Four Approaches to Supposition

Abstract

Suppositions can be introduced in either the indicative or subjunctive mood. There are also two types of judgments that may be initiated by suppositions of either sort: qualitative (binary) judgments and quantitative (numerical) ones. The former are judgments about whether a given proposition is acceptable and the latter are about how acceptable it is. We systematically explicate the relationships between canonical representatives of each of the four available types of theories. For the qualitative accounts, our representative theories of indicative and subjunctive supposition are based on the belief change operations given by AGM revision and KM update respectively; for the quantitative ones, we consider those given by conditionalization and imaging. This choice is motivated by the familiar approach of understanding supposition as ‘provisional belief revision’ wherein one temporarily treats the supposition as true and forms judgments by making appropriate changes to their other opinions. To compare the numerical judgments recommended by the quantitative theories with the binary ones recommended by the qualitative accounts, we appeal to a suitably adapted version of the Lockean thesis. Ultimately, we establish a number of new results that we interpret as vindicating the often-repeated claim that conditionalization is a probabilistic version of revision, while imaging is a probabilistic version of update.