Quantum Supervaluationism

TL;DR

This paper proposes a supervaluationist logical framework to interpret quantum superpositions, treating indefinite propositions as lacking truth-values, offering an alternative to classical logic for quantum states.

Contribution

It introduces a supervaluation approach to quantum superpositions, providing a novel logical account that handles indefinite propositions without assigning truth-values.

Findings

Supervaluationist logic can model quantum superpositions.

Indefinite propositions in superpositions lack truth-values.

The approach offers an alternative to classical interpretations of quantum states.

Abstract

As it is known, neither classical logical conjunction "and" nor classical logical alternative "either...or" can replace "+" representing a linear superposition of two quantum states. Therefore, to provide a logical account of the quantum superposition, one must either reconsider the standard interpretation of quantum mechanics (making it fit for classical bivalent logic) or replace the standard logic with a deviant logic suitable for describing the superposition. In the paper, a supervaluation approach to the description of the quantum superposition is considered. In accordance with this approach, the indefinite propositions, which correspond to the superposition states, lack truth-values of any kind even granting that their compounds (such as logical alternative "either...or") can have truth-values. As an illustration, the supervaluationist account of the superposition of spin states is presented.