A startling discovery of recent decades is that the laws of physics are fine-tuned for the possibility of life. That is to say, for life to be possible, certain numbers in physics had to fall in a certain narrow range. Some scientists and philosophers try to explain this by postulating an enormous number of universes, exemplifying a huge range of different numbers in their physics, making it statistically likely that at least one will have the right numbers for life by chance. The trouble is that this kind of inference is fallacious; specifically, it commits the inverse gambler’s fallacy.
Here’s the classic example of the Inverse Gambler’s Fallacy (IGF):
You walk into a casino and see someone roll a double six. You infer that there must be lots of people playing in the casino tonight, as it’s more likely that someone will roll a double six if there are many players.
This is a fallacious inference. You’ve only observed one roll, and postulating many other rolls in the casino does not make it any more likely that the roll you observed would be a double six. The challenge for the multiverse theorist to explain why the inference they make does not commit the same fallacy. We have only observed one universe and the postulation of many other universes does not make it any more likely that the universe we have observed would be fine-tuned.
The answer standardly given is that the fine-tuning case, in contrast with the classic IGF case, involves a selection effect: we could not have observed a universe that was not fine-tuned, whereas we could have observed someone rolling something other than double six. This clearly does mark a difference to the classic IGF case. The trouble is when we introduce an artificial selection effect into IGF cases, the fallacy doesn’t go away. Consider the following case:
Jane was conceived through IVF. One day she discovers that the doctor who performed the IVF had a nervous breakdown around the time, and as a result rolled dice to determine whether she would fertilise the egg, committing only to do so if 5 sixes were rolled. The doctor only rolled the dice once, and subsequently got some therapy and never did this again.
There is a selection effect here. Jane could not have discovered that the doctor failed to roll all sixes, because, if the doctor hadn’t rolled all sixes, Jane would not exist. And yet it would be fallacious for Jane to explain the remarkable improbability of her birth with the following hypothesis:
The Many Doctors Hypothesis: Many IVF doctors have been rolling dice to decide whether to fertilise eggs, in most cases failing to get the right numbers to proceed.
This would be another case of the inverse gambler’s fallacy: Jane’s evidence is that her doctor rolled five sixes, and the postulation of many other doctors rolling dice does not make it any more likely that her doctor would roll five sixes. If the multiverse theorist wants to defend the inference from a fine-tuning to the multiverse, they need to tell us why their inference is relevantly different to Jane’s clearly fallacious inference.
More Detailed Analysis
Part of what is objectionable about IGF cases, as pointed out by Roger White in his classic article on this, is that it involves setting aside a specific piece of evidence – this universe is fine-tuned – for the sake of a weaker piece of evidence – a universe is fine-tuned. White offers a nice example to illustrate how problematic this can be:
Suppose I’m wondering why I feel sick today, and someone suggests that perhaps Adam got drunk last night. I object that I have no reason to believe this hypothesis since Adam’s drunkenness would not raise the probability of me feeling sick. But, the reply goes, it does raise the probability that someone in the room feels sick, and we know that this is true, since we know that you feel sick, so the fact that someone in the room feels sick is evidence that Adam got drunk. Clearly something is wrong with this reasoning. Perhaps if all I knew (by word of mouth, say) was that someone or other was sick, this would provide some evidence that Adam got drunk. But not when I know specifically that I feel sick. This suggests that in the confirming of hypotheses, we cannot, as a general rule, set aside a specific piece of evidence in favor of a weaker piece (White 2002: 264).
Following Peter Epstein, we can call the general rule White is expressing here ‘the Requirement of Total Evidence,’ or RTE. As Epstein and others have noted, RTE does have exceptions. Take the example of the inference from the existence of complex organisms to the hypothesis of evolution by natural selection. The Darwinian hypothesis does not raise the probability that certain specific animals, e.g. Tony the Tiger, will come to exist, and hence if we take very specific information about which particular animals exist as our evidence, then we will not get evidential support for the Darwinian hypothesis.
I propose that we are permitted to violate RTE if doing so moves us from a fact that isn’t surprising to a fact that is. How do we define when an event is ‘surprising’? Here White adopts Paul Horwich’s account, which he describes as follows:
The crucial feature of surprising events seems to be that they challenge our assumptions about the circumstances in which they occurred. If at first we assume that the monkey is typing randomly, then her typing “nie348n sio 9q” does nothing to challenge this assumption. But when she types “I want a banana” we suspect that this was more than an accident. The difference is that in the second case there is some alternative but not wildly improbable hypothesis concerning the conditions in which the event took place, upon which the event is much more probable. On the assumption that the monkey is typing randomly, it is just as improbable that she types “nie348n sio 9q” as it is that she types “I want a banana.” But that the second sequence is typed is more probable on the hypothesis that it was not merely a coincidence, but that an intelligent agent had something to do with it, either by training the monkey or rigging the typewriter, or something similar. There is no such hypothesis (except an extremely improbable ad hoc one) which raises the probability that the monkey would type the first sequence. Of course by P1, the human intervention hypothesis is confirmed in the case of “I want a banana.” So what makes the event surprising is that it forces us to reconsider our initial assumptions about how the string of letters was produced (of course someone who already believes that the typewriter was rigged should not be surprised). (White 2000: 270)
The existence of intelligent organisms is surprising to a pre-Darwinian atheist, because the existence of complex organisms is much more likely on a design hypothesis than on the chance hypothesis that organisms came about through random interactions of particles. Of course, Darwin gave us an alternative to both chance and design: natural selection.
Whilst the fact that there are complex organisms is surprising, the fact that these specific organisms exist (e.g. Tony the Tiger) is not surprising. And that’s because there is no non ad hoc hypothesis that raises the probability that Tony the Tiger exists (the hypothesis that there is a designer who specifically wanted to create Tony the Tiger would raise the probability that Tony exists, but that’s ad hoc in the way that a designer who wanted a monkey to type “nie348n sio 9q” would be ad hoc). This, I suggest, is why it’s permissible to violate RTE by moving from Tony the Tiger (and a long list of all of the other particular organisms that exist) exists to complex organisms exist.
I propose, then, that we qualify RTE as follows:
RTE*: It is not permissible to set aside a piece of specific evidence in favour of a piece of weaker evidence, unless in doing so one moves from a piece of evidence that is not surprising to a piece of evidence that is surprising.
Turning to the fine-tuning, is it surprising that this universe is fine-tuned? One might think: ‘No, because there’s nothing special about this universe, as opposed to any other possible or actual universe.’ I see how that can seem to make sense at a very intuitive level. But the fact that our universe is fine-tuned is surprising in the sense defined above. This is because when we run the Bayesian fine-tuning argument, everything but the values of the constants is in the background information of the calculation. And so it’s already assumed that this universe exists. Against that background, the evidence that this universe is fine-tuned is more likely on design/teleology that it is on a chance hypothesis. This explains why it is not permissible to violate RTE in the fine-tuning case by moving from this universe is fine-tuned to a universe is fine-tuned: because this universe is fine-tuned is in itself surprising.
This at any rate is my attempt to formulate a theoretical principle to explain why IGF is fallacious. I may be wrong, and I would welcome potential counterexamples. But the point I am more confident about is that we should expect the correct theoretical principle to rule that the inference from fine-tuning to a multiverse is fallacious, given its similarity to the clearly fallacious Jane case. Or to put it another way, the correct explanation of why IGF is fallacious is unlikely to have anything to do with the presence of a selection effect, given that the presence of a selection effect in the Jane case does not undermine the fallacy.
Response to Quentin Ruyant
Quentin Ruyant has just written an extensive blog post responding to this argument, with lots of very interesting thought experiments. It’s a long piece, and time constraints don’t allow me to answer of all of his objections, but I’ll give here my reaction to some of his thought experiments, and then use that to develop in more detail my analysis of the IGF.
[I have made some edits after initial publication, in response to Tweets from Quentin.]
Quentin claims that is that it would be equally fallacious for Jane to infer that the dice were loaded, which would seem to imply the IGF applies not only to the inference from fine-tuning to the multiverse but also to inferences from fine-tuning to design or teleology (for those who don’t know, I reject the omni-God hypothesis but think the fine-tuning supports something god-ish, e.g. the simulation hypothesis, or Nagel-style teleological laws). That seems to me wrong. Suppose the doctor rolled all five dice for an hour, determining only to fertilise the egg if all sixes came up every single time. This is wildly improbable and it would surely be rational for Jane to infer that the dice must have been loaded.
Quentin then tries out a twist on the Mary experiment which is supposed to be analogous to the inference from fine-tuning to the multiverse:
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 would say that Jane and Tarzan’s inference does not commit IGF because it does not violate RTE*. It is not surprising that Jane and Tarzan were conceived, as there is no non ad hoc hypothesis that would raise the probability of Jane and Tarzan in particular being conceived. But it is surprising that some humans were conceived on the hypothesis that there are few doctors. My account thus allows Jane and Tarzan to set aside the specific evidence that Jane and Tarzan exist in favour of the weaker evidence that some humans were conceived.
Here’s another thought experiment Quentin raises:
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.
I would say that in this case, Jane* is not committing IGF because she has some observational data that is made more likely by postulating many doctors, namely that her mother got pregnant. This contrasts with the real-world fine-tuning case, in which our observational evidence, namely that this universe is fine-tuned, is not made more likely by the existence of multiple universes.
Quentin expects this response, based on our Twitter discussion, and objects as follows:
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.
It should now be clear that Quentin’s point that Jane*’s existence entails that her mother was pregnant is beside the point. The point is that Jane* doesn’t need to violate RTE* in order to get a piece of evidence that would support a many doctors hypothesis, because she can take as evidence that her mother got pregnant. However, the Jane in my original thought experiment described above would need to violate RTE*: the many doctors hypothesis would not raise the probability that Jane’s mother got pregnant, and hence in order to try to get evidence for the many doctors hypothesis, Jane would need to set aside the specific evidence that her doctor rolled all sixes to decide whether to perform IVF in favour of the weaker evidence that a doctor rolled all sixes to decide whether to perform IVF, and this would not involve moving from a piece of evidence that isn’t surprising to a piece of evidence that is surprising (because the evidence that her doctor rolled all sixes to decide whether to perform IVF raises the probability that the dice were loaded). Similarly, the multiverse theorist also violates RTE* by setting aside the specific evidence that this universe is fine-tuned in favour of the weaker evidence that a universe is fine-tuned, which does not involve moving from a piece of evidence that is not surprising to a piece of evidence that is surprising (the evidence that this universe is fine-tuned is in itself surprising, as it raises the probability of teleology/design).
At the end of the day, what Quentin needs to show is that my Jane analogy is relevantly different to the real-world fine-tuning case. I’m afraid I found the discussion here a little bit hard to follow. He claims that what marks the instances of fallacious inference is that ‘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.’ So, for example, in the classic IGF case, my latching on to the particular roll I observe has nothing to do with whether it is a double six. In contrast, according to Quentin, in the fine-tuning case, ‘…we came to refer to our universe not by some direct acquaintance with the process of selection of physical constants, but by acquaintance with what this universe produced after the constants were selected, and the existence of the selection process is theoretically inferred from its products.’
But how is this different from my Jane case? Just as in the real-world fine-tuning case, Jane is only able to refer to herself and the improbable circumstances of her conception after she comes to exist as a result of the right numbers coming up. Maybe it’s my fault for not understanding the point Quentin was making, but I’m not yet seeing a relevant disanalogy here, and in the absence of that, we ought to conclude that the person who infers a multiverse from fine-tuning commits the inverse gambler’s fallacy.
In a Tweet after initial publication of this post, Quentin clarified that his point is that an instance of IVF needn’t be caused by the rolling of dice, whereas a universe’s having the constants it does had to be caused by the kind of probabilistic processes referred to by multiverse theorists. But the latter claims seems to me false. A universe could exist, having certain constants, without there being any more fundamental explanation of why it has the constants it does.
I know I haven’t responded to all of Quentin’s objection, but I’ve run out of time, and I hope my detailed analysis of IGF will enable reader to work out (if they’re very bored!) how I would respond to the other points he raises.