Semantic analyses for dyadic deontic logic
David K. Lewis · Cambridge University Press eBooks · 1999
INTRODUCTION It ought not to be that you are robbed. A fortiori , it ought not to be that you are robbed and then helped. But you ought to be helped, given that you have been robbed. The robbing excludes the best possibilities that might otherwise have been actualized, and the helping is needed in order to actualize the best of those that remain. Among the possible worlds marred by the robbing, the best of a bad lot are some of those where the robbing is followed by helping. In this paper, I am concerned with semantic analyses for dyadic deontic logic that embody the idea just sketched. Four such are known to me: the treatments in Bengt Hansson [4], Sections 10–15; in Dagfinn Føllesdal and Risto Hilpinen [2], Section 9; in Bas van Fraassen [9]; and in my own [8], Section 5.1. My purpose here is to place these four treatments within a systematic array of alternatives, and thereby to facilitate comparison. There are superficial differences galore; there are also some serious differences. My results here are mostly implicit in [8], and to some extent also in [7]. But those works are devoted primarily to the study of counterfactual conditionals. The results about dyadic deontic logic that can be extracted thence via an imperfect formal analogy between the two subjects are here isolated, consolidated, and restated in more customary terms.