Substance-Function-Telos: The Meta-Axiom Set of Ontology

Core Proposition: Substance-Function-Telos is not merely a theoretical-construction template; it is a self-referentially-closed meta-axiom set for ontology. It does not answer the traditional ontological question “what is being?”; instead, it stipulates the structural conditions that any minimally-complete ontology must satisfy to be discussable. Every ontology axiom set constitutes a steady-state instance under this meta-axiom set. Substance-Function-Telos (structural meta-axioms) together with ontological folding (high-order meta-operator) form the complete meta-layer operating system on the ontological side. Paired with the top-level meta-layer on the metacognitive side, they constitute the two ultimate foundations of the entire cognitive-ontological system. Abstract For more than two-and-a-half millennia, the intellectual history of ontology has been trapped within one recurrent cycle: countless thinkers have advanced diverse concrete ontological pictures of “being-itself” and debated which ontology corresponds to reality. Almost no one has pressed the more antecedent question: what structural conditions must a theory fulfil to qualify as an ontology? Breaking this cycle, this paper formally establishes Substance-Function-Telos as the meta-axiom set of ontology. Its three meta-axioms read: 1. Substance: Every discussable being possesses a substrate; without substance, frameworks hang unsupported in mid-air. 2. Function: Every substrate undergoes evolution; without function, it becomes static and inert. 3. Telos: All evolution is governed by constraining directional tendencies; without telos, evolution descends into complete randomness. These three are framework constraints; they do not stipulate what the substrate concretely is. They impose one rigid criterion: if one seeks to construct an ontology that speaks of being, the system must decompose into three mutually-irreducible components of substance, function and telos. Failing this, the ontology is innately defective and lacks minimal completeness. Substance-Function-Telos satisfies strict self-referential closure: the meta-axiom set itself also follows the substance-function-telos tripartite structure. It is neither induced from empirical facts nor a direct metaphysical allegory inherited from Confucian, Buddhist or Daoist traditions. Traditional substance-function discourses represent only phenomenological observational records of this meta-structure by ancient thinkers; this paper accomplishes its axiomatic formalisation. Substance-Function-Telos does not abolish lower-order ontology axiom sets; rather, it renders their possibility intelligible. The convergent-orientation axiom set All Stable Structures are Mathematizable, The World Prefers Parsimony, Topological Unification, alongside other ontology axiom sets, are all steady-state-attractor instances generated under the constraints of the Substance-Function-Telos meta-axioms. Complementing Substance-Function-Telos is ontological folding, acting as the high-order meta-operator. Substance-Function-Telos governs the generation, decomposition and completeness-verification of ontology axiom sets; ontological folding executes cross-paradigm homologous verification, boundary localisation and the preservation of legitimate inter-paradigm tensions. Together they transform ontology from textual speculation into ontology-engineering. The paradigm shift carries disruptive consequences: the illusion of self-grounding for natural science comes to an end. Empirically successful scientific systems are fundamentally unfoldings from an unconsciously mounted ontology axiom-set, rather than transparent discoveries about things-in-the-mselves. The “incommensurability moat” sheltering the humanities and social sciences is dismantled. The underlying presuppositions of every humanistic doctrine can be decomposed via Substance-Function-Telos and subjected to homologous comparison through ontological folding. This entire transformation operates purely at the axiomatic-structural level. It requires neither AGI deployment nor large-scale computational power; it takes effect once logical self-consistency is achieved.