On the Fine Tuning Argument for the Existence of God

Does God exist? Or, put another way, do we have good reason to believe that God exists? Proponents of the Fine Tuning Argument (FTA), such as Robin Collins and Luke Barnes have outlined their reasoning (in both written and oral form) as to why they would answer yes to the second formulation of the question. Each has put forward their own formulation of the common theistic argument from fine tuning, in the form of a Bayesian inference. For those unfamiliar with Bayesian inference here are a few good youtube primers: Veritasium 3Brown1Blue.

The purpose of this post will be to highlight what I perceive to be a critical error in the reasoning used by the above proponents. In the spirit of Bayesian inference, I am not suggesting that my reading of their position is definitively true, I’m just saying that I believe they are making an error in reasoning by misrepresenting the position of naturalism, or what I will refer to here as Brute Fact Naturalism (BFN). There may be an issue with my reading of their collective position, or with my interpretation of certain information, and I am open to updating my calculation, should that error be demonstrated. The issue, as I perceive it, is that the FTA outlined by theists* begs the question against BFN by ascribing a low probability to the likelihoood of the given evidence, which in this case is a a Life Permitting Universe (LPU) under BFN.

At this juncture, it might be worth pointing out (and at the same time shamelessly plugging my own work) that I should be a proponent of the FTA, since it would massively support the thesis laid out in The God Conclusion – AAtheism: From Rock Bottom to a God of My Own Understanding. The FTA would [arguably] support a Pantheistic inference over any other theistic interpretation. Pantheism doesn’t require such an argument, but if the Bayesian inference for theism were indeed stronger than for BFN, then it wold be stronger again for Pantheism. However, I remain unconvinced by the theistic FTA.

*Here, I simply mean proponents of the theistic inference from the FTA.

 

What is Brute Fact Naturalism

Here BFN is simply the idea that our universe exists as a brute fact. Sean Carroll outlines this position in a discussion with Luke Barnes. Barnes references Carroll on naturalism in his paper, A Reasonable Little Question: A Formulation of the Fine-Tuning Argument,  “there is only one world, the natural world . . . [which] evolves according to unbroken patterns, the laws of nature”. Collin’s references Keith Parsons in his paper, The Teleological Argument: An Exploration of the Fine-Tuning of the Universe:

if the universe and its laws are all that is or ever has been, how can it be said that the universe, with all of its ‘finely tuned’ features, is in any relevant sense probable or improbable? Ex Hypothesi there are no antecedent conditions that could determine such a probability. Hence, if the universe is the ultimate brute fact, it is neither likely nor unlikely, probable nor improbable; it simply is.

So, this is simply the BFN hypothesis, namely, our universe, it’s initial conditions and laws of nature, with all of its finely tuned features is the “ultimate brute fact”. In effect, it is pretty much just the theistic hypothesis but with God deleted from the equation. Instead of God being the ultimate brute fact, the laws of nature and initial conditions of the universe are the brute fact.

Parsons states that we have absolutely no empirical basis for assigning probabilities to ultimate facts; that, if the universe is the ultimate brute fact then it is neither probable nor improbably in any relevant sense. Collins objects this claim, stating that Parson’s objection is “deeply mistaken” as it fails to recognize what is called epistemic probability or inductive probability (Bayesian probability in this case). Indeed, the FTA put forward by Collins and Barnes employs this form of epistemic or Bayesian probability, which is perfectly legitimate. There is nothing wrong with attempting a Bayesian argument. The issue, as I read it, is with the misrepresentation of the BFN by those authors.

 

Theistic Bayesian Claim

As you may have seen from the videos linked above, Bayesian probability is somewhat different from frequentist probability, which is the probability we usually think of when it comes to things like rolling a die, tossing a coin, or winning at roulette. Essentially, the question being asked [when it comes to Bayesian inference] is how likely it is that a specific piece of evidence would occur, assuming that the given hypothesis is correct.

In his “Teleological Argument” paper, Collins outlines what he calls the Expectation Principle:

According to the Expecation Principle, if an event or state of affairs e is more to be expected under one hypothesis, h1, than another, h2, it counts as evidence in favor of h1 over h2 – that is, in favor of the hypothesis under which it has the highest expectation. The strength of the evidence is proportional to the relative degree to which it is more to be expected under h1 than h2.

In short, if the event (evidence) is more likely to occur in theory A than in theory B, then the evidence favours A over B. This is what forms the basis of Barnes’s Big and Little Questions, with regard to naturalism:

The Big Question: of all the possible ways that a physical universe could have been, is our universe what we would expect on naturalism?

The Little Question: of all the possible ways that the fundamental constants of the standard models could have been, is our universe what we would expect on naturalism?

(Barnes suggests that the Big Question is, at present unanswerable, but the Little Question is more tractable and representative of the Big Question)

The essential claim by theists is that the Bayesian probability of getting a Life Permitting Universe (LPU) under BFN is vanishingly small, but not so under the theistic hypothesis. Theists argue that in the set of all possible, naturalistic universes the ratio of elements which are LPU is vanishingly small, therefore the probability of an LPU under BFN is vanishingly small. Essentially, theists claim that an LPU is not at all likely under naturalism, or that our universe is not what you would expect under naturalism.

The conclusion Barnes draws in his “Little Question” paper:

What physical universe would we expect to exist, if naturalism were true? To systematically and tractably explore other ways that the universe could have been, we vary the free parameters of the standard models of particle physics and cosmology. This exercise could have discovered that our universe is typical and unexceptional. It did not. This search for other ways that the universe could have been has overwhelmingly found lifelessness.

In short, the answer to the Little Question is no. And so, plausibly and as best we can tell, the answer to the Big Question is no. The fine-tuning of the universe for life shows that, according to the best physical theories we have, naturalism overwhelmingly expects a dead universe.

 

The Issue

In principle, there is nothing wrong with attempting to apply Bayesian probability to the question of the origins of the universe, although in practice there might be some limitations to its applicability. However, if one is going to attempt a Bayesian inference, the hypotheses under consideration must be fairly represented. My reading of the arguments put forward by Collins and Barnes is that they don’t fairly represent BFM.

If we look again Barnes’s Big and Little Questions, he says, of all the possible ways that a physical universe could have been… (Big Question) / of all the possible ways that the fundamental constants of the standard models could have been… (Little Question). [Focusing on the Little Question] how do we determine all the possible ways the fundamental constants of the standard models could have been? Barnes tells us,  we vary the free parameters of the standard models of particle physics and cosmology.

When we do this, the theist argues, we get the set of all possible, natural universes and, of the elements of that set, those elements which are LPU are vanishingly small.

Barnes’s treatment is representative of the theistic argument and relies on a sort of counterfactual element, which Collins says is essential to any account of conditional epistemic probability, if we are to connect degrees of conditional epistemic probability with actual rational degrees of belief, which we need to do if judgments of conditional probability are to serve as guides to life.

The critical issue here, however, is that BFN simply doesn’t allow for counterfactuals. As per the statements from Carroll and Parsons above, BFN says that this universe is all that is and ever was, or ever could have been. It says the Universe simply couldn’t have been any other way. When representing BFN fairly, Parsons’ claim that there are no antecedent conditions that could determine the probability for it’s existence is not “deeply mistaken”, it is a simple statement of fact. Robin Collins references an objection by John Earman in which Earman says, talk of the existence of a fine-tuned universe’s being improbable “seems to presuppose a creation account of actuality: in the beginning there is an ensemble of physically possible universes – all satisfying the laws of our universe but with different values of the constants – awaiting to be anointed with the property of actuality by the great Actualizer . . .” Collins dismisses this claim saying that such a representation of BFN doesn’t presuppose a creation account rather it represents the epistemic probabilities of an LPU under BFN.

Collins is technically correct when he says the theistic argument doesn’t presuppose a creator or “Great Actualizer”, however, what it does presuppose is an ensemble of possible universes from which our Universe comes. Again, this is a misrepresentation of BFN, which says our Universe with all of its ‘finely tuned’ features is the ultimate brute fact. [Leaving the Multiverse hypothesis aside, for now] the set of all possible BFN universes is a set containing only one element, and that single element is our LPU, or BFLPU. Therefore, if we are to treat BFN fairly as a hypothesis when attempting a Bayesian inference, we need to ask what the probability of an LPU is given BFLPU. The answer to that question is, of course, 1, since the likelihood of our universe occurring given our universe is the ultimate brute fact is inevitable.

 

Theistic Justifications

Theists might object by reiterating Collins’s claim that:

some sort of counterfactual element, however, is essential to any account of conditional epistemic probability if we are to connect degrees of conditional epistemic probability with actual rational degrees of belief, which we need to do if judgments of conditional probability are to serve as guides to life.

Indeed, Collins and Barnes offer some pretty clear examples to support their justification in using counterfactuals to ascribe a low probability to an LPU under BFLPU. Collins says:

when there is a range of viable natural variables, then one can only legitimately speak of the range of possible probabilities, with the range being determined by probabilities spanned by the lower and upper bound of the probabilities determined by the various choices of natural variables

To justify what he refers to as the Restricted Principle of Indifference he asks us to consider the case in which we are told that a factory produces cubes between 0 and 10 meters in length, but in which we are given no information about what lengths it produces. Using the aforementioned principle, the epistemic probability of the cube being between 9 and 10 metres in length is calculated. This, however, is not representative of the question in hand, since [analogously] we know the cube is between 9 and 10 metres in length. For the question to be representative, the question would have to be what the probability is, of the factory producing a cube between 9 and 10 metres in length given it is set to produce cubes between 9 and 10 metres in length.

He goes on to use the example of a never-before-rolled 20-sided die (the first ever produced) to justify the use of probabilities outside those cases involving relative frequencies i.e. the frequency of something occurring given N number of trials. Collins says, and he is correct, that we all immediately know that upon being rolled the probability of the die coming up on any given side is one in 20, this is despite the fact that a 20-sided die has never been rolled before in the history of the universe. This is supposed to be representative of the case in hand, since we don’t have N number of trials of the universe to judge the probabilities. However, again, it assumes an ensemble of possible outcomes where BFN says that there was only ever one possible universe. A more representative example would be a one-sided die.

In a discussion with Alex Malpass, on the Capturing Chirstianity youtube channel, Barnes uses roulette as an example, which again presupposes a set of more than one possible outcome. In the same video he makes explicit the misrepresentation of BFN when he says, “it’s not the case that the Universe had to be this way and couldn’t have been any other way*”, however, that is precisely what the BFN/BFLPU hypothesis says – that the universe had to be this way and couldn’t have been any other way. Barnes even acknowledges this in a discussion with Sean Carroll where he says that “the price of naturalism” is that we just have to “grin and smile and say those are the ultimate brute facts of reality and if they look fine-tuned….you just say that’s the ultimate principles, we’ve explained reality, then high-five and go to the pub”.

 

Eternal Conflation

I suspect the underlying issue here is a subtle, inadvertent conflation on behalf of, not just theists but perhaps on behalf of some proponents of naturalism also – although not those I have referenced here. My reading of it is that theists are conflating the notion of the set of possible models we get, by varying the fundamental constants, in an attempt to find the correct model of this singular Universe, with the idea of possible ways the Universe could have been. Applying Bayesian reasoning here aids us in our attempt to distinguish between the competing models of the BFLPU. The models represent our attempts to get a handle on how the Universe actually is, they do not represent possible ways in which Universe could have been – at least, not according to BFLPU. When we accurately represent the BFLPU in this way, it completely changes the Bayesian inference.

Theists might perhaps argue that this stacks the deck in favour of BFLPU but that simply means that the Bayesian inference for a BFLPU is stronger. Contrary to Collins’s claim that counterfactuals are necessary if epistemological probability is to be a guide for life, the proponent of BFN could also argue that acknowledging how the world is is a better guide for life than ruminating over counterfactuals. However, it might be worth nothing that the counterfactuals in the case of the fine tuning argument are provided by the competing hypotheses, not by the misrepresentation of BFN as the idea that there were a number of possible ways the Universe could have been. The Bayesian inference is then between the competing hypotheses, of which the BFN emerges stronger than the theistic hypothesis.

Again, I want to stress that I am open to correction and again, I want to shamelessly plug my work by saying that having the theistic hypothesis win the Bayesian argument would favour the thesis laid out in my book, since Pantheism would be a stronger inference again (since it is the thesis that God is the Universe). Incidentally, the Pantheistic thesis still has a stronger Bayesian inference so theists such as Collins and Barnes should embrace Pantheism over Christianity*.

 

*Popular forms of Christianity, since it is [not in so many words] argued by David Bentley-Hart in the Experience of God that the God espoused by Christian scholars is effectively the same as that espoused in Hinduism.