The classical boundaries of the EPR argument and quantum ontology

Von Neumann's Hilbert-space formalism of quantum mechanics constitutes a logico-physical theory of observed or measured reality. Imposing the logical constraint of Booleanity, essential for objectively shareable descriptions among observers, reveals the physical meaning of classicality inherently embedded within the formalism itself. Starting from this consideration, the present work reformulates the quantum-classical transition via Hilbert-space classical mechanics (HCM), grounding classicality not in the dynamical limit $hbar → 0$, but in the logical constraint of Booleanity (i.e., the mutual commutativity of preparable states). Within this state-centric framework, applying the Einstein-Podolsky-Rosen (EPR) criterion alongside locality and measurement independence reduces standard quantum mechanics to the HCM model. Thus, the EPR argument reveals not quantum incompleteness, but the implicit classical boundaries of its own premises. To resolve this impasse, we articulate a nuanced quantum ontology grounded in a fundamental structural bipartition between the observational environment and the observed object, which accommodates three categorical distinctions: ontic, processional, and tropos-existential. Building on this, we propose a criterion of objective reality wherein descriptive objectivity is treated as merely a sufficient condition for physical reality. This addresses the historical Bohr-Einstein ambiguity, enabling the quantum formalism to ontologically unify objective measured phenomena and non-objective observed interference within a context-dependent framework.