Agustina Borzi (IIF-SADAF-CONICET, UBA) – Analytic and Synthetic Entailment

(w/ Martina Zirattu)

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 renements 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 renement of said systems applied to classical logic, where the variable inclusion requirement is met unconditionally. Most notably, our alternative systems dier 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, where the analytic/synthetic distinction on inferences can be understood as an analogical extension of the usual Kantian distinction between analytic/synthetic judgements.