For over two thousand years, the philosophy of mathematics has been trapped in the ontological dilemma of "whether mathematics is invented or discovered", while long plagued by core problems such as Wigner’s puzzle of unreasonable effectiveness, Gödel’s incompleteness theorems, infinity paradoxes, and the legitimacy of mathematical axioms. Existing schools of mathematical philosophy can only explain partial phenomena, failing to achieve the underlying logical closed loop between mathematics, authentic physical reality, and conscious cognition, let alone touch the ultimate ontological root of mathematics. Based on the author’s original Cognitive Succession Ontology system, starting from the unfalsifiable first principle that "the essence of cognition (faculty) is succession", this paper derives the ultimate ontological definition of mathematics: mathematics is an unambiguous abstract expression of the universal meta-rule of succession governing all domains, made by humans with self-created symbolic systems. Taking geometrized construction, which is strictly 1:1 aligned with existential ontology, as the intermediary, this paper opens up the full-chain logic of "ontological meta-rule → authentic physical causality → conscious cognition → symbolic abstraction", thoroughly resolves all millennial and centennial problems in the philosophy of mathematics, proves the underlying homology between mathematics, the authentic physical world, and conscious cognition, and finally completes the cross-domain logical closed loop of ontology, physics, consciousness science, and mathematics. This theory provides the ultimate ontological support for the absolute truth of mathematics, lays a legitimate foundation for the cross-domain application of mathematics, and offers a brand-new paradigm-level path for the development of the philosophy of mathematics.
Mingxiang Liu (Tue,) studied this question.