Logical Inferentialism & Attacks on Classical Logic

Abstract

This paper undertakes a foundational inquiry into logical inferentialism with particular emphasis on the normative standards it establishes and the implications these pose for classical logic. The central question addressed herein is: “What is Logical Inferentialism & How do its Standards challenge Classical Logic?” In response, the study begins with a survey of the three principal proof systems that is, David Hilbert’s axiomatic systems and Gerhard Gentzen’s natural deduction and his sequent calculus, thus situating logical inferentialism within a broader proof-theoretic landscape. The investigation then turns to the core tenets of logical inferentialism by focusing on the role of introduction and elimination rules in determining the meaning of logical constants. Through this framework, natural deduction is evaluated as a system that satisfies key inferentialist virtues including harmony, conservativeness and the subformula property. Ultimately, the paper presents challenges to classical logic from intuitionist and revisionist perspectives by arguing that certain classical principles fail to uphold inferentialist standards, consequently undermining their legitimacy within a meaning-theoretic framework.