Logics of deontic inconsistencies and paradoxes

Abstract

Usually, a deontic paradox consists of a set of sentences in natural language which are, intuitively, logically independent and jointly consistent but, when formalized in standard deontic logic (SDL), the set derives contradictory obligations and/or has logical dependencies. In this paper, following the approach initiated in [8], two deontic systems based on Logics Formal Inconsistency are proposed: the first one is closer to SDL because contradictory obligations trivialize but contradictory sentences do not. The second one is a bimodal extension of system DmbC introduced in [8] by adding a modality for deontic inconsistency as a primitive, such that contradictory obligations do not trivialize. This approach overcomes deontic paradoxes such as Chisholm’s paradox by allowing a richer repertoire of connectives which avoids logical dependencies, and by avoiding logical collapse in the presence of contradictory obligations.