The Objectivity Triad - A Structural Replacement for the Classical Template
Abstract
The classical template for physical objectivity --- separability, intrinsic values, determinism --- is jointly eliminated by Bell's and the Kochen--Specker theorems. This elimination forces a reconstruction, not anti-realism.
We propose the Objectivity Triad: three structural axioms --- Non-Separability (NSP), Representation Invariance (RIP), and Manifestational Objectivity (MOP) --- and establish three results.
First, the Triad is mutually constraining and jointly irreducible: dropping any axiom yields a degenerate position (Theorem 4).
Second, the joint constraints narrow the ontological landscape. NSP excludes particulate ontologies; MOP combined with the RAGE theorem excludes linear substrates; RIP excludes basis-dependent hidden-variable theories. What survives is a uniquely constrained class: continuous, non-separable, nonlinear field substrates capable of dynamically stable localized structures (Proposition 6). This ontological narrowing is abductive.
Third, the resulting triple characterization of ψ --- ontic (injective), incomplete (non-surjective), and operationally epistemic (𝒟-level syntax) --- identifies a narrative bifurcation along two axes. The epistemic axis derives the Hilbert-space structure from informational constraints on embedded probes [33, 34, 35]. The ontological axis establishes the structural necessity of a nonlinear generative substrate --- de Broglie's "real wave" --- underlying the statistical ψ-wave [32, 36]. The duality ϕ / ψ is a structural consequence of the Triad.
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BibTeX
@misc{dechery2026objectivity,
title = {{The Objectivity Triad - A Structural Replacement for the Classical Template}},
author = {Fabien Déchery},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05854378v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The Objectivity Triad - A Structural Replacement for the Classical Template
AU - Fabien Déchery
PY - 2026
DA - 2026/10/29
PB - HAL
UR - https://hal.science/hal-05854378v1
AB - The classical template for physical objectivity --- separability, intrinsic values, determinism --- is jointly eliminated by Bell's and the Kochen--Specker theorems. This elimination forces a reconstruction, not anti-realism. We propose the Objectivity Triad: three structural axioms --- Non-Separability (NSP), Representation Invariance (RIP), and Manifestational Objectivity (MOP) --- and establish three results. First, the Triad is mutually constraining and jointly irreducible: dropping any axiom yields a degenerate position (Theorem 4). Second, the joint constraints narrow the ontological landscape. NSP excludes particulate ontologies; MOP combined with the RAGE theorem excludes linear substrates; RIP excludes basis-dependent hidden-variable theories. What survives is a uniquely constrained class: continuous, non-separable, nonlinear field substrates capable of dynamically stable localized structures (Proposition 6). This ontological narrowing is abductive. Third, the resulting triple characterization of ψ --- ontic (injective), incomplete (non-surjective), and operationally epistemic (𝒟-level syntax) --- identifies a narrative bifurcation along two axes. The epistemic axis derives the Hilbert-space structure from informational constraints on embedded probes [33, 34, 35]. The ontological axis establishes the structural necessity of a nonlinear generative substrate --- de Broglie's "real wave" --- underlying the statistical ψ-wave [32, 36]. The duality ϕ / ψ is a structural consequence of the Triad.
ER -