Conditional Obligation

Abstract

Let us rehearse what may be termed the standard account of the meaning of the monadic deontic operator ◯. Relative to each possible world, including our own, there is a non-empty class of possible worlds that are deontic alternatives to the given world. A sentence of the form ◯ A is adjudged true at a possible world just in case A itself holds true at each of the world’s deontic alternatives. The picture is of a non-empty class of worlds functioning collectively as a moral standard: What is true at all such worlds is what ought to be true. Let us call the logic of ◯ that arises from this account standard monadic deontic logic, or D*. On the basis of ordinary propositional logic, it is given by the rule of inference ${\text{ROM}}{\text{. }}\frac{{A \to B}}{{\bigcirc A \to \bigcirc B}}{\text{,}}$ together with the axioms ${\text{OD}}{\text{.}}\left. {\overline {\, {} \,}}\! \right| \bigcirc \bot {\text{,}}$ ${\text{ON}}{\text{.}}\bigcirc {\text{T,}}$ and $\begin{array}{*{20}{c}} {OK.} & {(\bigcirc A \wedge \bigcirc B) \to \bigcirc (A \wedge B).} \\ \end{array}$

I wish to thank Audrey McKinney for valuable advice and assistance in preparing this paper.