James Joyce Title: "Do Imprecise Credences Make Sense?" Abstract: Many have suggested that states of uncertain belief in light of evidence, hereafter credal states, are best represented by sets of probability functions rather than single probability functions. The following ideas seem essential to this picture: IMPRECISION. A rational believer’s creedal state in light of evidence is often best represented by a set of probability functions P defined over a Boolean algebra of events ? COMPLETENESS. If my credal state is P and yours is Q, then we have the same total system of beliefs if and only if P = Q. SUPERVALUATION. If some claim about probabilities ?(P) holds for every P ? P, then ? is a determinate truth about what the believer believes. Some add the following to this picture: SET. For A, B ? ?, if the set of values for A in P, P*(A) = {P(A) : P ? P}, is identical to the set of values for B in Q, then P represents the believer as having the same beliefs about A that Q represents her having about B. So, P*(A) = Q*(B) = same belief state in re B. I will explain why SET is false, and show how certain recent objections to imprecise credences – found in White (2009) and Titelbaum (2009) – fail because they presuppose its truth.
