Roger Penrose's Theory of Consciousness Through the Lens of the Theory of Axiomatic Necessity (TNA): Objective Reduction versus Failure of Local Closure

The paper analyzes Roger Penrose's Orch-OR theory of consciousness using the formal framework of the Theory of Axiomatic Necessity (TNA). It argues that Objective Reduction (OR) — the physical threshold where quantum superposition collapses into definite states — maps onto an admissibility domain (N₁) rather than emerging from the operational domain (N₀) of biological structures like the brain's microtubular network. Through a theorem of Failure of Local Closure, the authors claim that the brain does not generate consciousness internally but acts as a structural antenna tuned to non-derivable conditions of admissibility. This reconciles Gödelian incompleteness in human thought by showing that conscious experience requires irreducible external structural support beyond algorithmic computation.

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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.