A Formal Study of Ought Implies Can and Other Metaethical Principles

Abstract

This article provides a comprehensive logical study of the metaethical principle referred to as “ought implies can” (OiC, for short). We analyze and formalize ten OiC interpretations from the philosophical literature and develop a class of sound and strongly complete deontic agency logics axiomatizing these ten principles. To do so, we adopt a non-normal modal logic approach to the agency formalism of ‘seeing to it that,’ that is, STIT logic. The resulting logics are employed to demonstrate a formal taxonomy of OiC in STIT, logically determining the (in)dependencies between the various interpretations. Additionally, we extend the class of logics with four other prominent metaethical principles discussed in the literature, analyzing their relation to OiC. These include the principles of “no vacuous commands,” “deontic contingency,” “deontic consistency,” and “no deontic dilemmas.” Last, to address a common objection, we extend the developed class of logics with restricted forms of monotonicity and aggregation that take into account the variety of OiC. Through this, we restore and enhance some of the inferential power lost in adopting a non-normal modal approach.