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Classical Harmony and Separability.

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This study introduces a new formalization for classical logic, demonstrating it can be both harmonious and separable. This challenges the view that classical logic cannot be explained using inferentialist principles.

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Area of Science:

  • Formal Logic
  • Philosophy of Language
  • Proof Theory

Background:

  • Inferentialism posits that logical expression meaning derives from usage rules.
  • Harmony and separability are key proof-theoretic requirements for admissible logical rules.
  • Standard formalizations of classical logic fail to meet these requirements, posing a challenge for inferentialist accounts.

Purpose of the Study:

  • To challenge the prevailing view that classical logic is incompatible with inferentialist semantics.
  • To present a novel formalization of classical propositional logic that satisfies harmony and separability.
  • To demonstrate that classicality can be an emergent structural feature within an inferentialist framework.

Main Methods:

  • Development of a new assertion-based, single-conclusion formalization for classical propositional logic.
  • Proof-theoretic analysis to demonstrate the satisfaction of harmony and separability conditions.
  • Examination of the structural properties of the proposed logical framework.

Main Results:

  • A formal system for classical propositional logic is introduced that is both harmonious and separable.
  • The proposed framework successfully accounts for classical logic within inferentialist terms.
  • Classicality is shown to arise as a structural characteristic of the logic, rather than a predefined axiom.

Conclusions:

  • The presented formalization overcomes limitations of previous systems, reconciling classical logic with inferentialism.
  • This work offers a new perspective on the relationship between logical practice and semantic theories.
  • The findings suggest that inferentialist explanations can be extended to encompass classical logic effectively.