Research Group
in Analytic Philosophy

Abstract

In this talk, we critically discuss what has become known as “variable inclusion logics”: logical systems where validity requires that the propositional variables occurring in the conclusion are included among those appearing in the premises (right variable inclusion), or vice versa (left variable inclusion). We object that most variable inclusion logics and refinements thereof allow for some striking exceptions to the variable inclusion requirement for the sake of maintaining the Tarskian (or structural) character of the notion of logical consequence. The main goal of this talk is to present a new refinement of said systems applied to classical logic, where the variable inclusion requirement is met unconditionally. Most notably, our alternative systems differ from other proposals present in the literature in that they are characterized proof-theoretically and are both substructural. After reviewing what we deem as advantageous of this new approach, we provide a philosophical interpretation for them: as the logics of (classically valid) analytic and synthetic arguments, following the definition of analytic/synthetic inference introduced by Szmuc (2017), which can be understood as an analogical extension of the usual Kantian distinction between analytic and synthetic sentences.

References:

Szmuc, D. (2017b). “El sentido del sinsentido”, Análisis Filosófico, 37(2): 195–212.