Title: What is Classical Reasoning in a Natural Deduction System?

■ Keywords (Google Search SEO)

classical reasoning, natural deduction, proof-theoretic semantics, harmony, purity, separability, Dummett, Prawitz, logic paradox, analytic philosophy.

■ Abstract & Description

Within the framework of proof-theoretic semantics, it is natural to call a derivation classical when it essentially depends on a classical rule. The present paper argues that the familiar criterion is insufficient for characterizing classical reasoning thoroughly. 

The research explores the underlying circularity problem and re-examines foundationalist principles such as harmony, purity, and separability in natural deduction systems. It provides a critical philosophical and logical analysis of how classical logic behaves under proof-theoretic constraints, challenging standard assumptions established by Dummett and Prawitz.