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Reconstruction of Mathematical Philosophy and Fundamental Axiom System Based on Unified Complex System Theory



Author(s)

CUI Weicheng

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DOI:10.17265/2159-5313/2026.03.008

Zhejiang Engineering Research Center of Micro/Nano-Photonic/Electronic System Integration, Hangzhou, China
Westlake University, Hangzhou, China

The Unified Complex System Theory (UCST) takes the mind-ether dual ontology as its core foundation, constructing a global complex system framework encompassing matter, energy, and information. Based on the dual ontology and hierarchical coupling principle of UCST, this paper breaks the millennia-old dual opposition between the “pure discovery” and “pure invention” of mathematics in traditional philosophical discourse, and puts forward the core proposition that mathematics is the hierarchical isomorphic mapping of the objective structure of the real world by the cognitive subject mind. On this theoretical premise, this paper innovatively establishes the UCST mathematical fundamental axiom system containing six interlocking core axioms, systematically reinterprets key core frontier topics in the foundations of mathematics such as infinite essence classification, intrinsic logic of set theory, physical attribution of continuum, and practical boundary of computability theory, and effectively dissolves the long-standing inherent logical paradoxes and theoretical dilemmas within traditional mathematical philosophy and the classical foundations of mathematics. Meanwhile, taking the self-consistent UCST axiom system as the unified critical normative criterion, this paper systematically sorts out and reveals the universal cognitive deviation arising from the forced arbitrary transition of abstract high-dimensional mathematical formal models to concrete four-dimensional empirical physical reality in the theoretical construction process of modern mainstream physics. It further scientifically clarifies the essential ontological, epistemological, and methodological boundary between instrumental mathematics and empirical physics in the whole scientific research system. This research advocates that academic circles should return mathematics to its original instrumental essence of fitting and describing four-dimensional empirical natural laws, and theoretical physics should firmly adhere to the basic research boundary of observable, verifiable, and falsifiable real spacetime entities. Ultimately, the research realizes the self-consistent unity of the essence connotation of mathematics, the standardized reconstruction of the foundations of mathematics, the ontological logic of complex systems, and the core principles of physical empiricism, providing a novel, rigorous, and operable complex system comprehensive perspective for the innovative development of contemporary philosophy of mathematics and the normative rectification of philosophy of science.

Unified Complex System Theory (UCST), philosophy of mathematics, mind-ether dualism, mathematical fundamental axiom, high-to-four dimensional transition, boundary demarcation between mathematics and physics

CUI Weicheng. (2026). Reconstruction of Mathematical Philosophy and Fundamental Axiom System Based on Unified Complex System Theory. Philosophy Study, May-June 2026, Vol. 16, No. 3, 269-282.