Why Christian Theism Is Still Almost Certainly True: A Follow-Up Reply to Cale Nearing

A couple of weeks ago, readers of this blog may recall, I posted "Why Christian Theism Is Almost Certainly True: A Reply to Cale Nearing."[1] Though offered in good faith to meet the challenge he issued to Christian apologists like me, that reply was not well received by Cale Nearing – which should really surprise no one. It's his argument that was under scrutiny, after all.[2] And as I mentioned in the comment box of that article, after posting it I was quite ready to abandon the subject and move on to another. Cale, however, asked me to give his argument another look and reconsider the prospect that theism is indeed "almost certainly false." At Cale's request, then, I will here revisit the argument, taking into account his five main criticisms in order. His rebuttal begins:

First, there is no question that A1, A2, and A3 are at least coherent (possible) in the logic in use. I'm glad you don't actually try to pursue an outright elimination of them, but you then move on to assign them low priors for completely arbitrary reasons: a clear mistake, which leaves your response clearly irrational.

For readers unfamiliar with all this: A1, A2, and A3 are what Cale refers to as Random Universe Generators (RUG's), which he presents as alternative hypotheses to theism. Now is it really beyond question that these RUG's are coherent? Well, it's not as if the coherence of an entity that is (1) metaphysically necessary, (2) mindless, and (3) capable of generating a life-permitting universe which includes minds, is self-evident. According to many theologians, for any being to be necessary (whose essence is existence, the ground of all other being) would require it to be "Pure Act" (actus purus), which would require it to be omnipotent,[3] which would require it to be omniscient, which would require it to be – or at least "have" – a mind. A RUG that is both necessary and mindless, then, is arguably incoherent. A similar argument could be made in reference to the notion of a mindless being giving rise to mindful, i.e., rational and intelligent beings.[4]

Honestly I don't recall "assigning" low priors to these RUG's. (Nor for that matter do I believe that any response involving a "clear mistake" is clearly irrational. If making mistakes – even mistakes that are obvious to others – is irrational, I'm afraid we're all doomed to a life of irrationality.) I did suggest then, as now (above), that RUG's appear incoherent. Additionally I suggested that the postulation of RUG's specifically as a defeater for theism "seems completely ad hoc." Thus: Given that coherent hypotheses are antecedently more probable than seemingly incoherent alternatives, and given that serious explanatory hypotheses are antecedently more probable than ad hoc hypotheses devised for the sole purpose of defeating them, it would be rational for these non-arbitrary reasons alone to assign a higher prior to theism than to RUG's.

Second, the A hypotheses say nothing about multiple universes, and (further) multiple universes are not actually a more complex hypothesis than Theism. Complexity is actually a good way to look at priors, but if we actually take this route, we can show that my demand for equivalent priors becomes inarguable: both Theism and A1, for instance, are hypotheses which cannot be fully specified in any finite computable string, which means that they both actually have infinite complexity (and, hence, must have equivalent priors).

Here I may have simply misunderstood, not just what Cale's argument entails, but what a certain technical definition of "complexity" might entail. In that case I stand corrected. Even so, my appeal was not to Kolmogorov complexity or algorithmic complexity, but to a more time-honored understanding that a hypothesis invoking prima facie fewer ontological or explanatory elements is prima facie less complex, hence epistemically preferable, than one invoking more. Some 600 years before Kolmogorov developed algorithmic complexity, William of Ockham famously championed the concept now known as Ockham's Razor, the general principle that in the formation of hypotheses entities that should not be "multiplied beyond necessity." On that score theism appears more epistemically promising than a multiverse hypothesis – or for that matter, an imaginative distribution of ad hoc RUG hypotheses.[5]

Thus Cale's assumption of equivalent priors ignores certain points of background knowledge which suggest a higher prior for theism – and which are not equally entailed by any RUG hypothesis. For example, theism entails the deliberate creation of the universe by God. Take two hypothetical beings, each of which is presumed "metaphysically necessary" and each of which has the power to create a universe, but one has various purposes and intentions while the other has no purposes or intentions whatsoever. Even assuming equal prior probability of God and a given RUG simply existing, the probability of an omnipotent God intentionally creating our universe – i.e., directing his power to actualize the possibility of creation – has to be much higher a priori than the probability of a mindless RUG accidentally creating our universe. In that case Cale needs to explain why P(T) is not substantially higher than P(A1), or even substantially higher than P(A1 v A2 v A3).

Third: the RUG hypotheses are ad hoc, but this doesn't actually matter. Theism is ad hoc. If this were grounds for dismissing A1, A2, and A3, it would also be grounds for dismissing Theism.

Okay, I will concede here that in one sense that's a reasonable objection. In terms of “predictive power,” theism doesn't really compare with, say, a scientific theory like General Relativity. Here theists like Wilko van Holten agree with Cale: "So it would be fair to say that theism is manifestly ad hoc; it merely explains retrospectively, not predictively."[6] However, certain factors tend to dull the force of this objection:

First of all, the celebrated cases often referred to in connection with the ad hoc-ness requirement – like the theories of Newton and Einstein – are not entirely accurate historically. As some have pointed out, these theories were initially accepted on the basis of their ability to account for known observations, that is, for their ability to solve ‘old problems,’ and acquired universal reception long before the required confirmation of the relevant predictions was given….Further, the ad hoc-ness requirement is too restrictive to be applied rigorously to all theories for there are some well-established scientific theories that do (as yet) without confirmed predictions. Darwin’s theory of evolution by natural selection is a case in point: this theory is also manifestly ad hoc, for it was probably designed with the facts in mind, as a response to them. Finally, the rule against ad hoc-ness does not provide the hoped for means of demarcating scientific from non-scientific theories (Popper). As Banner argues, the criterion ‘fails to solve the very problem it was designed to solve, for just as any number of theories may fit with known observations, so any number of theories may yield confirmed predictions.’"[7]

Swinburne argues more directly to the point,

The suggestion that hypotheses must predict successfully…if they are to be rendered probable by evidence is certainly not implied by Bayes's theorem. It is a matter of indifference, as regards that theorem, whether e is observed before or after the formulation of h….. Newton's theory of motion was judged to be highly probable on the evidence available in the late seventeenth century, even though it made no immediately testable predictions.[8]

Theism is not only, as previously mentioned, a long-standing and altogether serious hypothesis[9] offered to explain the origin of our universe and life within it, but is supported by various lines of physical and propositional evidence (evidence nowhere specified in Cale's argument other than by the letter E in his various formulations). Theism is further a stand-alone hypothesis, in that it bears no immediate relation to other theories. To the contrary an ad hoc hypothesis, at least in the sense in which I refer to it, is an auxiliary hypothesis devised specifically to insulate an existing claim or theory from falsification or refutation. Ptolemy’s geocentric invocation of epicycles to account for observed retrograde motions of planets is the classic historical case in point. In our case, RUG's are postulated for the express purpose of reducing the probability of theism, thereby rescuing atheism from the implications of fine-tuning and other forms of evidence for theism.

Fourth: your analogy to the shape the earth is not an analogy at all, and it reveals that you didn't actually understand the argument. The cone, cylinder, and cube hypotheses make clear predictions that we can use to falsify those hypotheses: the likelihoods they offer for our available evidence do not even begin to approach the likelihood that the sphere hypotheses offers. This issue of likelihoods is something I spend a fair bit of time talking about in my argument, but you seem to have missed it entirely.

Here is the crux of the matter, I think. Of course Cale is correct to argue that the cone, cylinder, and cube hypotheses do not really compare with the sphere hypothesis in terms of likelihood, P(E|H), because the other three do not have nearly the same power to predict the evidence. But as I was careful to clarify in a footnote, that's just the point. In principle, evidence serves to differentiate among hypotheses otherwise assumed to be equiprobable, so that we can update our beliefs, or at least better evaluate the probability of our beliefs being true, on the evidence. This is the very purpose of Bayes' theorem.

The reason the "shape of the earth" analogy (or parody, as he says) works is that it, like Cale's argument, presupposes that the only relevant source of "evidence" is equivalent to, or else implicitly contained within, the assumptions used to derive the prior probability distribution in the first place.[10] Taken as a general principle, that presupposition turns out to be demonstrably false, as the “shape of the earth” analogy makes clear. Similarly, the fact that T, A1, A2 and A3 are all equally possible does not entail that these hypotheses are equally probable. Again, likelihood per Cale’s argument is not a function of physical or propositional evidence given theism – the sort of thing normally meant by "evidence" – but rather the evidence is presumed to be no more than a function of Cale's contrived probability distribution. 

Why then, someone might ask, would anyone not want to evaluate evidence from cosmology, fine-tuning, consciousness, the resurrection of Jesus, etc., in assessing the likelihood of the evidence on theism relative to competing hypotheses? That leads us to Cale's final objection:

Fifth: Swinburne's attempt at a Bayesian argument fails trivially specifically because he does not understand how alternative hypotheses affect the relationship between the prior and the normalizing constant. He's not wrong that some things do constitute evidence for Theism, thanks to theism's retrodictions, but what he misses is that there are any number of alternatives which make the same retrodictions (if we limit our hypothesis space to those hypotheses which acknowledge common human knowledge, then there is no evidence for Theism at all). This is why a hypothesis based on pure retrodiction is doomed to failure, and this is indeed why theism fails. Swinburne doesn't understand the logic, as my argument illustrates nicely. The evidences he offers cannot in principle pull Theism out if its hole, because there will always be other similarly ad hoc hypotheses making the same retrodictions that Swinburne calls upon for evidence.

According to Cale, no evaluation of the evidence on theism relative to competing hypotheses is necessary, because theism depends entirely on "retrodictions," and "there are any number of alternatives which make the same retrodictions." We've already addressed prediction versus retrodiction in the context of ad-hocness. Clearly the fact that competing hypotheses often make claims on the same store of evidence does not render them equally probable. Otherwise we would have to conclude that evolution by natural selection, theistic evolution, young-earth creationism, old-earth creationism, and intelligent design hypotheses are all equally probable, because they all retrodict from the same set of available facts. Likewise juries could almost never rationally reach a verdict, because the same facts in evidence are subject to radically different interpretations by the prosecution and the defense.

Essentially Cale's prior probabilities and subsequent calculations are based on the presumption that the evidence is no better for theism than it is for any number of alternatives. Now that may be an argument worth consideration in its own right, but it hardly qualifies as a true premise in a valid argument to the effect that theism is no more probable than alternative hypotheses! The very fact that these hypotheses are mutually exclusive suggests the possibility that they do not predict or explain the evidence with equal force, which is why I asked in the previous post, “Does any rational thinker honestly believe that consciousness is not vastly more probable on theism than on the mindless RUG hypothesis?” With all due respect to Cale (and he's due some respect, for sure), his argument is starting to look like an elaborate exercise in question-begging.

"Swinburne's attempt at a Bayesian argument,” says Cale, “fails trivially specifically because he does not understand how alternative hypotheses affect the relationship between the prior and the normalizing constant." But that seems to be just what Swinburne addressed concerning the prior probability of theism against the disjunction of many or limited gods. Given that Swinburne, Emeritus Professor of Philosophy at Oxford, specializes in philosophy of science and is known particularly for his use of Bayes' theorem to rationally justify inductive inferences, it is Cale's burden to justify the claim that Swinburne lacks understanding of how Bayesian inference works. For now I see no reason to think that Swinburne's Bayesian argument "fails trivially." He concludes:

Once we understand your misunderstanding of the logic, Don, as well as Swinburne's, it becomes clear that my conclusion is indeed correct: Theism cannot be rationally affirmed, and only by eschewing the logic of probability theory – or simply failing to understand it, as you and Swinburne obviously have – can one conclude otherwise.

That is simply a non sequitur. Even if I, along with Swinburne, William Lane Craig and every Christian apologist who ever lived, completely, hopelessly misunderstood the logic behind Cale's argument, it would not follow that his conclusion is correct. Until he can explain why all hypotheses should be considered equally probable regardless of the evidence, or alternatively, why evidence should be considered a function of probability rather than the other way around, I have no reason to believe that my arguments for Christian theism given the evidence are not sound. In that case I have reason to believe that Christian theism is still almost certainly true.

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[1] Don McIntosh, "Why Christian Theism Is Almost Certainly True: A Reply to Cale Nearing," http://christiancadre.blogspot.com/2017/05/why-christian-theism-is-almost.html. I want to thank Cale for presenting his argument and challenging Christian apologists like me to answer it. I have learned a few things in the process – always a good thing – and I appreciate the opportunity to explain why Christian theism is almost certainly true.

[2]   Readers again may find Cale’s argument in full at https://m.facebook.com/groups/870345023006950/permalink/1501101383264641/?__tn__=R (requires logging in to Facebook and joining the "Reasonable Faith Debunked" group).

[3] "Omnipotence follows upon God's essence as pure act, having within Himself His own fullness of actuality. Since one thing is able to cause another insofar as it is itself in act, God alone is capable of giving existence to created things." – "Omnipotence," New Catholic Encyclopedia (The Gale Group, 2003), http://www.encyclopedia.com/religion/encyclopedias-almanacs-transcripts-and-maps/omnipotence.

[4] See for example Victor Reppert, "The Argument from Reason," http://www.lewissociety.org/reason.php.

[5] As mentioned in my previous post, Richard Swinburne suggests that "the hypothesis that there are many gods or limited gods" should be a singular alternative hypothesis rather than a host of hypothetical competitors: "I have argued that the hypothesis of theism is a very simple hypothesis indeed, simpler than hypotheses of many or limited gods…. In that case, theism is going to be more probable than…the disjunction of hypotheses of many or limited gods; and there is much less reason why they should bring about a universe at all or one of our character – they may not be able to do so, and not being perfectly good may not have much reason to do so (unless we complicate these hypotheses further by building into them the requisite propensity)." – The Existence of God (New York: Oxford, 2004), p. 340.

[6] Wilko van Holten, "Theism and Inference to the Best Explanation," Ars Disputandi, Volume 2, Issue 1, November 8, 2002, pp. 262-281. van Holten goes on to argue that despite this caveat, theism has considerable explanatory power: “If a theory’s explanatory power is foremost a measure of its observational success, i.e. of how well it accounts for known observations, and not necessarily of its predictive success, the argument in favour of theism will largely depend on its power to do justice to our experience of the world in the widest possible sense of that term.”

[7] van Holten, p. 273.

[8] Swinburne, p. 69.

[9] That's on an "evidentialist" apologetic, anyway. I fully sympathize with fellow defenders of the faith who maintain that belief in God is properly basic, or that theism is better argued along deductive lines, or that Bayes' theorem does not really apply to metaphysical questions. See Joe's recent article, "Bayes' Theorem and the Probability of God: No Dice!", http://christiancadre.blogspot.com/2017/05/bayes-theorem-and-probability-of-god-no.html.

[10] An example of “built-in” non-evidentiary assumptions used to determine not only priors but likelihoods would be, to paraphrase Cale for brevity, “A1: There exists a RUG so characterized that the probability that it generates a universe including observational evidence E is equal to L [or P(E|T)] + (1-L)/2.” So we know that likelihood for A1, P(E|A1), is L + (1-L)/2. The justification for this hypothesis? It’s a possible alternative. And since there are in his scenario three such RUG hypotheses and one theistic hypothesis, the prior probability of each is “approximately equal to 1/4.”