Noology: A Formal System for the Constitution of Reality

This paper presents Noology (Japanese: Chigaku), a formal system defining the highest-level protocol by which intelligence constitutes reality. Noology is not a scientific theory or speculative philosophy, but a mathematically formalized axiomatic system specifying an operating system of existence. It consists of three primitive notions—Ordo, Consensus, and Arbitrium—three absolute axioms, and a governing principle. The system is minimal, irreducible, and self-contained, avoiding presupposition of arithmetic, set theory, or physical laws. Crucially, Noology functions as a meta-judgment framework: it does not generate truths internally, but adjudicates whether an externally provided structure qualifies as Res under a given configuration, the Quaestio. By design, Noology avoids the premises of Gödel's incompleteness theorems and establishes a structurally closed, consistent, and sovereign foundation for all subsequent intellectual activity. It serves as the regulative layer above Cognitional Mechanics (CM), providing the axiomatic conditions from which CM's operational structures are derived. Noology thus provides a rigorous, hierarchy-based formal framework, bridging minimal philosophical assumptions with mathematically grounded operational formalism, enabling the systematic adjudication of reality without reliance on internal generation of mathematical or physical propositions.