Is the Existence of God a Matter of Probabilities?

To treat the question whether God exists as a matter of probabilities seems to some people completely natural and to some utterly perverse. Believers and non-believers are found in both camps. I agree with Duncan Richter in finding such a way of thinking deeply wrongheaded, but I find his attempt to say what is wrong with it unsatisfactory.

I was delighted to find my previous two posts (1, 2) on ancient polytheism and the concept of evidence cited and discussed by Duncan Richter in his blog Language on Holiday. Richter’s discussion includes a parenthetical remark that approaches some lines of thought that I have pursued. He remarks that arguments for the existence of God that are founded on empirical observations, whether concerning religious experience, miracles, or design, all try to establish their conclusion as a matter of probability. (For the sake of simplicity, I shall in this entry equate questions of the existence of a divine being with the question of the existence of God, i.e., an inherently unique deity, leaving polytheism out of account.) He says of this way of thinking:

It is a logical and ethical mistake, an error in grammar and theology, to think of the existence of God as a question of probabilities. This might become clearer if one tried to calculate the odds, although I think people have done this and not achieved the clarity I have in mind. In case it isn’t clear, it’s a mistake because it treats God as the same kind of thing as a fluke gust of wind, i.e. something whose odds we might calculate or at least estimate, i.e. as something natural, however super. To think of God this way is to misunderstand what believers believe in a way that is both simply wrong (that isn’t what they believe) and insulting (it is to treat God as something less than what they believe). This is complicated by the fact that some believers (or “believers”) are idolaters in just this way, but that isn’t the kind of belief that interests me. There’s also the question whether non-believers like me should care about the alleged badness of insulting God, but we can at least respect the feelings of believers. And I think we can respect the concept of God, too, and want to do justice to it.

I suspect that the passage was written with some haste and impatience, for two reasons: first, it is rather long and contentious, not to say blustery, for a merely parenthetical remark; and second, saying exactly what is wrong with treating the existence of God as a matter of probability is no easy matter—or so, at any rate, say I. In this piece, I will give reasons for finding Richter’s presentation of the case unsatisfactory. I hope, though I dare not promise, to make a stronger case of my own in a subsequent entry to this blog.

Richter finds fault with probabilistic discourse about theism in two respects. One concerns the way in which it treats theistic believers. According to him, it insults them by treating God as “something less than what they believe [in].” He also implies that it fails to “respect their feelings.” Now it is possible that I am missing something here, but to me such claims seem simply irrelevant. If—and this is a large “if”—there is no fundamental conceptual error inherent in inquiring whether probability favors the existence or the non-existence of God, then I can see no compelling reason why those making such inquiries should care in the least whether they hurt the feelings of theistic believers or denigrate the object of their beliefs. At most, such considerations would be reasons to pursue such inquiries out of public hearing, so that they not offend the delicate ears of believers. But one could just as credibly argue that it is insulting to believers to assume that their sensibilities require this kind of protection. In any case, if they do, then it’s hard cheese for them and nothing more.

So it seems to me that Richter’s would-be ethical objection can be set aside. The entire weight of his objection must rest on its logical and grammatical part—“grammatical” here in Wittgenstein’s sense of concerning what one can intelligibly say and under what conditions. I believe that if this element of the objection could be satisfactorily articulated, the ethical aspect would emerge by itself. In fact, if I may mix the terms of the later Wittgenstein with the phrasing of the earlier, I would say that on this point grammar and ethics are one: if we could understand exactly what is so perverse about talking probabilistically about the existence of God, we would not distinguish a logical an ethical objections. Richter seems to me to move, or at least to face, in this direction when he describes theistic believers who take the question of divine existence to be a matter of probability as “idolaters,” a term that implies perversion of both intellect and will; but to make such a heavy charge stick would require an argument than I, for one, have not got at the ready.

What, then, is wrong with trying to assess the probability of divine existence? Richter holds that to do so “treats God as the same kind of thing as a fluke gust of wind, i.e. something whose odds we might calculate or at least estimate, i.e. as something natural, however super.” To take the first point first: what are the conditions under which we can calculate or at least estimate the odds of something? Richter may be assuming that we can do this only when we are talking about a type of event that occurs and recurs unpredictably under certain specifiable conditions, such a gust of wind of such and such a character that occurs a certain number of times in a certain location over a certain period of time. Given such specifications, we can observe a sample of cases and calculate the relative frequency of the event in question. The larger the sample that we have observed, the more confidently can we identify this relative frequency with the probability of a gust of wind occurring under the specified conditions.

Obviously, none of this is applicable to the existence of God, since that is not a repeatable event. So, if those who think of the existence of God probabilistically operate with a frequentist interpretation of probability, then they are hamstrung from the outset. But, of course, they do nothing of the sort; or at least, they need not do so. Here is the philosopher and Christian apologist—and, if Richter’s assessment is just, idolater—William Lane Craig on his website Reasonable Christianity answering a correspondent who is perplexed by the application of probabilistic terms to the question of the existence of God. Craig’s correspondent understands probability not in terms of relative frequency but according to what is known as the classical interpretation of probability, in which probability values are equated with the ratio of the number of cases in which a certain event occurs to the total number of possible cases. But Craig’s reply is equally applicable to the frequentist interpretation:

Probabilities are always relative to some background information. . . . Now the atheist says God’s existence is improbable. You should immediately ask, ‘Improbable relative to what?’ What is the background information? . . . The interesting question is whether God’s existence is probable relative to the full scope of the evidence.

Had you asked that question of your friend, it would have been evident that he is considering no background information at all! He seems to be talking about a sort of absolute probability of God’s existence Pr (G) in abstraction from any background information B and specific evidence E. That’s a pointless exercise. He seems to be imagining all the possible deities that could exist and asking, “What are the chances apriori that a certain one of these exists?” How silly! That’s like inquiring about the absolute probability that a certain person, for example, you, exists, given the infinite number of possible persons there could be. Nobody is interested in such absolute probabilities, if there even are such things. What we want to know, rather, is the probability of your existence or God’s existence relative to our background information and specific evidence: Pr (G|E & B).

Craig operates with a subjectivist or, as it is widely known, Bayesian interpretation of probability. On this interpretation, the values that are assigned to probabilities of events represent degrees of confidence in the occurrence of those events. Such assignments do not require that the events be repeated or repeatable at all: one can attribute a degree of probability to any event whatever, even the existence of God (or of a god of some specific description). (“Event” here is a technical term in probability theory for that to which a probability value is assigned and is not contrasted with “fact” or “state of affairs.”)

The competition among interpretations of probability is a vast and complicated issue, into which I don’t propose to enter any farther. My point here is simply that, if one holds there to be a confusion inherent in treating the existence of God as a matter of probability, one cannot support that claim by simply assuming an interpretation of probability that requires a repeated event or a countable set of possible outcomes, as there are interpretations of probability that don’t require those things. To Richter’s remark that to talk of the existence of God in probabilistic terms treats it as “something whose odds we might calculate or at least estimate,” Craig would reply, or anyway could reply, “Yes; so what?” So, for that matter, could Richard Dawkins.

I can imagine one of these probabilists saying to Richter (and, for that matter, to me): “I suspect that the reason why you dislike this talk of the probability of God’s existence is that it seems to kill all the existential drama and to make the business of believing or not believing in God out to be a matter purely of the intellect. But, look you, I am not touching at all on the question of what moves people to believe or disbelieve in God, or what difference their belief or lack of belief makes to their lives. I am just assuming that when we ask, ‘Does God exist?’, we are posing a genuine and well-formed question—one that has a correct answer. The correct answer is either ‘Yes, God exists’ or ‘No, God does not exist.’ To determine which is the correct answer, one has to determine where the preponderance of evidence lies. To do this is to assess the probability of the proposition ‘God exists.’”

I do not think that this argument is unanswerable, but I do think that to answer it is not easy. In any case, I leave the task for a later post.