Is this just funny games?
Eh, yes.
Is there something to the proposed limitations of Bayes' theorem they present?
Pretty much, no. The questions they are trying to answer, of "how does a system deal with a lack of exact numbers" and such, are approached with tools like replacing discrete probabilities with probability distributions and using maximum ignorance or Kolgomorov complexity-approximating priors.
More broadly, be skeptical of any weakenings. Going from quantitative posterior probabilities to qualitative "probably or approximately yes" judgments is suspicious (especially because posterior probabilities are about "probably or appoximately" yes or no answers). Similarly, moving from cardinal probabilities (posteriors that are a decimal between 0 and 1 representing how likely a thing is to happen) to ordinal probabilities as Richard Carrier (see quote below) does is likely bad.
you can at least say that something wouldn't be less likely than X or more likely than Y
Thanks for the comment. This lines up with my [basic-level] thinking on this. It struck me as similar to EY's point in Reductionism with his friend insisting that there was a difference between predictions resulting from Newtonian calculations and those found using relativity.
In a similar vein, they seem to insist that this area isn't governed by Bayes' theorem.
Lastly, I might have not credited Carrier well enough. He does assign cardinal values to his predictions. He simply makes the point that when we don't know, we can use a "fringe" number th...
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: