I'm about 2/3 through an apologetics book that was recommended to me, Menssen and Sullivan's, The Agnostic Inquirer, and was quite surprised to run into a discussion of Bayes theorem and wanted some input from the LW community. The book is quite philosophical and I admit that I am probably not following all of it. I find heady philosophy to be one of these areas where something doesn't seem quite right (as in the conclusion that someone pushes), but I can't always identify what.
In any case, the primary point of the book is to attempt to replace the traditional apologetics method with a new one. The status quo has been to appeal to "natural theology," non-theological areas of discussion which attempt to bring one to the conclusion that some kind of theistic being exists, and from there establish that Christianity is the true formulation of what, exactly, this theistic being is/wants/does, etc by examining revealed theistic truths (aka the Bible). Menssen and Sullivan attempt to suggest that revelation need not be put off so long.
I don't want to get too into it, but think this helps set the stage. Their argument is as follows:
Issues Menssen and Sullivan have with Bayes applicability to this arena:
Then they begin trying to choose the best method for evaluating revelatory content. This is where Bayes comes in. The pages are almost all available via Google books HERE in Section 4.2.1, beginning on page 173. They suggest the following limitations:
- Bayesian probability works well when the specific values are known (they use the example of predicting the color of a ball to be drawn out of a container). In theology, the values are not known.
- The philosophical community is divided about whether Bayesian probability is reliable, and thus everyone should be hesitant about it too if experts are hesitant.
- If one wants to evaluate the probability that this world exists and there are infinitely many possibilities, n, then no matter how small a probability one assigns to each one, the sum will be infinite. (My personal take on this is whether a literal infinity can exist in nature... 1/n * n is 1, but maybe I'm not understanding their exact gripe.)
- In some cases, they hold that prior probability is a useless term, as it would be "inscrutable." For example, they use Elliott Sober's example of gravity. What is it's prior probability? If such a question is meaningless, they hold that "Has a good god revealed?" may be in the same category and thus Bayesian probability breaks down when one attempts to apply it.
- There are so many components to certain questions that it would be nearly impossible or impossible to actually name them all and assign probabilities so that the computation accounted for all the bits of information required.
- If Bayes' theorem produces an answer that conflicts with answers arrived at via other means, one might simply tweak his/her Bayes values until the answer aligned with what was desired.
- If a hypothesis sufficiently approximates an ideal explanation of an adequate range of data, then the hypothesis is probably or approximately true.
- h1 sufficiently approximates an ideal explanation of d, an adequate range of data.
- So h1 is probably or approximately true.