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The Logico-Algebraic Approach to Quantum Mechanics

Volume I: Historical Evolution

  • Book
  • © 1975

Overview

Editors:
  1. C. A. Hooker

    1. University of Western Ontario, Ontario, Canada

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Part of the book series: The Western Ontario Series in Philosophy of Science (WONS, volume 5a)

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Table of contents (31 chapters)

  1. Front Matter

    Pages I-XV
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  2. The Logic of Quantum Mechanics

    • Garrett Birkhoff, John Von Neumann
    Pages 1-26

  3. The Logic of Complementarity and the Foundation of Quantum Theory

    • Martin Strauss
    Pages 27-44

  4. Mathematics as Logical Syntax — A Method to Formalize the Language of a Physical Theory

    • Martin Strauss
    Pages 45-52

  5. Three-Valued Logic and the Interpretation of Quantum Mechanics

    • H. Reichenbach
    Pages 53-97

  6. Three-Valued Logic

    • Hilary Putnam
    Pages 99-107

  7. Reichenbach’s Interpretation of Quantum-Mechanics

    • Paul Feyerabend
    Pages 109-121

  8. Measures on the Closed Subspaces of a Hilbert Space

    • Andrew M. Gleason
    Pages 123-133

  9. The Logic of Propositions Which are not Simultaneously Decidable

    • E. P. Specker
    Pages 135-140

  10. Baer *-Semigroups

    • David J. Foulis
    Pages 141-148

  11. Axioms for Non-Relativistic Quantum Mechanics

    • Neal Zierler
    Pages 149-170

  12. Probability in Physics and a Theorem on Simultaneous Observability

    • V. S. Varadarajan
    Pages 171-203

  13. Semantic Representation of the Probability of Formulas in Formalized Theories

    • Jerzy Łoś
    Pages 205-219

  14. The Structure of the Propositional Calculus of a Physical Theory

    • Franz Kamber
    Pages 221-245

  15. Boolean Embeddings of Orthomodular Sets and Quantum Logic

    • Neal Zierler, Michael Schlessinger
    Pages 247-262

  16. Logical Structures Arising in Quantum Theory

    • Simon Kochen, E. P. Specker
    Pages 263-276

  17. The Calculus of Partial Propositional Functions

    • Simon Kochen, E. P. Specker
    Pages 277-292

  18. The Problem of Hidden Variables in Quantum Mechanics

    • Simon Kochen, E. P. Specker
    Pages 293-328

  19. Logics Appropriate To Empirical Theories

    • Patrick Suppes
    Pages 329-340

  20. The Probabilistic Argument for a Nonclassical Logic of Quantum Mechanics

    • Patrick Suppes
    Pages 341-350
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Keywords

About this book

The twentieth century has witnessed a striking transformation in the un­ derstanding of the theories of mathematical physics. There has emerged clearly the idea that physical theories are significantly characterized by their abstract mathematical structure. This is in opposition to the tradi­ tional opinion that one should look to the specific applications of a theory in order to understand it. One might with reason now espouse the view that to understand the deeper character of a theory one must know its abstract structure and understand the significance of that struc­ ture, while to understand how a theory might be modified in light of its experimental inadequacies one must be intimately acquainted with how it is applied. Quantum theory itself has gone through a development this century which illustrates strikingly the shifting perspective. From a collection of intuitive physical maneuvers under Bohr, through a formative stage in which the mathematical framework was bifurcated (between Schrödinger and Heisenberg) to an elegant culmination in von Neumann's Hilbert space formulation the elementary theory moved, flanked even at the later stage by the ill-understood formalisms for the relativistic version and for the field-theoretic altemative; after that we have a gradual, but constant, elaboration of all these quantal theories as abstract mathematical struc­ tures (their point of departure being von Neumann's formalism) until at the present time theoretical work is heavily preoccupied with the manip­ ulation of purely abstract structures.

Editors and Affiliations

  • University of Western Ontario, Ontario, Canada

    C. A. Hooker

Bibliographic Information

  • Book Title: The Logico-Algebraic Approach to Quantum Mechanics

  • Book Subtitle: Volume I: Historical Evolution

  • Editors: C. A. Hooker

  • Series Title: The Western Ontario Series in Philosophy of Science

  • DOI: https://doi.org/10.1007/978-94-010-1795-4

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1975

  • Hardcover ISBN: 978-90-277-0567-9Due: 30 September 1975

  • Softcover ISBN: 978-90-277-0613-3Published: 30 September 1975

  • eBook ISBN: 978-94-010-1795-4Published: 06 December 2012

  • Series ISSN: 1566-659X

  • Series E-ISSN: 2215-1974

  • Edition Number: 1

  • Number of Pages: 622

  • Topics: Philosophy of Science

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