How convincing is the ‘fine-tuning’ argument for God’s existence?

Introduction

The fine-tuning argument for God’s existence is in effect a piece of natural theology. Natural theology takes agreed facts about the world, from the intricacy of the human eye to the occurrence of particular historical events, and argues that theism is the best or only explanation for them. This method has attracted many critics, some arguing that it is illegitimate in principle to treat theism as an explanatory hypothesis.[1] However, in this essay I shall grant its legitimacy, arguing simply that there is no convincing reason to think theism the best explanation of the evidence employed in the fine-tuning argument.

This evidence comes from contemporary science, which tells us that what can loosely be called the cosmological constants (which range from the strengths of the four fundamental forces—gravitational, electromagnetic, strong and weak—to the early expansion rate of the Big Bang) fall within a narrow range of values which allow life. I shall assume that this claim is correct; its details, and the science behind it, are summarised with exceptional brevity and clarity in Leslie 1982:141-142. Unlike some arguments for God’s existence, the fine-tuning argument draws on evidence which non-theists can accept, and so might have a chance of convincing them. I will consider whether it should do so, focussing on the rigorous presentation in Swinburne’s (1990) paper, ‘Argument from the Fine-Tuning of the Universe’.

Swinburne puts the argument in terms of Bayes’ theorem.[2] Where h is the theistic hypothesis[3], e is the evidence that intelligent life exists, and k is our background knowledge:

Besides tautological knowledge, the background knowledge used in calculating these properties covers only “the existence of a Universe governed by natural laws”.[4] This is taken to specify the form of our universe’s natural laws and boundary conditions, but with the values of fine-tuned constants left unspecified.[5] I shall call laws and conditions of this form Α-conditions. In defence of specifying in k that Α-conditions hold, Swinburne[6] simply points us to Leslie 1982:143. Here Leslie compares our universe, which is fine-tuned relative to its laws, to a target on a dartsboard which is filled mainly with other targets, except in the area surrounding that particular target. He claims that just as a dart’s hitting this target would suggest that it had been skilfully aimed rather than thrown at random, even though a randomly thrown dart would likely hit some target, so our universe’s fine-tuning suggests an explanation such as theism, even if most possible universes contain life. I think this analogy fails: we know that darts players tend to aim at impressive targets, whereas we lack reason to think God would pick a universe with laws of the kind we know, as opposed to any universe which permits life. However, I shall not press this objection, and accept that k is as Swinburne understands it, omitting it for brevity:

For clarity, I will alter this equation by writing G for h, and E for a variant of e:

Here, E states that the cosmological constants referred to above fall within the narrow life-permitting range. This is weaker evidence than Swinburne’s e, which states that intelligent life actually exists. This will not affect my discussion of Swinburne’s argument, which relies on e rather than E only in a peripheral discussion of the conditions for intelligent life’s evolution.[7] Fine-tuning arguments are normally limited to the fine-tuning of cosmological constants, and that is why E states only that “There exists a universe with Α-conditions, and with constants in the life-permitting range”, with this last clause the only addition to Swinburne’s k, and so all that can make P(G|E∧k) greater than P(G|k).

To decide whether E raises the probability of G in this way, we need to evaluate P(E), P(E|G) and P(G). (We cannot simply calculate , the relative amount by which E raises G’s probability, without knowing P(G). Though Swinburne is not fully explicit about this, and his language sometimes suggests otherwise[8], we shall see that P(E) depends on P(G).)

P(E|G)

Swinburne argues that P(e|h) is high, because we would expect God to create intelligent life embodied within a physical universe.[9] (Since e entails E, and h is G, this would make P(E|G) at least as high; I shall henceforth speak only of E and G.) Put briefly, his defence of this is that such life is a good thing. On Swinburne’s account, God’s motivation comes only from his comprehensive knowledge of what is good, and He has the power to enable life’s emergence, so He has both motive and opportunity to do so. Not all theologians would share this understanding of God’s choices, but I’ll allow Swinburne to define the form of theism he is defending.

One difficulty with this argument is that Swinburne[10] concedes that there is no best possible Creation containing all good things; this poses notorious problems for arguments which rely on expectations about what God would create, such as his fine-tuning argument and some forms of the problem of evil.[11] Nonetheless, Swinburne plainly regards life (or rather what it enables, for which see Swinburne 1991:97-99) as so especially valuable that we can perhaps allow his confidence that a benevolent God would enable it. Many nontheists will agree that life is particularly valuable.

Unfortunately, beneath this surface agreement there lurks discord. To mount his argument, Swinburne has to understand life as being objectively valuable before any human mind or natural thing existed, with God’s knowledge of this value helping to motivate His choice of Creation.[12] This involves a non-naturalist realism about value which many nontheists reject in favour of naturalism, constructivism, non-cognitivism or Mackiean scepticism. Such people will not agree with Swinburne that an omniscient God would know that life was objectively valuable when choosing His Creation. So they lack this reason for thinking G (which describes a benevolent God who promotes life[13]) more probable on k than, for example, G∗ (which describes an otherwise identical god who is motivated not by benevolence but by a whim to create carbon chemistry). And it is hard to see what other reason they can have for thinking that P(G) > P(G∗); they cannot favour G for its simplicity in the way we shall see Swinburne does.[14] But if P(G) ≤ P(G∗), G would be no better an explanation of E than G∗: since fine-tuning for carbon chemistry involves roughly the same as fine-tuning for life, P(E|G∗) ≅ P(E|G). That would devastate Swinburne’s argument, for reasons I explore more fully after discussing P(G).

The argument can therefore be convincing only if we accept non-naturalist realism about value. There are many problems with this position[15], but there are also religiously neutral reasons to accept it.[16] I am inclined to accept it myself, and shall do so to give the argument a chance. To this end, I shall not only accept Swinburne’s claim that P(E|G) is high, but treat it as 1, which is a more favourable assumption than most theists would want to make. This will significantly simply the discussion, because it means that E cannot lower the probability of G, freeing us discuss how much (if at all) it increases it. This almost certainly overestimates the argument’s power; throughout this essay, I have tried to be charitable to it, while pointing out where others would cease to be convinced.

P(G)

The prior probability of G is far harder to determine than P(E|G). It depends on two factors: theism’s intrinsic theoretical virtues, and the strength of other arguments for and against theism. I shall discuss the effect of these other arguments first, since I suspect that they play a larger role in convincing people that G is a better explanation of fine-tuning than are rival hypotheses which make fine-tuning equally likely.

Many such arguments have been proposed. I cannot evaluate all of them here, though my next essay discusses the most prominent anti-theistic one. Fortunately, most of them should be applied only after the fine-tuning argument, because the evidence they rely on (religious experience, suffering, organisms’ designs, etc.) entails E and so is not independent of it. To build their impact into P(G) would thus be to count E more than once. We should instead leave them to be applied after the fine-tuning argument, with the proviso that they must then include E in their background evidence k.

Most of the remaining arguments claim that theism is necessarily true or necessarily false. Examples are the ontological argument, and suggestions that the concept of God is contradictory. These, too, need not be considered here, because they would render the appeal to fine-tuning superfluous: if P(G) equals 1 or 0, then so will P(G|E). Besides, someone who thought theism necessarily true would not need convincing; and someone who thought it necessarily false would be inconvincible.

Given the limited background knowledge Swinburne allows, the only arguments which he thinks should be taken into account before the fine-tuning argument are “arguments from the existence of the universe and from its conformity to [orderly] laws of nature”[17]. E entails the existence of an orderly universe, so these pieces of evidence should be considered beforehand, and then built into the background knowledge k on which we evaluate the priors in the fine-tuning argument.

If you find these other arguments convincing, fine-tuning will have to bear less evidential weight. But I am considering whether the fine-tuning argument is significantly convincing by itself, so I shall not assume that independent arguments increase P(G). Instead, I shall, as promised, question Swinburne’s[18] claim that theism’s theoretical virtues accomplish this before other arguments are considered.

First of all, we lack agreed criteria for theoretical virtue. Like most Bayesians, Swinburne focuses primarily on ‘simplicity’ (he also considers theoretical scope, but I shall only discuss simplicity). Jeffreys’ (1939) ‘simplicity postulate’ famously assigned simpler hypotheses higher prior probabilities. But while it may be plausible that Kepler’s heliocentric laws of planetary motion were preferable to empirically equivalent Ptolemaic ones because they were simpler in some sense, there is no agreed understanding of this. And it is even harder to compare the simplicity of theism and a rival multiverse hypothesis of the sort discussed later. Since the Keplerian and Ptolemaic accounts involved equations with common variables, we can at least compare the number of free parameters in those equations. Modern Bayesians like Dowe et al. (2007) rely on this to provide formal definitions of simplicity. Forster (2003) argues that such approaches can never succeed. But they are anyway inapplicable to theism and its rivals, because they are not comparable in this way.

It is thus unsurprising that many Bayesians leave simplicity undefined, and rely on our ability to know it when we see it. But since intuitive judgements of theism’s simplicity vary wildly, a proponent of the fine-tuning argument cannot rely on these. Besides, they threaten to make simplicity a subjective property unconnected to truth. Swinburne rightly find this unacceptable, and attempts to articulate objective criteria for simplicity: “An explanatory hypothesis is simple insofar as it invokes few substances, few (accessible) properties (including powers and liabilities to exercise powers), these being caused by each other in mathematically simple”.[19] To fully explain these criteria would take us too far into the metaphysics of substances, properties and liabilities on which they depend. Suffice it to say that they are controversial, partly because the metaphysics is controversial too. My time is better spent showing that, even granting that Swinburne’s criteria for simplicity indicate real theoretical virtues[20], he provides no real reason for thinking theism exceptionally simple.[21]

I shall use Swinburne’s argument that theism is simpler than polytheism as a representative example. This begins with the claim that theism is extremely simple because it posits only one substance.[22] If this is how he interprets his “few substances” test, it is implausible: positing sub-atomic particles inflates the number of entities in our theories, but that does not thereby make them worse. We might, perhaps, favour theories which posit few types of substances, but that would not aid theism against polytheisms which involve many gods of the same type.

Swinburne also claims that positing one God is “simpler and so less arbitrary”[23] than positing, say, 333, because that raises the question of why that particular number. But he does not explain why 1 is any different from 333 in that respect. This also applies to his assertion[24] that limited properties are less arbitrary than limitless ones like omnipotence, omniscience, eternality and complete freedom, from which he thinks all God’s essential properties follow.[25] Just as one can ask “Why this particular finite limit?” one can also ask “Why no limit?” Swinburne thinks that only the former “cries out for an explanation”, and that “there is a neatness about zero and infinity that particular finite numbers lack”[26], but these look like subjective reactions of the sort he rightly deems irrelevant. Equally subjective is scientists’ alleged preference for “hypotheses that some particle had zero mass to hypotheses that it had some very small mass”[27] – even if that preference exists, which Bradley[28] argues is doubtful.

Swinburne has other arguments for theism’s simplicity but they all share similar weaknesses, the most fundamental being their reliance on subjective verdicts about simplicity which those whom the fine-tuning argument wishes to convince may not share. This underscores my point that we lack an objective measure of theism’s simplicity. For the reasons already given, we cannot plausibly apply an algorithmic complexity measure like Colmogorov-Chaitin, AIC, or MML.[29] Those which measure maximal compressions of the information an algorithm encodes might have vindicated Swinburne’s intuition that limited properties are more complex because specifying their limit involves additional information. But without formal measures, we can only see that “There is an agent who can do anything” is a simpler statement than “There is an agent who can do anything within limit L”, which is merely an idiosyncrasy of English. If English didn’t contain words like ‘agent’, both statements would have to be more complex, so this is a hopeless measure of theism’s simplicity. Similar points apply to formulations of theism in formal languages. Perhaps it would help to restrict predicates to ‘genuine’ or ‘basic’ properties, but whether being an agent is one of these will be highly controversial. In general, the prospects for any objective measure of simplicity seem grim.

In sum, Swinburne has given us no reason to assign theism higher prior probability than polytheisms involving many benevolent gods of the same type, or modifications of theism which assign God finite power sufficient to bring about E. Where n is the number of such theories, we’ve no reason to think that . Since n is large, P(G) will be low. Furthermore, E is equally likely on these theories, so they will prevent G from being the best explanation of E in the same way that we saw G∗ threatened to do. I shall explore the impact of these alternative explanations of E by considering P(E), the final variable left in our equation.

I shall restrict my discussion to more thoroughly non-theistic alternatives than those considered so far. The reason for this restriction is obvious: if these modifications of theism were the only good alternative explanations of fine-tuning, E would suggest that something like theism were true, even if P(G|E) were only around . Theism could then be justified by further arguments which showed (perhaps by appealing to evidence from revelations or miracles) that it was sufficiently superior to the modifications of it. Since these arguments occur only after E has been considered, they are not my present concern, but they make it relevant to show that there are other non-theistic explanations of fine-tuning.

P(E)

We have seen reason to think that, insofar as we can evaluate P(G), it is low. But this could be compensated for were P(E) almost as low. To decide this, we can use the equation:

Now, using the following ratio…

…we can rewrite 1):

Substituting this for P(E) in Bayes’ theorem, we get:

Cancelling out, we get:

So rather than working out an absolute value for P(E), we need only estimate the ratio variable in (2). Even leaving aside my scepticism about our ability to estimate the prior probabilities (2) involves, I doubt that we can do this, because we don’t know all the possible non-theistic explanations of fine-tuning.[30] This makes us run the risk of underestimating P(E|¬G), just as those unfamiliar with Darwin’s theories underestimated P(SPECIES-EXISTING|¬G).

But even already-developed non-theistic hypotheses provide reason to suspect that ratio is low, and thus that P(G|E) is low. I shall use as an example the hypothesis that for every combination of values the fine-tuned cosmological constants could take, there is a universe[31] with that combination of values. Call this simple ‘multiverse’ theory M. Everett argues that M has significant scientific support, but let us here grant Swinburne’s claim that this is not so[32], and simply treat it as a speculative non-theistic explanation of E. (It is not strictly incompatible with theism, but since P(G) and P(M) are apparently independent[33] my arguments that P(G) is negligible imply that P(M&G) is equally negligible relative to P(M&¬G).) Now, favouring the theist by pretending that M is the only non-theistic hypothesis, and by still treating P(E|G) as 1, we can turn (2) into (6):

Since P(E|M) is 1, because M entails that there will be a universe with the fine-tuned values found in our universe:

From which it follows that if , then , which (5) shows would make . That would stop the fine-tuning argument from convincing anyone of theism by itself, though not from increasing G’s probability significantly and thereby helping other theistic arguments. To prevent even this, we would need to drop the pretence that M is the only non-theistic hypothesis, and provide others which significantly increase P(E|¬G) × P(¬G). I believe such hypotheses exist, and although I cannot survey them all here, I shall mention one below. But my current point is only that, even allowing Swinburne’s test of simplicity, there’s no clear reason to think P(M) lower than P(G). Swinburne[34] argues that it is, comparatively speaking, “absurdly low” because M vastly multiples the number of universes, but we saw that multiplying entities of a single type was no real sin. M is free of the alleged complexity of specifying the particular values of our universe’s cosmological constants. k specifies the forms of the physical laws into which those constants slot, so M does not have to. (If we exclude this from k, M could be revised to state simply that each possible set of laws obtains in some universe. However, my criticism of Leslie’s dart-throwing analogy would then apply, and calculating P(E) would become even harder[35], making the argument more inconclusive.)

That defuses the charge that fine-tuning in particular forces non-theistic hypotheses towards unacceptable complexity. There remain Swinburne’s claims that theism is especially simple regardless, so presumably simpler than M. But I have already criticised these. The main criticism levelled against M is not that it is over-complex, but that it cannot explain a datum which theism can, namely that this universe is fine-tuned. I shall conclude my argument by rebutting this challenge, which has been advanced by White (2000), Dowe (1999) and Hacking (1987).

Leave aside the questionable claim that we’d expect God to fine-tune this universe, and not some other. Leave aside the tricky question of what essential property individuates ‘this universe’ for White and company. (It cannot be ‘containing us’ or ‘having such-and-such constants’ since they are supposing it could lack such properties. Manson[36] suggests they will have to resort to ‘haecceities’.) Even if these questions have answers, the criticism of M cannot be accurate. Bostrom proves this formally, but the central point can be sketched informally: the claim that M does not increase the likelihood of this universe being fine-tuned is inconsistent with the fact, which White, Dowe and Hacking all accept, that it increases the likelihood of some universe being fine-tuned, which is all that E involves. At least, it is inconsistent unless M makes it less likely that this specific universe be fine-tuned than that another specific universe be fine-tuned, which it does not. The full proof of this is at Bostrom 2002:20. So M does make it more likely that this universe be fine-tuned.[37]

There are anyway alternative hypotheses which increase the likelihood that any specific universe in a multiverse be fine-tuned. An example is Smolin’s hypothesis that black holes form new universes with constants only slightly different from those in the parent universe.[38] This would lead to a high proportion of universes having constants which increase the likelihood of black holes: and these are just the constants which enable the formation of stars, carbon, and, as a byproduct, life.

Smolin’s hypothesis has only weak support from physics, and may be less ‘simple’ than M. But it is no worse an ultimate explanation of fine-tuning than theism, absent reasons to think theism especially theoretically virtuous.[39] Furthermore, it is merely an example of the many non-theistic explanations of fine-tuning that could be offered, each one raising P(E) further above P(G), and thereby diminishing the effectiveness of the fine-tuning argument. The argument is thus unconvincing, even absent an alternative to theism as powerful in cosmology as evolutionary theory in biology. Given the impressive growth in what science has explained over the past few centuries, this may yet present itself.

Conclusion

The fine-tuning argument should convince us no more than the argument from the intricate ‘designs’ of species should have convinced pre-Darwinians. In both cases, theism is just one possible explanation of the evidence. None of the reasons advanced for thinking it a better explanation than the alternatives are persuasive, even allowing that we can compare their theoretical virtue with that of theism – which I have tried to show is problematic both in principle and in practice. We also saw that the claim that we would expect God to create a life-permitting universe is only as plausible as a contentious view of the objectivity of ethics. But, for the reasons I have given, even someone convinced of this objectivity should reject the fine-tuning argument.