On the dilemma for partial subjunctive supposition

Abstract

In ‘The logic of partial supposition’, Eva and Hartmann present a dilemma for a normative account of partial subjunctive supposition: the natural subjunctive analogue of Jeffrey conditionalization is Jeffrey imaging, but this rule violates a natural monotonicity constraint. This paper offers a partial defence of Jeffrey imaging against Eva and Hartmann’s objection. I show that, although Jeffrey imaging is non-monotonic in Eva and Hartmann’s sense, it is what I call status quo monotonic. A status quo monotonic credal revision rule is monotonic in Eva and Hartmann’s sense if it is conservative in the sense of Meehan and Zhang (‘Jeffrey meets Kolmogorov’), but Jeffrey imaging is in general non-conservative. On the other hand, Jeffrey imaging satisfies a different constraint that I call convexity, and the only rule that is both convex and conservative is Jeffrey conditionalization. To this extent, the real dilemma for a normative account of partial subjunctive supposition is not between monotonicity (broadly construed) and Jeffrey imaging, but between convexity and conservativeness.