Saturday, September 15, 2012

Bayes’ theorem and the Moral Argument

Maverick Christian put up a post on Bayes’ theorem and the moral argument for God. This is not the first time Bayes’ theorem has been used to argue for religious belief, but I’d like to use this example to illustrate a generic problem with such attempts to use Bayes’ theorem.

To define some terms, propositional evidence is evidence that consists of one or more propositions; e.g. I believe evolution, in part, on the basis of certain similarities in Earth organisms, and Maverick Christian believes “objective morality exists” is evidence for theism. For want of a better nomenclature, let’s call a piece of propositional evidence veridically evidential if and only if (1) the proposition is true; (2) the claim it is evidence for is also true. Thus, where M symbolizes “objective morality exists” and G symbolizes “God exists,” the probability that objective morality is veridically evidential for theism is Pr(M & G), since it is the probability that both M and G are true. That probability can be calculated like so:

Pr(M & G) = Pr(M) × Pr(G|M)

The generic problem in using Bayes’ theorem to argue for religious belief is that we are seldom 100% certain of the evidence, and the evidential use of propositional evidence will depend on the probability of the proposition(s) being used as evidence. Suppose, as Maverick Christian suggests for his hypothetical agnostic, that Pr(G|M) = 0.8. What if the agnostic gives “objective morality exists” a probability of only 60%, making Pr(M) = 0.6? Then the probability that objective morality is veridically evidential for theism is only 48%, and by my lights the agnostic should remain agnostic even with the “evidence” of objective morality.