result of dice trials and some of which weren’t, but that is not the question. What we’re pondering is the existence of bajillions of dice trials anywhere in the world — because in M vs S we’re pondering the existence of bajillions of other worlds anywhere in existence.

12. But if this a valid objection it would then seem to apply to any standard case in e.g. thermodynamics where we commonly use the ensemble technique even though we don’t have an actual ensemble in reality. For example, there is only one room X where I am now and it’s either true or false that the molecules of air are about to coalesce into a dinosaur shape (call that hypothesis D). Following your objection, I can say that there can’t be an ensemble where for some members room X satisfies D and for some it doesn’t, and therefore I can’t draw probabilistic inferences about D based on a supposition that it’s a random member of a suitably constructed ensemble (i.e. consistent with the known evidence such as temperature, volume etc). If I’m not strawmanning your reasoning, it would seem to invalidate much more than I think you intended.

I of course think that the ensemble technique is valid in thermodynamics and for the same reason in the IVF case. Suppose for instance you knew Dr. X flipped a coin to decide on M vs S (many or single trial). Here’s the premise that I affirm:

(EP) The credences I should assign are not affected by whether or not there are other doctors here on Earth (or even in galaxies far far away) that have performed similar . (independent) experiments, or how many such doctors there are; in fact for all I know, if the cosmos is huge enough, there actually are many other such experiments!

Notice that no inconsistency arises in this formulation because these doctors are not all Dr. X, only one of them is.

• Hi Reason Me This,

You’re quite right that I certainly wouldn’t want to rule out ensemble analysis for questions like your thermodynamic example, so if I’m doing so then I’m making some sort of mistake. I have to show that there’s some important difference here.

To be honest, I’m struggling to articulate this clearly to my satisfaction, but I’ll try. What follows, unfortunately, seems even to me a bit like waffle.

I think the difference is that whether or not there is a multiverse is inherently a claim about what is true for all observers, and so you have no choice but to model it that way. The condition S asserts the non-existence of the condition M, and so denies the possibility of the existence of any observers for whom M might be true.

But the existence of the possible room configuration D does not rule out the existence of other possible room configurations. And I think for analysis of D it’s the possibility space you need to quantify over not over different observers in the same world some of whom observe D and some of whom observe other configurations at the same time.

You are quite right that I would say you can’t make a coherent ensemble “where for some members room X satisfies D and for some it doesn’t” as long as you are construing it as all members inhabiting the same world and X being the same room at the same time for all members. But this is not a sensible way to construe this question.

The normal way to model this question would be build your ensemble as the possibility space for how X could have been configured. It doesn’t especially matter that each X must be the same room in the same world, indeed when we’re in a possibility space they explicitly aren’t — these are explicitly different possible worlds. We could even empirically test ideas about the most probable ways X can be configured by actually building physical duplicates of X. Each member of your population is just a different point in the possibility space and doesn’t make claims of the existence of other members of the population.

I can see that you could try to argue for doing something similar with observers in S versus M, saying that these are just different possible worlds and we’re not obliged to take them all at the same time. The reason I think this is wrong is that S is explicitly a hypothesis about the non-existence of M observers and vice versa. S and M are only intelligible if we take them as existence claims, rather than claims about the properties of the universe. As claims about the universe we actually observe, they are entirely empty. So S being true of our universe is not really a claim about our universe at all but a claim about the non-existence of other universes. D, on the other hand, is actually saying something about the configuration of X and is not merely a denial of the existence of other configurations.

I hope that helps.

13. Can’t we just say that S and M are just mutually exclusive claims about the properties of the actual world (as opposed to talking about observers) in all cases: the multiverse question, the Dr. X question, and the property D question, so they are all on equal footing? Or at least maybe all but the multiverse question are.

What do you think of EP formulation though, it seems to avoid any hint of an inconsistency altogether?

• I think S and M are different because they are mutually exclusive claims about all of reality, not claims about the actual world at all (unless by actual world you mean all of reality), and there is only one instance of all of reality, by definition. So if you want to build good analogies to S and M, you have to limit yourself to one possible world, meaning that you can’t have mutually exclusive claims about that world. So we can’t abide mutually exclusive states of affairs in our ensemble. Once we start thinking about different versions of Dr. X or Loki in different possible worlds, we’re breaking the analogy to the multiverse. The question we’re asking of Dr. X and Loki has to be what actually happened in this world, and we have to forget that a multiverse with other instances of Dr. X or Loki is possible. So I would say that EP isn’t a great analogy to the multiverse any more.

We’re not so limited in the property D question, as this isn’t really supposed to be an analogy to S and M but is rather an example of valid ensemble analysis. For property D, there’s no need to limit ourselves to one possible world.

Again, S says nothing at all about our universe. It’s not really a claim about our universe. It’s a claim that other universes do not exist. There is no other content to it. If we imagine one version of our universe where S is true and another where it is false, there is literally no difference between these universes. The difference is only in what exists outside the universe. This also distinguishes it from D.

This comes back to my comparison to the ontological argument. Once we start treating existence as a property that things have just like height or weight or what have you, we run into trouble. This is off the cuff but I think we need some rules like (1) positing the hypothetical existence something in a thought experiment or argument is equivalent to saying it actually exists in the fictional world of the thought experiment or argument and (2) the existence of something in the fictional world of a thought experiment or argument can have no bearing on whether it actually exists in reality. By (1), you cannot posit an entity and treat its existence as a property it may or may not have. Just positing it is claiming that it exists (for the sake of the argument, not claiming that it actually exists in reality). This then means that you can’t posit S observers and M observers at the same time in the same argument. By (2), we rule out the ontological argument.

• Alex Popescu says

“ So if you want to build good analogies to S and M, you have to limit yourself to one possible world”

But that just doesn’t follow I think. Just as we can say “possibly all of reality has x property” and “possibly all of reality lacks x property”.
Note that in modal logic (basically all systems) those two statements are not contradictory. That’s true even for system 5, because we’re not interpreting “all reality” to mean all possible universes. So we don’t get possibly-necessarily(x) entails necessarily(x).

You are taking the term “possible universe” too literally, when such claims are not meant to be actual. Instead, you can think of possible states of all reality to be like properties of reality (so that reality has the property that it could have been different).

Or alternatively, you can interpret such claims to be mental ones (e.g. I imagine that reality could have been different). They are not meant to be “actual” claims unless you subscribe to modal realism.

In other words, we are not making claims about all of reality, but rather about the possibility of all reality being different. As long as we believe this possibility exists (i.e. it could have been that the world could have been such); we can draw sound logical conclusions from such reasoning.

14. I think I understood a little better what you were saying: basically for the multiverse question S means not only that the actual object of interest (the cosmos) can’t have property M, but also that NO OTHER object could have property M – because by definition there can’t be other cosmoses. Right?

Then that would not apply to the room X case or to the Dr.X case, correct?

• Sounds about right, yes, depending on what you mean by cosmos. If the cosmos is the universe we inhabit, such that there are other cosmoses on M, I would say that S and M aren’t really properties of the cosmos but properties of all of reality. They’re maximally universal zeroth order predicates, like mathematical conjectures.

15. And since you don’t think that applies to the room X case (since the object of interest is the room here), you would agree that also doesn’t apply to the Dr. X case?

• The Dr X case is supposed to be an analogy to the multiverse. If we start considering that there may be many doctors, including doctors on other planets or in other universes, then I think we break the analogy somewhat, or at least muddy the waters. This is because there is only one reality, So there should be only one Dr X.

But if we forget that it’s supposed to be an analogy to the multiverse, then maybe it wouldn’t apply to the Dr. X case. We could then for example appeal to the many worlds interpretation of quantum mechanics. Instead of assuming that Dr X must have rolled the dice a bajillion times in sequence, we could reason that of course we were born in the one branch where he happened to roll all sixes, all the other dice rolls happening in other brances.

16. Hey Alex and DM

If I understand DM correctly, he is now fine with the Ensemble Premise, which in the IVF case is:

(EP) The credences I should assign are not affected by whether or not there are other doctors here on Earth (or even in galaxies far far away) that have performed similar . (independent) experiments, or how many such doctors there are; in fact for all I know, if the cosmos is huge enough, there actually are many other such experiments!

he is fine with it in all cases where it’s not contradictory to have a bunch of such experiments *within ONE possible world*. Out of all cases under discussion he says it’s contradictory specifically for the multi/uni-verse case, because that case is very special – by definition there can’t be a bunch of these “verses” (I used the term cosmoses before) within one reality!

If I got that right then the only disagreement is about whether the EP technique can still be applied to the special case of the cosmos. Alex, you think it can because you don’t think an ensemble needs to be able to “fit” within just one possible world, it can be spread over a bunch of possible worlds.

Is that correct?

• Alex Popescu says

“If I got that right then the only disagreement is about whether the EP technique can still be applied to the special case of the cosmos. Alex, you think it can because you don’t think an ensemble needs to be able to “fit” within just one possible world, it can be spread over a bunch of possible worlds.

Is that correct?”

That’s right. Not only does it not need to fit within one possible world, but nor do our potential observers have to represent the entire class of hypothetical observers (we can quantify over some hypothetical observers). Further, I didn’t understand DM’s point about existence as a property (I have no idea how he is inferring that we have to postulate that). But even if it were true that we have to say existence is a property, we can just easily translate such talk into quantified form: So that Ea Ex(x=a)

Which means: a has the property that it exists, if and only if, there exists an x such that it is identical to a. Which is basically the same thing, and we have thus solved all potential issues that crop up with the “existence is a property” approach.

• Alex Popescu says

Ea ↔ Ex(x =a)

Not sure why it didn’t go through the first time.

17. Or in the case of IVF (forgetting about the original “verse” question), are you DM saying the credences you would assign depend on how many similar doctors (you estimate) there are (within only our quantum branch)?

• What I’d say is that the more we consider the possibility of other ways of bringing people into existence, the less the analogy works. If we want it to be as like the multiverse question as possible, then I think we probably need to make a number of awkward unrealistic stipulations. We have to say that we don’t know of any other ways for observers to be brought into existence, and that we don’t know of any observers. Because we don’t know of any other fine-tuned ways for universes to be brought into existence or of any other fine-tuned universes. If we knew of lots of fine-tuned universes that had been designed by a creator, for instance, then paradoxically fine-tuning would be no evidence for a multiverse (but of course we’d already know that there is a multiverse).

Without these amendments, a problem shared by Dr X and by Loki is that even the assumption of bajillions of trials doesn’t eliminate all the surprising aspects of the story. It’s still surprising to learn that you were created in such an absurd manner rather than like everybody else. But in general, I would assume that any amazing coincidence suggests the existence of some large class of failed coincidences. So either lots of trials from Dr X or lots of such doctors or just lots of people with really striking coincidences of some kind somehow required to explain their existence.

If you want me to tackle the IVF case on its own merits then we’d need to clarify a lot of these points.

18. “nor do our potential observers have to represent the entire class of hypothetical observers (we can quantify over some hypothetical observers).”
I got lost in the terminology here, can you define potential and hypothetical, what the difference is?

And I thought about your definition of Ea. Isn’t it identical with the trivial property of being true for everything the way you defined it? Seems like by this definition [for any]yEy.

• Alex Popescu says

I don’t mean “potential” in a technical way; it just refers to the observers we intended to use in our ensemble. “Hypothetical” I intended as a more technical term, synonymous with possible (an observer existing in a possible universe).

As for the definition of Ea, ‘a’ here represents a constant, not a variable. Typically the terms for variables are represented by the letters x, y, and z. Whereas constants start with the beginning of the alphabet (a,b,c). The difference being that a variable is the thing we are quantifying over (with the ‘all’ or ‘some’ quantifiers). Whereas this is not so for a constant; which is meant to pick out a specific thing. For example, I could use the letter a to represent the individual Alex (myself).

So Eg, where I define g as god, just means that god exists. And Ex means there exists an x, or some x. So even instantiating a non-specific variable (Ex) doesn’t entail all things (x) exist. We would actually represent that statement thus: (x) Ex

So basically ‘Ea’ is meant to stand in for the specific thing that the property “exists” is used to apply to in whatever instance DM thinks it would. Another thing to consider is that typically the existential quantifier is represented by this symbol: ∃

But I just used E to simplify. Keep in mind however that when philosophers express existence as a property, they typically just use E though. So the correct symbology is:
Ea & ∃x

I hope that helps.

19. Hi Alex,

Yeah, thanks for the conversation. It’s great!

I’m not sure you can talk about all peanuts being salty and all peanuts lacking salt in the one ensemble. That doesn’t seem to make sense to me. Seems like a dichotomy. You can talk about one case or the other case and do statistics on each case separately. I don’t think you can do statistics on both cases combined.

> There is no contradiction here unless you believe:
□∃x:S & □∃y: ¬S

Fine so far.

> when surely the actual translation is this no?
“(x ∈ P ∧ S) v (y ∈ P ∧ ¬S)”

No. Because P is the set you’re doing statistics on. When you do statistics on P, you are not considering two different ways P could be constituted. You have x and y in P at the same time. So you should turn that ‘v’ upside down.

> You just stipulated that we are saying that x has to be in both S and ~S

Well, more x and y than x and x. x is defined such that S and y is defined such that ~S, and x and y are both in P, so we need S and ~S at the same time.

> The only way it would follow that the ensemble analysis entails (x ∈ S) & (x ∈ ¬S)

S is not a set to me, or even a first order predicate, so it doesn’t make sense to me to say x ∈ S.

> Ultimately, I think your contention that such analysis demonstrating that fine tuning plays no role is an “absurd result”, is rather unfair and uncharitable.

Agreed, sorry. This was me being a bit facetious. Though it does seem wrong to me and cause for suspicion.

> we wouldn’t have to assign the observers captured by the x predicate and the y predicate to the same population class

But when you do statistics on them together then you are constructing a combined class. Otherwise you’d end up with two different incomparable probabilities, not one.

> But that just doesn’t follow I think. Just as we can say “possibly all of reality has x property” and “possibly all of reality lacks x property”.

Sure. But then you don’t get to do statistics on the observers of both possible realities combined. The combined population is incoherent. You can only do statistics on both populations separately.

> Which is basically the same thing, and we have thus solved all potential issues that crop up with the “existence is a property” approach

It’s fine as long as you don’t assert that some entity doesn’t exist and then put that entity in a class you’re doing statistics on regardless. But I think that’s what one is doing when one has people from S and M in the same population, because S asserts the non-existence of M observers and vice versa.

• Alex Popescu says

Hey Disagreeable Me,

I would like to quickly point out that you didn’t address my first point about it being possible to quantify over a limited sub-set in each possible world like so: “◇∃x:S & ◇∃y: ¬S”

That would in fact entail that your objections about universal quantification are not applicable (even if they were correct).

Also, I’m not quite sure what you mean about S not being a set (in my defense, I was just copying your language here) or not even a first-order predicate! You say that you think it represents a zero-th order ‘predicate’. But typically zero-th order logic is just propositional logic, where no predicates or quantification are employed. Do you mean S to represent the proposition “there is a single universe” then? However, just because S can be expressed via zero-th order logic does not entail that it can’t be expressed in higher level logics. On the contrary, it’s the other way around, because the higher order logics are more reducible we can definitely express the same thing that exists in a lower order logic, in a higher order logic. But I digress now.

Moving on now to the objections about universal quantification. Again, I don’t quite understand your objections other than the fact that you keep iterating that it would incoherent to quantify in the specified way. I’m not really seeing your reasoning here (other than your adamantly saying that this is so). Therefore, I can’t really give a counter here since I don’t know wherefrom your objections come. However, as mentioned, we can sidestep this issue by resorting to existential quantification from two different populations (without incurring an existential burden) and, I can give counter-examples to show that your approach, if true, would lead to absurdities.

Let’s consider the peanuts example again; is it really true, as you claim, that such quantification leads to incoherent statistics? Well we should start by noting that the ‘class’ which is picked out by the universal quantifier is purely arbitrary. Therefore any sub-class of entities (for example, the number of peanuts in my jar, which is a subset of all peanuts) can be captured by the universal quantifier. So, I can just create a predicate P, which stands for peanuts in Alex’s jar, and then create an ensemble wherein either all the peanut’s in my jar have been eaten or not. According to you, you wouldn’t be able to engage in statistical reasoning regarding the likelihood of the peanuts being eaten or not, because we have expressed this scenario using universal quantification (over the entirety of the class of peanuts in my jar), and there are two mutually exclusive outcomes.

It should quickly become apparent that not only are all the modal logics impermissible under your approach, but that worse, the ensemble analysis becomes a completely illegitimate technique. That’s because any possible ensemble analysis of two sets of things (like the IVF example) can be translated to a scenario using the language of universal quantification. For example, in the IVF case, we can just create two new predicates, A:(is an embryo implanted by doctor x in the single scenario) and B:(is an embryo implanted by doctor x in the multi-IVF scenario). And we can then use a universal quantifier to set up our ensemble analysis. This basically applies to all statistical reasoning.

A way to save your approach would be to argue that as long as an ensemble scenario, involving mutually exclusive scenarios, can be set up without universal quantification, then such a scenario is an acceptable one. The problem is that I have showed that we can do without universal quantification in the multiverse/single universe cosmology.

Best,

Alex

20. Alex Popescu says

To make one last clarification:

The point about the items of the lower-order predicates being possibly expressed in the higher order logics is key. If you wanted to maintain that S isn’t a set to which x belongs, or can’t be captured by first order logic, you would actually have to say that S is an item which is quantified over in a higher order logic. For example, if S was a relation between properties, then it could be captured by a second order logic and quantified over by a third order logic, but it couldn’t be expressed in first order logic.

Hence, it makes no sense to me for you to deny that it is illegitimate to speak of x not falling under the predicate S, on the grounds you stated. With all due respect, I think I’m going to call it a day. I do enjoy such conversations, but I’m afraid that I simply can’t follow your logic here regarding many of your assertions. And so I’m hardly equipped to even begin to tackle them. Thanks for your time.

Best,

Alex

21. Hi Alex,

> I would like to quickly point out that you didn’t address my first point about it being possible to quantify over a limited sub-set in each possible world like so: “◇∃x:S & ◇∃y: ¬S”

I said that I agreed. Where I think we split ways is where you don’t recognise you’re putting x and y in P at the same time. So I was using an AND where you wanted to use an OR. You can quantify over observers for the S case and for the ~S case separately, but not both at the same time.

> I’m not quite sure what you mean about S not being a set (in my defense, I was just copying your language here)

But I never said x ∈ S, I said ∃x:S. The former implies S is a set or a first order predicate (i.e. S(x)). But I claim that S needs no parameters. It’s a zeroth order predicate, so any parameters are superfluous and misleading. It’s not that you can’t treat it as a set or a first order predicate, it’s that it gives the wrong idea. If it’s a first order predicate, then S(x) & ~S(y) is not a contradiction. If it’s a zeroth order predicate then it is, because the parameters make no difference. S(x) is equivalent to S(y) is equivalent to S. S is just a synonym for N=1 and M is just a synonym for N>1, where N is the number of universes. No parameters are needed.

> However, as mentioned, we can sidestep this issue by resorting to existential quantification from two different populations

But I have no problem with that. It’s doing statistics on the combined population I have a problem with. We might be able to say that there are n observers in condition S and m observers in condition ~S. But I say it is incoherent to jump from this to say that the ratio of observers in the combined population is n:m. The combined population is not a coherent object.

> So, I can just create a predicate P, which stands for peanuts in Alex’s jar, and then create an ensemble wherein either all the peanut’s in my jar have been eaten or not. According to you, you wouldn’t be able to engage in statistical reasoning regarding the likelihood of the peanuts being eaten or not,

Of course you can. But I’d need to see the actual analysis to assess whether it makes sense or not. You can have an ensemble of peanuts, some of which are salty and some of which are not, or some of which are in a jar and some of which are in a stomach. What you can’t have is an ensemble of peanuts for which “All peanuts in this ensemble are salty” is true for some peanuts and “All peanuts in this ensemble are not salty” for other peanuts. Members of the ensemble probably shouldn’t be making claims about the existence of other members of the ensemble, but that’s what S and M are doing.

• Alex Popescu says

Disagreeable Me,

You’re just repeating your claims over and over again. You haven’t actually brought up reasons for why we should believe them; worse, each claim is terribly problematic. Let me summarize:

1) “It’s not that you can’t treat it as a set or a first order predicate, it’s that it gives the wrong idea. If it’s a first order predicate, then S(x) & ~S(y) is not a contradiction. If it’s a zeroth order predicate then it is”

Claim: That the same claim can be incorrect in zero-th logic but true in first order logic.
Counter: That’s simply false. The reason they give different conclusions is because they’re not actually the same claim. S & ~S means (there is a single universe cosmology and there is not a single universe). Whereas,

(x)Sx & (y)~Sy means (everything in population x is in a single universe, and everything in population y is in a multiverse)

So they are expressing two entirely different things. Notice the first-order logic claim doesn’t entail the former claim, or vice versa. And it should be obvious that we need first-order logic to fully capture the necessary conditions for the ensemble analysis.

2)“I said that I agreed. Where I think we split ways is where you don’t recognize you’re putting x and y in P at the same time. So I was using an AND where you wanted to use an OR.”

Claim: We have to categorize x and y as being in the same, combined population.
Counter: I don’t think you understood what I was saying in that quote you took. The part where I used the OR statement was related to the universal quantification translation. But notice the separate translation using the existential quantification has an AND symbol in it. I’m saying that if we use the existential quantification then we can maintain both statements are true simultaneously without contradiction. That’s because using the existential quantifier by definition allows us to draw two separate populations (x does not necessarily have to be y). So it doesn’t follow that the existential translation (which I showed is legitimate) necessitates that we combine the two populations, they can be from two subset populations of possible observers. That’s because the statement “all of reality” isn’t used to represent all of reality in actuality, but just a subset of some possible space (i.e. a possible universe which is a multiverse or single universe)

The only way to dispute this would be to argue that counting the odds ratio between two populations necessitates first combining the population, and I think you agree that that is completely absurd.

3) “Members of the ensemble probably shouldn’t be making claims about the existence of other members of the ensemble, but that’s what S and M are doing.”

Claim: That classifying a population as belonging to either a single universe or multiverse necessitates invoking an existential claim on the behalf of the population (or denying it for the opposite population).
Counter: Using either the universal or existential quantifier (in modal logic) does not carry an existential burden if done appropriately, that’s basic logic. More importantly, describing a population as being in S or M doesn’t carry an existential burden. When we say that S is in a possible state, we aren’t saying anything about the existence of the population in M.

4) “Of course you can. But I’d need to see the actual analysis to assess whether it makes sense or not. You can have an ensemble of peanuts, some of which are salty and some of which are not, or some of which are in a jar and some of which are in a stomach. What you can’t have is an ensemble of peanuts for which “All peanuts in this ensemble are salty” is true for some peanuts and “All peanuts in this ensemble are not salty” for other peanuts”

Claim: That we can’t do analyses on combined populations if the potential results are mutually exclusive.
Counter: The whole point of modal logic, and the logic of possible universes, is to take one population and then subject it to counterfactual (mutually exclusive) descriptions. That after all, is the point of much of statistics too. Also, I don’t think you understood my reasoning here either, which was that, because the class over which the universal quantifier operates is arbitrary, I can capture any possible mutually exclusive scenario under the quantifier. So, according to you, all reasoning regarding mutually exclusive scenarios would have to be invalid. For example, I could construct a predicate P(lives in room y in house x) which only I satisfy. Hence, saying all x that are P [i.e.(x)Px] is just another way of referring to me. And this can be done with all subsets and objects. Therefore, we couldn’t do any ensemble analysis regarding any mutually exclusive scenario (like the IVF case).

So the bottom line is that I think with all due respect you have been very free in your claims. I haven’t seen much reason on your behalf for invoking any of them, and furthermore they would have absurd results if true that you haven’t addressed.

Good day.

• Alex Popescu says

In other words, this I feel, all boils down back to our original discussion on possibility vs actuality. You can’t have some peanuts being salty in the population of non-salty peanuts, and you can’t have some single universe observer existing in a multiverse in actuality. All of that is true, but you can definitely reason towards the possibility of either scenario (i.e what if a salty peanut was not salty?). Again, all of modal logic (one population in different counterfactual scenarios) and all of ensemble analysis goes out the window according to your claim. I think we should probably just give up the fine tuning claim instead perhaps?

I just wanted to make that last response of mine as a summary for posterity; you’re right that all conversations must end. I’ll definitely read your responses, but sorry if I choose not to continue. Thanks.

Best,

Alex

22. DM,

– if the Ensemble Premise holds for Dr. X, aliens creating planets, etc then, since Philip and Steven seem to be more interested in the logic of the inference to Multi involved in all these situations, rather than caring specifically and exclusively about the multiverse question, it seems for the question they are discussing the ensemble technique is legitimate. Of course if they are also right that the answer for the multiverse question is the same as for all these analogies then even better.

– Of course they both would then be wrong about the actual answer, since the ensemble technique gives the result that the odds of M vs S do get a boost (contrary to what the “this universe” argument would seem to imply), but the boost is by a factor of N, the number of rooms / universes etc in the Multi scenario, and is unaffected by P, the degree of fine-tuning (contrary to Steven).

– I disagree with the idea that the multiverse case is special. One way to explain why is to note that a “verse” doesn’t necessarily contain all observers, there could be other “parallel” multiverses, not contiguous with ours. Roughly speaking, a multiverse is not defined to be all of reality.

– I have a separate argument for the same answer, I called it the Characteristics based argument, it’s on Steven’s blog but I will probably add it on my site too.

• Hi RMT,

While I think it makes sense for there to be a hierarchy of multiverses, and parallel multiverses not contiguous with ours, for fine tuning we are only interested in the maximal scope of all universes in any multiverse. So in this discussion I’m defining the multiverse as the set of all universes anywhere (in any of your multiverses), where the number of such universes is > 1. All we need to explain fine-tuning is the idea that there are lots of universes anywhere in reality. We don’t need any of those universes to be in any particular subset of reality. If there are enough universes anywhere then some of them will appear to be fine-tuned. This makes the multiverse case special.

• Hey DM,
Of course if you stipulate by definition that there can’t be more than one multiverse in any possible world, then sure, an ensemble of them won’t fit in one possible world.

However, I don’t think there is a good reason why we must use this definition in the context of fine-tuning, I think my definition is at worst no less reasonable Why? Because there is no reason to think that other parallel multiverses necessarily obey the same laws as ours, and therefore conditions there can be wholly unlike ours. In particular maybe there every universe is compatible with life, and is also 42-dimensional to boot. So what we really want to know when it comes to fine-tuning is whether our “local” contiguous piece is a single or a multi-verse.

23. Hi Alex, if you’re still reading.

I’m sorry that you are leaving the conversation, but all such conversations must end. Thanks for sticking around as long as you did. I accept I’m not always very good at expressing myself and I don’t blame you for not following. These issues are particularly difficult to express cleanly.

I did just want to bring up one other way of talking about it, in case it might help. This is how I was led to thinking of the problem in this way.

Like you and Reason Me This, I think ensemble arguments are a great way of thinking about probability. Where probabilities are hard to calculate or prove for some reason, we can often get good approximations by simulating such ensembles. So when thinking about this problem, my first reaction was to imagine how I would go about simulating it in a computer to see what we would get.

So here’s the setup. I design a new cryptocurrency ObserverCoin which is more or less a clone of Bitcoin, except the we imagine the coins to be observers with a point of view. We don’t have to simulate a mind or anything, but maybe we can print some templated lines from their point of view to console. As with Bitcoin, to have a chance of creating a coin, we have to perform a time-consuming calculation which is incredibly likely to fail. The S condition is just “only one ObserverCoin mining calculation has ever been carried out”. The M condition is “many ObserverCoin mining calculations have been carried out”. With this setup, it’s easy to simulate either S or M, and we can think about what a typical ObserverCoin should expect to be true.

But, we can’t do both. If we only ever run the ObsererCoin mining calculation once, then S is true (and we’ll almost certainly generate no ObserverCoins). As soon as we run it more than once, M is true. So it turns out that we cannot simulate an ensemble where S is true for some ObserverCoins and M is true for others.

We can try to get around this by trying to put a limiting scope on our claims. We could try to say that S is instead analogous to “only one ObserverCoin mining calculations has been carried out today” and M is “many ObserverCoin mining calculations have been carried out today”, and some days S could be true and some days M could be true. Then you can try to do statistics about what should be true for a typical ObserverCoin, and what should feed into a particular ObserverCoin’s credence for S vs M (i.e. does the difficulty of the mining calculation have anything to do with it). But you’re only able to do so by having a whole lot of instances of the system, when for the multiverse versus universe the very question we’re trying to answer is whether we should believe there are a whole lot of instances of the system, or rather how having many instances of the system affects what we should expect to see. The limiting scope is artificial, and does not adequately represent S. By running the simulation many times, observers in the system should expect to see just what observers would see in a system that corresponds to M, not S. You just can’t represent condition S in a simulation adequately unless you only ever have one instance of the system in your simulation, because while the observers in condition S may be alone on the day, they are nevertheless members of a class with many members (all the other ObserverCoins who have ever been generated). For fine tuning, the real question is not “how many universes are there in this particular scoped subset of physical reality” but “how many actual universes are there in the maximal scope imaginable”.

We could use such a simulation to show that most observers will be in M, but only by running the simulation many times and so presupposing that M is true, since we are incredibly unlikely to get any observers if S is true and we run it only once. So while I was hoping to use such arguments to show that we should believe M, I rejected the argument as useless.

• Alex Popescu says

I would say you are correct that you cannot do both. But we all accept that both M and S cannot be true (no one argued otherwise). So I don’t quite see your point here unless you’re trying to say that the specific act of simulating (i.e. constructing an ensemble analysis) must instantiate the other scenario.

But I don’t think this follows; it only was true in your case precisely because your statement’s soundness depended on the simulation being put into effect (you stipulated this). But notice that the real S and M don’t say anything about their truth values depending on our undertaking a certain ensemble analysis. So I don’t think it’s the same.

24. Hi Alex,

Since you said you’ll read my responses…

I’ve had a bit of a sleepless night trying to sort this out and find the best way to concisely explain my position. I’ll do so after a brief apology.

You say I’ve been very free with my claims, and that’s a fair point. I guess I wanted to get my claims out there, see which ones you disagree with and then argue for them. One problem is that I don’t always agree with your interpretation of my claims, and another related issue is that I can see that I haven’t communicated them very well, partly because they’re tentative or unclear in my own mind. Yet another problem is that I don’t always understand your points, e.g. when you say “So I don’t quite see your point here unless you’re trying to say that the specific act of simulating (i.e. constructing an ensemble analysis) must instantiate the other scenario.” I don’t know what “other scenario” refers to.

I confess that I find discussing this question extraordinarily confusing. I have a strong sense that there is something wrong with your argument but I have not succeeded in articulating it clearly to this point.

Since you’d rather not continue the conversation, I’m not sure there’s much point in getting stuck in the weeds addressing all your counters to my claims in detail. I’d rather focus on big-picture issues.

Part of the problem is that we are talking at cross purposes. The way I’m modelling the scenario in logic does not match how you are modelling it. The reason for this is that you don’t seem to take up my suggestion that we need to model S and ~S as zeroth order predicates which must have the same value for all of the members of our population. This really goes back to the disagreement on whether our population is in effect a multiverse — to you it is just a collection of possible worlds and is not in effect a multiverse but to me it is. As such it makes sense for you to consider that x might be in a single universe whereas y might be in a multiverse and then to do statistics on a population containing both x and y, but this does not make sense on my assumptions.

So I need to explain why I make the assumptions I do. I think that there are conflicting reasons why we both must and must not treat the ensemble as effectively a multiverse and so the analysis cannot be made to work. Since you’re on board with why we cannot treat it as a multiverse (it’s begging the question), I must show why viewing it as just a collection of possible worlds does not really work for the specific case of trying to decide whether fine-tuning is suggestive of a multiverse, even though it does for just about any other question you might want to investigate.

Note that in your original argument you referenced the IVF problem, and your analysis imagines “that there are an infinite number of parallels universes”. So this original analysis of the IVF problem works perfectly, but only if we imagine that there are infinite parallel universes. I suspect you’re happy for these universes to be imaginary, but I think this loses sight of the fact that we need bajillions of trials to account for our existence if the doctor has to roll 20 dice. As such we need either that the doctor runs dice trials bajillions of times in this universe or we need these infinite parallel universes to be actual for us to account for our conception. So your argument shows that indeed we have no reason to believe the doctor attempted to roll twenty sixes bajillions of times in our universe, but only if we can appeal to bajillions of trials occuring elsewhere in the multiverse.

I think that in order to bring this analysis to the actual fine-tuning question, you need to make a similar assumption. But since you don’t want to beg the question by assuming a multiverse, you need to change it to “there are an infinite number of possible worlds”. But an infinite number of possible worlds is not enough to account for our existence. Again, those worlds need to be actual, otherwise it is very unlikely that the one actual world is one which would be fine-tuned. This is why I think we must treat the ensemble as a multiverse. We then run into contradictions because we cannot have single-universe observers inhabiting our multiverse, and why I think the analysis begs the question by assuming a multiverse.

• Alex Popescu says

Disagreeable Me,

“I suspect you’re happy for these universes to be imaginary, but I think this loses sight of the fact that we need bajillions of trials to account for our existence if the doctor has to roll 20 dice. As such we need either that the doctor runs dice trials bajillions of times in this universe or we need these infinite parallel universes to be actual for us to account for our conception”

This is not an accurate representation of what our ensemble analysis does. We aren’t trying to account for our existence in the IVF or multiverse case.

“But an infinite number of possible worlds is not enough to account for our existence. Again, those worlds need to be actual,”

To add on to the above, since we aren’t trying to account for our existence we don’t have to postulate a multiverse. This is easily demonstrable once we look at the conclusion of the ensemble analysis. Which is that (if fine tuning) then ~(multiverse more likely). This is a conditional claim similar to the following one: If it were raining, then the ground would be wet

Conditional claims aren’t existential claims; it doesn’t have to be raining for the above to be true. And we don’t need to posit S or ~S to make the conditional claim about fine tuning.

“As such it makes sense for you to consider that x might be in a single universe whereas y might be in a multiverse and then to do statistics on a population containing both x and y, but this does not make sense on my assumptions”

I think this entire talk (along with the higher-order logic talk) is just a side discussion which needlessly confuses the issue. The real claim of yours is that one must infer a multiverse to show the ensemble analysis, and hence beg the question. This is an entirely different matter over whether it is in fact incoherent to do counterfactual analysis on a single population (it’s not). Let’s stick with the core claim.

Lastly, related to your earlier post about the ObserverCoin; what I meant is that the problem there was straightforward. You stipulated, through the definitions of S and M, that S or M can only be true on account of one doing a certain (mutually exclusive) simulation. Where the simulation was analogous to one running an ensemble analysis. Therefore, it is no surprise that your doing the simulation which proved S would negate M. However, the real S and M don’t say anything about an ensemble analysis, therefore it makes no sense to say that the cases are analogous.

They would only be analogous if they were to read:
P:(There is a single universe (S) and M is false if an ensemble analysis is done on S)
Q:(There is a multiverse (M) and S is false if an ensemble analysis is done on M)

The real statements of course say nothing of the kind.

• Alex Popescu says

So ultimately, I hope we can see that the higher order logic stuff and certain ensemble analyses being incoherent is just an unhelpful tangent discussion. Your real claim is about us having to invoke actuality at some point. For some reason this is a very strong intuition of yours; I urge you to think on it more and maybe explore why you feel this way. If you’re still curious you can come back with your best argument for this claim at some later date, and maybe we can continue the conversation then.

Best,

Alex

• Hi Alex,

I don’t think there’s much point in discussing the higher order logic stuff or the incoherence of the ensemble analyses until you understand why I think we need to invoke actuality. I think the rest would follow if I could communicate that. So it is unhelpful at this stage, I agree.

What your ensemble analysis shows is only that fine-tuning does not affect the ratio of observers in single universes versus in multi-universes for hypothetical observers in possible worlds. But this mistakes the motivation for the the inference from fine-tuning to the multiverse. Nobody (at least nobody who understands your argument) thinks that fine-tuning should increase the ratio of multiverse to single-universe hypothetical observers in possible worlds. Fine-tuning is motivated by the observation that we are real observers in an actual world. The ensemble analysis is inapplicable because we are not trying to assess some ratio within a hypothetical ensemble, but whether an ensemble physically exists in the first place (as a multiverse).

There’s a reason I set up ObserverCoin as I did. As far as I can see, my stipulations are necessary to make it analogous to fine-tuning. You’re free to propose any adjustments you like and we’ll see how that turns out. Just have a think about how the difficulty of mining an ObserverCoin should affect your credences if you are an ObserverCoin. Given that you observe yourself to exist, should you expect the experiment to have been conducted in condition S or in condition M?

If it’s hard enough to produce an ObserverCoin, it’s easy to see what will happen if we set up the experiment in condition S. No ObserverCoin will be produced, or the probability of an ObserverCoin being produced is negligible. You (the ObserverCoin) will never come to exist. Therefore, any ObserverCoin that actually exists should conclude M, that many ObserverCoin mining operations have been conducted.

Analysis with possible worlds will not do because I’m stipulating that this ObserverCoin is a real perspective in this real actual world, just like ours is, because for fine-tuning the realness of the perspective just is the explanandum, because the vast majority of possible worlds have no observers.

I really want to make this as concrete as possible for you, because concreteness is key. Ideally this should be so concrete you can almost believe it. This breaks the analogy, by using your perspective rather than that of the ObserverCoin, but clearly, if I am telling you right now that I went to the trouble of implementing ObserverCoin, and furthermore that I successfully mined one, then your credence that I ran it many times should be proportional to the difficulty. This seems undeniable to me. Perhaps you will agree and disagree that this is analogous to IVF because now the observer is not the ObserverCoin itself and could have observed no ObserverCoins at all. Perhaps we can get around this by saying that I only ever tell you that I was actually mining ObserverCoins in the event that I succeeded. The intention here is to weed out all the possible worlds containing observers where no ObserverCoins were produced, and so make your perspective an appropriate substitute for the ObserverCoin’s itself.

Can we not now apply your analysis to this situation? Imagine the probability of producing an ObserverCoin is 1 in a billion. Suppose there are an infinite number of possible worlds, half of which ran ObserverCoin once and half of which ran it a billion times. A billion times more ObserverCoins will be in worlds where it was run a billion times. And the same is true if the successful production of an ObserverCoin is guaranteed every time.

But if I tell you that I randomly decided at 50% odds to run ObserverCoin once or a billion times, then that I actually succeeded in producing an ObserverCoin, and that I had decided ahead of time I would only tell you all this if I was I was successful, are you really going to stick to your guns and say that your credence that I did the mining only once is unaffected by whether the chances of success are 100% or 1 in a billion?

I expect you won’t stick to your guns and will instead point out some perceived problem with my argument, because the conclusion is to me absurd enough to count as a reductio ad absurdum for your analysis, such that I am surer that there is some problem with your argument than that I have correctly identified it. Indeed it seems much more absurd to me than Philip’s conclusion. Philip’s argument is that M doesn’t help because while it does explain the existence of observers just like us (which you would perhaps dispute, per your analysis) it can’t explain the existence of us specifically — which I think is incorrect only because I conceive of personal identity differently than he. Philip at least agrees with me that the multiverse should help explain why some observers exist even if observers require fine-tuning.

25. Alex Popescu says

About the higher order logic side discussion:

I actually think that this is an irrelevant side discussion which needlessly confuses and complicates the issue. As a brief summary: the difference between the logic orders is just a result of the difference of the type of items being quantified. So in first order logic we have objects (e.g. individuals) being quantified; but we can assign predicate values or properties to these objects. Second-order logic just quantifies over these predicates (one level up), third order would quantify over the relations between the predicates themselves etc… Another way of looking at this is that we quantify over sets (3rd order) of sets (2nd order) of sets (1st order) the further up one goes in order.

Zero-th order logic is even more basic. Technically, in modern predicate (type) logic, zero order items are just truth values, they are completely void of content. Although it is convenient to say that propositions can also fill in for zero-order items. But this scaling is relative; you can choose to assign any item you want for your zero-order item (e.g. a set for example). Notice that it therefore makes no sense to say that you can’t include a certain item (i.e. S) in first order logic, unless you meant to say that we are breaking common convention. But of course this is not so, by convention predicates are things applicable to first-order logics, they are not the items of zero-th order logic.

So I think that claim is confused, as well as the claim that S can’t be a set. To say that we are treating S as a set is just to say that we are assigning set members (in this case our population) to S. It therefore makes no sense to say that S can’t be a set on account of the problems you mentioned. It doesn’t matter if our hypothetical set members are possible or actual; either type of entity can be a set member. Nor does it matter if the population is incoherent, that just means our set is incoherent as well, but at the end of the day its still a set by definitional fiat.

26. Alex Popescu says

“The ensemble analysis is inapplicable because we are not trying to assess some ratio within a hypothetical ensemble, but whether an ensemble physically exists in the first place (as a multiverse)“

This is just a matter of representation. Of course the items in our ensemble analysis are possible entities; the point is that these relations between possible entities are supposed to represent actual relations in the real world. Saying that the ensemble analysis (in the way I constructed it) doesn’t work because it’s just ratios between possible entities, is almost as silly as saying that we can’t capture any mathematical truths because writing (2 + 2 = 4) on the board only expresses relata in the form of numerical characters, and not mathematical items. By that logic, no model can ever work.

So we don’t need an actual existing ensemble to make reasonable inferences. Instead of denying that there is no such thing as representation (which you seem to be doing); a better approach would attempt to point out some flaw in the representational aspect. Perhaps some salient feature of a multiverse/single universe or fine tuning wasn’t appropriately captured in the analysis. But you haven’t pointed this out.

“ But if I tell you…are you really going to stick to your guns and say that your credence that I did the mining only once is unaffected by whether the chances of success are 100% or 1 in a billion?”

In this case I think fine tuning does modify our credences on account of the fact that you would stop the observer coin calculation after a successful result. Consequently, we must take into account the chances that a single observer coin was produced. If you do the appropriate ensemble analysis; you’ll see that the odds of this do tilt relative to fine tuning.

But in the multiverse case we have to take into account the ratio of civilizations (or life forms) that exist in either cosmology. In any case, I don’t think it’s helpful to rely on intuition as a guide for whether it is reasonable to take into account fine tuning or not; these types of probabilistic outcomes are notoriously counter-intuitive.

• Alex Popescu says

I meant to write: *Instead of denying that there is such a thing as representation

Perhaps it was uncharitable of me to interpret your claim as an attack on representation. I was assuming that that was your main argument for why we need to invoke actuality, and I was also responding to this:

“But this mistakes the motivation for the the inference from fine-tuning to the multiverse. Nobody (at least nobody who understands your argument) thinks that fine-tuning should increase the ratio of multiverse to single-universe hypothetical observers in possible worlds.”

If you merely intended to repeat your claim about the ensemble having to be actual; I don’t really think that’s helpful. Like I said; I think you should think on this and come back with your best argument for why you think this is so.

• Hi Alex & RMT,

I agree that we should not rely on intuitions too heavily when looking at probabilities. But I not only think the ensemble analysis is wrong, I feel like I can see why it’s wrong, even if I’m struggling to articulate it. The conclusion you reach about the ratio of observers in one condition vs another in your thought experiment is clearly correct given your assumptions. But it’s less clear to me that your assumptions are applicable to this question, and that your conclusion means what you think it means (that fine tuning gives us no reason to increase our credence in a multiverse).

This is why I’d like to focus on the ObserverCoin question, because I think it makes it clear that the conclusion is wrong. We can figure out why once we agree on this.

Since I think we all agree that the conclusion would be wrong for ObserverCoin, you need to show how this is not analogous to IVF.

Alex has done so by suggesting:

“In this case I think fine tuning does modify our credences on account of the fact that you would stop the observer coin calculation after a successful result. Consequently, we must take into account the chances that a single observer coin was produced. If you do the appropriate ensemble analysis; you’ll see that the odds of this do tilt relative to fine tuning.”

I didn’t say that I would stop the ObserverCoin calculation. (Nor did I say that I wouldn’t, in fairness). I don’t see that it makes any difference though. The rules are just that I tell you that I have successuflly mined an ObserverCoin. You don’t get to know how many were mined, just like we only get to observe one universe. Just to keep it analogous, let’s stipulate that I run the mining operation a billion times in condition M and do not stop when I succeed.

Now, again, let’s run your analysis on this situation. Quoting myself:

“Imagine the probability of producing an ObserverCoin is 1 in a billion. Suppose there are an infinite number of possible worlds, half of which ran ObserverCoin once and half of which ran it a billion times. A billion times more ObserverCoins will be in worlds where it was run a billion times. And the same is true if the successful production of an ObserverCoin is guaranteed every time.”

So, on this analysis, the ratio of condition M vs condition S is unchanged by the difficulty of mining, and you should not conclude I ran the mining more than once with any more than 50% probability.

Again, I’m flailing around a little to articulate what exactly the problem is, and I’m sorry for that. I think you should take all my claims as suggestions, suggestions from which I’m prepared to back down if we can find a better one.

Here’s another, and I think this one may be the clincher.

Recall when RMT said: “What is the proportion of S vs M worlds? That’s your prior. For example, if, as far as you know, Loki had no preference between S and M, you effectively assume he flipped a coin. If that whole situation happened in G independent worlds, then you’ll have 0.5G S-worlds and 0.5G M-worlds.”

I think it may be a mistake to let our priors remain at 50% when we learn that an ObserverCoin was produced. So the analysis is wrong to let half of the possible worlds be in condition S and half of the worlds be in condition M once you know the ObserverCoin was produced. We are not after all reasoning in a vacuum. We have new information which should cause us to update our priors before conducting the ensemble analysis.

The reason the fact of the ObserverCoin being produced should cause you to update your priors is just the usual argument from those who think that fine tuning should affect your credence in a multiverse, which can be cast in a bayesian light.

Bayes Theorem is that P(A|B) = P(B|A).P(A)/P(B)

Let A be that only one universe exists (or ObserverCoin was run once).
Let B that a fine-tuned universe exists (or ObserverCoin was run successfully).

We start with priors of 50% each way, so P(A) and P(B) are both 0.5, and P(A)/P(B) cancel out. We’re left with P(B|A) only.

So to calculate our credence that this is a single universe given that we have observed fine tuning, all we need to do is to calculate the probability that a single universe would be fine-tuned. For ObserverCoin, this credence is a billionth. So given that we have observed an ObserverCoin, it’s a mistake to let half of the possible worlds be in condition M and half in condition S. Rather, a billion times more possible worlds should be in condition M, so now fine tuning does actually impact the ratio of observers after all.

QED?

27. “The ensemble analysis is inapplicable because we are not trying to assess some ratio within a hypothetical ensemble, but whether an ensemble physically exists in the first place (as a multiverse).”

This is linguistic confusion again, a multiverse is not an ensemble. I think I understand now that you think the very definition of the multiverse is:
A. multiverse = mereological sum of all universes (in a given possible world)

Then, combined with your belief that:
B. Ensemble analysis is only legitimate if the ensemble can fit in one possible world

you conclude:
C. There is no possible world containing an ensemble of multiverses and single universes (follows just from A)
———–
D. Ensemble analysis for multiverses/universes is not legitimate (follows from B and C)

The problem is Alex doesn’t see a good argument for B, and I definitely deny A.

• Hi RMT,

I think in light of my Bayesian argument above, I’m on the verge of recanting many of my earlier arguments — I’m unsure if there is any merit in them or not. The Bayesian argument is certainly clearer, and seems to cast the problem in your own terms, whereas the other arguments I presented better reflect how I’m inclined to think of the problem.

In particular, I’m prepared to accept that proposition B above is probably a mistake.

However I still think you’re wrong to deny A (and C) in the context of this question. I agree with what you say here:

“Because there is no reason to think that other parallel multiverses necessarily obey the same laws as ours, and therefore conditions there can be wholly unlike ours. In particular maybe there every universe is compatible with life, and is also 42-dimensional to boot.”

But I don’t think I need to assume that universes are the same as ours apart from constants. If there are enough universes of all kinds of structures, then it is no surprise that we find ourselves in a universe that supports life. In fact, what you’re saying here only strengthens the argument for a multiverse, since I would argue that we not only have to explain why the constants are fine tuned, but why the mathematical structure of the laws of physics parameterised by these constants is such that life can exist given some set of constants. It’s very easy to imagine a universe with no entities, with no complex structure, with no contstants, where the only law is that nothing ever happens. I think we not only need to explain why our laws of physics are parameterised as they are, but why they exist in the first place when they needn’t in all possible worlds, and when presumably most imaginable universes with radically different laws of physics wouldn’t support life either.

• Confession time: I am actually a modal realist (I believe in Tegmark’s Mathematical Universe Hypothesis), so for me all possible worlds are actual worlds, so I can’t conceive of a possible world which is in condition S, as such a world is inconsistent with the existence of other possible worlds. I think this may have infected my thinking a little, even while I was attempting to suspend my belief in the MUH.

• Alex Popescu says

Hey DM,

Two points:

1) About ObserverCoin: RMT has already touched on this, but the principal distinction here is that it matters what you are trying to measure. If you are trying to measure whether a (single) fine tuned universe (or ObserverCoin) exists, then fine tuning does modify the odds ratio. If instead you are just concerned with the ratio of civilizations, or the ratio of ObserverCoins, then fine tuning doesn’t matter.

The former situation can come about by the stipulated conditions of the simulation (e.g. simulation ends after one ObserverCoin produced); or it can come about as a result of the way you define the desired outcome. Sorry I wasn’t clearer on that point earlier. In your updated case, even though you didn’t stipulate that the ObserverCoin must stop after a successful run; you nevertheless set your Bayes’ condition as “Let B that a fine-tuned universe exists”.

Thus, since you’re just measuring the probability that a (single) fine-tuned universe exists; it follows that fine tuning will tilt the odds. However, the real measurement must be the ratio of civilizations (because we assume that we could have been born in any fine tuned universe).

I don’t think this actually matters. Since your brand of modal realism is Tegmark’s mathematical multiverse; that’s basically analogous to all logically possible universes (or at least all mathematically possible ones). But RMT already made this point earlier (which I think you misunderstood); which was that the multiverse cosmology we envisioned is actually but a very small subset of logical space. That’s because we’re using the the term multiverse to refer to the inflationary/string theory landscape of physical universes that are bounded by the standard model.

Therefore, even if the universes in our ensemble analysis were real entities; they would only pick out a very small subset of all the logically/mathematically possible ‘actual’ universes. As such, Tegmark’s mathematical space is more than capacious enough to allow single universe observers to exist side by side with multiverse observers. That’s because the word ‘universe’ (as previously mentioned) only refers to the space-time continuum that cosmologists envision, and not all of reality. In other words, by accepting modal realism you’ve changed the definition of “all of reality” to mean not just physical space, but all of mathematical space as well.

Therefore single universes can exist in possible space, as long as they are not subsets of larger physical space (but still a subset of all possible space). Of course we can go back to saying that modal worlds aren’t actual, but then you need to give an account of why we must invoke an actual world for our possible worlds analysis.

• Hi Alex,

I don’t understand why you think the question is the ratio of civilisations. The observation I understand scientists to be trying to explain when they posit the multiverse is that the world is fine-tuned. I take the surprising thing about this to be that such a fine-tuned world exists at all. Perhaps you will disagree. In any case, what I think we need to explain is captured well by “Let B be that a fine-tuned universe exists”.

From my point of view, I don’t think the ensemble analysis adds anything, and the ratio of civilisations is unimportant. If we were to do the ensemble analysis correctly, we would need to adjust the proportion of possible worlds between S and M according to our updated credences given the results of my Bayesian analysis, and we would derive no interesting or surprising conclusions, arriving back at square one where we were with the Bayesian analysis.

On Modal Realism — forget it. I tried to think like a modal non-realist and I possibly failed. My modal realist assumptions may have led me into making arguments that wouldn’t work for a modal non-realist. Let’s not get into a digression about whether they even make sense on modal realism, unless perhaps you’re interested because you’re also a modal realist. I have the instinctive urge to respond to your points but this conversation is long enough as it is! I’m really keen to figure out what’s going on with ObserverCoin, Bayesian analysis and RMT’s introduction of E3 into the mix.

All the best, and thanks for sticking around.

• Alex Popescu says

Hey DM,

The reason I (and RMT) think the ratio of civilizations matter is quite simple. We are trying to answer the question, does fine tuning increase our credence in the multiverse? To do so, we must ask what are the odds that a hypothetical observer is born in S or M, before and after fine tuning is taken into account.

Analogously, if we wanted to ask “if a person exists, is it more probable that they were born in China or Chile?”, we would clearly need to take into account the populations of both. It would be misleading to simply measure the likelihood that a single person exists in either country.

We can see this more clearly in the countries example, because in this case it’s 100% for both. So clearly something has gone wrong in our analysis here; we would have to give 50/50 odds if that’s correct!

Notice it doesn’t matter if the population of China was 1 and if Chile had a 1/1000 chance of hosting just a single person (more analogous to the M and S situation). That’s because we’ve just changed the absolute population numbers; but it still follows that a hypothetical observer is more likely to be born in China. So therefore, population (and ratio of civilizations) have to be taken into account.

Not doing so means that you are denying that it could have been equally likely for us to be born in any fine tuned universe within the multiverse. Here I’m not talking about the odds ratio between S and M, but rather that we have an equal probability of being born among all fine tuned universes in M.

And yes I think this is a good time for me to bow out of this conversation.

Best,

Alex

• Hi Alex,

> To do so, we must ask what are the odds that a hypothetical observer is born in S or M, before and after fine tuning is taken into account.

That’s fine, I can get on board with that. So to do it before taking fine tuning into account, you set up the ensemble with the naive prior, 50% M worlds and 50% S worlds. To take fine tuning into account, you set up the ensemble with your updated Bayesian priors, where now you have 99.999% M worlds and 0.001% S worlds. The ratios are therefore affected after all, and we find that fine-tuning should impact our credence. The reason I say the ratios don’t matter is because you get the right answer just from the Bayesian analysis and you get nothing useful from the ensemble analysis in this particular case.

> “if a person exists, is it more probable that they were born in China or Chile?”, we would clearly need to take into account the populations of both.

Agreed, but this is not analogous. We don’t know the populations of “China” or “Chile” in the case of the multiverse/single universe. That’s why we assign them credences instead, which are affected by fine-tuning.

If you want to bow out now that’s fine, especially if RMT sticks around. But in any case, to be perfectly honest, I’m satisfied with my answer now. I am no longer puzzled that I can’t find a satisfactory explanation of what’s wrong with your argument. I’m only puzzled as to why you still think it works, and I’d be interested in exploring that, especially on the off chance that I’m missing something.

• Alex Popescu says

It doesn’t matter that we don’t know the populations. What’s important is that we know that population should play a factor in the China/Chile case, and that still remains true even if we don’t know what the population is. Similarly, what’s important here is that we know the number of fine tuned universes in M should play a factor; even if we don’t know the actual number. Remember that our claim is a conditional one; we aren’t actually trying to come up with the correct figures here.

And you are just presuming that we should modify our credence for M on the basis of fine tuning, but that is exactly what is in contention here! One must first demonstrate that fine tuning plays a role in the odds ratio before one allows fine tuning to modify our credences. And you have only demonstrated this for the single universe case, and not for the ratios between civilization. I hope you agree that the latter ratio doesn’t change based on fine tuning (you seemed to admit this earlier).

So the question is if we should adopt the ratio between civilizations or the single fine tuned universe approach. I laid out a clear case for the former; in response you just said that we can’t do that because we need to modify our credences on the basis of fine tuning. But that would be begging the question.

Since I’ll no longer be responding (sorry); I urge you to think on why you believe that we should reject the ratios between civilization approach, and to read RMT’s post on his site in more detail if you are curious.

Take care.

• Alex Popescu says

Since I am leaving; here’s one more post. It’s also important to point out that we do in fact know something crucial; which is that the population of observers will be greater for the multiverse relative to a single universe. So that piece of information is enough to deduce that all things being equal, a multiverse is more likely. Of course all things are not equal; we don’t start off by assigning 50/50 odds. Instead, we should assign our priors based on evidence and belief regarding the likelihood of the multiverse existing.

If we think there is little such evidence, then we are absolutely justified in assigning a very low prior to M. But note that our point is that regardless of the prior, fine tuning will play no role. And this is demonstrable in the ratios between civilizations case. Hence, the actual prior one assigns is irrelevant to refuting the conditional claim that (if fine tuning) then ~(multiverse more likely).

And like I said, whether we take into account fine tuning for our prior is going to depend on whether fine tuning modifies the odds ratios. If it doesn’t then fine tuning is an independent variable, and we shouldn’t take it into account. I hope that makes sense.

28. – With Bayes you don’t need an ensemble at all, it’s just trickier to figure out what should count as evidence.
– Alex and I are not saying the posterior credence for M should be equal to the prior, we are saying it doesn’t depend on P, the degree of fine-tuning
“Bayes Theorem is that P(A|B) = P(B|A).P(A)/P(B)

Let A be that only one universe exists (or ObserverCoin was run once).
Let B that a fine-tuned universe exists (or ObserverCoin was run successfully).

We start with priors of 50% each way, so P(A) and P(B) are both 0.5, and P(A)/P(B) cancel out. We’re left with P(B|A) only.”
This is all completely correct, you have proven that *evidence B* should increase the credence in A by a factor dependent on N and P.

The crucial point is you have more evidence than just B. It’s tricky to see what it is in this formulation, that’s why the ensemble analysis is so helpful. I described the extra evidence here on Novella’s blog: http://disq.us/p/2fiq0v

And here’s a compact version of the Bayesian calculation: http://disq.us/p/2fitxt5

I didn’t just paste it all here because there are some surrounding questions and answers there that may shed more light on the analysis.

29. Apologies, the first link is wrong, use https://theness.com/neurologicablog/index.php/multiverse-again/#comment-5292004589

Also, Philip talks about this evidence too, but in his article he doesn’t do the calculation that demonstrates why we should shift the credences towards the multiverse and away from a single universe, even though fine-tuning is not evidence of the multiverse.

This is what I think is at the root of the confusion between him and Steven.

30. Which first link? Did you lose a comment? The link still doesn’t seem to work — I’m not sure which comment you’re referring to. I think it may not load on first page load as there are too many comments.

As far as I can tell, Philip’s argument is completely different than yours and he rejects the inference for completely different reasons having more to do with personal identity (he thinks a mutliverse might explain why there are observers just like us, but not us specifically). But from trying to follow the thread between you and Philip Jones and others, I’m wondering if identity is key to your position too.

31. Hey DM,
sorry, yes, my previous comment is “awaiting moderation”. Briefly, I was saying I have more evidence than just “there is at least one IVF baby / universe with life / etc” if I am that baby /…

It’s tricky to see though, the ensemble technique makes it easier, but is not required. The first link should work but yes, it loads slowly and you might have to scroll up or down to get the comments to appear. The comment in the first link is just:
He knows:
E1 = at least one baby exists
E2 = this embryo got the lucky roll of the dice (fine-tuned)
E3 = this embryo existed/was picked to do the dice rolls in the first place

32. The comment in the second link http://disq.us/p/2fitxt5 is just this two line calculation that basically reconciles, imo, Philip’s and Steven’s positions (kind of):

P(E2|E3&M) = P(E2|E3&S) – independence, but
P(E3|M) = N * P(E3|S)
——-
P(E2&E3|M) = N * P(E2&E3|S)

I am not sure if this makes sense without the surrounding discussion, that’s why I wanted to give the links.

33. Hi RMT,

On your introduction of E3, I think it almost works but I have concerns. Open to correction as I may have misunderstood.

For this to apply to the actual multiverse argument, you have to conceive of the cosmos picking and choosing randomly from a population of possible worlds and deciding what to instantiate. E3 would then be the knowledge that this particular world is a possible world available for selection. I don’t think that is informative, I think it’s a tautology. A possible world is a possible world. E2 seems to imply E3 anyway, so once you know E2 I don’t think E3 is informative.

Pointlessly changing analogies, just to check we’re on the same page, and also just because it’s a bit more down to earth than the crazy IVF situation

Suppose
E1 = is at least one winning lottery ticket was sold.
E2 = 1,2,3,4,5,6 is a winning combination for which a ticket was bought
E3 = A ticket with 1,2,3,4,5,6 was bought

S = one lottery ticket was sold
M = many lottery tickets were sold

Fine tuning = each individual lottery ticket is highly unlikely to win

If I’m understanding your correclty, your analysis seems to have a problem

P(E2|E3&M) = P(E2|E3&S)

This does not seem to me to be correct. It works if we construe E2 as “1,2,3,4,5,6 is a winning combination for which a ticket may or may not have been bought”. The number of tickets sold doesn’t affect whether it is a winning combination. It does not work if we construe E2 as “1,2,3,4,5,6 is a winning combination for which a ticket was bought”, as the number of tickets sold factors in here (this is more or less your conclusion). But your E2 is
“this embryo got the lucky roll of the dice (fine-tuned)” which clearly implies “this embryo existed/was picked to do the dice rolls in the first place”, so I think we need to add “for which a ticket was bought”.

That said, I’m happy to accept your conclusion. I just think we can jump there straight away without all the steps and without making E3 explicit. Simplified, this is just the statement P(E2|M) = N * P(E2|S).

Does this reconcile Philip’s and Steven’s positions?

I think you’re more or less saying with this statement that fine-tuning is irrelevant, because it’s crazily improbable that this specific world would exist on S even without fine tuning. For our particular possible world to have a chance of existing, there must be many actual worlds and so many opportunities for this world to be one of them.

I doubt either Steven of Philip would go along with this, actually.

For me, and perhaps Steve, it seems to place too much significance on our world being special, perhaps relying on intuitions about identity I don’t share. It seems like being impressed that of all the particular spermatozoa that could have fertilised your mother’s egg, it was the one that resulted in you that succeeded.

34. ” Simplified, this is just the statement P(E2|M) = N * P(E2|S).”
I think you thought E2 = embryo with my DNA was picked AND dice roll for embryo with my DNA was successful
In my notation that’s not E2 but E3 AND E2. This might be confusing but I thought I needed to clearly separate the part that is independent of S or M (E2) from the exact event whose probability depends on S vs M (my embryo being chosen).

But you are right that we can do the calculation with just one step:
P(E3&E2|M) = N * P(E3&E2|S).

The identity stuff is tricky, that’s why the ensemble analysis is much cleaner I think. But the Bayesian way is ok too. We can defend it by saying that we must use all evidence available to us, and we know more than just E1. We have mounds of data that might seem irrelevant, but if it were truly irrelevant then it would still not be a mistake to include it, it just wouldn’t affect the final result. It can’t be illegitimate to use the maximum amount of evidence.

In one sentence the logic is: I know my total experience has been actualized in reality, since I am the one experiencing it. It is N times more likely to have been actualized if there are N universes instead of one (assuming it was very unlikely even on M).

35. Hi RMT,

“I know my total experience has been actualized in reality, since I am the one experiencing it. It is N times more likely to have been actualized if there are N universes instead of one (assuming it was very unlikely even on M).”

Take this back to the inverse gambler’s fallacy, where somebody witnesses a very improbable sequence of dice rolls (say 10 sixes in a row) on entering a casino. Fine tuning is just that such a remarkable roll happened. No fine tuning is just that an unremarkable roll happened.

Could you now help me please by distinguishing the above argument from the following?

I know that 3, 5, 3, 3, 1, 6 (the intention here is that this is unremarkable — on the off chance that this is your ATM PIN or something please substitute some other sequence!) has been rolled in reality, since I am the one witnessing it. It is N times more likely to have been rolled if there were N rolls instead of one. Therefore I should adjust my credence in M accordingly. And exactly the same thing would have happened if I had witnessed 6, 6, 6, 6, 6, 6, therefore fine tuning has nothing to do with it.

In my view, your argument only works if I buy that there’s something special about you (or about me) such that we should be very impressed with the amazing fact that we exist as opposed to somebody else. I don’t buy that, I’m afraid. Fine tuning, on the other hand, does seems special. Which is why fine tuning should cause us to increase our credence.

36. Hey DM,
“Could you now help me please by distinguishing the above argument from the following?

I know that 3, 5, 3, 3, 1, 6 (the intention here is that this is unremarkable — on the off chance that this is your ATM PIN or something please substitute some other sequence!) has been rolled in reality, since I am the one witnessing it. It is N times more likely to have been rolled if there were N rolls instead of one. Therefore I should adjust my credence in M accordingly. And exactly the same thing would have happened if I had witnessed 6, 6, 6, 6, 6, 6, therefore fine tuning has nothing to do with it.”
———

It’s subtle but this situation is fundamentally different because there is no observer selection effect. First, let’s make sure we completely specify your example. I am assuming what you had in mind was that if it was rolled N times you would be shown only one random roll, and not for example only shown 353316 if and only if it came up on one of the rolls and otherwise killed (turned into a non-observer), right?

In that case in your example
P(353316 | M) = P(353316 | S),

but in the IVF case, letting MTE = my total experience actualized ( = E3&E2 roughly speaking)
P(MTE | M) = N * P(MTE | S)

37. “In my view, your argument only works if I buy that there’s something special about you (or about me) such that we should be very impressed with the amazing fact that we exist as opposed to somebody else. I don’t buy that, I’m afraid. Fine tuning, on the other hand, does seems special. Which is why fine tuning should cause us to increase our credence.”
——

The logic doesn’t rely on us being impressed. Think about it this way: you think it’s legitimate to use the evidence that you are alive as opposed to being a bunch of random particles, or a rock, or a discarded embryo, right? Can you use the fact that you are specifically an intelligent observer and not a plant? Or a lizard? Or a chimp? Or a 5 month old baby? Or a nine year old who is intelligent enough but can’t yet think about Bayesian inferences? Or a person who can but wouldn’t want t? Why would some parts of your makeup be legitimate to use but others not?

38. Hi RMT and Alex,

It’s interesting that both of you now seem to be making very different points. I wonder if you still agree with each other. RMT’s argument is now that we need to account for our existence specifically, and that this should feed into the Bayesian analysis. Alex’s argument is mostly to stick with the original ratio argument, insisting that it’s begging the question to do the Bayesian analysis first and having this feed into the ratio argument, and an additional observation that there are more observers if M is true than if S is true and that this should influence us.

(1) RMT’s argument

RMT, you’ve taken my unremarkable dice roll analogy and turned it into a remarkable dice roll analogy, by saying that only this specific roll could have saved you from being killed. So, by again tying the dice to your existence, you’re confirming that your argument boils down to the belief that your existence, as opposed to the existence of someone else who could have existed in your place, is remarkable and needs explanation, increasing your credence in the multiverse. I do not have that intuition at all. You are impressed with your own existence the way you would be impressed to observe 20 sixes in a row. I don’t think you should be.

As to your question, there is no evidence that is illegitimate to use, but the evidence is only impressive (and so warranting explanation) if there’s something about it that singles it out from other possibilities such that an objective observer might have reason to be impressed. Unimpressive information can be attributed to chance — something had to happen, so why not that? The fact that you specifically are a sentient person as opposed to some other sentient person is not particularly impressive. I’m not even impressed that you are not a rock. The fact that this universe allows sentient people to exist, on the other hand, is impressive to me.

On whether I’m neglecting the observer selection effect, consider again ObserverCoin, the crypto coin to which we attribute a perspective. Suppose every ObserverCoin gets attributed a random ID (a UUID). Suppose I run the mining operation once, and the difficulty of mining is set such that I’m guaranteed to generate an ObserverCoin. Imagine the ObserverCoin printing it’s message to console as follows.

“Hello World! ObserverCoin b92ce94b-74c2-4562-9689-a7845271430a here! Wow, the chances of me being generated are 1 in 2¹²² (the number of possible UUIDs)! The ObserverCoin algorithm must have been run many many times for me to exist!”

From our perspective, this is wrong, as ObserverCoin b92ce94b-74c2-4562-9689-a7845271430a is entirely unremarkable as compared to the class of other ObserverCoins who might have existed instead. Even if it’s remarkable from that ObserverCoin’s perspective (because this UUID is special to it), this is only because this perspective is radically biased. We would be wrong to think we should infer M, and so is that ObserverCoin.

(2) Alex’s argument

Alex’s argument seems to be that the definitive tool to answer the question of whether fine-tuning should impact credence is the ensemble/ratio argument, and we can use this to assess the efficacy of other tools such as Bayesian analysis. To use Bayesian analysis to update the ensemble analysis therefore is begging the question.

This seems obviously wrong to me. I’m not begging the question because I have an ostensible Bayesian proof for my conclusion. What we have is two different ostensible proofs producing different conclusions. It’s not obvious to me why we should accept the ensemble proof over the Bayesian proof. But by allowing the Bayesian proof to update the ensemble analysis, we can reconcile the two and the contradiction is resolved.

Think about a similar situation with a toy problem. Should our knowledge that a coin is weighted impact the expected value of a coin flip? This is not strictly analogous to fine-tuning, it’s more of a demonstration of the problem with the “but that is exactly what is in contention here!” objection.

Let’s start without this knowledge, and do an ensemble analysis. There are two possibilities, therefore our ensemble is {H,T} and we have 50% expectation either way.

Now lets add the knowledge that the coin is weighted such that we should have a credence of 4:1 that it will come up heads, but without updating the weighting of the ensemble to reflect our new credences. We can’t update the ensemble to reflect this knowledge because “that is exactly what is in contention here!” and so we get the same, incorrect answer.

The analogy to fine-tuning is rather imperfect because you did update something about the ensemble in fine-tuning’s case (the fraction of worlds with observers), but as with the coin example you did not update the weighting between the different S-worlds and M-worlds as you should have.

“It’s also important to point out that we do in fact know something crucial; which is that the population of observers will be greater for the multiverse relative to a single universe.”

This isn’t China vs Chile, both of which exist. I think your observation only matters if the multiverse exists. If it doesn’t exist, then neither do those observers, and the chance that we could have been one of those observers is 0. There are 2¹²² possible ObserverCoins. That doesn’t at all suggest that I will run the mining operation lots of times. To have their possible existence weigh in favour of their actual existence is the same mistake as the Ontological Argument. You can’t posit something into existence.

• Also, RMT, the fact that you exist is just a very special case of fine tuning — the universe is set up just so that you specifically, against all odds, happen to exist.

If you did your ensemble analysis again but counted worlds where you existed instead of worlds which were fine-tuned, wouldn’t you get the same results and prove that your existence does not give reason to increase credence in M?

• Alex Popescu says

“This seems obviously wrong to me. I’m not begging the question because I have an ostensible Bayesian proof for my conclusion.”

You have a legitimate Bayesian proof that fine tuning modifies the odds that a single universe exists, and not that it does so for the ratios of civilizations case, as in the ensemble analysis. So we don’t have two contradictory proofs at all; it’s just a question of which is more applicable.

• You have a legitimate Bayesian proof that fine tuning modifies the odds that *only* a single universe exists. If we were 100% sure that only a single universe exists, then the correct ensemble analysis would not have any M worlds at all. You have to update the credences in the ensemble analysis for this reason.

• Alex Popescu says

No I meant that fine tuning tilts the S and M odds in the case where you are asking whether a (single) fine tuned universe exists. I didn’t mean that it tilts the odds for S in all cases.

It doesn’t in the scenario where we ask whether it is more probable that we were born in M or S (ratio between civilizations).

• Alex Popescu says

So notice there is nothing contradictory between the two statements:

1)Fine tuning doesn’t modify the odds that an observer is born in M or S

2)Fine tuning modifies the odds that a single observer (or fine tuned universe) exists in either M or S.

They are fully compatible, and so we can’t somehow use 2 to refute 1. Which you would be doing by modifying the odds ratio in the ensemble analysis on the basis of fine tuning.

• If the population of Narnia is 1 million, and the population of Lichtenstein is 50,000, it doesn’t mean that I’m more likely to be born in Narnia than Lichtenstein, because Narnia doesn’t exist.

You have to update the ensemble to reflect your credences about what exists.

• Alex Popescu says

This is just about whether fine tuning modifies the ratio; we’ve discussed this many times. I completely agree you with you that we have to update the credences because Narnia very likely doesn’t exist (notice the many times I said the same for the multiverse). That has nothing to do with the question at hand; we aren’t actually trying to know whether S or M is more likely.

• Fine tuning modifies the ratio because it modifies our credences. When we update the ensemble as we should, we get a different ratio. If I have effectively 0.000% credence that S is true (because of Bayesianism applied to fine tuning), then my model should be updated to reflect that and should have no S worlds in it — just as we should discount the probability of being born in Narnia because Narnia doesn’t exist. The ratio argument does not establish that we should not update our credences, because it insists on incorrect credences of 50% (or whatever they were before we learned of fine tuning). If I’m begging the question by assuming we should update the weighting in the model to reflect fine-tuning, then you’re begging the question by assuming we should not.

If you are sticking around I’d be interested in hearing whether you agree with RMT’s argument “In one sentence the logic is: I know my total experience has been actualized in reality, since I am the one experiencing it. It is N times more likely to have been actualized if there are N universes instead of one (assuming it was very unlikely even on M).”

• Alex Popescu says

“ Fine tuning modifies the ratio because it modifies our credences”

That is exactly what I am disputing. You argued that we should update our credence for the odds ratio in the civilizations case because of fine tuning, on the grounds that your Bayesian analysis proved that fine tuning modifies the odds ratio when we ask “what is the probability that a single fine tuned universe exists?”. I showed that one does not follow from the other.

“The ratio argument does not establish that we should not update our credences, because it insists on incorrect credences of 50%“

I’m sorry but this is just false; in fact I made the exact opposite point in my last post. I think you’re not fully understanding our position here, and this is causing a lot of headaches. I agree with RMT, but note that he’s just saying that N modifies the odds. Not that we should assign a certain prior to M, and not that we’re prohibited from concluding that M is very unlikely.

• It’s occurred to me that we’re losing sight of the fact that M and S are mutually exclusive (or so I say at least) as well as our credences that populations exist in the first place when we compare to China and Chile.

In China and Chile, I have 100% credence that both exist. If China has 10x the population of Chile, then my credence is straightforward — 10:1 odds I will be born in China.

In Narnia/Lichtenstein, suppose I have a 1% credence that Narnia exists and a 100% credence that Lichtenstein exists. Now it gets more complicated. I posited that Narnia had 20x the population of Lichtenstein. So what should my credence be now? Naively, I just discount the population of Narnia, so now Narnia effectively has 0.2x the population of Lichtenstein, and my credence should be 1:5 in favour of Lichtenstein. But I don’t think that’s right, as it means that no matter how unlikely I think a population is to exist, I can give myself a reasonable credence to be found in such a population if I make it big enough. I think the correct calculation is that I should first consider all possibilities and weight them accordingly. If Narnia exists, at a 1% chance, then I have a 20:1 credence in favour of Narnia. If Narnia doesn’t exist, at 99% credence, then I have a 0:1 credence in favour of Lichtenstein. So, just taking the probability that I should be in Narnia, it becomes 0.01 * 20/21 + 0.99 * 0, which is about 0.0095 — a very different answer.

In M/S, the two are mutually exclusive, since the question is whether the number of actual universe is =1 or > 1. Assume the number of observers in M is effectively infinite if you like, such that it has the maximal power to drown out the size of S’s population. Since they’re mutually exclusive, the sizes of the population are now irrelevant. To see why, do the above calculation (Narnia/Lichtenstein) again, and assume that my credence is 50% for M vs S, but that the probability that I’m born in S is 1 if S is true and the probability that I’m born in S is 0 if M is true. So now the probability that I am in S is 0.5 * 1 (if S is true) + 0.5 * 0 (if M is true). I’m left back where I started, with a credence of 50%. The only way the relative population sizes matters is if there is a chance that both kinds of worlds can co-exist.

• Hi Alex,

“That is exactly what I am disputing.”

Me too! So where does that leave us? If you assume A, then you can show A. If I assume ~A, I can show ~A. We disagree about how the ratio analysis should be conducted, so using the ratio analysis to prove anything is circular.

I have an independent argument from Bayesian analysis that fine tuning increases our credence in M. I’m not seeing an independent argument from you, other than that the size of the population in M weighs in favour of M, which you seem to walk back when you agree that the size of the population doesn’t matter (at least if the scenarios are indeed mutually exclusive).

>1)Fine tuning doesn’t modify the odds that an observer is born in M or S
> 2)Fine tuning modifies the odds that a single observer (or fine tuned universe) exists in either M or S.

OK, this is interesting, because they look contradictory to me. Other than the opposites (doesn’t modify)/(modifies), the differences are only that one sentence uses (an) vs (a single) and (is born) vs (exists) and then (either/or) vs (or). Those all seem synonymous to me

• For clarity, I realise you dispute that my Bayesian analysis shows what I think it shows. But I don’t understand your point. That’s why I’m trying to clear up why you think there is no contradiction between sentences (1) and (2).

• Alex Popescu says

Okay, (as you can see) I decided to keep posting.

“uses (an) vs (a single)”

This is the relative difference. They are different because 1 takes into account the selection effect, and 2 does not. 1 is saying, assuming that we could have been born in M or S (both are possible), is M or S more likely? We then add fine tuning (before and after) to see if it makes a difference between the M and S odds ratio. So answering 1 requires that we look at all possible observers.

2 however, asks if M or S, then how likely is a single observer to exist? Then after we’ve answered that, we take into account before and after fine tuning, to see if either case has a different odds ratio between M and S (it does). Why not the other way around (i.e. if single observer, then M or S)? Because the latter question has to take into account the selection effect; which is the exact same question as 1. If you still wanted to maintain that 2 was analogous to the latter question, but nevertheless distinct from 1, then you would have to maintain that there is something special about this single observer, so that only one such observer could have been produced even in an infinite M. Of course if you thought 2 was analogous to 1 the way I defined it; then it is true that fine tuning plays no role in 2 either (and they are the same).

Notice that both 1 and 2 stipulate by default that N matters. That’s because in 1 we have to take into account all possible observers, but in 2 it’s also true that N changes P. If N is very low in M, then P doesn’t make as much of an impact on the comparative odds between M and S, as if N were huge. That’s because if N were astronomically high, the chance of a single fine tuned universe existing in M is basically ~100% before and after P, whereas the odds shift enormously before and after P in S.

If N is very low, it approximates more closely the situation in S; so that in both M and S the odds ratios shift enormously, before and after P. Which is analogous to saying that P doesn’t matter as much (we need a discrepancy in how the odds ratios are affected by P; to say that P heavily matters).

So N matters for both 1 and 2. A tangential discussion is whether we should even take into account N on the grounds that there are absurdities regarding N being infinite. There are ways to address this critique of course. But even if the critique is legitimate (I tend to think it is; RMT thinks it is not); we have to argue that the ratios of M and S remain fixed by our priors. So that would be saying that if we think M is 10% likely, we should maintain a fixed probability of M to S of 1:10 odds, no matter the population of M. Since 1 and 2 entail by default that N has to matter; we would therefore have to reject the relevancy of 1 and 2. And we can only do that by denying the assumptions of 1 and 2.

What are these assumptions? That M (and S) are physically possible; meaning that it is possible that an observer could have been born in M. So we would have to argue that assigning a prior of .1 to M means that we think that the chance that M is possible is 10%. Therefore, we infer that M is not possible, and that we can’t reason to either 1 or 2. But notice this is just an argument about favouring M or S; it says nothing about whether P would play a role in the calculations of M. That’s because we base our likelihood of M being possible on the evidence/reasons we have (i.e. is it compatible with the standard model? Is there evidence for cosmological inflation? etc…).

To say that fine tuning should play a role regarding the likelihood of M being possible; is just to beg the question, since that assumes that fine tuning makes M more likely. I do dearly hope that helped; considering the length of the post (and many of my others).

• Alex Popescu says

Also this:
“I have an independent argument from Bayesian analysis that fine tuning increases our credence in M. I’m not seeing an independent argument from you, other than that the size of the population in M weighs in favour of M, which you seem to walk back when you agree that the size of the population doesn’t matter”

You misunderstand what I wrote. Our independent argument that fine tuning plays no role is the ensemble analysis itself. I gave a critique of your position (that we can use your Bayesian analysis to demonstrate that the ensemble analysis conclusions regarding fine tuning are bunk), which argued that because your analysis and my analysis are compatible; your argument can’t work. As I showed below, the point about N factoring in here is just an interesting side discussion; it’s not crucial to the conversation regarding whether fine tuning plays a role in the likelihood of a potential observer being born in either M or S.

So the ultimate question, which is “should fine tuning modify our credence in M” boils down to the question regarding a potential observer being born in either M or S (1); if you accept that N should matter. If it doesn’t matter to you, then the ultimate question just reduces to the question of how likely it is that M is physically possible. In which case, we still don’t take into account fine tuning; since that plays no impact. Why? Because by rejecting that N plays a role, you’ve also rejected 2; so you can’t now use 2 to reason that M must be physically possible.

• Alex Popescu says

I meant to write:
*you can’t use 2 to reason that M is more or less likely to be physically possible.

• Alex Popescu says

Also I wrote: “but in 2 it’s also true that N changes P.”
When I meant to say, ” but in 2, it’s also true that N changes the way P modifies the odds ratio between M and S”

Sorry about that! Hopefully it was more obvious what I mean to say from the context of the posts.

• Hi Alex,

Just a quick note that I’ve tried to follow your latest posts, for which I’m grateful, but as yet they’re not making sense to me. I haven’t given up on parsing them, but if you’re waiting for a response then that’s the delay.

I might mention some points of confusion in the meantime in case you can clarify.

What is the word “single” is doing or meaning in statement 1 vs 2? Is this supposed to be a solitary/unique observer, or do you mean a particular observer? Or an observer in a single universe?

Is statement 1 vs 2 about what you’re taking as a given and what you’re trying to predict? Like, what are the odds that I would exist on S vs M, and what are the odds of S vs M given that I exist?

What’s P? The probability of what? Sorry you’ve probably clarified this somewhere but it’s not easy to search for, and it’s a long conversation.

Similarly, when you’re talking about N, is that the number of universes in a multiverse or something else?

As I’m not following this I’m still unclear on what the difference is betweeen what I have concluded with my Bayesian analysis and what I would need to prove to establish that fine tuning should update our credence in M.

Alternatively to the above you could perhaps start again and explain the above in other terms. Again: I think I’ve shown that by Bayes’ Theorem, if I start with prior credence 50/50 for M vs P, then update with evidence of fine tuning, I end up with greater credence for M vs P than before, which seems to prove that fine tuning is reason to increase credence in M. Is this not what I’ve shown and if not why not, and if so then what are we disagreeing about? It’s not enough to show by other means that I should have reached a different conclusion (especially if I disagree with those other means), you ought to be able to point to some specific mistake.

One quick argumentative response to a point I think I do understand:

“Our independent argument that fine tuning plays no role is the ensemble analysis itself. ”

Well that’s just not independent (by which I mean: independent of the disagreement about how to apply the ensemble analysis correctly). When I apply it my way, I get the result I want. When you apply it your way, you get the result you want. I need some other argument which doesn’t depend on the ensemble analysis, such as I’ve asked for above.

That said, I’m aware that you’re not obligated to be my teacher. The point of continuing with this from your point of view would be if you allow any possibility that you might be wrong and you’re interested in exploring. That’s why I’m still in this, although to be honest I’m about 90% sure I’m right at this point. If you’re 100% sure that you’re right and I’m wrong, then I think from your perspective, for your own sake you should probably call it a day if you’re not enjoying it any more.

• Gah, I said M vs P a few times when of course I meant M vs S.

• Alex Popescu says

It appears I have you at a disadvantage; in that I’m 100% sure that I’m correct here. Alas, I think RMT has outfoxed us both; for he is 110% sure! I kid I kid.

In all seriousness; this is quite a complicated issue. Especially in the way that you and I have approached it. I would say that it’s unfortunate that we’ve approached it in the way we have (in the sense of trying to explain why one Bayesian analysis shouldn’t impact our credences for the ensemble). But that was the natural turn of our conversation it seems.

I think the semantics here are very tricky; the slightest missteps or differences in interpretation can wreak havoc. It would be very difficult for you to follow, through no fault of your own, even if you understood the meaning of relevant variables like P and N. Perhaps you can keep discussing this with RMT if you and him desire.

Best,

Alex

• Alex Popescu says

My apologies, I didn’t address your post more thoroughly. P is just fine tuning. And I disagree that I ought to be able to point out a mistake in your analysis. That’s because I think your conclusion that fine tuning modifies the odds ratio between M and S when we ask “what is the probability that a single fine tuned universe exists?” is correct. The problem I have with it, is that I think it answers the wrong question. Therefore, this is simply a matter of which analysis better captures/answers the question “should fine tuning modify our credence in M?”.

I think I showed in my posts above why the ensemble analysis better captures this, and why yours doesn’t. I apologize for not being a better communicator.

39. Alex Popescu says

1 does not entail that nothing should modify the odds ratio between M and S! Or that we shouldn’t update them on evidential grounds.

40. Hi DM,
Alex and I both think that the ensemble analysis is the cleanest way to do this, it lets us sidestep confusing issues of identity and indexicals. The Bayesian argument is a separate argument, which I find somewhat more intuitive in some regards and less in others.

You asked me to tell you the difference between one of my statements and a parallel statement about dice. It seems you misinterpreted my response as me changing your dice scenario into a different story with dying and such:
DM: “RMT, you’ve taken my unremarkable dice roll analogy and turned it into a remarkable dice roll analogy, by saying that only this specific roll could have saved you from being killed. ”
But that’s not what I did. RMT:

First, let’s make sure we completely specify your example. I am assuming what you had in mind was that if it was rolled N times you would be shown only one random roll, and *not* [irrelevant jibber jabber 🙂 ], right?

In that case in your example
P(353316 | M) = P(353316 | S),

but in the IVF case, letting MTE = my total experience actualized ( = E3&E2 roughly speaking)
P(MTE | M) = N * P(MTE | S)

• Hi RMT,

No, I understood what you meant about the dice. The argument about the dice was intended to show a flaw in your presentation of your argument. It was not intended as an argument with a correct conclusion, but an argument with a false one. I asked you to show the difference, and you did it by changing my story to reflect the difference. That’s perfectly fine, I’m not accusing you of misrepresenting me or misunderstanding the dice analogy. It makes the dice roll special by making it the only dice roll compatible with your existence. What your change makes clear is that they key point your argument rests on is that the existence of your particular perspective is remarkable, a point I reject.

“No, because in the ensemble there would be N times more Dmitriys living in a multiverse than Dmitriys living in a single universe”

The same is true of fine tuning. The point is that the improbability of generating a Dmitriy (or of fine tuning) doesn’t affect the ratio, so the existence of Dmitriy should not give us reason to increase our credence in M. Let’s suppose that the proportion of planets the aliens create that have a Dmitriy on it (i.e. someone exactly like you in all respects) is p.

M S
Galaxies 0.5 gazillion 0.5 gazillion
Planets 42*0.5 gazillion 0.5 gazillion
Planets w/Dmitriy p*42*0.5 gazillion p*0.5 gazillion
Odds 42 1

41. “If you did your ensemble analysis again but counted worlds where you existed instead of worlds which were fine-tuned, wouldn’t you get the same results and prove that your existence does not give reason to increase credence in M?”

No, because in the ensemble there would be N times more Dmitriys living in a multiverse than Dmitriys living in a single universe.

42. ADDENDUM: that ratio was under the assumption that as far as I know “God” had no preference between M and S; or, string theory and such don’t have an obvious preference towards M or S.

• “as far as I know”

Indeed.

Perhaps fine tuning should cause you to update your credences about God’s preferences.

• DM,
I am not sure if you are disagreeing with anything in the ensemble version of the calculation, because you quoted a table from my article, with which I of course agree (and yes, it makes no difference whether p refers to fine-tuning or the chance of making a Dmitriy):

M S
Galaxies 0.5 gazillion 0.5 gazillion
Planets 42*0.5 gazillion 0.5 gazillion
Planets w/Dmitriy p*42*0.5 gazillion p*0.5 gazillion
Odds 42 1

The first line represents the aliens’ preferences, in this case we believe they literally or effectively flipped a coin. The final line shows the credences a Dmitriy should assign to living in M vs S. So if you agree with this result, then it seems you should agree that:

– The posterior odds are modified from the prior odds by a factor N shift in favor of M.
– The shift is the same whether p = 1(no fine-tuning) or p = 1/10^229
– If for some theoretical reason the two scenarios are not wildly different in plausibility (for example, evidence from cosmology seems to give us some, but not overwhelming, reason for either inflation, in which case it predicts M with a huge N, or no inflation, resulting in S) then updating the credences to take the observer selection effect into account (doing the table) will cause us to assign only a tiny credence to us living in S.
– the only way p can affect the final credences is if p somehow factors into our estimates for the priors or N (which is not the logic of the inference to M that Steven, or anybody else I know, defends – the dispute is essentially over the *factor* by which the odds change, given N)

Finally, I think there is some confusion about the relationship between the evidence of Dmitriy’s existence and the ensemble analysis. The table just IS one clean way to account for the different probabilities of a Dmitriy existing on the two competing hypotheses, that’s why the table is counting Dmitriys.

The Bayesian, non-ensemble, argument is an alternative way to account for this evidence, we shouldn’t combine one way on top of the other somehow, that would be double dipping into the evidence.

• Hi RMT,

I think you’re missing my point.

What I’m trying to show is that you are advancing two positions that are incompatible with one another. One position you advance seems to suggest that the fact that your experience exists gives you reason to raise your credence in M. Another position you advance seems to suggest the opposite.

The former is “I know my total experience has been actualized in reality, since I am the one experiencing it. It is N times more likely to have been actualized if there are N universes instead of one (assuming it was very unlikely even on M).”

The latter is that your own fine-tuning argument shows that the existence of a Dmitriy gives you no reason to increase your credence of M, because “it makes no difference whether p refers to fine-tuning or the chance of making a Dmitriy”

Neither of these positions really accords with mine, both because you’re not that special (no offense). So I don’t think your existence gives you reason to increase your credence in M (rejecting position 1), and I do think it makes a difference whether p refers to fine-tuning or making a Dmitriy, because the former is remarkable and needs an explanation and the latter is not and can be attributed to chance alone.

43. Alex Popescu says

Hey DM,

“But I don’t think that’s right, as it means that no matter how unlikely I think a population is to exist, I can give myself a reasonable credence to be found in such a population if I make it big enough.“

Yes I made a similar argument in another forum. But note that this doesn’t attack the point that fine tuning doesn’t modify our credences. Rather, if true, you’ve only demonstrated that the number of population (N) plays no difference in our calculations. It doesn’t follow from that that therefore P should make such a difference.

• It shows that the relative number of observers in M vs S plays no role in our calculations iff M and S are mutually exclusive. That seems to be an important point, as you raised the number of observers in M as weighing in favour of M.

• Alex Popescu says

Right; which isn’t the same as saying that P (fine tuning) plays a role.

• Alex Popescu says

We all agree that M and S are mutually exclusive. Rather, it’s just that if we stipulate that N shouldn’t be taken into account, on the grounds that you mentioned (namely, that it leads to absurdities involving infinities); it follows that we don’t take into account N. But that doesn’t demonstrate that P (fine tuning) should play a role.

So it’s not an important point to the argument about whether fine tuning plays a role. But it’s an important point regarding whether we should prefer the M or S hypothesis.

• Ok, if you’re conceding that point, then great. Progress! Or did I misunderstand the point you were making?

44. Hi Alex and DM,
see my longish comment above. Alex, I think we probably agree on the points there, but let me know if that’s not the case.
—–
DM,
“But I don’t think that’s right, as it means that no matter how unlikely I think a population is to exist, I can give myself a reasonable credence to be found in such a population if I make it big enough.“
Alex
Yes I made a similar argument in another forum. But note that this doesn’t attack the point that fine tuning doesn’t modify our credences. Rather, if true, you’ve only demonstrated that the number of population (N) plays no difference in our calculations.
——

Priors are to some degree inherently subjective, but that doesn’t mean it’s rational or justified
to just “give myself” credences by “making” the population big enough. We don’t just adjust priors based on what posterior credences we want to get to, that’s not how rational Bayesian reasoning is meant to work.

In the multiverse case, N is not arbitrary, it’s determined by the theory, for example by how many metastable string vacua there are.

• Alex Popescu says

I completely agree; I was referring to the more general argument that DM invoked regarding infinities specifically. Where basically I made a similar point on your site to justify our needing to adopt a two tier process regarding how we treat low possibility vs low probability priors. I’ll have more to say about this in the email I plan to send you.

Ultimately, the point about discarding all reasoning that relies on N on the basis of infinity issues, is related to our preferences regarding M or S; it doesn’t impact the reasoning about fine tuning not playing a role. I wrote two posts above where I elaborated more on this. Basically, I think it would be illegitimate to use DM’s Bayesian analysis (the likelihood that a single observer/fine tuned universe exists in M or S) as evidence that we should use fine tuning to update our credences for the possibility of M.

Why? Because DM’s analysis depends for its soundness on M being possible, and on N making an impact on the degree that P modifies the odds ratio between M and S. But to adopt the two-tier possibility/probability dichotomy I spoke of, is to reject the assumption that N can make such a difference (because we’ve discarded N).

So DM’s point can’t work even if we adopt my hypothetical method of “getting away” with discarding reasoning based on N. Also, we have to use my method or something like it if we discard reasoning based on N; it’s not just one possible alternative among many. I show why in my posts above.

• > Priors are to some degree inherently subjective, but that doesn’t mean it’s rational or justified to just “give myself” credences by “making” the population big enough

I mean, we can make up any crazy theory we like. We shouldn’t be more inclined to believe the theory just because it has more observers in it. This justifies my treatment in my comment about China/Chile vs Narnia/Lichentstein vs M/S. It’s a total side issue unless you think I got anything wrong in my analysis of those comparisons, which was just supposed to show the importance of incorporating credences properly in ensemble analysis.

45. Hi Dmitriy,

> The Bayesian, non-ensemble, argument is an alternative way to account for this evidence, we shouldn’t combine one way on top of the other somehow, that would be double dipping into the evidence.

This is an interesting point, and prima facie a plausible objection. But I don’t buy it. I don’t think it’s really double dipping because just updating the populations doesn’t really change any relevant probabilities (as your table shows), and I think you have to make the relative frequencies of the populations match all the evidence and reasoning you have at your disposale before conducting the ensemble analysis. As far as I can see, this includes the Bayesian conclusion.

But I don’t really want to argue about this any more unless you think you have some knockdown argument in your back pocket.

What I desperately want from you at this point is just a clear reason why either my Bayesian conclusion is faulty or why it doesn’t disagree with your conclusion. Again, I don’t think the ensemble argument will do as all that would achieve is contradicting my conclusion without pointing out where I went wrong. Meanwhile I have already reason to believe the ensemble argument is mistaken (because it doesn’t adopt the Bayesian update).

As it happens, my earlier Bayesian calculation was incorrect. I incorrectly stated that the probabilty that a fine tuned universe existed was 50% when I meant to say that the probability of M vs S was 50% each. It doesn’t affect the outcome much. It changes a negligible probability to another negligible probability.

Here’s the argument again, from beginning to end, stating all my assumptions (at least those I’m aware of), and finishing with the conclusion I think you reject: “Fine tuning should cause us to update our credence in M). Please point out where you think I go wrong.

Definitions:
N: The number of possible universes in consideration, e.g. the string theory landscape
p: (fine tuning parameter): the proportion p of possible universes that support observers
S: the hypothesis that only 1 of the N possible universes is actual.
M: the hypothesis that many possible universes are actual
C_prior(x): Our prior credence in x, before engaging in analysis (about fine tuning)
C_posterior(x): Our credence in x, after engaging in analysis (about fine tuning)
P(A|B): The probability or credence of A given B.
O: The hypothesis that there exists a universe which supports observers (is fine tuned).

Assumptions for simplicity: (I’m stating more than I’m explicitly relying on in the argument, just want to be clear on where I’m coming from)
(i). On M, let’s just say that all possible universes are actual, and there’s one of each
(ii). S and M are the only alternatives and are mutually exclusive, i.e. P(S) + P(M) = 1
(iii). N >> 1, e.g. 10^500
(iv). Fine tuning is true, i.e. p < the single actual universe is randomly chosen from our population of N possible universes.
(vii). I am not special. The fact that I exist as opposed to some other observer who could have existed instead is not treated as significant. That is, I will not be using my feelings about the importance of my personal identity or my particular universe to reason. This is contentious, but I want to be absolutely clear if this is the one point we disagree on. In the following argument I think this will be reflected in that I mostly ignore E1 and work with O instead.

Empirical evidence:
E1: This universe supports observers.

Argument:
1. If C_posterior(M) > C_prior(M), then fine tuning should cause us to update our credence in M. (rephrasing)
2. C_posterior(S|O) = P(O|S) * C_prior(S)/P(O) (Bayes theorem)
3. E1 => O (obviously)
4. O (from E1 and 3)
5. C_posterior(S) = P(O|S) * C_prior(S)/1 (updating 2 in light of the fact that we take O to be true from 4)
6. P(O|S) = p (From (vi) and the definitions of p and O)
7. C_posterior(S) = p * 0.5, which is approximately 0 on (iv) (substituting values into 5)
8. C_posterior(M) = 1 – C_posterior(S), which is approximately 1 (from 7 and ii)
9. If 1 > 0.5, then fine tuning should cause us to update our credence in M (substituting values into 1)
10. 1 > 0.5
11. Fine tuning should cause us to update our credence in M. (from 9 and 10)

QED.

I expect that you will reject the argument because I’m not using E1 for more than deriving O, and so rejecting evidence I could have used.

But as I’ve managed to prove what I wanted without this evidence, this evidence could only count against my conclusion if it brought our credence back to 0.5 or below. That is what Philip Goff wants to say, actually — he doesn’t think we have reason to believe in a multiverse because it doesn’t explain why we specifically exist. He thinks that using E1 leaves us back at 0.5, right where we started.

But this seems to be the opposite of what you want to say — you want to say (well, some of the time) that fine tuning doesn’t increase our credence in a multiverse because the fact that we exist at all is reason enough whether or not fine tuning is correct. But this line of argument is contentious (as I’ve noted, you seem to reach the opposite conclusion yourself sometimes), so it is interesting that fine tuning works all on its own to increase our credence in M whether or not we adopt this contentions argument about your personal existence increasing credence in M.

As I don’t think our specialness should matter, I’m hoping against hope that you can point at something else. At least if you can’t, it can focus the debate on that alone and we won’t have to argue about the ensemble any more.

46. Sorry, some text was accidentally deleted from the middle of the assumptions

(iv). Fine tuning is true, i.e. p < the single actual universe is randomly chosen from our population of N possible universes.

• Ah, it seems to be the at WordPress is stripping out some text for some reason to do with using less thans and greater thans.

Allow me to rephrase.

Assumption (iv) is that fine tuning is true, i.e. p is much less than 1, e.g. 10^-9
I forget what Assumption (v) was, but I don’t appear to have used it so hopefully it’s not important.
Assumption (vi) is that on S, the single actual universe is randomly chosen from our population of N possible universes.

• Pretty sure assumption (v) was that C_prior(S) = C_prior(M) = 0.5

47. Hey DM, I appreciate you putting your argument in this precise way. There are two important problems.

A. 1 is not correct; to say “*fine-tuning* should cause us to update credences in M” is an arguably slightly more ambiguous way of saying that fine-tuning is evidence of M, which doesn’t mean C_posterior(M) > C_prior(M). Instead it means (denoting PM(N, p) = C_posterior(M) = P(M | ALL available evidence, not necessarily just O) ):

PM(N, p1) > PM(N, p2) for p1 < p2
—–

B. Your line of argument still can show that P(M | O) gets bigger if we decrease p from p2 to p1, but even then you still don't get QED because you would need to show that P(M | O) = = P(M | ALL available evidence, not necessarily just O).

48. DM,
this is not part of my objections to the logic of your argument, but here is my reason for why I would say B above not only relies on an unsupported assumption (which is enough to contest the QED, but is in fact unfixable.

I believe we also know :
– E3 = either M or, if S, this universe was the one out of N possible ones that for whatever reason turned out to be actual a 1/N chance event)
– this universe is fine-tuned, which you may or may not think is already entailed by E3 depending on how you understand the setup, either way is totally fine with me
——
Call all of that E.
Clearly E entails O, so if updating based on E gives a different result than updating on O, and it does, then it seems B is a big problem.

49. Sorry, I should have proofread better, it should be

…actual (a 1/N chance event)