A. A Probabilistic Defeater?

Precisely how would such a defeater work? Suppose we begin by considering a probabilistic antitheistic argument from pluralism. J. L. Schellenberg asks us to “Consider first the case of one who supposes there to be a number of mutually exclusive religious alternatives to a certain religious belief r having probabilities equal to the probability of r.”⁵⁵⁹⁵⁵⁹   “Pluralism and Probability,” Religious Studies, 33 no. 2 (June 1997), p. 147. He then suggests that such a person ought to suppose that r is improbable (less likely than its denial)—at any rate if she thinks there is more than one alternative having a probability equal to that of r; hence she ought not believe it. Schellenberg then concedes that the typical believer will not suppose that what she believes is no more probable than alternatives to it (if she did, why would she be believing it?); but he thinks his argument can nonetheless be restated as follows:

Summarizing (and allowing for a non-uniform assignment of probabilities to alternatives), we can say quite generally that the following may be held by the critic to be a sufficient condition for the improbability of any religious belief r with an epistemic status superior to that of each of its alternatives: r is improbable if the number of times by which its probability exceeds that of each of the available mutually exclusive alternatives (or the average of their probabilities) is exceeded by the number of those alternatives.

By way of example:

Even if a Christian were to suppose her trinitarian belief to be significantly more likely to be true than each of the various Jewish, Hindu, Buddhist . . . alternatives, the application of the approach here described could still yield the conclusion that her belief was probably false. For it might upon reflection seem intuitively obvious or at any rate very likely to the Christian that the degree of superiour probability she could credibly claim would not be sufficient to prevent the combined probability of the relevant alternatives from outweighing that of the beliefs she holds. (p. 148)

The basic idea, therefore, is that reflection on the facts of pluralism should lead the believer to think that the probability of her belief is relatively low, perhaps even less than .5. But here is the crucial question: probability with respect to what? What is the body of evidence 442with respect to which Schellenberg thinks the Christian’s belief must be more probable than not, if she is not to be irrational? If it is the set of beliefs actually accepted by the believer, then, of course, the probability of her beliefs will be 1. After all, the believer doesn’t just think it likely that, for example, Jesus Christ is the divine son of God; she believes it; it is a member of the set of propositions she believes; hence its probability with respect to that set is 1. If that set isn’t the one Schellenberg has in mind, however, which one is it? What is the body of beliefs Christian belief must be probable with respect to in order to be reasonable? Schellenberg’s approach (like so many others) seems to make sense only if the believer, to be rational, must hold her Christian beliefs on the basis of their relation to other beliefs she has—or, at any rate, only if those Christian beliefs are probable with respect to those other beliefs. One of the main burdens of this book, however, is that the believer can be perfectly rational in accepting some of her beliefs in the basic way—not on the basis (probabilistic or otherwise) of other beliefs.

No doubt there are subsets S of her total set of beliefs with respect to which Christian belief is indeed improbable; perhaps, in fact, it is improbable with respect to the rest of what she believes (supposing, for the moment, that there is some neat way to segregate her Christian belief from her other beliefs). But how is that relevant? The same will be true, no doubt, with respect to many other beliefs she holds in perfect rationality. She is playing bridge and is dealt all the sevens and eights. The odds against this are pretty formidable; there are many alternatives that are at least equally probable; does that mean that her belief that she was dealt all the sevens and eights is irrational? Of course not. The reason, clearly, is that this belief has a source of warrant independent of any it gets by way of its probabilistic relations to her other beliefs. The same goes for Christian belief. If there is a source of warrant for Christian belief that is independent of any it acquires by way of probabilistic relations to other beliefs, then the fact (if it is a fact) that Christian belief isn’t particularly likely with respect to those others doesn’t show anything of much interest. It certainly doesn’t provide a defeater for Christian belief.