On Knowability and Unknowability: Correction of Four Core Contradictions in Mathematical Physics -- with a Rectification of Gödel's Incompleteness Theorems

Abstract

Human mathematical and physical systems are trapped in the tension between knowability exploration and unknowability limitations. The four core contradictions in existing theories—opposition between finiteness and actual infinity, conflict between the law of excluded middle and intuitionistic logic, artificial division of Euclidean and non-Euclidean geometry, incompatibility of classical and quantum mathematics—are not inherent cosmic paradoxes, but result from the academic community equating human cognitive shortcomings with objective cosmic laws, imposing unproven implicit rules, and misinterpreting Gödel's Incompleteness Theorems. With objective realism as the core, this paper supplements key concepts to form a logical closed loop. Based on π’s original geometric formula and differential calculation essence, it overturns the dogma that "π is infinite and non-recurring", proving π is a definite finite real number. It clarifies infinite recurring decimal classification to reconstruct a consistent number system, unifies geometry with spatial curvature parameters, eliminates intuitionistic fallacies by adhering to the law of excluded middle, and explains quantum apparent randomness via cosmic determinism, thus comprehensively correcting the four contradictions. Strictly based on Gödel's Incompleteness Theorems and his realist stance, this paper acknowledges the proof boundary of formal systems, rejects vulgar misinterpretations, and upholds the knowability of objective truth. By absorbing core viewpoints of Plato, Gauss, Hilbert and other scholars, it constructs a unified, internally consistent mathematical physics framework, breaks the conservative barriers of the existing system, restores the discipline’s essence of describing cosmic deterministic truth, and solves the dilemma of "unattained knowability and misinterpreted unknowability".

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