Indexical Expressions in Model Theory and in Truth Theory. 1 defend Davidson's truth-theoretic approach to the semantics of natural language as against the form of model-theoretic semantics exemplified in Kaplan (1979b). First 1 question Kaplan's assumption that the actuality operator is an indexical, on the ground that it · is irnproper to speak of the world of the utterance. 1 then point out sorne properties of genuinely indexical utterances that Kaplan's logic of demonstrative seems unable to account for. It turns out that these properties, as weIl as Kaplan's basic insights, can be captured in a truth-theoretic framework without assuming an ontology of possible worlds.