Routes to Relevant Logics - Guest Lecture Dr Shawn Standefer

Relevant logics are a family of non-classical logics characterized by the behaviorof their implication connectives. They are characterized by the rejection of principles of irrelevance for their implication connectives. In the purely implicational fragment, this means rejection of the paradoxes of material implication.

• A --> (B --> A)

• B --> (A --> A)

Unlike some other non-classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. The common core to relevant logics is the adoption of Belnap’s variable sharing criterion, which says that if A --> B is valid, then A and B share a propositional variable. This condition on formal relevance is standardly adopted as a necessary condition on being a relevant logic. Many logics common in philosophy, such as classical and intuitionistic logic, violate this criterion. Beyond the variable sharing criterion, there is much disagreement between relevant logicians on the philosophical views behind relevant logics. In this article, we survey five major views motivating the adoption of relevant logics. The major views are the Use Criterion, sufficiency, meaning containment, theory construction,and truth-making. We will present these views and highlight their philosophical differences. The views seem to favor different logics as well as different presentations of the logics.