This study shows that the Turkish expression hani exhibits interesting properties for the study of the semantics and pragmatics interface, because, on the one hand, its function is merely pragmatic, but on the other hand, it is subject to the truth-conditional effect of other constituents at LF. This notwithstanding, studies on this expression are remarkably scarce. The only attempts to describe its properties are Erguvanlı-Taylan (Studies on Turkish and Turkic languages; proceedings of the ninth international conference on Turkish linguistics, 133–143, 2000), Akar et al. (Discourse meaning, 57–78, 2020), and Akar and Öztürk (Information-structural perspectives on discourse particles, 251–276, 2020). In the present study, we introduce the first formal semantic and pragmatic treatment of clauses containing hani. Unlike previous accounts, we claim that hani can have one of the following two major pragmatic functions: making salient a proposition in the Common Ground or challenging one in a past Common Ground, therefore requiring a Common Ground revision. Despite its variety of occurrences, we argue that hani has a uniform interpretation and provide a compositional analysis of the different construals that it is associated with. Furthermore, we show that a formally explicit and accurate characterization of hani clauses requires operating on indexical parameters, in particular the context time. Therefore, if our proposal is on the right track, hani clauses may provide indirect empirical evidence in favour of the existence of “monstrous” phenomena, adding to the accumulating cross-linguistic evidence in this domain (see Schlenker in Linguistics and Philosophy 26(1):29–120, 2003 and much work since then). The definition of monsters is intended as in Kaplan (Themes from Kaplan, 481–563, 1989).