Quantum Interpretation of Semantic Paradox: Contextuality and Superposition

Abstract

We employ topos quantum theory as a mathematical framework for quantum logic, combining the strengths of two distinct intuitionistic quantum logics proposed by Döring and Coecke respectively. This results in a novel intuitionistic quantum logic that can capture contextuality, express the physical meaning of superposition phenomenon in quantum systems, and handle both measurement and evolution as dynamic operations. We emphasize that superposition is a relative concept dependent on contextuality. Our intention is to find a model from the perspective of quantum theory that accommodates semantic paradoxes. We refine Aerts et al.’s interpretation of the liar paradox using models from quantum mechanics and present a model based on quantum theory, incorporating contextuality and superposition to interpret semantic paradoxes. We associate the truth values of statements in semantic paradoxes with quantum states in a given context, interpreting statements with unclear truth value assignments as superposition states within the current context. Dynamic operations are employed to distinguish the truth value assignments of statements among different times. Unlike the classic interpretation of paradoxes, we accept the reasonable existence of semantic paradoxes and point out the difference between paradoxes and contradictions.