From Mathematical Logic to Quantum Logic: The Dilemma and Solution of the Logical Methodology of the Ideal Language School

Abstract

Mathematical logic, as the foundational tool of the ideal language school, seeks to eliminate the ambiguity and vagueness inherent in natural language through formalized symbolic systems and rigorous reasoning rules, striving for precise philosophical analysis. However, in practical applications, it encounters limitations such as formal isolation, static rigidity, and linear unidimensionality, which hinder its ability to address dynamic changes and complex, multidimensional relationships. Quantum logic, as a pioneering logical methodology, transcends these limitations with its core characteristics: contextual relevance, dynamic evolution, and nonlinear multidimensionality. It emphasizes the integration of logical expressions with specific contexts, adapts to changing systems, and adeptly manages multidimensional complexity. Quantum logic thus offers an innovative tool and theoretical foundation for formal language logic systems, potentially revitalizing the ideal language school.