This paper argues first that, contrary to what one would expect, metaphorical interpretations of utterances pass two of Cappelan and Lepore's Minimalist tests for semantic context-sensitivity. I then propose how, in light of that result, one might analyze metaphors on the model of indexicals and demonstratives, expressions that (even) Minimalists agree are semantically context-dependent. This analysis builds on David Kaplan's semantics for demonstratives and refines an earlier proposal in (Stern, Metaphor in context, MIT Press, Cambridge, 2000). In the course of (...) this argument, I also discuss some new examples of linguistic phenomena that motivate a semantic structure underlying metaphorical interpretation, phenomena I argue that neither Minimalists nor Contextualists can explain. (shrink)