In my paper on “pragmatics and justification”:http://brian.weatherson.org/cwdwpe.pdf, I make a big song and dance about the fact that by definition of belief in probabilistic terms allows for multi-premise closure, or at least a plausible version of it. More precisely, it says the coherent agent believes the conjunction of any two things she believes, if all three are salient. What I didn’t go back and check, because I could hardly believe it could be an issue, is whether we still have single-premise closure. And, to my horror, it turns out that in the theory as presented there, we don’t. But there’s a small fix that solves the problem it turns out. Because the symbols get rather messy in HTML, I put the write up of the problem and the fix into a PDF file below.

* “Single Premise Closure in the CCNCP Theory of Belief”:http://brian.weatherson.org/ccncp-single.pdf

CCNCP is my new and uncatchy shorthand for Conditionalisation Changes No Conditional Preferences, which is the full name for the theory, though sadly not quite a full description of it!