LOGICAL MATRIX, MATHEMATICAL ESSENCE, AND THE MODAL DISCIPLINE OF OBJECTIVITY: a critical–propositional analysis of Hugang Cui in confrontation with the Theory of Objectivity

This article presents a critical–propositional analysis of Hugang Cui’s Spacetime Substantivalism XXI: The Completeness of Logic and the Incompleteness of Mathematics —— The Logical Matrix is the Sole Truth of the Universe, published on Zenodo in 2026. The study examines Cui’s thesis that the incompleteness of mathematics, semantics, computation, physics, social theory, and epistemology does not indicate the failure of logic, but rather confirms the superior completeness of logic as a Logical Matrix.

The article confronts Cui’s Logical Matrix with the Theory of Objectivity (TO), especially with the First Absolute Truth of TO, according to which Nothingness is a Primitive and Eternal Mathematical Essence. It argues that Cui’s critique is philosophically relevant, but depends on a restrictive identification between mathematics and incomplete formal systems. From the standpoint of TO, primitive mathematical essence must be understood not as a formal axiomatic system, but as an originary ontological structure of determination, distinction, boundary, relation, and possibility.

The analysis also articulates Cui’s notion of logical tracks with the logical tracks of TO, the phenomenic elements, the Inducer Effects, the cosmogonic theorem, the cosmological Eras, and the TO conception of transcendent substance as knowledge or information produced in atomic relations, equivalent to atomic radiations. The article concludes that Cui’s work offers a highly relevant dialogue with TO, while also requiring critical distinction between logical metaontology and modal–cosmogonic ontology.

This analytical text counted on the analytical support of ChatGPT.

Keywords: Theory of Objectivity; Hugang Cui; Logical Matrix; Spacetime Substantivalism; mathematical essence; Nothingness; modal ontology; incompleteness; Gödel; logical tracks; Inducer Effects; phenomenic elements; transcendent substance; atomic information; cosmology; cosmogony.