Monday, August 12, 2013

More on Thinking Probabilistically

We typically use the plural noun “probabilities” only when speaking of events that are potentially repeatable, like throws of a pair of dice. But the notion of probability has another aspect, namely the degree of strength of belief warranted by evidence. This seems to apply, at least potentially, to the question of divine existence. But one may doubt whether the “God” about which some reason probabilistically can be identified with the God worshiped and served in any actual religion.

According to this page, these actually work

My previous entry addressed, but—characteristically, I confess—did not answer, the question “Is the existence of God a matter of probabilities?” I wish now that I had used the singular form of the noun “probability” rather than the plural, as the latter has associations that I don’t welcome. The plural form “probabilities” tends to suggest numerical values or measures of probability, which in turn (and this is the most unwelcome part) suggests the sort of case in which an event of a specific, repeatable type occurs under specific conditions—for instance, the event of a hand of five playing cards containing a pair, given that the five cards are dealt randomly from a deck of 52. Even if we are speaking, say, of the probability that candidate So and So will win the upcoming election, which is not a repeatable event-type but a single occurrence, we may consider that outcome as belonging to a type specifiable more or less broadly according to country, locale, time period, type of office, characteristics of the candidate, and so on; and we can then calculate the chances accordingly.

But what if we are speaking of the probability of a possible fact that is not an instance of a repeatable type? Discussions of the existence of God would be a case of this. The idea of assigning the existence of God to some type of repeatable event seems senseless. Perhaps some diligent analytic metaphysician somewhere has reckoned the probability of divine existence as the proportion of God-made possible worlds to Godless ones; but I don’t care to take account of all conceivable products of academic invention. If the concept of probability applies only to repeatable event-types, and if, as seems plain, the existence of God is not an event of a repeatable type, then the answer to the question “Is the existence of God a matter of probability?” is a flat and rather uninteresting “No.”

But the concept of probability is not restricted to such cases. When Bishop Butler remarked in the “Introduction” to his Analogy of Religion (1736) that “to us, probability is the very guide of life,” he was not referring to the calculus of chance, which was then in its infancy. He was speaking of probability in contrast with absolute certainty, and of the condition of finite intellects in contrast with that of an infinite one:
Probable evidence is essentially distinguished from demonstrative by this, that it admits of degrees; and all variety of them, from the highest moral certainty, to the very lowest presumption. . . .

Probable evidence, in its very nature, affords but an imperfect kind of information, and is to be considered as relative only to beings of limited capacities. For nothing which is the possible object of knowledge, whether past, present, or future, can be probable to an infinite Intelligence; since it cannot but be discerned absolutely, as it is in itself, certainly true, or certainly false. But, to us, probability is the very guide of life.
Probability is our guide in life because our knowledge of the world is, by our nature, limited. To follow probability in the pertinent sense is not to reckon odds but to weigh what Butler calls “presumptions,” or reasons for belief. There is more to probability than mere chance. As Ian Hacking remarks in his historical study The Emergence of Probability,
Probability has two aspects. It is connected with the degree of belief warranted by evidence, and it is connected with the tendency, displayed by some chance devices, to produce stable relative frequencies.
Hacking dubs the first aspect of probability the “epistemological” (from Greek epistēmē, “knowledge”) and the other the “aleatory” (from Latin ālea, “die” or, by derivation, “game of chance”). I think “epistemic” is a more widely used term for the former, although, since it is belief and not knowledge that is in question, “doxic” (from Greek doxa, “belief”) would be more apt. Whatever the terminology, and however we may try to understand the relation between these two aspects of probability, it is the doxic or epistemic aspect that is pertinent when the existence of God is treated probabilistically. The fundamental thought is not that we can calculate the chance that God exists as we can the chance of getting a certain result from throwing a pair of dice, say, but that some degree of strength of belief that God exists is warranted by the evidence available to us.

The question “Is the existence of God a matter of probability?” is a question about a question. It concerns how the question “Does God exist?” may be answered—what sort of thing one has to do, or may do, to answer it. Anyone who assumes that the question must be, or may be, answered by weighing what Butler terms “probable” evidence (meaning empirical evidence, as contrasted with the “demonstrative” evidence of proofs a priori) assumes that the answer to the first question is “Yes”—that the existence of God is a matter of probability.

Most writers who argue for atheism seem to make this assumption. They typically argue either that there is no evidence that God exists or that there is evidence that God does not exist. It seems to go without saying for them that to answer the question of God’s existence otherwise than by evaluating the available evidence would be incompatible with intellectual integrity. For instance, Richard Dawkins entitles one chapter of his book The God Delusion “The God Hypothesis” and another “Why There Almost Certainly Is No God.” For Dawkins, to treat belief in God as a “hypothesis” is what it means to take the proposition “God exists” seriously as a contender for truth. As for the probabilistic qualification “almost certainly,” it is not for him a sign of weakness but a point of strength, as it shows that he, like any good scientist and in contrast to the great majority of theistic believers, founds his opinion in the matter on where the preponderance of evidence lies. “What matters,” he says at one point, “is not whether God is disprovable (he isn’t) but whether his existence is probable”; which, of course, it isn’t, according to him.

I am inclined to agree, in a certain guarded fashion, with Dawkins that the existence of God is not probable—not, however, because it is improbable, as he thinks, but because it is not a matter of probability at all. I said in my previous entry that it is not easy to defend this claim. This evoked some interesting comments from Tommi Uschanov, who does not share my sense of difficulty on this point. The following two observations, which, he says, “have been presented often in Wittgensteinian philosophy of religion, by O. K. Bouwsma or D. Z. Phillips, for instance,” he finds “do the work so well that nothing more needs to be said”:
1) If someone has lived his life atheistically or otherwise irreligiously through a wrong assessment of probabilities, due to an innate lack of talent for mathematics and statistics, this would seem to mean that God condemns him to perdition through a failure to endow him with sufficient talent to make the required calculations. But this is obviously contrary to the moral teaching of the religion itself. And indeed to the whole official self-image of the religion.

2) The importation of the probabilistic way of speaking to properly religious language makes this language (not unintelligible, which would be the positivist critique, but) uproariously funny.

For instance, . . . Psalm 23 does not say: “The Lord is probably my shepherd; I probably shall not want. . . .” [Other examples follow.]
The first argument seems to me an effective objection to anyone who, like William Lane Craig, uses probabilistic arguments to defend the reasonableness of Christianity; but only because Christianity, at least in some of its varieties, holds the non-acceptance of Christian doctrine to be a sin subject to divine retribution. There are, of course, interpretations of Christianity that reject this belief, but it has been a part of Christian doctrine historically and is, so far as I know, not found in any other major religion. In any case, it is not a part of theistic belief per se. The objection, therefore, tells only against probabilistic defenses of some varieties Christianity and not to probabilistic approaches to the question of divine existence in general. Further, the objection seems to be just a variant of the ancient one that if God makes human beings sinful that he cannot justly punish them for their sins: so if he makes someone inept at forming beliefs, he cannot justly punish that person for failing to arrive at the right beliefs. In any case, the most that this objection can show is that it is imprudent for a Christian to try to make probabilistic arguments for the existence of God. It doesn’t show that there is anything inherently wrong with doing this in general or with treating the question of God’s existence probabilistically in the first place.

Uschanov’s second argument may seem even less effective, as it can be rebutted on several grounds. For one thing, to make a probabilistic argument means only that the premises from which one argues provide reasons to accept one’s conclusion without entailing it with logical necessity. It does not mean that the conclusion has to include a probabilistic qualifier. For instance, if I know that Smith fell into a piece of industrial machinery and was ground to bits, and I conclude on that basis that he is dead, I am reasoning probabilistically; that does not mean that I am obliged to say only, “Smith is probably dead.” In such a case, my premise warrants my conclusion with moral certainty, which is certainty beyond a reasonable doubt (though not beyond all logically conceivable doubt). For another thing, if someone tries to show that there is sufficient empirical evidence to conclude that God exists, it does not follow that she is bound to import probabilistic language into her religious practices, such as prayers, or to rephrase scriptural passages to include such language. Finally, to advance a probabilistic argument for belief in the existence of God does not commit one to holding that theistic believers should base their belief on such a justification. One might offer the argument purely for the purpose of refuting skeptical doubts of God’s existence and showing that theistic belief is rationally warranted. (As I said in my reply to Tommi’s comment, William Lane Craig seems to be trying to do something parallel to this, but specifically for certain Christian doctrines, not for bare theism.)

With all that said, I think that there is at least potentially more to Uschanov’s objection (or to the sources from which he draws it) than such replies recognize. The point of the objection, as I understand it, is not to argue, “To defend theism probabilistically commits you to saying things like these; these things are patently ridiculous; therefore, it is misconceived to defend theism probabilistically.” At least, I think that the objection is much more effective if it is taken differently, as an attempt to bring out something incoherent in the probabilistic approach to divine existence precisely by taking it seriously. It is as if one were to say: “You want to treat the existence of God as a matter of probability? Fine! Let’s do that consistently and see what happens!”

The suggestion, in other words—at least, this is the suggestion that I derive from the objection as stated—is that if you adopt a probabilistic approach to the question of God’s existence, the “God” that you reason about, no matter whether your conclusion is theistic or atheistic, will be a philosophical fetish or idol and not that which is worshiped and served in any of the world’s religions. Probabilistic reasoning and religious practice are not two different ways of relating oneself to the same entity; rather, one is a way of relating oneself to God, if God exists, and the other is a way of relating oneself to a figment of the intellect mistakenly called by the same name. To put the point another way, a possible object of religious devotion is not a possible object of probabilistic reasoning.

That, at any rate, is the idea that Uschanov’s comment suggests to me. I think it can also be taken as a development of the objection that Duncan Richter was making in the blog entry that I discussed in my previous entry here, when he said that a probabilistic approach to the question of divine existence “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.” If the objection can be satisfactorily worked out, it should be applicable to polytheistic religions as well as to monotheisms—or rather, not to the religions, but to probabilistic treatments of the question of the existence of their gods. It may even be applicable to probabilistic would-be defenses of revealed religion, such as that offered by Craig, who incorporates scripture into his evidence base.

I find it an attractive idea, but I don’t entirely trust it, and I certainly don’t have a defense of it ready. So, once again, I close with unfinished business.


Joseph Butler, Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature, ed. by G. R. Crooks (New York: Harper and Brothers, 1860), p. 84.

Richard Dawkins, The God Delusion, paperback ed. (Boston and New York: Houghton Mifflin, 2008), p. 77.

Ian Hacking, The Emergence of Probability, 2nd ed. (Cambridge: Cambridge University Press, 2006), p. 1.

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