There is no tenable notion of global metainferential validity

The use of models to assign truth values to sentences and to counterexemplify invalid inferences is a basic feature of model theory. Yet sentences and inferences are not the only phenomena that model theory has to take care of. In particular, the development of sequent calculi raises the question of how metainferences are to be accounted for from a model-Theoretic perspective. Unfortunately there is no agreement on this matter. Rather, one can find in the literature two competing model-Theoretic notions of metainferential validity, known as the 'global' notion and the 'local' notion. In this article, I argue that, given certain plausible considerations about metainferential validity, the global notion collapses into the local notion.