Abstract
Collins (The Blackwell companion to natural theology, 2009) presents an argument 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 given fine-tuning. As an argument for God’s existence, this is a serious failing. Second, his analysis of what is appropriately restricted background knowledge, combined with the credences of a specially chosen ‘alien’, do not allow him to establish the premise \( \Pr (LPU \mid NSU~ \& ~k') \ll 1\).
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Notes
See Collins (2009, p. 202), for the argument being referred to as an argument for the existence of God. In other places he drops ‘for the existence of God’.
Significance is hard to evaluate. Someone testifying to someone else that God exists is evidence for God’s existence, 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 probability of the hypothesis, but less is required than showing the posterior probability is greater than that of the denial of the hypothesis.
This does not entail anything about the probability that such a universe in fact does contain life, other than that it is not ruled out.
Which, I remind the reader, is what Collins has directed us to as justification for the Likelihood Principle.
The conclusion of his argument is phrased as the likelihoodist would phrase it, and not as the Bayesian would. In another context ((Collins 2009, p. 210)), he again uses confirmation in a clearly likelihoodist and not 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.
Emphasis in original.
The restriction on the Principle of Indifference is to let it apply only to “natural” variables, which are variables that appear in the simplest formulation of a law. This move is designed as an answer to the challenge that different ways of expressing the laws lead to different probability assignments. There are concerns with this as an answer to the challenge—for example, the assumption that the simplest formulation is the appropriate 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.
There may be many propositions with important truth values which are deemed unimportant to make explicit. For example, in the game of chance it would be important to know if there was a laser that instantly vaporises the die if it is going to come up as 6. We can assume, as charitable and reasonable people, that this is the sort of thing that would be made explicit by the one asking the question, if it were important.
We may find this view plausible when we consider the gravitational force. If the gravitational force is increased sufficiently, then the universe re-collapses rapidly. If we keep all other constants the same, and continually increase the gravitational strength, it seems implausible to think that we will get anything but a rapidly re-collapsing universe. Likewise, if we reduce the strength, and the universe expands too quickly for anything to cohere together, then continually reducing the strength until it is nothing is unlikely to produce anything else but a universe that expands too rapidly.
It may be argued that the alien will not actually know anything about whether or not other regions of space are interesting. This does not seem a reasonable possibility to consider, however. Suppose that the alien only has 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 universes but not other ‘special’ kinds of universes. Having such a capacity and lacking others would surely figure in its calculations. The alien would rightly wonder why it is able to determine a universe’s fitness for life, but not 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 the universe had not been life-permitting, it would have been special in some other interesting way. And so it seems that the argument requires that the alien be aware of other special regions of possibility space, and also know that such regions are uncommon.
It seems to me that the alien would be very reasonable in suspecting this. And indeed, this is in a way the correct answer! Collins has carefully chosen \(k'\) and placed it in the alien precisely because the remaining constant is life-permitting.
It may be thought that this is the wrong way to approach it. The alien is not confronting the particular assignment of values for the \(n - 1\) constants, and being asked what to make of that. Rather, the alien would just 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. The alien decides in advance its response to any given assignment. This response, however, won’t help escape the above concerns. What in fact the alien will know is, “If I were to discover that these \(n - 1\) constants had 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 particular case where the constants are as they are in our universe. That is the case that interests us.
References
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Acknowledgments
This paper was written with the support of the Monash Postgraduate Publications Award. I also thank Lydia McGrew for her helpful feedback on this paper.
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Saward, M.D. Collins’ core fine-tuning argument. Int J Philos Relig 76, 209–222 (2014). https://doi.org/10.1007/s11153-014-9453-6
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DOI: https://doi.org/10.1007/s11153-014-9453-6