Abstract

In an earlier defense of the view that the fundamental logical properties of logical truth and logical consequence obtain or fail to obtain only relative to contexts, I focused on a variation of Kaplan’s own modal logic of indexicals. In this paper, I state a semantics and sketch a system of proof for a first-order logic of demonstratives, and sketch proofs of soundness and completeness. (I omit details for readability.) That these results obtain for the first-order logic of demonstratives shows that the significance of demonstratives for logic exceeds their behavior as rigid designators in counterfactual reasoning, or reasoning about alternative possibilities. Furthermore, the results in this paper help address one common objection to the view that logical truth and consequence obtain only relative to contexts. According to this objection, the view entails that logical consequence is not formal.