Scott Sturgeon's paper and handout available
They're pouring in now! See the sidebar.
Scott says he'll also talk about results from Jim's paper, "The Logic of Confidence and Belief", during his session. It's available on the sidebar as well. The first comment below describes it's relevance.
1 comment:
Scott,
I completely agree with your points about confidence and credence -- that confidence is a "thicker notion" and is "prior to" credence. And I find your examples really compelling.
I've done some work on formalizing the comparative confidence relations that I think fits well with what you are saying.
One may set down axioms for the "is at least as confident that" relation (a version of the axioms of qualitative probability -- aka comparative probability), and then show via a representation theorem that quantitative probability functions (i.e. credence functions) are simply a convenient representation of comparative confidence relations.
However, the usual axioms for qualitative probability include a "completeness axiom" that says that for each pair of statements A and B, the agent is either at least as confident that A as that B or is at least as confident that B as that A. But there is a way to axiomatize confidence without this sort of completeness, so that confidence is only a partial order on statements (or propositions). I think that this way of doing it yields confidence relations that are "thick" in the sense you describe. Each such thick confidence relation turns out to be representable by a set of credence functions, just as you might expect. But now the confidence "horse" has come first, and the credence "cart" follows after. There is also a way to extend the qualitative logic of relative confidence to include belief thresholds.
For those interested in the formal details, I'll attach a link on the blog sidebar to an overly long paper about it.
Jim
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