• DOI:10.1086/psaprocbienmeetp.1980.2.192607
• Corpus ID: 123587170

Quantum Logic and Meaning

@article{Hellman1980QuantumLA,
  title={Quantum Logic and Meaning},
  author={Geoffrey Hellman},
  journal={PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association},
  year={1980},
  volume={1980},
  pages={493 - 511}
}

• G. Hellman
• Published 1 January 1980
• Philosophy
• PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association

Quantum logic as genuine non-classical logic provides no solution to the "paradoxes" of quantum mechanics. From the minimal condition that synonyms be substitutable salva veritate, it follows that synonymous sentential connectives be alike in point of truth-functionality. It is a fact of pure mathematics that any assignment Φ of (0, 1) to the subspaces of Hilbert space (dim. ≥ 3) which guarantees truth-preservation of the ordering and truth-functionality of QL negation, violates truth-functionality of QL ∨ and $\wedge $. Thus, from within both the classical framework and that of any QL that preserves elementary set theory, two distinct (nonsynonymous) sets of connectives are discernible. Classical derivations of QM paradoxes are all available unless the language of QM is not classically closed. Maintaining this requires a strong and selfdefeating verification theory of meaning, the philosophical cornerstone of the Copenhagen interpretation to which QL was to provide an alternative.