David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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History and Philosophy of Logic 28 (2):107-122 (2007)
By quoting extensively from unpublished letters written by John von Neumann to Garret Birkhoff during the preparatory phase (in 1935) of their ground-breaking 1936 paper that established quantum logic, the main steps in the thought process leading to the 1936 Birkhoff?von Neumann paper are reconstructed. The reconstruction makes it clear why Birkhoff and von Neumann rejected the notion of quantum logic as the projection lattice of an infinite dimensional complex Hilbert space and why they postulated in their 1936 paper that the quantum propositional system should be isomorphic to an abstract projective geometry. Looking at the paper now I see, that I forgot to say this, which should be said somewhere in the first ?: That while common logics did apply to quantum mechanics, if the notion of simultaneous measurability is introduced as an auxiliary notion, we wished to construct a logical system, which applies directly to quantum mechanics ? without any extraneous secondary notions like simultaneous measurability. And in order to have such a consequent, one-piece system of logics, we must change the classical class calculus of logics. (J. von Neumann to G. Birkhoff, November 21, 1935)
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References found in this work BETA
J. Michael Dunn (2001). Algebraic Methods in Philosophical Logic. Oxford University Press.
Miklos Rédei (1996). Why John von Neumann Did Not Like the Hilbert Space Formalism of Quantum Mechanics (and What He Liked Instead). Studies in History and Philosophy of Science Part B 27 (4):493-510.
Miklós Rédei, Michael Stöltzner, Walter Thirring, Ulrich Majer & Jeffrey Bub (2001). John von Neumann and the Foundations of Quantum Physics. Springer Netherlands.
Citations of this work BETA
Miklós Rédei (2014). Hilbert's 6th Problem and Axiomatic Quantum Field Theory. Perspectives on Science 22 (1):80-97.
J. Michael Dunn, Lawrence S. Moss & Zhenghan Wang (2013). Editors' Introduction: The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing. [REVIEW] Journal of Philosophical Logic 42 (3):443-459.
Mauri Cunha do Nascimento, Décio Krause & Hércules de Araújo Feitosa (2011). The Quasi-Lattice of Indiscernible Elements. Studia Logica 97 (1):101-126.
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