dimanche 5 juin 2022

Fine-tuning and Multiverses

There has been a discussion on Twitter regarding the view, expressed by Philip Goff, that the multiverse hypothesis is not a good explanation for fine-tuning (or, as he would probably say, cannot be inferred from the fine-tuning of our universe).

Short summary of Philip’s position

The constants of our universe seem to be fine tuned for life, which would be miraculous. How can we explain this? An apparently good explanation is a multiverse hypothesis together with a selection effect. The idea is that there are many universes with different values for constants, so the fact that some of them are suitable for life is not miraculous, and of course, we happen to be in such a universe.

According to Philip, an inference to this explanation is fallacious. It is an inverse gambler fallacy: seeing a double six when entering a casino, and inferring that there were many trials. The usual response is that it is not, because of a selection effect. If we are only allowed to enter the casino when a double six is rolled, we can infer that many trials were made before we were shown one. In the case of fine-tuning, we would not exist if the constants were not right, so there is a selection effect. But according to Philip, this move is fallacious.

After discussion, he reaches this case in a document published on his website (corrected on Twitter, I report the correction). It is supposed to be analogous to the problem of fine tuning with a selection effect, and the analog of an inference to many universes would still be fallacious:


Jane is the product of IVF. One day she discovers that the doctor who performed the IVF which led to her existence rolled dice to see whether to fertilise the egg, determining to do so only if she rolled a double six. The doctor only adopted this procedure once. Given that she exists, Jane concludes that other different doctors must have adopted this decision procedure in the case of many other potential IVFs.

The doctor rolling a dice corresponds to our universe “choosing” its physical constants, and the double six corresponds to the values of these constants that favour life. According to Philip, the final inference is fallacious.

“Her evidence is that a double six was rolled to decide whether her conception would go ahead. How many times [other doctors] have done this with respect to other potential conceptions has no bearing on how likely a double six was to come up in the case of her conception”

So, the existence of other unviverses cannot explain why the constants of our universe are suitable for life. The intuition behind this rejection can be given by comparing with a lottery case:


Jane buys a lottery ticket and wins. Given that she won, Jane concludes that many other people bought a lottery ticket as well.

This inference is absurd: what other people do does not change Jane’s probability of winning the lottery. This example does not have any selection effect, but the point is that it would be irrelevant. For example:


Jane buys a lottery ticket. Her enemy will kill her in her sleep if she loses the lottery. However, she wakes up and sees that she won. Given that she won, Jane concludes that many other people bought a lottery ticket as well.

The inference is still absurd with a selection effect. But are we in such a case with fine-tuning?

On the one hand, I am not personnally convinced that fine-tuning is a real problem (because I think it’s a theory-laden problem). But on the other hand, I think that Philip is wrong: were fine-tuning a problem, the multiverse would be a solution.

I will give three problems and a diagnostic for Jane3 case. Then I will return to the gambler fallacy and selection effect, and finally, briefly discuss whether the problem should be framed in inferential or explanatory terms, because this point came up in the twitter discussion.

First Problem

A first problem with Jane3 is that it’s analogous to the standard explanation for why the earth is habitable. The dice roll is analogous to the earth “choosing” its distance to the sun, its having a big satellite that stabilises its orbit, its being of the right mass not to lose its atmosphere, and all other unlikely factors that are necessary for life. This gives us the case:


Life is a consequence of the formation of the earth. The characteristics of the earth that make it habitable are very unlikely to occur. Given that life exists, we conclude that many other planets with different characteristics have been formed in the universe. We just happen to be on one with the right characteristics.

In this case, the inference does not seem invalid at all to me, and it’s almost if not identical to the standard explanation for why there’s life on earth that nearly everyone accepts. But in order to be coherent, Philip should conclude in this case too that:

“Our evidence is that the earth has the right conditions for us to exist. How many times the process of planet formation occurred in other solar systems has no bearing on how likely the right conditions were to come up in the case of the earth.”

So, knowing that other planets exist is of no importance, it has no bearing on our problem, because what we want to explain is why the earth in particular had the right conditions for life, and we’re not interested in other planets. Then we should reject the widely accepted explanation for why the earth is habitable.

Philip’s response is that the standard explanation for why the earth is habitable is acceptable because we already know that there are other planets. However, it would be fallacious to infer that other planets exist from the mere fact that there is life on earth. But I think that this response is not acceptable. In the lottery case, we know that other players exist, and this does not change the fact that the inference is invalid. So, either the existence of other planets has no bearing on why the earth has the right conditions for life (then the standard explanation fails), or it has (then it succeeds), and this does not depend on our knowledge that other planets exist. Rather, as I will argue, it depends on the exact question being asked and what we want to explain.

Second Problem

The second problem with Jane3 (noted by Keith Frankish in the twitter discussion) is that the fine-tuning argument for the existence of God or any kind of designer seems to be fallacious as well if we try to apply it here. But Philip accepts this argument in the case of fine tuning. Take the following case, which is just Jane3 with a different conclusion:


Jane is the product of IVF. One day she discovers that the doctor who performed the IVF which led to her existence rolled dice to see whether to fertilise the egg, determining to do so only if she rolled a double six. The doctor adopted this procedure only once. Given that she exists, Jane concludes that someone loaded the dice so that the result of the roll was a double six.

I don’t think that this argument is particularly persuasive. Jane’s existence was unlikely, but that’s no reason for her to conclude that the dice were loaded, unless we have independent reasons to assume that someone really wanted her to exist. If not, she might as well not have existed.

[Added part]
Is it somehow surprising that there was a double six given the odds? If Jane is very special, yes, otherwise, we could assume that the procedure was adopted thousands of times by other doctors before her conception, and Jane is among the few successes. For Jane to ask “why me in particular?” would be like for a lottery winner to ask “why me?”. There has to be a winner. Jane was lucky, that’s all.
[End of added part]

However, Philip accepts the argument for design in the case of fine-tuning, and I think that he is right to do so (if fine-tuning were a real problem, that is). So what goes wrong? Maybe we could adapt the case to make the design argument work.

The point where this case departs from the standard fine-tuning argument is that the stakes are low: Jane is not special, there’s no reason someone would want her in particular to exist, so there’s no reason to assume that someone loaded the dice. But God would want life to occur. If we want to get closer to a design argument, we must therefore adapt the case and raise the stakes.


Jane and Tarzan are the last humans on earth. They are the product of IVF. One day they discover that just before the apocalypse, the aliens that were in control of the earth at the time obliged the doctor that performed their IVFs to roll dice each time to see whether to fertilise the eggs, determining to do so only if they rolled a double six. The doctor only performed two IVF following this procedure. Given that they both exist, Jane and Tarzan conclude that someone loaded the dice so that the results of the roll were each time a double six.

This is now more persuasive because we would understand why someone would do that: the existence of Jane and Tarzan is desirable. And it’s unlikely that this desirable result would obtain without the trick. But what if we go back to the original multiverse argument and make the same change?


Jane and Tarzan are the last humans on earth. They are the product of IVF. One day they discover that just before the apocalypse, the aliens that were in control of the earth at the time obliged all doctors performing an IVF to roll dice each time to see whether to fertilise the eggs, determining to do so only if they rolled a double six. Doctors can only perform two IVFs in their career. Given that they exist, Jane and Tarzan conclude that many different doctors must have made trials before to succeed.

I dare say that the inference is much more plausible now, and that unless we have independent evidence that only one doctor could perform IVFs, this is the best explanation for the existence of Tarzan and Jane. It’s even better than the loaded dice explanation. Shall we object that “how many other doctors have done this with respect to other potential conceptions has no bearing on how likely a double six was to come up in the case of [their] conception”? This seems simply irrelevant: Tarzan and Jane would not exist if doctors had not tried hard.

So, not only the design argument does not seem much more persuasive than the multiverse argument in Jane3, but attempting to make it more persuasive also saves the multiverse argument.

One could think that the idea that there were many doctors, or that dices are loaded, is deduced from the premise that people at the time really wanted humanity to survive, and not from the premise that Jane and Tarzan exist. I don’t think this is right: the will of the doctors merely reinforce the inference, but it is not necessary. I will come back to this soon.

Third Problem

A third problem (noted by @ Disagreeable_I on Twitter) is that the intuitions we have in Jane3 seem to be sensible to details that are apparently irrelevant. This means that the case is not very robust, and we might suspect that it was fine-tuned (!) to make us accept a particular conclusion. We have seen with Earth and with TarzanAndJane that different alterations prompted different intuitions, but we can already see it with a case that is much closer, almost equivalent to the original:


Jane is the product of IVF.  She learns that the success of IVF depends on the co-presence of many contingent factors. Any trial has only one chance over a thousand to be successful, and gives rise to a different baby when it succeeds. A doctor can only make an IVF once, but parents can see many doctors. Given that she exists, Jane concludes that her parents saw many doctors before her conception.

This case is almost identical to the original Jane3, with the dice replaced by a more realistic probabilistic process. Another important difference is that the many trials of the conclusion concern specific parents. But although similar, the inference does not seem as problematic as before, for some reason. People born from IVF would be right to suspect that given the randomness of the process, many trials were made before the success that resulted in their existence. Why this difference?

One view mentioned before would be that it is the high stakes that explain that many trials were made, and not their existence: parents that do IVF want a child, so they are likely to make many trials. The same rationale could be given for JaneAndTarzan. But this does not do justice to the intuition that what needs to be explained is that it would have been very unlikely for Jane to came to life after only one trial, whereas her birth is no surprise if many trials were performed.

We can make another change to the case in order to remove this parasitic effect of stakes.


Jane is the product of natural fecondation. She learns that her father is almost infertile: any intercourse has only one chance over a thousand to result in fecondation (each intercourse resulting in fecondation will give rise to a different baby). Furthermore, Jane learns that her parents never really wanted to have a baby. Given that she exists, Jane concludes that her parents probably had many intercourses, and that one of them accidentally resulted in her fecondation.

The inference still seems valid: it would be a miracle for Jane to exist if her parents only had one intercourse, so an explanation is that they had many. And this conclusion is not reached from the fact that they really wanted a child, but only from the fact that Jane exists. Indeed, Jane only has evidence for one intercourse, the one that resulted in her existence. She has no independent reason to assume that her parents had others. Only her existence and the infertility of her father favours this hypothesis.

This case is relevantly similar to the case of fine-tuning: the laws of nature as described by contemporary physics are “almost infertile”, they need very specific constants to produce life, and yet we exist. One explanation is that there were many “intercourses” with the same laws, but different constants.

Philip argues that in this case, the relevant evidence is not Jane’s existence, but her mother’s pregnancy. There’s something right in this diagnostic: relevance matters. But it cannot be the whole story, because the mother’s pregnancy can be deduced from Jane’s existence, and so, if we can infer many trials from pregnancy, we can also infer many trials from Jane’s existence. So, why wouldn’t it work in the original case too?  Is the fact that the conclusion concerns only Jane’s parents the main difference? But then in the original case too we could infer that many trials were made by her parents, with different doctors.

The most relevant difference seems to be this: in the original case, we only assume that the weird dice procedure was adopted in the case of Jane’s birth. It could be used elsewhere, but it’s not necessary. In the last case, and, actually, in all cases where the inference seems valid, we assume that a probabilistic procedure is necessarily involved in all possible members of a relevant set of possibilities (all planet formations, all the IVF that could have occurred before the apocalypse, or all the fecondations from Jane’s parents). Actually, the sole replacement of dices with probabilities associated with IVF does this, the relevant set being IVF born children: by natural necessity, these children are subject to a random process (the set of children born from the dice procedure is more ad-hoc, whereas IVF does not have to be chancy by definition, but it happens to be).

Note in passing that in the case of fine-tuning that interests us, it seems fair to assume that the probabilistic procedure (selection of physical constants) is necessary rather than contingent, that is, that it is involved in all possible universe creations (even if there’s only one universe).

We can now see how Jane3 is specially designed to prompt anti-multiverse intuitions: it insists that the dice procedure is only contingently attached to specific instances of fecondation that have nothing else in common (not even being performed by the same doctor). My diagnostic is that this tiny difference changes the question being asked, or what is relevant for the explanation and what needs to be explained.

The Diagnostic

I will frame my diagnostic in terms of explanation, because I think that this is the appropriate setting: we are looking for an explanation to fine-tuning (I will discuss Philip’s inferentialist approach in the last section, but we can get to the same results). What happens in all our cases is that someone infers an explanation from something that seems unlikely.

An explanation is a response to a why question. A why question is generally analysed by means of a contrast class: why X rather than Y? We could add that an explanation generally takes for granted a background context C that remains fixed in counterfactual reasoning (whether X or Y is the case), some kind of “all other things being equal” clause. The explanation normally takes the form of a counterfactual: an answer “because Z” could be analysed as: “given C, if Z had not been the case, then we would have had Y instead of X (or X would have been less likely)”.

Example: “why did my house burn (rather than not)?”
Answer: “because the candle fell”, analysed as: “all else being equal (there is oxygen in the air, this is a wooden house, etc.), if the candle hadn’t fallen, your house wouldn’t have burnt”.

My diagnostic is that the contrast class is different in all cases, which is why the inference is valid in some cases and not in others. The contrast class is induced by the presentation of the case.

The original Jane3 case prompts us to ask “why does Jane exists rather than not?” (this is at least the question implicit in the objection provided by Philip), and the LoadedDice case as well. The problem with this case is that this is a weird question to ask. There is no answer to why a random process gives a certain result, no relevant counterfactual to give: it’s like that.

The Earth case prompts us to ask a different question: “why is life possible at all?” The contrast class is not “why the earth in particular has these characteristics rather than not?” but “why is there a planet with these characteristics in the universe (which happens to be the earth) rather than none?”. The right answer is “because there are many planets with different characteristics” (had it not be the case, habitable planets would probably not exist). Only then can we infer, by means of the selection effect, that the earth must be one of these possible objects, because we’re no more troubled by the impossibility of its existence.

We saw that raising the stakes makes for a more convincing case. What raising the stakes does is switching the contrast class of the explanation. In JaneAndTarzan, what interests us is no more why Jane and Tarzan in particular exist rather than not, but rather why some people (who happen to be Jane and Tarzan) exist rather than nobody. What stakes do is point to what is special about the instance we wish to explain, and this gives us the right contrast class. In the original case, Jane is only special as the person on which the case focuses. On the other hand, Jane and Tarzan are special qua last survivors of an apocalypse.

Finally, specifying that all members of a class of object must necessarily be subjected to a random procedure also gives us a potential contrast class, which are these objects. The question can then become: why is there an instance of this class rather than none? Refusing to attach a random procedure to a specific class of objects, as Jane3 does, dissuades us from using this constrast class.

Depending on what question is asked, an inference or explanation can be valid or not. If the question is “why Jane in particular exists rather than not?” then no explanation is really valid. If the question is “why an IVF born child (Jane) exists rather than none?” then many explanations become relevant: perhaps it’s God, or some kind of design, or perhaps it’s many trials, and unless we have evidence that there was only one trial, invoking God should probably be avoided (why would God want life to occur in our universe rather than in any other?). And the same goes if the question is “why do these parents have a child (Jane) rather than none?”.

Interestingly, the design explanation and the multiverse explanation are relevant for exactly the same kind of questions. The questions where they are not relevant are indexed to particular instances of random processes and their outcomes. These questions are contrived and uninteresting, the only response being “it just is, it’s random”. Philip forced us to answer this kind of uninteresting question to make his case against the multiverse, in particular because his setting implies that the random process is only contingently attached to particular instances.

The problem of fine-tuning is not this kind of uninteresting question. The process of selection of constants is presumably involved not only with our universe, but with all possible universes. We do not want to know “why this particular universe has the right constants rather than not?”. What we want to know is why a universe suitable for life is possible at all given the apparent unlikelihood of such a universe, that is, “why a universe of this kind (ours or any, really) exists rather than none”. And the multiverse hypothesis gives us an adequate explanation.

Gambler Fallacies, Selection Effects and Rigidity

What was said in the previous section can be shown by providing very abstract cases and making variations that will imply a relevant contrast class. Take for example:


X is an object of type A. Instances of A are necessarily the result of a random process of type P with a very tiny probability of success. Given that X exists, we infer that many processes of type P occurred, and not just one.

The inference seems valid in this abstract setting. It doesn’t seem right to say “how many processes of type P occurred has no bearing on the likelihood of this particular instance”, because we are interested in X only as an instance of a A, and had not many processes occurred, there would probably be no object of type A. So the inference from “there is a A” to “there are many Ps” is valid.

Now moving to a case where the procedure is not necessary:


X is an object of type A. Instances of A can be produced in many ways, but X in particular was the result of one specific random process of type P with a very tiny probability of producing an object of type A. Given that X exists, we infer that processes of type P occurred many times.

In this case, is the inference valid? If the contrast class is still A, then many occurrences of P do not really explain that there are As because had these occurrences not been there, there would still be other As. But I think that with this presentation, we are drawn into thinking that the relevant contrast class must be X alone. “There is a A” is not the right starting point for the inference, because there is no strong link between As and Ps. However, there is a strong link between X and an instance of P. Now the inference could be valid in the sense that many P increase the likelihood of existence of the particular P that led to X. This amounts to introducing an artificial class of objects to which X belongs: the products of instances of P, asking why there are instances of this class rather than none. But this class is ad-hoc, and the contrast class “why X exists rather than not” is more natural.

But what about the lottery case in the introduction? And what about the inverse gambler fallacy? They seem to be instances of Abstract1: my winning the lottery is an instance of lottery winning, the result of a random process of type buying a ticket with tiny probability of producing a winning. But given my winning, I do not infer that many people bought a ticket. The double six I see is an instance of successful dice roll, the result of a process of type dice roll with tiny probability of success. But given the double six, I do not infer that many dice were rolled. What goes wrong?

In these cases, the problem does not come from an induced contrast class, but from an induced background context. The fact that I bought a ticket is part of the background, it is kept fixed in the inference. So, many people buying a ticket does not change the probability of me buying a ticket. Same for the fact that I saw a dice roll just after entering the casino.

[Edited part]
What is part of the background context or not depends, I would say, on the way our relevant evidence is identified. In particular, it seems, from the lottery and casino example, that when the random process we are interested in is causally related to us (its reference is fixed) in a way that is independent of its outcome, then the existence of this process instance will be part of the background context. We rigidly refer to it, so to speak. This forces us to ask questions about this instance in particular. So, for example, I would buy a lottery ticket come what may, my causal relation to the lottery ticket is independent of whether it is a winning ticket, the outcome. The same goes for the dice roll I see in the casino. But if we add a selection effect, if I am only allowed to enter in the casino when a double six is rolled for instance, then the specific instance I see is causally related to me in a more complex way that crucially depends on its outcome, the result of the roll. The reference can be fixed only after the outcome. Then the rigid reference is not reference to the particular instance of random process, but rather to a type or a property: what is fixed “in all possible worlds” of the explanation is not the particular object that constitute my evidence, but the fact that the object, whatever it is, with which I will be in contact will correspond to a particular outcome, if I am in contact with an object at all. Not all selection effects have this result though. If someone kills me or not depending on whether I won the lottery (as in FatalLottery), or if someone shows me one particular roll only if its result is a double six, I am still causally related to a specific lottery ticket or dice roll independently of its result: this is how the instance is first identified and the reference fixed.

In the special case where I am myself the product of a random process, the reference is not fixed independently of its outcome. There can be no reference (by me) to the process prior to its outcome.

Taking this into account, we can propose the following case:


Random processes of type P have a very tiny probability of producing an object of type A. We came to identify and be interested in a particular process p of type P by means of causal relations that are independent of the fact that p produced an object of type A. We observe that p produced X, an object of type A. Given the existence of X, we infer that many other processes of type P occurred as well, and not just p.

This is an invalid inference. Since the existence of p is part of the background context and since X is identified as the product of P, and not as any A, the contrast class that is forced upon us is “why p produced X rather than not?” and the number of instances of P becomes irrelevant. (In Abstract2, rigid reference to a process was induced by the relevant contrast class. In this case, it is the other way around.)

Abstract1 now appears to be vague, and we could amend it to reflect the fact that no particular instance of P was referred to before we could know whether it would produce an X or not.


X is an object of type A. We came to identify and be interested in X by means of causal relations that crucially depend on the fact that X is a A. Instances of A are necessarily the result of a random process of type P with a very tiny probability of success. Given that X exists, we infer that many processes of type P occurred, and not just one.

In this case, the inference is valid.

The main factor of rigid reference is whether random processes are merely identified qua generators of a general class (AbstractNonRigid) or by means of reference to particular objects (AbstractRigid and Abstract2). When a process is not attached to a class of object, but only contingently to its instances, as in Jane3, the process can only be identified by means of particular objects. This is the trick Philip used because he wanted us to refer rigidly to a particular random process (to our universe), even though he had to depart from the AbstractRigid case because of some criticisms. When the random process is necessarily attached to a class of object, as in Lottery, Earth or Jane3bis, both kinds of identification are possible, but the right kind of filter effect removes rigidity.

What kind of case is the case of fine-tuning? I think that the answer is clear: it is an AbstractNonRigid case. We came to identify and be interested in our universe not by some direct acquaintance with an instance of selection of physical constants, independently of its outcome, but by acquaintance with what this universe produced after the constants were selected. Our capacity to refer to the universe crucially depends on the fact that it is suitable for life, so the right kind of selection effect is present. This excludes AbstractRigid. Furthermore, the relevant random processes are identified theoretically, qua hypothetical constants generators attached to the class of objects to which our universe belongs. They are not contingently attached to our universe in particular. This excludes an Abstract2 case.

Hence, we should not rigidly refer to our universe in our reasonning (assuming its existence in the background context), but only to the kind of properties that it features, which is what we are really interested in: life, etc. This makes it possible to concentrate on the contrast class “why is is there a universe with the right constants for life rather than none” instead of “why does this particular universe have the right constants for us to be there rather than not”. The same goes in many of the cases analysed before: JaneAndTarzan, Earth, etc.
[end of edited part]

Explanations or Inferences?

All this is framed in terms of explanations, but Philip complains that we should think in terms of inferences: from our evidence that we exist, or that the constants in our universe have such values, can we infer that there is a multiverse, using Bayesian inferences?

I should first say that I’m not convinced at all that the problem should be couched in terms of Bayesian inference. We could say that A explains B just in case prob(B|A & C) > prob(B|~A & C), but this is just an old model of explanation that has been abandoned because it suffers from the problem of relevance and from the problem of symmetry (our barometer could explain a storm with this account). Explanations are not simple deductive relations: they are better analysed by a counterfactual, as already explained.

Yet it can still be instructive to understand what is going on from a purely inferential point of view, without bothering us with these problems. For this purpose, we can take our three abstract cases. Note that in Bayesian inferences as well we have to condition on a background context (the C in the formulas of the previous paragraph). Also note that it is legitimate to deliberately remove part of our knowledge from the background, which is done for example to account for old evidence in favour of new theories.

In AbstractNonRigid, the likelihood of having a A given many processes of type P is clearly higher than if there’s only one P, so a Bayesian inference to many P is valid. The likelihood of our direct evidence X is increased as well, because the likelihood of occurrence of the particular process leading to X is increased. We should not assume that the existence of this process is part of the background context (in the fine-tuning cases, we should not assume as background that our universe exists, as is often done in the literature in order to block the multiverse hypothesis).

In AbstractRigid, the induced interpretation is that a particular instance of P, which happens to produce a X, is part of the background context (its likelihood is 1). This makes the inference from X to many processes invalid, as expected, because given that P is instantiated, other Ps will not increase the probability of our evidence.

In Abstract2, which corresponds to Philip’s Jane3, the probability of having a A can be marginally increased by many Ps, but the natural interpretation is that the process leading to X is part of the background context, so the inference from X to many Ps is invalid too for the same reasons.

So, we get the same right results. As argued in the previous section, the problem of fine-tuning is an instance of AbstractNonRigid, and therefore the inference from our evidence to the multiverse is valid.

So, despite framing the discussion in terms of explanations, I think that we can retrieve the same results by focusing on Bayesian inferences. The interest of talking in terms of explanations is only that it makes clear that before making an explanatory inference, we must assume a background context and a relevant contrast class, and these are sensitive to the kind of counterfactual/causal statement that is involved in the explanation, something that pure Bayesian inference cannot capture.

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