Because of a paper I am working on regarding Hume's theory of belief in the Treatise, and some connections between the topic of that paper and the interpretation of Hume as a Baconian about probabilistic reasoning, I started looking into formalizations of non-Pascalian probabilities.

My as-yet-unschooled understanding of Baconian probabilities is that they differ from Pascalian probabilities in a couple of important ways. One is that they are ordinal rather than algebraic (meaning that they cannot be summed or multiplied). The other major difference is that the 0 point on the scale does not reflect disproof (as it does for Pascalian probabilities), but maximal uncertainty. In other words, on the Pascalian model, if P(H) = 0 that is equivalent to it being the case that P(~H) = 1. On the Baconian model, this is not so. Since that pretty much exhausts my current knowledge of Baconian probability, I figured that I should find out more about it.

A cursory google search alerted me to a book by L. Jonathan Cohen in which he (allegedly) shows how to use a generalized version of the modal logic S4 to model Baconian probabilities. I say 'allegedly' not because I am particularly doubtful that he does so, but only because I have yet to get my hands on that book. Someone else had it checked out, so I issued a recall (after first making sure that the book was not checked out by one of my professors or by another student in the program), and am now waiting for it to come back in.

Luckily, I do not lack reading material while I wait, though, because, in my search of the library's online catalogue for that Cohen book, I noticed that he had also written something called "An Essay on Belief and Acceptance" which piqued my interest despite (or perhaps because of) the fact that it was not particularly related to any of the issues I had been intending to investigate.

So, I've been reading that book, which I am finding very interesting. In fact, any readers who are familiar with it and have (a) thoughts about it or (b) recommendations of other good work on the same topic should post them to the comments.

I don't want to make it sound like this has stalled progress on my original investigation (the original investigation being the Hume paper, in case that wasn't clear). Luckily, I spend enough time working on philosophy that such off-topic excursions don't outright interfere with getting my work done.*

But there is a potential danger with having too many topics under investigation at once, which is what makes it worrisome for me that pursuing legitimate connections to a given topic seems to be the major trigger for launching me on increasingly unrelated investigations.

*In this case, enough time is roughly equivalent to all of it.