Title: The future of MFL: pure math or seriously interdisciplinary? Abstract: The call for this event asks for "rethinking" research directions in MFL from three seemingly quite different point of views: (1) pure mathematical logic, (2) philosophical motivations, (3) computer science applications. We argue that currently MFL is mainly pursued as a research endeavor within the methodological boundaries of pure mathematical logic (1), with only quite superficial attention to problems arising from fields (2) and (3), so far. We contend that future and wider success of MFL will depend on the ability to address this imbalance and to bridge the gap between the admittedly impressive purely mathematical progress and the so far largely just intended impact on the foundations of reasoning and on applications in computer science. Motivated by this diagnosis, we attempt to locate some research challenges that have the potential to *combine* all three of the above mentioned perspectives. In particular, we single out the following topics: - modeling reasoning with (vague) natural language - justifications, consequences, and limits of truth functionality - fuzzy logics as logics of costs - efficient reasoning with graded truth We argue that these topics call for a truly interdisciplinary approach that builds on current knowledge and techniques in MFL, but - crucially - also require serious engagement with themes, methods, and perspectives that are (as yet) outside its focus. If time permits, we will also discuss further candidates for extending the above list.