**Theism, Naturalism and Fine-Tuning**I'm comparing theism and naturalism. I take naturalism to be the claim that the natural world is all that exists. I take theism to be the claim that there exists a perfectly good, maximally powerful being that exists necessarily (the reason for its existence is found in its own nature, not an external source). This is not a debate about the coherence or prior probability of these ideas.

We need to consider the consequences of these ideas. Keep in mind that "what does X imply?" is a different question to "what do advocates of X believe?". Ideas have implications, independently of what their advocates believe.

**What is Fine-Tuning?**First things first: ‘Fine-tuning’ is a metaphor, one that brings to mind an old radio set. This metaphor unfortunately involves a guiding hand that sets the dials, giving the impression that 'fine-tuned' means cleverly arranged or made for a purpose by a fine-tuner. Whether such a fine-tuner of our Universe exists or not, this is not the sense in which I use the term.

Fine-tuning is a technical term borrowed from physics. It refers to a suspiciously precise assumption. To illustrate, suppose that a bank vault was robbed. The armoured door was opened without force; the robbers used the access code. The police arrive on the scene.

*Drebin:* Maybe they guessed the code.

*Hocken:* No way, Frank. There are a trillion combinations. The system shows that they entered the code correctly on the first attempt. Surely the odds against that are astronomical.

*Drebbin:* But it's still possible, right?

Here is one way to see the problem with Drebin’s theory. To explain the data, we need to fine-tune the theory by assuming that the code that the robbers guessed was the

*correct* code. That is a suspiciously precise but totally unmotivated assumption, which tells against Debbin's theory.

(To forestall a common reply, this is an illustration, not an analogy. I'm not saying that the universe is analogous to a crime scene. I'm illustrating a principle.)

**The Set-Up**How do we test theism and naturalism? I'll treat them as "theories" in the context of Bayesian theory testing. We want to know their probability, given everything we know. We use Bayes theorem: break what we know into two pieces, A and B. For each theory T, calculate the probability of A, given T and B (the likelihood). Also, calculate the probability of T on B alone (the prior). Bayes theorem often comes attached to a narrative about "evidence" and "background information" and "updating", but none of this is essential. It's a

*theorem*. It works for any propositions. We divide into A and B for convenience.

Naturalism and theism are ultimate or fundamental statements about the universe - if they are true, then there are no "deeper" statements, so to speak. We can and should, then, ask what kind of universe we would expect. That is, what is the likelihood of this universe on naturalism and theism?

Now, that's a rather large question. The first thing to consider is: what universes other than this one are possible? When we use a physical theory to predict, say, a reading on a meter attached to our experimental apparatus, the likelihood is defined against the backdrop of all the possible readings, even though only one may actually be observed. This is necessary: the likelihood is normalised over this set of possibilities.

On naturalism, the existence and fundamental properties of the universe are brute facts. There is no reason why this particular universe exists, or indeed why any universe exists. If you think that this renders our search for probabilities impossible, then naturalism is inscrutable. There is literally nothing at all that could possibly said in support of it. The success of science would not lend it one iota of support.

But this problem is familiar to the physicist. When faced with a seemingly infinite set of possible theories or observations or whatever, we get modelling! Focus on a subset of the problem that a) we can handle, and b) seems to represent the larger problem in an unbiased way. We consider a finite number of theories, or a suitably broad model of our instrument and what it may observe.

So, here is a proposal. Rather than consider every possible way that a physical universe could be, we will restrict our attention to a well-characterised, as-best-we-know unbiased set of possibilities, generated in two ways.

**1.** We vary the values of the constants in the equations of the laws of nature. This has several advantages. Since the equation is familiar, we are more likely to be able to predict what would happen in a universe with the different value of the constant. Further, when testing physical theories, we need to posit a prior probability distribution of the free parameters of the theory. The constants are treated as "nuisance parameters" for theory testing.

**2.** Similarly, we can vary the initial conditions of the same equations. Roughly, physical theories tell us how the world changes, but not how it is. For example, Newtonian gravity tells us how masses pull on each other; to describe the Solar System, we need to know where the planets are and how they're moving. We specify this with initial conditions (or, more generally, boundary conditions). The set of possible initial conditions maps precisely onto the set of physical scenarios that the theory dictates is possible.

This subset of possibilities has much to recommend itself to us. It stays very close to our best scientific theories of the universe. It allows to use familiar results and methods from our physics. Furthermore, looking ahead, we have not biased our search against finding life. In fact, if anything, we have biased out search

*in favour* of finding life-permitting universes. The reason is that we have started our search at a known example (our universe) of what we are looking for (life-permitting universes).

Additionally, this set of possibilities comes with probability measures derived from theory testing in physics. These probabilities are a measure of our state of knowledge, not a statement about any supposed chancy-ness in reality.

What about the possibilities on theism? God can create anything. Perhaps surprisingly, this is similar to the situation given naturalism, where because the universe exists for no reason at all, anything could exist. I propose, then, that we consider the same range of possible universes. The difference will be the probabilities placed on the set of possibilities. Here, we ignore the question of why a physical universe exists at all on naturalism and theism. (That's the contingency argument.)

**Testing Naturalism and Theism**In all its detail, the Bayesian approach says we need to calculate the probability of everything we know about this universe (the likelihood). The key, in practice, is to focus on

*decisive* pieces of data. When we compare Newtonian gravity with Einstein's general relativity, we don't bother comparing the data about the orbit of Neptune, where the theories make extremely similar predictions. We certainly don't calculate the probability of every crater on the moon. Feel free to try, but the likelihood is going to be the same, so there is no net effect on the probability of the theory. Instead, we consider the orbit of Mercury, where there is a measurable difference between the predictions.

The fine-tuning argument invites us to consider this particular fact about our universe: it supports the complexity required by life forms. Over the last 40 years, physicists have found that the necessary conditions for life are extremely rare among the set of possible universe we are considering.

Here's just one example. Einstein's cosmological constant causes the expansion of the universe to accelerate. Other forms of energy can have the same effect, so we speak of their combined effect as an effective cosmological constant (ECC). Within our equations, ECC can range between -m

_{Pl} and +m

_{Pl}, where m

_{Pl} is the Planck mass. (In this case, it is not just a possible value: there are reasons to expect the Planck scale to be the ECC's natural scale. But put that aside for now.) Within this range, we can quite safely identify a subset outside of which life will not form. If ECC < -10

^{-90} m

_{Pl}, then the universe recollapses into a big crunch in a matter of seconds. If ECC > 10

^{-90} m

_{Pl}, then absolutely no structure forms in the universe at all. The expansion is too rapid, and soon every proton in the universe is isolated in empty space.

So, in Bayesian fashion, we represent our state of knowledge with a probability. If all we knew was that a) naturalism is true and b) that the equations of physics describe the universe, we would be ignorant of the value of the ECC. In probability jargon, naturalism is a non-informative theory. This isn't pejorative: some theories don't make precise predictions. If all we knew was that robbers guessed the code, we'd have no reason to expect any particular code to be entered rather than another. Similarly, naturalism gives us no reason to expect any possible physical universe rather than another. So, with respect to the ECC, we model our ignorance with a uniform probability distribution. Then, the probability of a life-permitting universe is no greater than one in 10

^{90}. Other examples of fine-tuning reduce this number even further.

What about on theism? Here, we must ask how likely it is that God would want to create a universe that supports embodied moral agents. Here, God's essential goodness is relevant. A good God might want to create a good state of affairs, and the existence of beings who can can live, learn, labour and love is a good state of affairs.

A cynic might complain that this "divine mind-reading" is entirely speculative. But observe two things. Firstly, such "speculation" pre-dates the discovery of the fine-tuning of our universe by a couple of millennia, so one can hardly accuse the theist of ad-hocery.

Secondly, consider the crime scene again. There are a seeming infinity of means, motives and methods that come under the umbrella of the "inside job" hypothesis. Must we read the minds of the robbers? Actually, given the extremely small probability of the data on the "guessed" hypothesis, we need only argue as follows. Only if the probability of an inside job is comparable to one in a trillion (the likelihood on the "guessed" hypothesis) will such considerations make any difference to the investigation. Similarly, the force of the fine-tuning argument is only turned back by a "divine mind-reading" skepticism if the probability of God creating a life-permitting universe is comparable to one in 10

^{90}. That, I contend, is not much of a burden on the theist.

Thus, even if the probability of a life-permitting universe given theism is one in a trillion, the fine-tuning of the universe for life still confirms theism over naturalism by some enormous number like 10

^{78}. That's how we test theories, and naturalism takes a rather large hit.

**Conclusion**The intuition behind this argument is that the naturalist, faced with all the ways the physical universe could have been, can only shrug their shoulders. For naturalism, the question "why this universe?" is in principle unanswerable. The theist can see a rationale for the way the universe is, one that is neither ad hoc nor jerry rigged. Note that these are not really rival explanations. Theism offers an explanation for the ultimate facts of physics where naturalism offers none.

There are a large number of possible moves for the naturalist to make at this point, so I'll discuss those as they arise. If the details of fine-tuning are in question, I've got a whole book of more examples:

www.cambridge.org/fortunate. If you think that fine-tuning is a theist invention, then you should know that my co-author is an atheist.