Studia Logica

, Volume 101, Issue 5, pp 901–913

Weakly Intuitionistic Quantum Logic


DOI: 10.1007/s11225-012-9401-3

Cite this article as:
Hermens, R. Stud Logica (2013) 101: 901. doi:10.1007/s11225-012-9401-3


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.


Quantum logicIntuitionistic logicWeakly Heyting algebras

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Theoretical PhilosophyUniversity of GroningenGroningenThe Netherlands