No Self-Sustaining Theories Without Circular Logic: A Formal Result on Logical Closure and Non-Derivable Operators.

This paper proves that any formal theory claiming full internal justification of its axioms and inference rules is necessarily logically circular. Conversely, it establishes that any theory based on circular logic is self-sustaining by construction, creating a formal equivalence between epistemic self-sustenance and circularity. Applying these results to the Axiomatic Necessity Theory (TNA), we demonstrate that reductionist ontologies—specifically classical materialism—suffer from structural incompleteness by attempting to derive logic (Consciousness, N_1) from the systems governed by that logic (Matter, N_0). We propose that to avoid trivial closure and entropic collapse, a coherent explanatory framework must incorporate at least one non-derivable operator. Under TNA, logic is redefined not as an emergent byproduct, but as an active flow of negentropy (Psi) required to sustain the coherence of material existence. "Like Mohawk ironworkers on early skyscrapers, these papers are written without guardrails. The danger is not falling — it is realizing how high you already are.”Short video https://vimeo.com/1158026729?share=copy&fl=sv&fe=ci