Man Muss Immer Umkehren Johan van Benthem Abstract: Choosing a semantics validates certain axioms. But as the 19th century German geometrist Jakobi said already: "One Should Always Convert'. Modal correspondences are a way of stepping back from statements of validity, and asking the converse question 'what sort of models would make the given axiom valid'. Analyzing a sequence of well-known principles using standard correspondence techniques for pure modal logic, we find the bare mechanics of the models for systems that superficially look different: spatial and temporal geometry, dynamic-epistemic update, and eventually even first-order predicate logic itself. The result of the correspondence analysis is often a generalized class of models over which even new logics can arise, which are of interest by themselves.