Fine Tuning and the Multiverse

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Do Multiverse theorists commit the Inverse Gambler’s Fallacy when inferring the existence of many universes from the scientific evidence of fine tuning? According to Associate professor of Philosopbhy [at Durham University] and author, Philip Goff, the answer is yes they do. This is a claim repeatedly made by professor Goff in a number of discussions (here, here, and here), and one he reiterates through his personal blog posts – here and here. 

For those that may not be familiar with the Gambler’s Fallacy, it is the fallacious reasoning often associated with the compulsive gambler where they believe that their luck must be about to change because it is unlikely that they could be unlucky all evening. For example, the gambler at a craps table who has failed to roll a double-six believes that they are more likely to roll the lucky combination in their next roll, despite the probability of doing so being unaffected by the previous rolls. The example of the Inverse Gamblers Fallacy, as outlined by Goff here, is the case of a person who walks into a casino and witnesses someone rolling a double-six (on the first roll they witness) and then concluding that the person must have been rolling for a long time previously – or that there are many other rollers in the casino. In both cases, the gambler and the witness, the inference they draw is indeed an example of fallacious reasoning.  

The challenge for Multiverse theorists, Goff states, is to explain why the inference they make is not committing a similar [Inverse Gambler’s] fallacy. While I, myself, am not a proponent of the Multiverse – I am a proponent of a [single] Natural-Pantheistic Universe,  as outlined in The God Conclusion: AAtheism – From Rock Bottom to a God of My Own Understanding – I am interested in the fine-tuning problem and what I perceive as the tendency of theistic proponents of the fine-tuning argument (FTA) to misrepresent the naturalistic position. In a previous blog post I have outlined how the arguments made by Robin Collins and Luke Barnes, inadvertently, attack a strawman of what Collins calls the Naturalistic Single Universe (what I refer to as Brute Fact Naturalism).  

I will try to tease apart why I think professor Goff might, inadvertently, be doing something similar in his argument against the Multiverse hypothesis and how MV theorists are not committing the same IGF as outlined by Goff. I think it ultimately comes down to Goff attacking a strawman and inadvertently committing a bait and switch. 

Bait and Switch 

A recent reply to professor Goff’s tweet offers a useful jumping off point. 

https://twitter.com/BugRib/status/1534496238401335296?t=B6561IwAe2QSiEGtsuHQqA&s=19 

I believe the reason @BugRib has this feeling of seeing the argument, then not seeing it, is because professor Goff is inadvertently committing a bait and switch fallacy. He begins his analysis of the Multiverse theorist’s position by claiming they are inferring many universes from the fine-tuning evidence, as represented by his casino roller and Jane IVF analogies. However, his argument then proceeds along the lines of an argument from Bayesian inference. While attempting to infer many universes from the evidence of fine tuning simpliciter – let’s call it Plain Old Inference (POI) – would indeed be a case of the IGF, under Bayesian inference the direction of reasoning is reversed and the claim that an IGF is being committed doesn’t stand-up. This is because, under a Bayesian inference, the hypothesis is not being inferred from the evidence, the likelihood of the evidence is inferred from the hypothesis. Hence, why I believe @BugRib experiences something similar to the Rabbit/Duck illusion. 

In Goff’s defence, it may well be the case that there are some multiverse theorists who attempt to infer many universes from the evidence of fine tuning simpliciter, and Goff would be correct that these, specific multiverse theorists are committing the Inverse Gambler’s Fallacy. It’s also quite likely that some MV proponents don’t fully articulate their reasoning and make it seem like they are using POI to infer the existence of many universes. However, I don’t believe this to be the case for all proponents of the MV. In any case, it is preferable to try to articulate the steelman position of a position. When Goff’s argument moves to an argument from Bayesian inference, the MV hypothesis should be considered in this context and the IGF no longer applies.  

Selection Effect 

Goff’s misrepresentation of the MV hypothesis may explain his attempts to dismiss the selection effect. He is right in saying that the selection effect doesn’t resolve the IGF for the MV proponent by helping them to move from the weaker evidence to the stronger evidence. However, that is only the case when considering the MV hypothesis through the lens of POI. In the Bayesian context, the MV hypothesis gives us the weaker evidence that a single Universe is fine-tuned, while the selection effect is what guarantees that our universe is that Universe (or at least one of a possible number). 

Goff’s reference of Roger White’s Drunk Adam analogy might speak to certain cases of trying to setting aside a specific piece of evidence for the sake of weaker evidence, but it doesn’t appear to represent the case in hand. A better analogy might be that the presence of a virus increases the likelihood that someone in the room is sick. My feeling sick increases the likelihood that I have the virus. Goff’s “simpler” analogy of Jack and the butterknife doesn’t appear to involve any selection effect or necessarily speak to the case in hand. A stronger analogy might be that Jack finds himself in police custody. The likelihood of Jack being in police custody is increased as the number of suspects arrested by the police increases. Jack doesn’t infer (using POI) that there are many suspects, he uses Bayesian inferences and hypothesises that the more suspects that are arrested increases the likelihood of his arrest.  

This reasoning also applies to all the other Jane IVF and sleeping analogies when considered in the context of a Bayesian inference, as opposed to POI. 

Inferring Many Worlds – POI 

Having given some thought and consideration to the question of the IGF and inferring the MV from the FT evidence, I am inclined to think that an inference can be made, not from the fine-tuning evidence simpliciter, but rather from the insistence that fine tuning is improbable under naturalism, which is the claim made by theistic proponents of the fine-tuning argument such as Luke Barnes, Robin Collins, and Philip Goff.  

A key argument made by theistic proponents of the FT argument is that, under naturalism, fine tuning is improbable. In their respective papers, Robin Collins and Luke Barnes outline their reasoning as to how they arrive at a figure for the probability of the constants of nature being what they are, under the naturalistic hypothesis – what Collin’s refers to as the Naturalistic Single Universe (NSU). Similarly, Goff uses a number of analogies involving dice, to illustrate the improbability of fine-tuning under the naturalistic hypothesis. Their arguments rely on the idea that the initial conditions and the values for the constants of nature could have been different. Their arguments, I believe, commit the fallacy of counterfactual definitenes or the “what if?” fallacy – for fun we might call it the Casablanca fallacy: of all the values, in aa the range of possible values, in all the constants of the Universe, they had to be fine-tuned to mine. I have outlined why, in a previous blog post However, if we grant that the fine-tuning of the constants of nature are improbable, then we might be able to infer many universes from the improbability, not the fine tuning simpliciter.  

If we consider in what sense the constants of nature “could have been different”, we might consider the dice analogy used by Goff to illustrate the IGF. To make things simpler, let’s consider a single n-sided die, where we can increase or decrease the number of sides to represent the probability figures as necessary. 

Let’s start with the simple example of one, fair, six-sided die. The probability of rolling a 6 is 1/6. If we walk into a dimly lit casino and can only see an object with 6 dots on its face, if someone tells us that the probability of seeing the 6 was 1/6, we might infer from that, that there are 5 other sides to the die. This is the case for any n-sided die where we might infer n-sides. If there were no other sides to the die, we would ask in what physically meaningful sense could the number shown have been different and the probability of seeing the 6 dots be 1/6. In this case, each side of the die represents a Universe with it’s given constants, where only one is fine-tuned for life and the selection effect ensures we see the face of the die with the constants that are life permitting. Without some ad hoc hypothesis each side of the die would represent an actualised universe. 

It might be tempting to suggest that what we are seeing could be the output of a random number generator and that explains the probability, however, this analogy would represent a scenario where the initial conditions of the universe go from non-existence to existence. Given a causal chain to the random number generator, this would mean that the number generator are the initial conditions of the Universe. That would require them to be fine-tuned and if they are deemed to be improbable, we end up in a loop.