New Foundations for Imperative Logic I: Logical Connectives, Consistency, and Quantifiers*
Peter B. M. Vranas · Noûs · 2008
Abstract Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: “kiss me and hug me” is theconjunctionof “kiss me” with “hug me”. This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives istrueexactly if both conjuncts are true, the conjunction of two imperatives issatisfiedexactly if both conjuncts are satisfied—what more is there to say? Much more, I argue. “If you love me, kiss me”, aconditionalimperative, mixes a declarative antecedent (“you love me”) with an imperative consequent (“kiss me”); it issatisfiedif you love and kiss me,violatedif you love but don't kiss me, andavoidedif you don't love me. So we need a logic ofthree‐valued imperatives whichmixesdeclaratives with imperatives. I develop such a logic.