The Logic and Metaphysics Workshop will meet on February 23rd from 2:00-4:00 in-person at the Graduate Center (Room 9205) over Zoom (details via mailing list) for a talk by Sara Ayhan (Tohoku).
Title: Contradictions without negation and a proof-theoretic, bilateralist account of connexive logics
Abstract: I’ll present the negation-free fragment of the bi-connexive logic 2C and investigate its properties from the perspective of bilateralist proof-theoretic semantics. I’ll argue that eliminating primitive negation has two important conceptual consequences. First, it requires a reconceptualization of contradictory (also called ‘überconsistent’) logics: in a bilateralist framework, contradiction need not be understood in terms of negation inconsistency, but rather as the coexistence of proofs and refutations for certain formulas within a non-trivial system. Second, it challenges the standard definition of connexive logics, which typically rely on negation-based schemata. Instead, a rule-based conception of connexivity, grounded in bilateralist proof-theoretic semantics, is proposed. This reconception avoids dependence on the validation of specific formula schemata and thereby also dependence on negation.

