政治哲学圆融模型的数学表达与完整论述

This paper establishes a formal mathematical framework for the Political Philosophy Cohesion Model, the third and final core methodological pillar of the "Productive Political Philosophy" system. Utilizing three variables—Value completeness (V), Methodology completeness (M), and Tool completeness (T_tool)—combined with the Matrix Homogeneity coefficient (ρ), it defines a comprehensive formula for systemic integrity: Ω = ρ × min(V, M, T_tool). The completeness of the three dimensions determines whether a system is "threefold complete," while the Matrix Homogeneity coefficient determines whether it is "cohesive" or "hybridized." The judgment of ρ distinguishes between two criteria that can vary independently: logical homology (determining long-term stability) and functional homology (determining short-term effectiveness). The synthesis of the three dimensions follows the wooden barrel principle, but the nature of deficiencies differs: completable dynamic deficiencies versus non-completable static deficiencies, depending on the relationship between the deficiency and the underlying axiom. The model further distinguishes between active synthesis (providing positive incentives) and passive synthesis (merely setting moral boundaries). The evaluation of completeness is divided into theoretical completeness (textual logical analysis) and practical completeness (historical operational assessment), the gap between which serves as the analytical focus of the Dynamic Success Probability Model. Through numerical simulations of seven classic cases—the Zhou Rites, Shang Theocracy, Legalism, Confucianism, the Confucian-Legalist hybrid, Mohism, and Xunzi's Confucianism—the model intuitively demonstrates how it distinguishes between "complete," "incomplete," and "hybrid" systems. It ultimately concludes that the long-term efficacy of a political philosophy depends not only on the completeness of its components, but crucially on whether those components originate from the same underlying philosophical design. Keywords:Political Philosophy Cohesion Model; Matrix Homogeneity; Logical Homogeneity; Functional Homogeneity; Active Synthesis; Passive Synthesis; Systemic Integrity; Practical Completeness.