Question #2

2. What example(s) from your work (or the work of others) illustrates the role formal methods can play in philosophy?

In epistemology I have worked hard to integrate probability and more traditional epistemology in two areas: evidence and explanation. I am working hard on a phenomenal theory of evidence which satisfies essential bayesian theorems. Less originally I have both argued that traditional critiques of Orthodox Bayesianism are less than persuasive and that there are strong Neo-Bayesian strategies for evading them at any rate.

The twin pillars of the classical opposition to Orthodox Bayesianism are the problem of the priors and the weakness of a mere coherence constraint. The reply--which really needs to be shot back more forcefully than it has beenis that probability theory is a form of logic. It is, from a formal standpoint, no different than First Order Logic. FOL can't tell you what values you should have for the p's and q's--you must mind your p's and q's yourself--logic isn't the whole of epistemology (granted, many Orthodox Bayesians talk as if it is). Or if it is, then it isn't the whole story about rational belief (cognitive psychology has much to say). And ultimately all FOL can do is tell you when you're inconsistent (and in a much coarser granularity than probability theory). So though I think claims that probability theory exhaust epistemolog--has anybody really ever said just that--are clearly mistaken, I think the parallel between probability theory and first order logic is closer than most people appreciate.

A book which very nicely pursues this project is David Christensen's Putting Logic in its Place, though I disagree with him on keeping a closure constraint. One of my main projects is applying the theory of idealizations Weirich devised for decision theory in Realistic Decision Theory to probability theory. The proposed monograph is to be called _Realistic Bayesianism_.

Nevertheless there are ways of addressing the problems which have been developed but under-appreciated. Rather than rehearse them let me give an example which I have adapted from Kvanvig. Kvanvig and Riggs have suggested that traditional coherentists have missed the boat in not including non-doxastic--but still contentful--mental states (such as perceptions, memories, and appearance states generally) among the elements which must cohere. There's no reason Bayesian coherentists can't adopt this same strategy.

In fact, I think it makes perfect sense: I think we do often assign confidence levels to appearance states, as when we judge that we are seeing an optical illusion. I don't think this can be reduced to merely refusing to believe what is reported. We express a degree of confidence in the veracity of the appearance state itself. I think further analysis will bear this out.

I also would like to defend a limited form of Inference to the Best Explanation as a form of "poor man's bayesianism." That is, IBE is the way boundedly rational agents approximate bayesian inference. Often, the results of formal epistemology are judged to be inapplicable due to idealization. I agree and am keenly interested in adapting formal methods to cases of bounded rationality.