Weakly Intuitionistic Quantum Logic

Ronnie Hermens

doi:10.1007/s11225-012-9401-3

Weakly Intuitionistic Quantum Logic

Ronnie Hermens^*

^*Corresponding author for this work

Department of Theoretical Philosophy
University of Groningen

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	901-913
Number of pages	13
Journal	Studia Logica
Volume	101
Issue number	5
DOIs	https://doi.org/10.1007/s11225-012-9401-3
Publication status	Published - 1 Oct 2013
Externally published	Yes

Keywords

Intuitionistic logic
Quantum logic
Weakly Heyting algebras

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10.1007/s11225-012-9401-3

Cite this

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AB - 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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Weakly Intuitionistic Quantum Logic

Abstract

Keywords

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