Published March 16, 2026
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Kochen--Specker Contextuality and the Tetralemmatic Calculus of Quantum Mechanics
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Description
The contextual character of quantum observables—formalized by the Kochen--Specker theorem
and Bohr's complementarity—represents a fundamental rupture in classical binary logic.
In interference regimes, such as the double-slit experiment, polar questions
(e.g., ``Which path did the particle take?'') are operationally unaskable, yet standard
logical frameworks fail to formalize this unaskability without collapsing into truth-value
gaps or triviality. We resolve this by introducing a context-indexed formal logic that
adjoins an explicit \emph{applicability predicate} to the valuation space.
Drawing structural inspiration from the ancient \emph{catuṣkoṭi} (tetralemma), we map
quantum operational states onto four distinct logical sectors: \emph{Thesis/Antithesis}
(strong measurement and decoherence), \emph{Synthesis} (paraconsistent gluts realized
via weak measurement), and \emph{Holothesis} (paracomplete gaps representing typed
inapplicability). From this logical foundation, we generate a $*$-algebra equipped with
a positive warrant functional. Through the Gelfand--Naimark--Segal (GNS) construction,
we demonstrate that Hilbert-space structure—and the complex unit $i$ itself—emerge
canonically from an order-$4$ logical symmetry rather than being presupposed.
Contextuality is quantified via incompatibility graphs, with chromatic number bounding
minimal classical embeddings.
We establish a Noether-like correspondence wherein physical symmetry breaking dictates
logical polarity, while symmetry preservation dictates logical transcendence (self-duality).
This \emph{logic-first reconstruction} unifies Relational Quantum Mechanics (Rovelli) and
Consistent Histories (Griffiths, Omnès, Gell-Mann, Hartle) as regime-relative logical
stances within a pre-geometric ontology of \emph{interdependent origination} (contextual
co-arising of observer and observable), where the observer's contextual frame and the
system's observable reality are co-arising and non-separable. The framework yields
testable deviations in many-body interference ($I_3 \neq 0$), providing an empirical
pathway for detection.
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Additional details
Additional titles
- Subtitle
- The Formal Roots of the Unaskable in Quantum Measurement
Dates
- Submitted
-
2026-03-16