Why Christian Theism Is Almost Certainly True: A Reply to Cale Nearing

Some days ago at the Facebook group "Reasonable Faith Debunked" atheist Cale Nearing[1] laid out what he calls "A positive argument for atheism." The basic idea behind the argument, as I see it, is that since the evidence for theism is compatible not only with theism but with any number of coherent and mutually exclusive hypotheses explaining the origin and life-permitting structure of our universe, the probability of theism being the one true hypothesis is very low; and, since atheism is simply the negation of theism, the probability that atheism is true is very high. Or as Nearing asserts, "Any rational inductor will conclude that Theism is almost certainly false, and therefore that Atheism (the negation of theism) is almost certainly true."

 

Now the argument as Nearing presents it appears quite sophisticated, making extensive use of the probability calculus generally and Bayes' Theorem in particular. Despite this apparent sophistication, however, I believe there are good reasons to doubt that the argument actually goes through. To the contrary, I believe there are good reasons to maintain that theism, Christian theism particularly, is much more probable than atheism.

 

An Overview of the Argument

 

Nearing's argument begins with a review of Bayes' Theorem, which, for the question of the probability of theism given the evidence available, P(T|E), may be written as:

 

P(T|E) = P(T) * P(E|T) / P(E)

 

The left side of the equation, P(T|E), is the posterior probability of theism given the evidence, which answers the question: How probable is theism when all the relevant evidence is taken into account? This is what we really want to know. P(E|T) is known as the likelihood of theism on the evidence, or the probability of our having the evidence we do have given that theism is true. According to Nearing, P(E|T) can be imagined in terms of a counter-factual world in which a hypothetical observer, Sue, "has not made any of the observations in E, but is certain that theism is true." P(E|T) then represents "the probability that this counter-factual Sue would assign to observing E in the future." P(T) is the prior probability of theism, a somewhat subjective estimate usually based on human experience and intuitive concepts like perceived simplicity of the hypothesis; And the lower term, P(E), represents "total probability" of the evidence, sometimes called the marginal likelihood of E. As Cale indicates, P(E) is equal to the likelihood of theism on the evidence times the prior probability of theism, plus the likelihood that theism is false – again on the evidence – times the prior probability that theism is false, or:

 

P(E) = P(E|T) * P(T) + P(E|Tc) * P(Tc).[2]

 

Now as Cale has it, P(T),  the prior probability of theism, is best described again in terms of counter-factuals, where a hypothetical observer "has made none of the observations in E. How probable would this hypothetical Sue find Theism to be is the value of the second term." A rational observer with no biases, and at the same time with no evidence to guide her decision making, he argues, would have to impartially consider all viable options before deciding upon the prior. 

 

Thus prior probability, at least according to Nearing, "depends essentially on how many other mutually exclusive hypotheses Sue is considering." And there may be a very large number of these alternate hypotheses, each of which is mutually incompatible with theism. For sake of illustration, Nearing imagines three such alternatives, A1, A2 and A3. For example, A1:

 

There exists a metaphysically necessary, mindless, genuinely random universe generator which is characterized by a distribution over the universes it could possibly have generated such that the probability that it would have generated a universe in which Sue observes E is equal to L + (1-L)/2.

 

Like theism, each of these alternatives has its own prior probability, so that together the prior probabilities for this particular four-hypothesis scenario sum to one. Or:

 

P(T) + P(A1) + P(A2) + P(A3) = 1(one)[3]

 

Since total probability of all possible and mutually exclusive alternatives has to equal one, and since for an unbiased observer each hypothesis, at least according to Nearing, should have an approximately equal prior probability, "P(T) is approximately equal to 1/4." Because the rest of the argument takes what for me is a yet more technical turn, and because I would likely take up more space rather than less trying to summarize it, I will quote Nearing for the remainder:

 

We can also now calculate the total probability term, P(E). Recall that:

 

P(E) = P(T)*P(E|T) + P(Tc) * P(E|Tc)

 

where Tc is the set of alternative hypotheses. Since our alternative hypotheses are A1, A2, and A3, we know that:

 

P(E) = P(T)*P(E|T) + P(A1)*P(E|A1) + P(A1)*P(E|A1) + P(A2)*P(E|A2)

 

Further, we know that P(A1), P(A2), P(A3), and P(T) are each approximately equal to 1/4, and we have expressions for each of the likelihood terms in terms of a single constant, L: 

 

P(E|T) = L

            P(E|A1) = L + (1-L)/2

            P(E|A2) = L + (1-L)/4

            P(E|A3) = L + (1-L)/8 

 

Which means we can finally put the whole thing together:

 

P(T|E) = [L * (1/4)] / [(1/4)*(L) + (1/4)*(L + (1-L)/2) + (1/4)*(L + (1-L)/4) + (1/4)*(L + (1-L)/8)]

 

With a little algebra, 

 

P(T|E) = 8 / (25 + 7/L) 

 

Recall that L must be in the interval (0, 1), and the limit of P(T|E) as L approaches 1

is 1/4.

 

Hence, P(T|E) < 1/4

 

And of course, any additional alternative hypotheses would make that probability lower still. From all this Nearing concludes not only that theism is "almost certainly false" (and therefore atheism is almost certainly true), but that there are only two ways to wind up with a substantially higher probability for theism: arbitrarily ignoring one or more of its alternative hypotheses, or arbitrarily boosting its prior probability.

 

Evaluating the Argument

 

Just as theism is not the only possible explanatory view of the world, so Nearing's is not the only possible conclusion that can be drawn from a "rational" consideration of theism and its rivals. Though I do not question Nearing's calculations, I do have serious doubts about how some of his terms are derived.  For example, it is not clear that the concept of "a metaphysically necessary, mindless, genuinely random universe generator" is coherent. A metaphysically necessary entity that is both mindless and yet capable of creating countless universes, at least one of which houses intelligent, sentient beings, has to be substantially less probable a priori than a metaphysically necessary, omnipotent being who intentionally creates our universe and intelligent, sentient beings within it for identifiable purposes (e.g., revealing his glory and sharing with others the freedom and life he enjoys).

 

For one thing, a single universe deliberately designed by a wise and loving self-existent God appears much less complex (hence much more probable) than a large, possibly uncountable, number of universes generated at random from a mindless (purposeless), unidentifiable in principle, and yet somehow self-existent generator. This much is certain: One universe (ours) is much, much less complex than an uncountable host of randomly generated universes which includes ours. And as philosopher Daniel Vecchio put it to Nearing concerning the Deity himself, "God's necessity is per se due to His essence being identical with His existence. This entails eternality, simplicity, immutability, and possessing all perfections like omniscience, omnipotence, and omnibenevolence." In other words these divine attributes hold together systematically. Being ontologically necessary implies also being simple, eternal, immutable, and so forth. By contrast there seems to be no reason to even suspect a mindless random universe generator (hereafter RUG) to be simple or immutable – certainly not omniscient or omnibenevolent – and therefore no reason to think it conceptually viable, let alone ontologically necessary.

 

At any rate, postulating a collection of RUGs for the express purpose of rendering theism improbable seems completely ad hoc. Indeed, from what I can tell the only reason most philosophers and cosmologists ever had for postulating anything like a RUG in the first place was to provide a potential defeater for theism, specifically a defeater for the fine-tuning argument. But with the use of such ad hoc devices, one could prove virtually any hypothesis improbable. All that is required is to postulate two or more logically possible and mutually exclusive alternative hypotheses to make the hypothesis in question less probable. So if someone suggests to me that the earth is a globe, I can simply postulate that, conceivably, it may also be a cube, a cylinder, or a cone, and then run it through Nearing's calculations to demonstrate the probability of sphericity to be P(S) < 1/4.[4] The same procedure could be used, with slightly more seriousness, to diconfirm general relativity, common descent, or virtually any theory, physical or metaphysical, one might care to name.

 

That is to say, Nearing's procedure, far from being rational, actually denies the role of reason to choose among competing propositions and hypotheses. Instead of using evidence and arguments to infer the  existence (or non-existence) of God – or, for that matter, the sphericity of the earth, mass-energy equivalence, etc. – we simply count up all the counter-scenarios we can imagine for the hypothesis in question and then calculate its (im)probability. Again, there is nothing especially rational or scientific about this approach, which is not so much a responsible use of Baye’s Theorem as an assertion of what amounts to cosmological relativism: Given an arbitrary increase in the number of explanatory possibilities based on the finding of increasingly trivial distinctions among them, the probability of any one selection being true diminishes accordingly.

 

The main problem I see with all this is that Nearing seems to redefine the central metaphysical question in terms of something like a random variable. The “evidence” for various answers to that question (such as theism), then, amounts to little more than a prior probability distribution. Prior probabilities, however, should not be based strictly on the number of interally coherent but mutually incompatible alternatives imaginable, but also on factors like human experience[5], simplicity, scope, and fit with general background knowledge, all of which basically means that not all priors are created equal. As I argued here a few months ago, certain forms of evidence tend to get overlooked when they should rightly be accounted for as background knowledge.[6] In that case the real utility of Bayes' rule is to update beliefs that are already based on a measure of existing evidence, in light of new evidence. Revising probabilities, hence updating beliefs, on the strength of incoming evidence constitutes the very purpose of Bayes' Theorem. Rather than revising these various probabilities in light of various lines of actual observational and propositional evidence at hand, however, Nearing simply concludes that theism is improbable and closes out the argument.

 

Updating Belief (on the Evidence for Christian Theism) 

 

It goes without saying that most theists believe there to be good evidence for the existence of God. According to Richard Swinburne, for example, there is a wide spectrum of evidence which, when properly "plugged in" to Bayes' Theorem, makes theism considerably more probable than atheism.[7] After carefully explaining the apologetic usefulness of inductive arguments and the broad outlines of Bayesian confirmation theory, and arguing for a relatively high "intrinsic probability of theism" (its prior probability), Swinburne includes as evidence for theism, defined here as observations that make P(T|E) > P(E), the following: 

 

1. Evidence of cosmology

2. Fine tuning

3. Consciousness

4. Morality

5. Miracles

6. Religious experience

 

As evidence against theism he has only the problem of evil, which most would agree has lost much of its force in recent years (thanks largely to Alvin Plantinga). Swinburne then suggests, in a superficial similarity with Nearing, that there are at least three serious alternative hypotheses to theism:

 

Let h₁ be the hypothesis that there are many gods or limited gods; h₂ be the hypothesis that that there is no God or gods but an initial (or everlasting) physical state of the universe, different from the present state but of such a kind as to bring about the present state; and   the hypothesis that there is no explanation at all (the universe just is and always has been as it is).[8]

 

Now there is a reason that Swinburne "lumps together" all these alternative gods or limited gods, a category which would include RUGs, under h₁:

 

I have argued [on the basis of evidence from cosmology, etc.] 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 h₁, 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).[9]

 

From similar considerations of Christian theism and the terms of Nearing's argument, I would suggest it is reasonable and rational to believe that

 

P(T|E) >> P(A1)*P(E|A1) + P(A1)*P(E|A1) + P(A2)*P(E|A2)

Or as another Facebook contributor put it more succinctly: P(T|E)>>P(An|E)

And thus, P(T) > P(~T)

It is therefore perfectly rational to believe that theism is more probable than atheism – but how much more probable? Just for the sake of argument I would be willing to grant Nearing that the evidence of cosmology suggesting a beginning of the observable universe (of matter, space and time) is compatible not only with theism but with the existence of a RUG or lots of RUGs, and that the probabilities of our universe are perhaps comparable on all of these hypotheses. I would be willing to say the same, again just for argument's sake, of fine-tuning of life-permitting physical constants and quantities regulating our universe.

 

But consider consciousness. Does any rational thinker honestly believe that consciousness is not vastly more probable on theism than on the mindless RUG hypothesis? Morality, likewise, can be explained in nontheistic terms, but clearly the straightforward impartation of moral awareness and responsibility from God is more parsimonious than, say, the evolutionary development of conspiratorial “selfish genes” that disguise themselves as noble and meaningful moral obligations but really only seek long-term physical survival for themselves. Skeptics may find it easy to dismiss miracle “testimony” wholesale, but we all are continually faced with incontrovertible evidence – being alive, namely – that somehow life originated on earth, in the face of extreme improbability, and yet just as recorded in Scripture. That certainly sounds like miracle. And like so many others, I have never found a satisfactory “natural” explanation for the empty tomb of Jesus, the postmortem appearances of Christ to the apostles, the birth of the early church in Jerusalem (of all places!), and the conversion of Saul of Tarsus, apart from the resurrection of Jesus Christ. Given that the resurrection did occur, the testimony of the apostles emerges not only from a rich supply of historical background evidence but from firsthand experiences of Jesus risen from the dead.

 

For myself, I know that the same kind of “religious experience” that gave such boldness to the apostles continues to the present. I know of Christ’s resurrection not only by inference from historical evidence but because I have experienced, as did the apostle Paul, the life-changing "power of his resurrection” (Philippians 3:10). I know firsthand the love of the Father, forgiveness of sins by the sacrifice of the Son, and the communion of the Holy Spirit. For me and billions of other believers, the existence of God is therefore self-evident, as uncontroversially true as the axioms of logic and probability might seem for a logician or statistician. So for me Christian theism is simply, certainly true. But in deference to Nearing's probabilistic sensibilities, here I will say merely that Christian theism is almost certainly true.

 

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[1] Cale Nearing is a Statistician who holds Bachelor's degrees in Technical and Professional Writing, Mathematics, and Statistics. Readers may find his 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).

 

[2] Nearing uses the convention P(Tc), where c is any "compliment" of T, or any hypothesis which, if true, would mean that theism is false.

 

[3] Nearing here adds a fifth term, P(C), the probablity of any and all alternative hypotheses Sue has failed to consider. Though I believe he is correct to note that any value for P(C) would make theism less probable, I leave it out for simplicity's sake.

 

[4] It could be objected here – rightly! – that the evidence for sphericity makes it far more probable than any alternative or disjunction of alternatives. But as an a priori matter it happens to be the only one of the four shapes postulated with no flat surface, which might lead a naïve ("unbiased") observer to conclude that the earth probably has at least one flat side. This underscores why observational evidence and background knowledge are more important than Nearing seems willing to allow.

 

[5] There appears to be no getting around the role of the individual's beliefs and biases in assessing priors, strength of evidence for and against the hypothesis, etc. In Bayesian Confirmation Theory this is known as conformational relativity: "Evidential relationships must be relativized to individuals and their degrees of belief" – James Joyce, "Bayes' Theorem," Stanford Encyclopedia of Philosophy (2003), https://plato.stanford.edu/entries/bayes-theorem/.

 

[6] Don McIntosh, "On the Prior Probability of the Resurrection," http://christiancadre.blogspot.com/2017/02/on-prior-probability-of-resurrection.html.

 

[7] Richard Swinburne, The Existence of God (2nd Ed.) (New York: Oxford, 2004).

 

[8] Swinburne, pp. 339-340.

 

[9] Swinburne, p. 340.