A Pragmatic Interpretation of Quantum Logic

TL;DR

This paper proposes a pragmatic interpretation of quantum logic, viewing it as a language about empirical justification in quantum mechanics rather than a quantum truth, aligning with a broader integrationist perspective.

Contribution

It introduces a novel pragmatic interpretation of quantum logic as a formalization of empirical justification, avoiding the notion of quantum truth and integrating with classical logic.

Findings

Quantum logic formalizes empirical justification, not quantum truth.

The interpretation aligns with global pluralism in logic.

Standard quantum truth notions are also clarified.

Abstract

Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be interpreted as a pragmatic language of assertive formulas which formalize statements about physical systems that are empirically justified or unjustified in the framework of quantum mechanics. According to this interpretation, QL formalizes properties of the metalinguistic notion of empirical justification within quantum mechanics rather than properties of a quantum notion of truth. This conclusion agrees with a general integrationist perspective that interprets nonstandard logics as theories of metalinguistic notions different from truth, thus avoiding incompatibility with classical notions and preserving the globality of logic. By the way, some elucidations of the standard notion of quantum truth are also obtained. Key words: pragmatics, quantum logic, quantum mechanics, justifiability, global pluralism.