Int J Philos ReligDOI 10.1007/s11153-014-9453-6

ARTICLE

Collins’ core fine-tuning argument

Mark Douglas Saward

Received: 7 February 2014 / Accepted: 4 April 2014© Springer Science+Business Media Dordrecht 2014

Abstract Collins (The Blackwell companion to natural theology, 2009) presents anargument he calls the ‘core fine-tuning argument’. In this paper, I show that Collins’argument is flawed in at least two ways. First, the structure, depending on likelihoods,fails to establish anything about the posterior probability of God’s existence givenfine-tuning. As an argument for God’s existence, this is a serious failing. Second, hisanalysis of what is appropriately restricted background knowledge, combined withthe credences of a specially chosen ‘alien’, do not allow him to establish the premisePr(L PU | N SU & k′) � 1.

Keywords God · Fine-tuning argument · Design

Introduction

Collins (2009) introduced an argument which he called the ‘core fine-tuning argumentfor the existence of God’.1 This paper will examine this argument in some detail, inwhat I hope will prove to be new ways independent of the usual criticisms of the Princi-ple of Indifference and applications thereof. Before beginning the examination of thisargument, I will first make some general remarks about fine-tuning arguments, whichare of general interest to the project of producing what might hope to be considered asuccessful or challenging fine-tuning argument. After these preliminary matters, thispaper will focus on two key areas: the structure of Collins’ argument, and the role ofbackground knowledge in establishing the first premise. In each case, I will argue that

1 See Collins (2009, p. 202), for the argument being referred to as an argument for the existence ofGod. In other places he drops ‘for the existence of God’.

M. D. Saward (B)Monash University, Clayton Campus, Wellington Rd, Clayton, VIC 3800, Australiae-mail: mark.saward@monash.edu

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Collins does not achieve what he sets out to, and so the argument cannot be consideredsuccessful as a fine-tuning argument.

Fine-tuning arguments

To say that our universe is fine-tuned is to make one or more claims among a class offine-tuning claims. These claims follow very broadly the following pattern: identifysome feature of our universe that appears contingent, and note that among all therelevant alternatives, ‘very few’ allow for life. So, for example, one may note that thestrength of gravity in our universe is in part determined by the constant G, and thatthere appears to be no logical or metaphysical reason why G must be the value it isand not some other real value. Furthermore, only a ‘small’ finite range of choices forG, or a ‘small’ finite range of choices for G so far as we can tell, allow for life to exist.That is, it gives the appearance of the existence of life being balanced on a knife’sedge. Claims about fine-tuning are not limited to just claims about constants in ourphysical laws, but also to the form of the laws themselves, or to the initial conditionsof our universe (such as the initial entropy of our universe). Such fine-tuning claimsfollow a similar pattern of specifying the range of alternatives for some apparentlycontingent feature of our universe, and noting that of all the alternatives, ‘very few’are life-permitting.

Fine-tuning arguments are arguments that include as a premise one or more suchclaims about our universe being fine-tuned, and have as a conclusion some statementabout the existence of God. Given the evidence, the conclusion is that God exists, or thatGod is likely to exist, or that the posterior probability of God’s existence is higher. Ofcourse, there can be infinitely many other arguments that have fine-tuning as a premisebut a conclusion that says nothing about God. Perhaps we could reasonably call those‘fine-tuning arguments’ as well, since they include fine-tuning as an indispensablepremise. However, what is commonly understood is that ‘fine-tuning argument’ is ashort hand way of saying ‘fine-tuning argument for God’s existence’. This is what Ishall mean by ‘fine-tuning argument’, or FTA. For such an argument to be consideredsuccessful, it must say something significant about God’s existence: that God exists,or that God’s existence is likely, or that God’s existence is significantly2 more likelygiven the evidence than it was before. At the absolute minimum, a fine-tuning argumentshould show that Pr(T | F) > Pr(T ) (where T stands for ‘God Exists’, and ‘F’ for‘Our universe is fine-tuned’, or something similar). If it does none of these things,then it is hard to understand how it is an argument for God’s existence, and thereforehow it is a fine-tuning argument.

2 Significance is hard to evaluate. Someone testifying to someone else that God exists is evidence for God’sexistence, but it is hardly a significant amount of evidence, ceteris paribus. So here we shall include the ill-defined phrase ‘significantly’ to show that more is required than simply increasing the posterior probabilityof the hypothesis, but less is required than showing the posterior probability is greater than that of the denialof the hypothesis.

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The core fine-tuning argument

Collins (2009, pp. 203–207) presents what he calls ‘the core fine-tuning argument’.The argument’s core form will be presented in full shortly, but first, here are some ofthe terms as Collins uses them in his paper:

LPU Life Permitting Universe—there exists a life-permitting universe which cansupport embodied moral observers,3 such as ourselves. By ‘life’, Collins has inmind embodied moral observers, not just living things.

T Theism—the claim that there exists “an omnipotent, omniscient, everlasting oreternal, perfectly free creator of the universe whose existence does not dependon anything outside itself” (Collins 2009, p. 204).

NSU Naturalistic Single Universe—There exists just a single universe, with physicallaws that do not vary in any important way for differing regions of spacetime,and there is no transcendent explanation of the universe. The existence of thisuniverse is an unexplained, brute given (Collins 2009, p. 204).

k′ Where k is our total background knowledge, k′ refers to some subset of k′which excludes appropriate knowledge, such as the fact that some constant hasa life-permitting value.

The argument itself is as follows (Collins 2009, p. 207):

1. Given the fine-tuning evidence, L PU is very, very epistemically unlikely underNSU: that is, Pr(L PU | N SU & k′) � 1, where k′ represents some appropriatelychosen background information, and � represents much, much less than (thusmaking Pr(L PU | N SU & k′) close to zero).

2. Given the fine-tuning evidence, L PU is not unlikely under T : that is, ∼ Pr(L PU |T & k′) � 1.

3. T was advocated prior to the fine-tuning evidence (and has independent motiva-tion).

4. Therefore, by the restricted version of the Likelihood Principle, L PU stronglysupports T over N SU

Collins makes it clear that his argument is making use of standard Likelihood tools,by referring the readers to the works of Edwards (1972), Royall (1997), Sober (2002),Forster and Sober (2004) for providing justifications for his approach. Now, if onewants to meet the absolute minimim standard for a successful fine-tuning argument, thatit render the posterior probability of the hypothesis higher than the prior, likelihoodisttools are the wrong tools to use, and likelihoodists are clear on this themselves. Letus see how the likelihoodist’s account is intended to work, and why it will not helpCollins.

The likelihood L(H | E) of some hypothesis H , given some evidence E , is definedto be proportional to the probability of the evidence given the hypotheses, Pr(E | H)

(Edwards 1972, p. 9). The likelihood does not tell us whether or not a particularhypothesis is true, or even that it is probable or likely to be true. For any piece of

3 This does not entail anything about the probability that such a universe in fact does contain life, otherthan that it is not ruled out.

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evidence, we can invent some contrived hypothesis A for which Pr(E | A) = 1.This in turn corresponds to a maximum likelihood for the hypothesis. If maximisinglikelihood told us something significant about which hypothesis to prefer, then wewould find that there are always ad hoc hypotheses that should be preferred at least asmuch as our best competing hypotheses, if not more preferred. Consider the followingexample of this sort, provided by Collins (2009, p. 206):

suppose that I roll a die 20 times and it comes up some apparently randomsequence of numbers—say 2, 6, 4, 3, 1, 5, 6, 4, 3, 2, 1, 6, 2, 4, 4, 1, 3, 6, 6, 1. Theprobability of its coming up in this sequence is one in 3.6×1015 , or about one ina million billion. To explain this occurrence, suppose I invented the hypothesisthat there is a demon whose favorite number is just the aforementioned sequenceof numbers (i.e. 26431564321624413661), and that this demon had a strongdesire for that sequence to turn up when I rolled the die. Now, if this demonhypothesis were true, then the fact that the die came up in this sequence wouldbe expected—that is, the sequence would not be epistemically improbable.

This story clearly demonstrates why likelihoods on their own cannot be used forchoosing among hypotheses. The demon hypothesis corresponds to a near maximumlikelihood, yet clearly we would not come to think that the hypothesis is true insuch circumstances. The probability of the hypothesis given the evidence depends onmore than just the probability of the evidence given the hypothesis. The meddlingdemon is a counterexample to the very implausible proposal that high probabilityof evidence given some hypothesis corresponds to high probability of that hypothesisgiven evidence. This implausible claim is not one made by likelihoodists. Elliott Sober(2002, p. 25), addressing this very point, says:

Likelihoodists can and should admit that the demon hypothesis is implausibleor absurd, notwithstanding the fact that it has a likelihood of unity relative tothe single observation under consideration. It’s just that likelihoodists declineto represent this epistemic judgement by assigning the hypothesis a probability.Likelihoodist epistemology is modest in its ambitions: support gets representedformally, but plausibility does not.

Since likelihoods are only telling us something about support (which we will havemore to say shortly), and not about which hypothesis is true or likely, the meddlingdemon is no counterexample to the likelihoodist. The likelihoodist can consistentlyclaim both that the meddling demon has a likelihood of unity, and that the demonhypothesis is very implausible even given the evidence. The role of likelihoods then isnot about determining which hypothesis is true or likely, but rather about a way of com-paring two hypotheses on some particular evidence. In line with this, the likelihoodisttakes the likelihood ratio of two hypotheses given some particular evidence, and thendefines ‘support’ to be this likelihood ratio, or the natural log of this ratio (Edwards1972, p. 31). Having thus defined ‘support’ as the likelihoodist might, we can thentalk about the support that some piece of evidence provides for one hypothesis overanother, remembering that high support does not entail anything about the posterior

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probability of the hypotheses, not even that the posterior probability is higher than theprior.

With this background in mind,4 let us return to Collins’ argument, and see how‘support’ appears in his argument. We see that premises (1) and (2) make claims aboutthe probabilities of our evidence of fine-tuning given particular hypotheses, and in turnwill allow us to determine the likelihoods, so defined, for the particular hypotheses andevidence. Let us set aside premise (3) for now, and examine the conclusion (4). Theconclusion makes the claim that the evidence strongly supports T over N SU , accordingto the restricted version of the Likelihood Principle. The Likelihood Principle, as givenby Collins (2009, p. 205), is as follows: if some evidence E is more probable given H1than H2, then E counts as evidence in favour of H1 over H2. Furthermore, the degreeof the favour is determined by the ratio of Pr(E | H1)/ Pr(E | H2).

Collins says of his conclusion that it follows from the premises. For this to be thecase, it must be that Collins intends for ‘favour’ to be interchangeable with ‘support’(and, in other places, ‘confirm’). Setting aside the restriction on the Likelihood Prin-ciple, if we take ‘favour’ to mean ‘support’, and that ‘A is supported over B’ just isthat Pr(E | A) > Pr(E | B), (with ‘strongly supported’ in the case of �) then giventhe premises the conclusion does indeed follow. In this case, Collins’ use of the word‘support’ would be for the most part compatible with how Edwards defines support.But if this is right, then we can summarise the argument as follows:

1. Pr(L PU | N SU & k′) � 12. ∼ Pr(L PU | T & k′) � 13. Therefore, Pr(L PU | T & k′) � Pr(L PU | N SU & k′)

This conclusion is very unsurprising given the premises. It is merely the statementthat the second number is much bigger than the first. The conclusion, as given, tells usnothing significant about God’s existence: It does not tell us God exists, or that God islikely to exist. However, likelihoods and the Likelihood Principle are only concernedwith a comparison between two or more hypotheses on some piece of evidence, andcannot tell us something about the posterior probabilities of those hypotheses. Andso, Collins’ argument does not even tell us that T is overall more probable given fine-tuning! That is, his premises and conclusion are perfectly consistent with it being thecase that Pr(T | L PU ) < Pr(T )! Collins’ argument fails to meet even an absoluteminimum standard of showing that Pr(T | L PU ) > Pr(T ), and therefore fails to bea successful fine-tuning argument.

However, while the likelihoodist notion of ‘support’ does not do the work thatwe would hope for a fine-tuning argument, perhaps Collins has in mind somethingdifferent by ‘support’. Collins (2009, p. 206), concerned with the meddling demonas a counterexample, proposes what he calls the restricted version of the LikelihoodPrinciple. The restricted version limits which hypotheses we consider to those whichare considered non-ad hoc. For a hypothesis to count as non-ad hoc, Collins proposeseither of the following as sufficient conditions: that we have independent motivationsfor believing the hypothesis apart from the evidence, or that the hypothesis was widelyadvocated prior to learning this new evidence [and hence the reason for premise (3)].

4 Which, I remind the reader, is what Collins has directed us to as justification for the Likelihood Principle.

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But this is a curious move. We have already seen how the meddling demon is no coun-terexample to likelihoods. It was only a concern to those who thought that likelihoodscould tell us something significant about the posterior probability of hypotheses. Sowhy introduce the restricted version, unless ‘support’ is intended to mean somethingmore, something about the posterior probability of hypotheses? And we may furthersuspect that this is indeed what Collins has in mind when, in the context of the meddlingdemon, he says:

Consequently, by the standard Likelihood Principle, the occurrence of thissequence would strongly confirm the demon hypothesis over the chance hypoth-esis. But this seems counterintuitive: given a sort of commonsense notion ofconfirmation, it does not seem that the demon hypothesis is confirmed.

The Likelihood Principle concerns a comparison between two hypotheses only, inthe context of the evidence under consideration, and tells us nothing about the posteriorprobability of those hypotheses on their own given the evidence. It therefore makesno sense to say that the demon hypothesis is ‘confirmed’, as though the hypothesis isconsidered on its own, and so no reason to introduce a restriction on the LikelihoodPrinciple. We can say, ‘the demon hypothesis is confirmed over hypothesis H uponthis evidence’, but not that ‘the demon hypothesis is confirmed’. But perhaps wecan try to make sense of Collins’ notion of confirmation if we take him to have inmind some Bayesian notion of confirmation. That is, a hypothesis is confirmed iffPr(H | E) > Pr(H), and disconfirmed iff Pr(H | E) < Pr(H). This seems to be amore natural interpretation of what we might ordinarily mean by ‘confirmed’, and italso makes sense of his reference to the commonsense notion of confirmation. On thismeaning of ‘confirmation’, we can indeed talk about whether or not a hypothesis isconfirmed. If this is Collins’ intention, then the conclusion as stated is poorly worded,and not entailed by the premises, since he has only offered us confirmation in the senseprovided by the Likelihood Principle.

Even if this non-likelihoodist notion of confirmation is what Collins had in mind, itis clear from the text that he is trying to use the likelihoodist notion of confirmation.5

And so if he intends to use a more Bayesian notion of confirmation and support, thenhis argument needs serious revision. Collins does not wish to make use of priors, butthis does not mean he must sacrifice saying anything about the posterior probabilityof T given LPU. For example, if he partitions the hypotheses into T and ∼ T , and isable to establish some reasonable estimates for Pr(L PU | T ) and Pr(L PU |∼ T ),then he may yet demonstrate that the posterior probability of T is higher given L PUwithout making use of priors. If Collins is successful in establishing premises (1) and(2) in his core argument, then much of the work towards this end has been completed.Unfortunately, Collins’ methods for making sense of Pr(L PU | N SU ) fail, and wewill now examine some of the ways in which they do.

5 The conclusion of his argument is phrased as the likelihoodist would phrase it, and not as the Bayesianwould. In another context (Collins 2009, p. 210), he again uses confirmation in a clearly likelihoodist andnot Bayesian way. It seems reasonable to infer then that in ambiguous contexts, it is this likelihoodist notion,which Collins has provided, that he has in mind.

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Estimating probabilities

The first premise of the argument is the claim that Pr(L PU | N SU & k′) � 1.Roughly put, arguments to this conclusion go along the following lines. Take, forexample, some constant such as G. Note that the range of the life-permitting values forG is very small compared with the range of possible values. Since we have no reasongiven naturalism to suppose that G would have any particular value, we thereforerepresent our ignorance by assigning an equal probability to equally sized regions.This method of ascribing a uniform distribution of probabilities to possibilities whoseprobabilities we are otherwise ignorant of is called the ‘Principle of Indifference’.Using it, whatever probability we ascribe to the constant being from the life-permittingrange, we must assign the same probability to other regions of equal size. If we acceptthis, what we can observe is that as the finite-sized life-permitting region remainsconstant, and as we increase the range of possible values for G to extend to all thereals, the probability that the constant falls within the life-permitting range approaches0. This, it may be supposed, gives us a crude way of calculating that Pr(L PU |N SU & k′) ≈ 0. The Principle of Indifference in general, and its application to fine-tuning discussions specifically, has been subjected to many criticisms that have beencovered well elsewhere. Rather than repeating them in detail here, I will simply referthe reader to McGrew et al. (2001) and McGrew and McGrew (2005).6 I consider theobjections of Tim McGrew, Lydia McGrew, and Eric Vestrup to be serious objectionsthat are not adequately answered by Collins (2009, pp. 250–252). It is also worthnoting that some of the likelihoodists that Collins refers to in order to justify usingthe Likelihood Principle do not think the Principle of Indifference a good principle,and for reasons not entirely unrelated to their motives for being likelihoodists (seeEdwards 1972, pp. 55–57, Sober 2002, pp. 22–23).

Setting aside concerns with the Principle of Indifference, let us consider the rolethat background knowledge plays in Collins’ argument, in order to show that it cannotdo the work he wants as he has set it up. Collins’ core argument highlights that heis using ‘appropriately chosen background information’, k′ (Collins 2009, p. 205).It is important to understand k′ correctly. If we choose to use our entire backgroundknowledge, k, then we run into trouble. Part of our background knowledge is that lifeexists, and that the universe is fine-tuned for the existence of life. So choose any theisticor atheistic hypothesis you like, and try to find the probability of fine-tuning giventhat hypothesis and our background knowledge, and the probability will be unity. Weare therefore required to restrict our background knowledge in order to get the rightanswers to the right questions. Collins makes use of an ‘alien’, whose backgroundknowledge has been (it is hoped) appropriately restricted, so that we can then matchour probability estimates for particular events to match the credences that the alien hasfor those events. However, Collins is mistaken in both what credences the alien wouldhold, as well as in thinking that these particular credences are relevant to the questionat hand—that is, the probability of L PU given N SU . The following discussion willmake clear some of the reasons why (and there are many).

6 See also van Fraassen (1989, chap. 12), and Hájek (2011).

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Collins (2009, pp. 241–244) examines some of the concerns with how to determinek′ (which we will not cover) before settling on the following method of removing fromour background knowledge the fact that some constant has a life-permitting value, inorder to establish k′. The method is as follows (Collins 2009, p. 243):

...we let k be axiomatized by the set of propositions expressing the initial condi-tions of the universe and the laws and fundamental constants of physics withinour currently most fundamental theory which we can do calculations. Since theconstants of physics can be considered as given by a list of numbers in a table,we simply subtract the proposition expressing the value of C from that table toobtain k. Thus, k′ can be thought of as including the initial conditions of theuniverse, the laws of physics, and the values of all the other constants except C .7

It is clear what Collins hopes to achieve by this. By thinking of it as a table of valuesfor the various constants, with one box empty, given NSU we have no information todecide what it could be. Any value is consistent with the knowledge we have, and so weuse a method such as his restricted8 Principle of Indifference (Collins 2009, pp. 234–236) to assign values to the probability for C being fine-tuned, and thus demonstratethe truth of premise (1).

But there are concerns as to how to use this particular way of setting up k′ to answerthe kinds of questions we are asking. Consider the way in which a question can beincompletely specified. Suppose I describe to you an imaginary scenario involving aperson rolling a fair six-sided die for a game of chance. I then ask you, “What numberwill the die come up with?”. You may answer that you do not have enough information.That is, you would need to know facts about the way the die rolls off the hand, thesurface that it lands on, environmental factors, and so on. And even given all thatinformation you would still lack the capacity to answer the question. To answer sucha question, we need the scenario to be maximally complete, or at least complete withregards to all facts that might play some influence on the die roll. Let us say that sucha question must be ontologically complete. Perhaps that it must specify enough detailsuch that a competent physicist or mathematician would be capable of answering thequestion.

Rather than asking a question about what the actual outcome will be, we can aska slightly different question about the probability the player should ascribe to the diecoming up as a particular number. In that circumstance we know how such a playerwould calculate the probabilities, and can answer the question. And so, depending onthe sort of question we ask, the information provided may or may not be sufficientlyspecified to answer it. In Collins’ case, we are dealing with an epistemic questionabout what the probability of a particular outcome is, rather than a question regarding

7 Emphasis in original.8 The restriction on the Principle of Indifference is to let it apply only to “natural” variables, which arevariables that appear in the simplest formulation of a law. This move is designed as an answer to the challengethat different ways of expressing the laws lead to different probability assignments. There are concernswith this as an answer to the challenge—for example, the assumption that the simplest formulation is theappropriate choice. However, I do not wish to discuss the many problems with the Principle of Indifference,but rather try to cover fresh objections to Collins’ argument.

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the actual value it will come up as. However, to answer an epistemic question, thescenario must be itself appropriately complete—let us say, epistemically complete. Aquestion about the probability of outcomes of a die roll can generally be answeredby those familiar with the behaviour of a die roll. However, suppose we modify thescenario so that we no longer specify that the die is six-sided, and then ask what theprobability that it will come up a particular number. In this case, the scenario is notcomplete enough. The answer will critically depend on how many sides the die has.More importantly, the question is one about the probabilities that the player wouldassign, not the probabilities that we (as people imagining the scenario) assign. And theplayer knows something important that we do not—the player knows how many sidesthe die has. Let us call a scenario epistemically incomplete, when there are propositionsimportant9 to the calculation, which the agent in the story knows the truth value of,but we do not.

In order to evaluate now what epistemic probabilities follow from k′, we need todo some further work. We cannot just present k′ and ask, “what is the probability ofthe nth constant rendering the universe fine-tuned?”, since the information given isincomplete to answer that question. If the universe is deterministic, then the probabilityis either 0 or 1, and the information given does not determine which of those two iscorrect. If the universe is chancy, we would need to be given information about thekind of distribution or mechanism that produces the variation. So instead we need tobe asking a question about epistemic estimations of similar questions. We cannot askourselves what we would take the relevant probabilities to be, for we already knowthat the constants are within the life-permitting range. Instead, much like we askedquestions about the probabilities that a player of a game of chance would arrive at, wemay think to ask what some hypothetical being with background knowledge k′ wouldconclude. This is precisely the method that Collins (2009, pp. 232–233, 245) attemptsto use:

...imagine an unembodied alien observer with cognitive faculties structurallysimilar to our own in the relevant ways, and then ask the degrees of credencethat such a being would have in LPU given that he or she believes in N SU&k′or in T &k′.

So now when we come to consider k′, we will need to take careful note of thepropositions whose truth values we know the being (alien) will be aware of, but werenot made explicit. These propositions may be of two sorts in the context of the scenario:

1. Propositions we also know the truth value of2. Propositions we do not also know the truth value of

In the game of chance scenario where the number of sides is not made explicit, anexample of the first kind of proposition would be that the being is aware of how gamesof chance typically work, and the sorts of probabilities that should be ascribed to fair

9 There may be many propositions with important truth values which are deemed unimportant to makeexplicit. For example, in the game of chance it would be important to know if there was a laser that instantlyvaporises the die if it is going to come up as 6. We can assume, as charitable and reasonable people, thatthis is the sort of thing that would be made explicit by the one asking the question, if it were important.

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dice in order to maximise winnings. An example of the second kind of propositionwould be how many sides the die has. In the discussion that follows, we will be lookingfor both of these sorts of propositions in order to see if the calculation that Collinshopes for is indeed justified by the scenario.

And now, using this epistemic tool of the unembodied alien, we open up a veritableflood of problems. Consider Collins’ claim that the alien observer have “cognitivefaculties structurally similar to our own”. We humans lack the capacity to say anythingmeaningful about the probability of life in universes with different constants, withouthaving computers (or at least a pen and paper) upon which to do our calculations. Inorder to avoid giving the alien a computer or a pen and paper, we will need to assumethat this alien has the capacity to do all such calculations in its mind. This immediatelysets the alien apart from us in terms of its cognitive faculties. But it gets worse. Wehumans know what our world is like, and for relatively small changes in the constantswe can make reasonable (we hope) guesses about how those other universes will look,and what that will say about life in those universes. This alien, however, will be inno similar situation. It will not have an existing universe to look at and tweak, withall the constants set, and life inside it. This alien observer will have to be able tocalculate for any choice of values for the constants what that universe will look like,at the very least in terms of whether or not that universe will permit life. Otherwise weneed to introduce into k′ some awareness of a universe like ours and no other, and thatwould be curious knowledge to include in k′ that would certainly influence the alien’sestimated probability. And so we must say that for a given table of n − 1 constantsspecified, the alien knows which (if any) of the values for the nth constant will renderthe universe life-permitting. Now, in the case of n constants, when the values for onlyn − 1 constants are known, we cannot say for sure whether those known constants arefine-tuned for life. It may be the case that:

1. There is no value for the nth constant that would render the universe fine-tunedfor life.

2. There is a value for the nth constant that would render the universe fine-tuned forlife, and that for nearly any choice of values for any choice of n − 1 constants,there is a corresponding value for the nth constant that would render the set life-permitting.

3. There is a value for the nth constant that would render the universe fine-tuned forlife, and that for nearly any choice of values for any choice of n − 1 constants,there is not a corresponding value for the nth constant that would render the setlife-permitting10

In the first and second cases, it does not seem that the constants can reasonably becalled ‘fine-tuned’. However, in the third case we might have room for some crudenotion of a ‘fine-tuned constant’. Of course, there are numerous variations between the

10 We may find this view plausible when we consider the gravitational force. If the gravitational force isincreased sufficiently, then the universe re-collapses rapidly. If we keep all other constants the same, andcontinually increase the gravitational strength, it seems implausible to think that we will get anything but arapidly re-collapsing universe. Likewise, if we reduce the strength, and the universe expands too quickly foranything to cohere together, then continually reducing the strength until it is nothing is unlikely to produceanything else but a universe that expands too rapidly.

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second and third cases above, but that should not be important for the point that follows.Now consider our alien’s background knowledge k′, which includes knowledge of allthe constants bar one, and includes the capability to evaluate whether or not a particularvalue for a constant will render the universe life-permitting. This being would know,then, if one of the three cases above applies given the particular set of n − 1 constantswith which it has been presented. In the first case, it would declare a life-permittinguniverse to be impossible. In the second case, we would have a situation that would givesome motivation to apply the Principle of Indifference (setting aside concerns with theprinciple)—it was unsurprising that the n − 1 constants would allow for some choiceof the remaining constant that renders the universe life-permitting, so all that remainsto do is evaluate the probability that the remaining constant is in the life-permittingrange. The third case, however, is an interesting one. Our alien would know that a verycurious and rare situation has occurred—a collection of constants that are just rightsuch that there remains a value for the remaining constant that renders the whole setlife-permitting. The alien will see that for the n − 1 constants, all of them point to noother special region of possibility space11 other than the one that allows for complexlife. With no other information, the being may reason along these lines: it is a curiousfact that of all the constants I could have been presented, I was presented with preciselythese ones, that can be called “fine-tuned”. I initially thought (it may be supposed) thatthere was nothing special about any constant being any particular value. However, if Iam asked to evaluate Pr(L PU | N SU & k′), I will rate it reasonably high. It was notat all expected that the n − 1 constants be just right for the last constant to be able tobe life-permitting, and so it seems like I was mistaken to think that there was nothingspecial about any one value for a constant over another. Perhaps there is some sort ofnecessity determining the values for the constants to be fine-tuned, or perhaps thereis another creature like myself12 that has seen this universe, chosen it for its specialfeatures, and put in me this situation with a curious set of knowledge. Given that then − 1 constants may be called “fine-tuned”, it seems likely to think that, given k′ andN SU , that the final constant is also fine-tuned, or at least far more likely than anyother constant assignment.13

11 It may be argued that the alien will not actually know anything about whether or not other regions of spaceare interesting. This does not seem a reasonable possibility to consider, however. Suppose that the alien onlyhas the capacity for determining whether or not a particular set of constants will render the universe life-permitting. It would be a curious fact if the alien possessed this capacity to detect life-permitting universesbut not other ‘special’ kinds of universes. Having such a capacity and lacking others would surely figure inits calculations. The alien would rightly wonder why it is able to determine a universe’s fitness for life, butnot to determine anything else special about it.

A second objection may be that the alien does in fact see many other special regions of possibility space.If this is the case, and if there are plenty of other different ‘special’ regions of space that are quite frequent,then it would seem that a life-permitting universe is not any reason to think that God exists. That is, if theuniverse had not been life-permitting, it would have been special in some other interesting way. And so itseems that the argument requires that the alien be aware of other special regions of possibility space, andalso know that such regions are uncommon.12 It seems to me that the alien would be very reasonable in suspecting this. And indeed, this is in a way thecorrect answer! Collins has carefully chosen k′ and placed it in the alien precisely because the remainingconstant is life-permitting.13 It may be thought that this is the wrong way to approach it. The alien is not confronting the particularassignment of values for the n − 1 constants, and being asked what to make of that. Rather, the alien would

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And so we have one very important fact that the alien knows, which we do not:Whether or not it is rare, given arbitrarily chosen values for n − 1 constants, that therebe a value for the nth constant that renders the universe fine-tuned. If true, the alienwill not necessarily conclude that L PU given N SU & k′ is unlikely. Importantly, wedo not know whether this is true or not. So the situation is epistemically incomplete,and cannot be used as a guide to determine the relevant probabilities.

So perhaps we can modify k′ to exclude values for any of the constants on the table.This would solve part of the above concerns by removing the reasoning process thatcould lead the alien to conclude that the nth constant is likely to render the universelife-permitting. In this case, N SU would seem to be in more trouble, needing toharmonise multiple values rather than just getting one right. So let us consider theepistemic scenario where k′ includes the table, but with the values for all the constantsobscured. If this is our background knowledge, then Collins will now have a problemwith his treatment of the epistemically illuminated range (EI). For Collins, the EI rangeis “the set of values for which we can make determinations of whether the values arelife-permitting or not” (Collins 2009, p. 244). Talking about an EI range grants Collinstwo advantages. First, it restricts the range of possible values to some finite range, andthus (hopefully) eludes the normalisation concerns that frustrate typical fine-tuningarguments (McGrew et al. 2001). Second, it escapes concerns that our best physicistsare not able to tell us much meaningful about how a universe with constants radicallydifferent to our own would look. That is, it escapes concerns that outside our localregion of possibility space life-permitting universes are common, and we just don’tknow it. If we are considering our earlier alien, then by modifying k′ to exclude allconstants, we are not restricting our consideration to any particular range. This alien,unlike our best physicists, is not restricted to knowledge about values for constantssomewhat similar to our universe’s current values. The alien knows what things looklike outside this area, and so the scenario is epistemically incomplete—the alien knowsimportant things which we do not know. Collins (2009, p. 245) supposed that we couldimagine the alien being restricted to knowledge about n − 1 constants, and then addto k′ the knowledge that the nth constant falls within our EI range, to stick to whatwe know with our modern physics and limited epistemic position. But how this issupposed to make sense in the context of the alien is unclear. Some respond to fine-tuning arguments by pointing out that, for all we know, life-permitting universes arecommon and it is our universe and its kin that are unusual in requiring fine-tuningfor life. That is, fine-tuning is not in general required for life. Consider the followinganalogy from John Leslie (2002, p. 17) that attempts to defuse this line of reasoning.Suppose that there is a mostly empty region of a wall, with a single fly in the center,and then outside this region the wall is covered with flies. While a bullet from a shooter

Footnote 13 continuedjust know the credences it holds for every particular assignment of values for the n − 1 constants of values.That is, the alien is not picking out any particular value assignments and paying special attention to them. Thealien decides in advance its response to any given assignment. This response, however, won’t help escapethe above concerns. What in fact the alien will know is, “If I were to discover that these n − 1 constantshad some particular set of value assignments, here is what I would think about the relevant probabilities”.And in the above discussion, we have simply examined what the alien’s reaction would be in the particularcase where the constants are as they are in our universe. That is the case that interests us.

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striking a fly is not surprising, it would be a remarkable fact if a bullet was to strikethe lone fly, rather than one of those in the densely covered parts of the wall. Thatseems fair, but if we make use of Collins’ alien, we can no longer take advantage ofthis line of reasoning. Suppose that outside our local region of possibility space thatlife-permitting universes are plentiful, and we ask the alien what the probability isthat the constants will be jointly life-permitting. The alien will answer that it almostcertainly will be, since the wall is full of flies. However, if you then require that thealien restrict itself to our local region, you are introducing curious knowledge. Underwhat kinds of circumstances would the alien know this? Did someone ask it to restrictits knowledge to a particular range? Was the range curiously specified so its verycentre was life permitting, but its edges were not? Such a move involves introducinginto our background knowledge information that is causally downstream from the factof which universe has been created, which leads to problems with this account. IfCollins wants to escape the earlier objections by removing from k′ knowledge of thevalues for all constants, then he must face the problems of an infinite range of values,along with the problem of our lack of knowledge of what possibility space looks likeoutside of our EI range.

Final remarks

If we take the time to reflect on the alien, the list of problems will rapidly grow. Veryobviously, the alien would be asking why it exists, where it came from, and why it hasno body (if indeed it has no body). If it knows that it is an immaterial mind, it is a shorterstep for the alien to move from naturalism to theism than it is for many naturalists, sothe alien cannot be considered as an idealised naturalist when asked for its estimate ofthe probability of LPU. And even if we can fill in the gaps of the alien’s story so thatwe can estimate its credences, the question remains: what does the alien’s credencefor some particular event have to do with our question of Pr(L PU | N SU & k′)? Therelevance of the alien to that question needs to be established. We cannot use the alienas a tool for establishing the first premise of Collins’ argument.

And even if Collins can establish Pr(L PU | N SU & k′), the form of his argu-ment needs to be corrected. For something to count as a fine-tuning argument forGod’s existence, it needs to say something about God’s existence. At the absoluteminimum, it should give reason to think that Pr(T | F)> Pr(T ). Using the likeli-hoodist’s tools, Collins’ argument fails to do this—likelihoodists do not make claimsabout the posterior probability of hypotheses, and that is reflected in their tools.Changes to the structure of Collins’ argument may improve it, and showing thatPr(L PU | T & k′) � Pr(L PU | N SU & k′) would indeed be a valuable result.As things stand, however, Collins’ argument does not meet the challenge of countingas a successful fine-tuning argument.

Acknowledgments This paper was written with the support of the Monash Postgraduate PublicationsAward. I also thank Lydia McGrew for her helpful feedback on this paper.

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References

Collins, R. (2009). The teleological argument: An exploration of the fine-tuning of the universe. In W. L.Craig & J. P. Moreland (Eds.), The Blackwell companion to natural theology (pp. 202–281). Hoboken:Wiley-Blackwell.

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Forster, M., & Sober, E. (2004). Why likelihood? In: The Nature of Scientific Evidence. Chicago: Universityof Chicago Press.

Hájek, A. (2011). Interpretations of probability. http://plato.stanford.edu/entries/probability-interpret/Leslie, J. (2002). Universes, kindle edn. New York: Routledge.McGrew, L., McGrew, T. (2005). On the rational reconstruction of the fine-tuning argument. 7(2), 423–441.McGrew, T., McGrew, L., & Vestrup, E. (2001). Probabilities and the fine-tuning argument: A sceptical

view. Mind, 110(440), 1027–1038.Royall, R. (1997). Statistical evidence, a likelihood paradigm. London: Chapman & Hall.Sober, E. (2002). Bayesianism-its scope and limits. Oxford University Press, 113, 21–38.van Fraassen, B. C. (1989). Laws and symmetry. Oxford: Clarendon Press.

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