Does The Fine-tuning Of The Universe Make It More Likely Than Not That God Exists?

Introduction

On first reading the very phrase fine-tuning suggests intentionality. That something is fine-tuned is perhaps suggestive of an end or goal. The argument I am alluding to is the cosmic variation of the teleological argument the idea that it is extremely improbable for the fundamental cosmic parameters of our universe to be life-permitting (i.e. fine-tuned) by chance, and so fine-tuning may be evidence of a designer or deity at work. Whilst several variations of the argument exist, I will turn towards a probabilistic argument as laid out by Collins using the prime principle of confirmation (PPC). I will begin by formulating a variation of Collins argument, followed by a thorough evaluation of both premises and the conclusion. Overall this essay will show that this argument, whilst intuitively appealing, simply fails to allay the objections raised by probability theory, the problem of God s intention, and the objection of invalid inference. Ultimately, I will conclude that the fine tuning of the universe does not make it more likely than not that God exists.

Cosmic argument via the Prime Principle of Confirmation

Collins takes the fine-tuning data (FT) of the universe to provide evidence for preferring theism over the atheistic single-universe hypothesis [ASU] (Collins 2003, 5). The ASU hypothesis holds that there is only one universe and it has life permitting cosmic parameters by chance. Theism however postulates that the fine-tuned universe is a product of God s design.

The crux of this argument is the use of the prime principle of confirmation. It holds that whenever we are considering two competing hypotheses, H₁ and H₂, an observation, O, counts as evidence in favour of H₁ over H₂ if O is more probable under H₁ than it is under H₂, (Collins 2003, 6). In other words, we can substitute H₁ for the theistic design hypothesis, H₂ for the ASU hypothesis and O as FT. The argument can therefore be laid out as follows (Collins 2003, 8):

P1) The existence of FT is very improbable under the ASU hypothesis

P2 The existence of FT is not improbable under theism

C1) From P1 and P2 and the prime principle of confirmation, it follows that the FT provides strong evidence in favour of theism over the ASU

As we can observe, this argument is logically valid. That is, if both premises hold than the conclusion will be true. In order to appropriately answer the question at hand, I will modify the argument to include:

C2) Therefore FT makes it more likely than not that God exists

To begin, I will evaluate the credence of Premise 1, that FT is improbable under the ASU.

Defence of Premise 1: Fine Tuning Data

The first substantial defence of the argument is to show that the values of the fundamental parameters of the cosmos have a very narrow life-permitting range, and it is therefore improbable that they occurred by chance (P1). For example, the gravitational constant G acts as gravitation G. As Craig notes, if G had been a little greater, all stars would have been red dwarfs, which are too cold to support life-bearing planets. If it had been a little smaller, the universe would have been composed exclusively of blue giants, which burn too briefly for life to develop, (Craig 2003, 156). In fact, Davies holds that a change in either G or electromagnetism by only one part in 10⁴⁰ would preclude the existence of stars like the Sun (Davies 1992, 5). In this it is clear to see that the chances of the life-permitting range of values of G is incredibly small, or rather fine-tuned.

There is a wealth of literature and examples that will further elucidate the fine tuning of cosmic parameters (e.g. the cosmological constant, entropy, proton/electron mass ratios), however the intuition remains the same, and has generated broad scientific consensus that some physical constant [C], must take a value in some very narrow range in order for (carbon-based) life to evolve (Colyvan, Garfield and Priest 2005, 327). Hereafter, this life-permitting range shall be donated as r.

However the issue here is that we cannot say something about the probability of a physical constant C taking a value within r. All we know is that r is narrow. If for example, there was an underlying bias factor that swayed cosmic parameters to take life-permitting values, then the probability of C taking a value within r, may not actually be low at all. Whilst such an objection is speculative, it demands a mathematical conception of defining the probability of C falling within r. If nothing can be said of r in relation to the range of possible real values, then the probability of C falling within r is mathematically undefined. A solution can be found however, in the principle of indifference.

Defence of Premise 1: The Principle of Indifference

The principle of indifference holds: when we have no reason to prefer any one value of a parameter over any other, we should assign equal probabilities to equal ranges of the parameter, given that the parameter in question directly corresponds to a natural parameter, (Collins 2003, 14). This therefore defines the relationship between r, and the range of all possible real values a constant can take, R. Indeed, as all values within R have equal probabilities, we can take the probability of a physical constant C taking a life-permitting value, as r/R. In this sense, the probability of C taking a value within r is mathematically defined, and thus Premise 1 can be made to stand.

I will now explore in detail one major objection to Premise 1 concerning probability theory.

Objection to Premise 1: Probabilities do not apply

The probabilities do not apply objection is a major refutation of the principle of indifference. The argument objects to the idea of assigning an equal probability to each unit subinterval in a range of values R for physical constant C. Thus, the probability of C being life-permitting (r/R) would not hold, and Premise 1 falls.

The central idea here as highlighted by McGrew, McGrew, and Vestrup (2001), is that the possible values of C have no defined upper or lower bound. According to modern science, there is no established finite range for most fundamental cosmic parameters, and thus we take the range of C to be infinite. It follows, When a probability distribution is defined over a space of possible outcomes, it must add up to exactly 1. But for any uniform distribution over an infinitely large space, the sum of the probabilities will grow arbitrarily large as each unit interval is added up (Ratzch, Del and Koperski, Jeffrey 2016). Therefore we cannot so much as assign a probability to a value within R, and so the probability of C taking any value is mathematically undefined. In this light we cannot say that FT is improbable under the ASU. In fact nothing can be said of its probability at all.

Response: Truncation

One solution to this objection is to truncate the range R of possible real values for C. As Ratzch et al., (2016) note, instead of allowing the real line of C to range from [0, ], one could form a finite interval [0,N], where N is very large relative to [r] (life-permitting range). A probability distribution could then be defined over the truncated range, and the principle of indifference could then be effectively employed to assign equal probabilities to each unit subinterval. Indeed, as Colyvan et al., point out the trick is to find some set of possible values that C could take that is large enough for [r] to seem small, but small enough for the resulting probability for [C] [r] to be non-zero (Colyvan, Garfield and Priest 2005, 329). If this can be done, the probability r/R may still hold.

Counter Response

Whilst one could certainly postulate the idea of truncation however, several questions must be asked. Firstly, how does one go about truncating a range R for every fundamental cosmic parameter, when as Manson points out, the physicists who provide the fine-tuning data [ ] do not give theoretical upper bounds on the values of the parameters in question, nor do they give theoretical reasons why some of those values are more likely to be actual than others? (Manson, 2009, 281). Indeed, it would be implausible to truncate a range R without sufficient scientific evidence or theory. Therefore, the only option is to arbitrarily truncate R. However, not only will this be meaningless if not backed up by proper evidence, but the defender of the truncation solution will first need to prove that fundamental constant C does not have an infinite real line. Otherwise, if one is to arbitrarily truncate the range, we are left with as McGrew et al., point out, an infinite number of finite-sized regions, which is mathematically implausible. (McGrew, McGrew, and Vestrup 2001, 203)

To summarise then, I believe the probabilities do not apply objection poses a serious threat to Premise 1 of the argument. If we cannot so much as validly assign a probability to any subinterval within the range of real values of C, then we cannot determine the probability of C taking a value within r. Thus it is difficult to see how we might say that the fine-tuning of cosmic parameters is improbable under the ASU, when the probability itself cannot be defined.

I will now explore a defence of Premise 2.

Defence of Premise 2: Argument for God s Intention

Even though Premise 1 has been shown to fall, in order to further my evaluation of the argument from fine-tuning it is important to explore the validity of Premise 2. The defender of the argument must show that FT is not improbable under theism. In this there are two main ideas a) that God has probable capability of fine-tuning, and b) that God has probable intention to do so. Collin takes a to be implicit in the idea of God, in that God is omnipotent. Indeed, the intuitive appeal is that the fine-tuning of the Universe would require divine power to be conceived, and so no further argument is needed for a. However the matter of God s intention is subject to much greater debate. Collin s provides us with the following justification (Collins 2003, 9):

P3) God is an all good being

P4) It is good for intelligent conscious beings to exist

C) Therefore, it is not improbable that God would create a world that could support intelligent life

From this it is plausible to interpret an argument for an Abrahamic God, in that such a God has probable cause to fine-tune the universe. Omni-benevolence is implied as God is an all good being. Omniscience is implied as God must surely always know what is good, and omnipotence follows in the idea of creation. This notion of God is of course widely popular amongst theologians and has received support in the field of fine-tuning arguments too (most notably Swinburne 1991). As we will see however, this defence ultimately fails to sufficiently argue for God s motive.

Objection to Premise 2: A Perfect God Speculation

Narveson undermines the very idea of arguing for God s intention. He claims that if God has a cause for fine-tuning the universe, he has acted with an end in view. Thus, in acting with an end in view he must necessarily be seeking something that he lacks (Spinoza 1982 [1677]: 59). It therefore follows, that if God lacks something, he must be imperfect. Narveson takes this to be logically invalid as God is necessarily perfect he cannot be otherwise (Narveson 2003, 9). In this light, no defence can be made for God s probable cause, and P2 falls.

Of course the assumption here is God s perfection. If we take this to be true, Narverson s response holds considerable weight it is difficult to see a way out of his logical formulation. The alternative however, is to argue for an imperfect God. Indeed, an imperfect God seems logically compatible with Collin s defence above.

However, even supposing that Collins argument could be formulated to allow for an imperfect God, Collins has not provided any justification for P3 or P4. Whilst P3 has considerable philosophical weight, especially in the Abrahamic conception of God, P4 however, is much weaker. It is difficult to see how one may argue that it is good for intelligent conscious beings to exist, certainly without detracting from the point at hand, which is an argument from fine-tuning. If the argument finds itself in philosophically deep waters, trying to define what is good, and whether conscious beings fit such a descri ption, the explanatory power of the argument will be diminished. In this light Collins defence is dismissed on account of being highly speculative and leaving the argument vulnerable to strong theological objection.

Thus, in summary, Premise 2 is considerably diminished as no adequate defence can be made for God s motive. Whilst other defences can be made in favour of God s intention, such discussion is beyond the scope of this essay. In light of Collins defence alone, P2 is undermined.

However, some proponents of the fine-tuning argument believe no substantial claim can be made for theism (Craig 2003, Behe 1996.) In this light, they employ a weaker design hypothesis that there is a designer but whom the designer may be is left open. I believe this to be a crucial limit to the argument presented in this essay. The cosmic argument via the PPC simply has no logically valid formulation for God s intention and thus, until such a justification can be made, is consigned to a weaker design hypothesis.

Objection to C2: Invalid Inference

As shown above, P1 fails, and P2 is considerably weak. Thus C1 hangs on a fine thread. However, even if C1 can be made to fly, there is a strong objection to C2. Bradley holds that, even if we can show FT strongly favours theism over the ASU, this does not mean that the fine tuning makes the existence of God more probable than not, (Bradley 2002, 378). The intuition here is that this argument has only justified the likelihood of God with respect to one concept that of fine tuning, against one scenario the ASU. In order to reasonably assert that God is more likely to exist than not, however, we must take into account a much greater sphere of background knowledge and theory. Indeed Swinburne, a defender of the argument from fine-tuning, holds that together with other evidence not discussed here [the fine-tuning argument] does, I believe ( ) render the existence of God significantly more probable than not (Swinburne 1990, 174). Special attention, however, should be given here to Swinburne s implicit acknowledgement that fine-tuning alone cannot make it more likely than not that God exists. As Bradley suggests, the fine-tuning argument is to be taken as an appendage to the array of arguments in favour of God s existence (Bradley 2002, 378). These arguments are likely to argue against alternative scenarios such as the many-universes hypothesis which may cast further doubt on theism, or defend arguments from consciousness or miracles, as Swinburne does (Swinburne, 1990). It is only in thoroughly exploring such alternative scenarios and arguments that we may then reasonably assert that God is more likely to exist than not. Therefore, at best, this argument based on fine-tuning alone, can go no further than C1.

Conclusion

In summary then, this essay has involved a thorough evaluation of the argument from fine-tuning via the PPC. Whilst the argument holds considerable intuitive appeal, it is subject to severe objections met with weak response. In the probabilities do not apply objection we can see that Premise 1 fails to hold on account of having undefined probabilities. In the objection to P2 we can see that Collins argument fails to justify God s intention without submerging into philosophically deep waters. As a result, C1 is made incredibly weak. However, even if C1 can be made to fly, the move from C1 to C2 is undermined by the objection of invalid inference. I therefore conclude that whilst the fine-tuning of the universe may in theory support an argument in favour of a designer, it does not make it more likely than not that God exists.

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