(Meta)inferential levels of entailment beyond the Tarskian paradigm

In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an alternative of our own. After that, we consider a number of objections to our account and evaluate a substantially different approach to the same problem.