The argument continues, but this is the core. Notation: k e [some interval], means k is contained (e) in [whatever goes here].
This was thanks to Eubulides who suggested Graham Priest.
CG ---------------------------
Problems With the Argument from Fine Tuning
1 Mark Colyvan Department of Philosophy, University of Queensland..Jay L. Garfield Department of Philosophy, Smith College..and Graham Priest Department of Philosophy, University of Melbourne...
Abstract
The argument from fine tuning is supposed to establish the existence of God from the fact that the evolution of carbon-based life requires the laws of physics and the boundary conditions of the universe to be more or less as they are. We demonstrate that this argument fails. In particular, we focus on problems associated with the role probabilities play in the argument. We show that, even granting the fine tuning of the universe, it does not follow that the universe is improbable, thus no explanation of the fine tuning, theistic or otherwise, is required.
1. Introduction
There has been a great deal of recent interest from both physicists and philosophers in the so-called fine-tuning argument.2 This is the argument that purports to deliver the conclusion that God exists from the fact that our universe seems remarkably fine tuned for the emergence of carbon-based life. In this paper we discuss several difficulties with this argument. Central to these concerns are the fact that the argument rides roughshod over crucial matters concerning probability.
Before we move to our objections it will be convenient to state the fine-tuning argument with some degree of precision.3
1. The boundary conditions and laws of physics could not have been too different from the way they actually are if the Universe is to contain (carbon-based) life.
2. The Universe does contain (carbon-based) life. Hence:
3 . The Universe as we find it is improbable.
4. The best explanation for this improbable fact is that the Universe was created by some intelligence.
Hence:
5. A Universe-creating intelligence exists.
First let us say a few words about the above presentation of the argument. Our presentation is a little more careful than those one usually encounters. There are two reasons for this. On the one hand, some versions of the argument are so vague that it is hard to take them seriously at all and we wish to focus on the strongest and most compelling version of the argument; and this, we believe, we have presented above. On the other hand, we believe that it is the lack of precision in many of the presentations that has allowed the argument to survive so long. Once the various premises and inferences are made explicit the shortcomings of the argument are plain to see. We have not set up a straw person though. The above presentation is true to the spirit of the argument as presented by its most influential advocates Leslie (1989; 1998), and Swinburne (1990; 1991).4
Next let us say a few words about the fine tuning mentioned in the argument. Although there are many fascinating examples of the fine tuning in question,5 of particular interest are the rather narrow ranges in which certain physical constants must fall if (carbon-based) life is to be possible. For example, for elements as complex as carbon to be stable, the electron proton mass ration (m_e/m_p = 5.44617013 x 10^-4 ) and the fine structure constant (a = 7.29735308 x 10^-3 ) could not have been more than a few percent from their actual values.
A great deal has been written on this evidence and even more on the issue of what the best explanation for this fine tuning is: God or multiple universes.6 We will have little to say about either of these debates. We will not question the scientific evidence for fine tuning. (That is, we grant premise (1) of the above argument.) Instead, we examine other aspects of the argument that deserve closer attention than they have thus far received. In particular, we focus on the argument from (1) and (2) to (3). We show that none of the fanciful explanations for fine tuning is required, because (3) simply does not follow from (1) and (2).
2. The Improbability of Fine Tuning
Consider the inference from (1) and (2) to (3). The first thing to notice here is that the argument presupposes that the laws of physics or the boundary conditions of the universe could have been other than they are. After all, if they could not have been different, the probability of the universe being just as we find it is 1, and no fine tuning has occurred. But what is the modality invoked here? Logical possibility? Conceptual possibility? Physical possibility? This is rarely spelled out in the usual presentations of the argument. One exception is Leslie, who explicitly invokes logical possibility (1989, p. 15) and so we will initially follow him on this.7 It certainly is logically possible that various physical constants, for instance, could take any real number as their value. Logical possibility, then, seems a promising option.
The central idea of the fine-tuning argument is that some physical constant, k say, must take a value in some very narrow range in order for (carbon-based) life to evolve.8 Let us suppose that the constant in question has to lie between the values v-d and v+e. (Where v is the actual value of k and d and e are small, positive real numbers.) The intuitive idea is that the interval [v-d, v+e] is very small compared to all the logically possible values k might have taken (i.e. the whole real line), and since there is no explanation of why k = v and not any other value, all possible values of k should be considered equally likely. Thus, the probability of k taking a value in [v-d, v+e] is also very small. That's the intuitive idea, but the problem is that it s not at all clear how this naïve intuition can be made rigorous.
One way to try to cash out this intuition is to compare the number of values that k can take in [v-d, v+e] to the all possible values it could take in the real line. But in each case there are 2^aleph-naught, values so the relevant probability would appear to be one.9 That, however, is misguided. We are not interested in the number of values k could take but rather the measure of the sets in question.10 Employing any standard measure (such as Lebesgue measure) will, as the fine tuning argument proponent suggests, indeed yield a very low probability for k e [v-d, v+e]. The problem for the proponent of the fine tuning argument, however is that the probability is too low! Such measures will yield a finite value for the interval [v-d, v+e] and an infinite value for the whole real line. The resulting probability for k e [v-d, v+e] is zero (or infinitesimal if you prefer a non-standard analysis take on this).11 What is more, the probability that k takes a value in any finite interval will be the same even those we intuitively think of as being extremely large. So, for example, the probability of k e [v-10^10^10, v+10^10^10] is also zero (or infinitesimal).12
The fine tuning argument, on its most plausible interpretation, hence not only shows that life-permitting universes are improbable, but, arguably, that they are impossible! Surely something has gone wrong here. Admittedly, the problem here has nothing to do with the fine-tuning argument; it concerns (standard) probability theory. Indeed, similar reasoning shows that an infinitely sharp dart cannot hit a dart board, no matter how big the board is; or that no one can win a lottery that has infinitely many tickets. It's true that such paradoxes of probability theory are well known and that there does not seem to be any consensus on how they are to be resolved. This does not, however, relieve the defender of the fine-tuning argument of the burden of proof. Anyone advancing this argument must demonstrate that the probability that the physical constants take life-supporting values is low, or the argument whatever its other merits or difficulties does not even get off the ground. If the only argument to show that the probability that the physical constants take values that permit carbon-based life is low also shows that it is impossible for them to take those values, that argument must be rejected and we are back to square one, without any reason to believe that there is any phenomenon needing explanation, least of all, explanation by an intelligent deity.
Now someone might be tempted to accept that the probability of the universe as we find it is zero, but deny that events with zero probability are impossible. This, however, will not help, for the objection can be recast without appeal to assumptions about how we should interpret zero probabilities. First, we reiterate our point above that the probability of finding the constant in question in any finite interval is zero. This makes a mockery of the claim that the class of life-permitting universes, in particular, is improbable. The defender of the fine-tuning argument is now obliged to tell us why this class of universes is more improbable than others.13 Accepting that this class of universes has probability zero but that this does not render it impossible does nothing to defuse the problem at hand. Second, there are other problems looming for anyone prepared to bite the bullet and accept that the probability that we find ourselves in this class of universes is zero. Accepting that the universe as we find it has probability zero means that the conditional probability of any hypothesis relative to the fine-tuning data is undefined. This makes the next move in the argument from fine tuning that the hypothesis of an intelligent designer is more likely than not, given the fine-tuning data untenable. Moreover, even if you focus, using a Bayesian hypothesis testing model of inference, on the inverse probability (the probability of the evidence, given the hypothesis), then on this assumption, no hypothesis is capable of raising the probability of a fine-tuned universe if the probability is zero, it stays at zero (using standard updating procedures like Bayes Rule).14 For now, we wish to simply point out that on any standard calculation of the probability of a fine-tuned universe, the probability of that universe comes out as zero and therein lies the problem. The defender of the fine-tuning argument must find another way to show how the intuition that [v-d, v+e] is small can be made to support the claim that the probability of k e [v-d, v+e] is low (but not zero).
One plausible way out of this problem is to retreat from logical possibility and restrict the range of values that k can take from all of the reals to something more manageable. The move, in essence, is to reject logical possibility, which cannot discount any real values, and adopt a weaker notion of possibility that allows a smaller range of values. Conceptual possibility? That can't be right though, because it also seems to be conceptually possible that the physical constants could take any real number as their value. Physical possibility (construed as consistency with the laws of physics and physical constants as we find them) however, restricts the range too much for the proponent of the fine tuning argument, leaving the actual values as the only possible ones, and hence setting the probability at 1! The trick is to find some set of possible values that k could take that is large enough for [v-d, v+e] to seem small, but small enough for the resulting probability for k e [v-d, v+e] to be non-zero. (That is, for the class in question to have a large but finite measure.) Putting it this way, however, illustrates how arbitrary this restriction is going to be. It's not going to be any obvious, naturally-occurring, sense of possibility (such as logical, conceptual or physical possibility). The class in question has to be hand picked: choose something too small ([v-d, v+e], say) and the probability of k e [v-d, v+e] is too large; choose something too large and the probability of k e [v-d, v+e] is zero. Indeed, it seems that the choice of the class in question needs to be fine tuned!
Leslie does seem to endorse such a move (for reasons not unrelated to the problems we have raised), despite explicitly invoking logical possibility as the appropriate modality:
``Imagine that a bullet hits a fly surrounded by a large empty area. The bullet's trajectory needed fine tuning to achieve this result, which can help to show that a marksman was at work. It can help to show it regardless of whether distant areas are all of them so covered with flies that any bullet striking them would hit one. The crucial point is that the local area contained just one fly.'' (Leslie, 1998)
Leslie does not think that there is anything problematic about the appeal to local area here but he is clearly wrong about this. As we have already argued, this local area needs to be specified in a non-arbitrary way and it needs to be the right size to get the probability of k e [v-d, v+e] right for the fine-tuning argument to work. There is clearly a significant task here for Leslie and other defenders of this version of the fine tuning argument: they must come clean about the specification of the local area. We do not see how this can be done in a non-question-begging way. In the absence of such a specification, we conclude that there is no argument from (1) and (2) to (3) and the argument as a whole fails...