The distinction between a merely ‘rigidifying’ dthat and a directly-referential take on dthat-terms is well known, and is explicitly highlighted by Kaplan in Afterthoughts, his 1989 commentary on Demonstratives. What is not equally widely recognized is that Afterthoughts also oscillates between three different directly referential proposals. This essay discusses the semantic and philosophical implications of these different directly-referential interpretations of ‘dthat’, paying particular attention to the relationships between syntactic and propositional structure, the structure and makeup of contexts in the semantics (...) of indexical languages, the significance of context shifting devices and of so-called operators on character, and the aims and scope of propositional semantics. (shrink)