Logical Inferentialism & Attacks on Classical Logic

TL;DR

This paper explores logical inferentialism's standards, examining how they challenge classical logic by analyzing proof systems and the meaning of logical constants, ultimately questioning classical principles' legitimacy.

Contribution

It provides a detailed analysis of proof systems within logical inferentialism and argues that classical logic fails to meet inferentialist standards, offering a critique from intuitionist and revisionist perspectives.

Findings

Natural deduction satisfies inferentialist virtues

Classical principles often fail to uphold inferentialist standards

Challenges to classical logic undermine its legitimacy within a meaning-theoretic framework

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.