Roger Penrose's Theory of Consciousness Through the Lens of the Theory of Axiomatic Necessity (TNA): Objective Reduction versus Failure of Local Closure
Zenodo (CERN European Organization for Nuclear Research) June 18, 2026 DOI: 10.5281/zenodo.20748965 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Keywords | Consciousness Axiomatic system Closure psychology Reduction mathematics Superposition principle Domain mathematical analysis Mathematical economics Through-the-lens metering Network theory |
| Key points | Argues that the brain's microtubular network does not generate consciousness internally but acts as an antenna tuned to non-derivable conditions of admissibility (N₁), reconciling Gödelian incompleteness in human thought. |
Abstract
This paper analyzes Roger Penrose’s Orch-OR theory of consciousness through the formal framework of the Theory of Axiomatic Necessity (TNA). By examining Objective Reduction (OR) as a physical threshold where quantum superposition collapses into definite states, we demonstrate that Penrose's non-computable foundational layer maps directly onto the admissibility domain ($N_1$), rather than emerging from the operational domain ($N_0$) of biological silicio-like structures. Through the theorem of Failure of Local Closure, we argue that the brain's micro-tubular network does not generate consciousness internally, but rather acts as a highly specialized structural antenna tuned to non-derivable conditions of admissibility. Ultimately, this formulation reconciles Gödelian incompleteness in human thought by proving that conscious experience requires an irreducible external structural support ($N_1$) that escapes the operational limits of pure algorithmic computation.