No Self-Sustaining Theories Without Circular Logic: A Formal Result and Its Implications for Ontological Reductionism

This paper presents a formal proof that any theory claiming full internal justification of its axioms and inference rules is necessarily logically circular. Conversely, any theory based on circular logic is self-sustaining by construction. This establishes a strict equivalence between epistemic self-sustenance and logical circularity. As a corollary, any coherent explanatory framework must include at least one non-derivable operator to avoid trivial or circular closure. The result is independent of physical interpretation and directly constrains reductionist ontologies that attempt to derive logic, consciousness, or foundational principles from the systems they govern. A structural refutation of classical materialism is provided, showing that postulating consciousness or logic as emergent from matter leads to incomplete circular logic. The Thermodynamic Necessity Architecture (TNA) resolves this by establishing the functional primacy of a non-derivable operator (N1) that sustains material coherence (N0) through measurable negentropic work (Ψ). The analysis builds on prior work in irreversibility of experience, Aleph as global incoherence functional, and N1 as measurable negentropy operator.