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Weakly Intuitionistic Quantum Logic

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Abstract

In this article von Neumann’s proposal that in quantum mechanics projections can be seen as propositions is followed. However, the quantum logic derived by Birkhoff and von Neumann is rejected due to the failure of the law of distributivity. The options for constructing a distributive logic while adhering to von Neumann’s proposal are investigated. This is done by rejecting the converse of the proposal, namely, that propositions can always be seen as projections. The result is a weakly Heyting algebra for describing the language of quantum mechanics.

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Authors and Affiliations

  1. Department of Theoretical Philosophy, University of Groningen, Oude Boteringestraat 52, Groningen, The Netherlands

    Ronnie Hermens

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  1. Ronnie Hermens
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Correspondence to Ronnie Hermens.

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Presented by Robert Goldblatt

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Hermens, R. Weakly Intuitionistic Quantum Logic. Stud Logica 101, 901–913 (2013). https://doi.org/10.1007/s11225-012-9401-3

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  • DOI: https://doi.org/10.1007/s11225-012-9401-3

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