I applaud the authors for putting their argument in a bayesian form. At the very least, it forces them to make their argument explicit. Also, in theory it lets one describe disagreement in terms of values of numbers (priors and conditional probabilities). However, I suspect that this is rarely going to happen in historical disagreements and the qualitative structure will capture most of the disagreement. (In principal, anyone should be able to supply numbers someone else's structure, but I'm skeptical that it is a useful comparison.)