Running back to the prior 1: More on why a partition is important

We turn technical again today with a discussion of why it's enlightening and useful to investigate the case for a historical claim using a full partition. Which explains the specific evidence better? "The claim is true" or "The claim is false"? This allows one to see if there is a "cost" to adding auxiliary hypotheses to ~H ("the claim is false") in order to make an attempt to explain the alleged evidence. And how "bad" is that cost? This doesn't of course guarantee that the evidence should be regarded as strong, much less that the hypothesis will turn out to be probable, all things considered. But it prevents one from focusing only on subhypotheses of ~H that are specifically designed to explain evidence that, in fact, favors H, which can easily lead to losing sight of the cost of ad hocness.Nor does considering a partition Bayes factor involve ignoring the prior probability or improbability of H. In fact, considering a partition Bayes factor provides an easy and obvious way of considering how low of a prior probability could be overcome by the specific evidence that supposedly supports H. This backsolving approach is what Tim and I took in our article on the resurrection. Here is the recent exchange with Brian Blais which I mention in the video: https://lydiaswebpage.blogspot.com/2026/07/probability-and-non-partition.htmlHere is a preprint version on my published paper on a Bayesian analysis of ad hocness: https://lydiamcgrew.com/wp-content/uploads/AdhocarticleforActaAnalytica.pdfHere is Tim's and my anthology article from some years ago on the resurrection:https://lydiamcgrew.com/wp-content/uploads/2023/11/Resurrectionarticlesinglefile.pdf