Abstract

This chapter turns to the notion of conditional belief: rationally believing a proposition given another proposition. Among other things, conditional belief plays a role for belief revision by entailing a disposition for how to revise one’s belief given new evidence. The numerical version of conditional belief is subjective conditional probability, and first the chapter calls to mind how the concept of conditional probability figures in the standard diachronic norm on degree-of-belief change. Afterwards the same is done for conditional all-or-nothing belief and the standard diachronic norm on all-or-nothing belief change, which rely on the so-called AGM postulates for belief revision. Finally, a stability account of rational conditional belief is developed according to which subjective conditional probability and rational conditional all-or-nothing belief cohere with each other just as their unconditional versions did in Chapters 2 and 3. From this, together with the standard diachronic norms on belief change, it follows that also rational degree-of-belief change and categorical belief change must cohere with each other once the stability theory is in place. Other than extending the stability account to conditional belief, the chapter also serves the purpose of supplying some of the mathematical machinery on which the theory in this book is based.