I finally finished the draft of my paper for the Formal Epistemology Workshop. Here it is.

bq. “Uncertainty, Probability and Non-Classical Logic”:http://brian.weatherson.org/upn.pdf

For all my complaining about how hard it was to do logic, there didn’t end up being much formal work in the paper. There’s actually very little formalism that goes beyond what I say in “From Classical to Intuitionist Probability”:http://brian.weatherson.org/conprob.pdf. But I think I make some of the epistemological points of that paper somewhat clearer, and I go into a little more detail about the pros and cons of using intuitionist probability as a constraint on credences. In particular, I think the new paper is a little clearer than the old about just what the significance of the Dutch Book result I proved there was meant to be, though it’s still not as clear as I’d like.

There’s also a small section on mixing probability with one of the Łukasiewicz logics (3-valued with 1 as the only designated value), but that turns out to have very few interesting formal properties. Thanks to one of Greg Restall’s comments in an earlier thread I was able to do (or at least sketch) a completeness proof for the intended axioms of that probability theor with respect to their intended semantics, which was nice. And there’s a nice Dutch Book argument that they are the right axioms too. But that’s not a new argument – I just noticed that all the features of intuitionist logic I used in the earlier Dutch Book argument are also features of the Łukasiewicz logic being discussed.

I have this dream where one day non-classical probability theory will be this huge field, and everyone will make a passing reference to me as being one of the pioneers. Not necessarily one of the pioneers whose work is particularly important in and of itself, and certainly not one whose results or methods you’d want to be leaning too heavily on. Maybe even indeed one whose work you’d give as homework refutation exercises to the not particularly talented undergraduates. And certainly not _the_ first in the area – although there’s been _much_ less work in this area than I expected. But still an early explorer. It’s an unlikely dream, but I think it’s helpful in philosophy to have high hopes from time to time.