Modern cognitive science, philosophy, and scientific methodology have long been trapped in empty speculation, linguistic games, and disciplinary fragmentation. Human thinking lacks a unified, rigorous, and universally applicable underlying foundation. This paper proposes Topological Paradigm Cognition (TPC), which takes geometry and topology as the ultimate basis of thinking, establishes a complete system of rigid axioms, and clarifies the nature of the mean, initiative, and cognitive logic. This paper systematically puts forward 9 core axioms including topological dominance, existential mathematization, proximal origin, hierarchical concealment, global isomorphism, cognitive completeness, topological mean, projective normalization, and paradigm initiative. It fundamentally solves the problems of empty philosophy, invalid mean, passive cognition, and incomplete methodology. Topological Paradigm Cognition is not only a cognitive methodology but also a universal meta-theory that can be applied to physics, mathematics, philosophy, complex systems, social governance, and strategic decision-making.
Zhenmin Wang (Thu,) studied this question.