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Journal of Philosophical Logic

Logical self reference, set theoretical paradoxes and the measurement problem in quantum mechanics

María Luisa Dalla Chiara

Published Jan 1, 1977• 53 citations
Publisher
DOI
10.1007/bf00262066

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Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in Tarski's hierarchy or paraconsistent logics. We propose a novel approach: a quantum circuit architecture that intrinsically enforces logical consistency during its unitary evolution. By encoding self-referential or contradictory propositions into a quantum state, the circuit uses interference effects to suppress inconsistent outcomes while preserving coherent ones. We demonstrate this with the Liar Paradox ("This statement is false"), showing that the quantum model naturally stabilizes truth values that would be paradoxical classically. The framework builds on orthomodular quantum logic treating logical propositions as subspace projectors and connects to belief revision and cognitive modeling by providing a physical mechanism for coherence restoration in epistemic states. This work bridges formal logic and quantum computation, suggesting that consistency can be embedded as a structural property of reasoning systems rather than imposed externally.
The observer problem remains one of the central unresolved questions in the foundations of quantum mechanics. This paper derives the logical structure of observation without assuming an observer, consciousness, measurement, or information as primitive concepts. Starting from the primitive notion of Meaning, the following logical sequence is derived: Meaning → Being → Closure → I₄ → Update → Time → 0 < δ < ∞ → Self-Reference → Observer → Observation → Record → Synchronization → Information. Within this framework, an observer is shown to emerge necessarily from persistent self-referential closure possessing finite residual relation. Observation is interpreted as the generation of persistent internal representations, while measurement is reformulated as synchronization between independent closures. Information is derived as synchronized records supported by an information medium. This logical structure provides a unified reinterpretation of Schrödinger's cat and Wigner's friend. The apparent paradoxes are shown to originate from synchronization between independent observers rather than from consciousness, observer-dependent reality, or wave-function collapse. The paper establishes an ontological hierarchy connecting Meaning, Being, observation, synchronization, and information within the MBC (Meaning-Based Constraint) framework.