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Arithmetical Foundations for Physical Theories

  • Yvon Gauthier
Part of the Studies in Universal Logic book series (SUL)

Abstract

The notion of analytical apparatus was introduced in the paper by Hilbert, Nordheim and von Neumann (1928) ≪ Über die Grundlagen der Quantenmechanik ≫ : The analytical apparatus <der analytische Apparat> is simply the mathematical formalism or the set of logico-mathematical structures of a physical theory. Von Neumann used the notion extensively in his 1932 seminal work on the mathematical foundations of Quantum Mechanics and he stressed particularly the auxiliary notion of conditions of reality <Realitätsbedingungen>. I want to show that this last notion corresponds grosso modo to our notion of model in contemporary philosophy of physics. Hermann Weyl, who has initiated group theory in Quantum Mechanics (1928), also exploited the idea in his conception of the parallelism between a mathematical formalism and its physical models.

Keywords

Hilbert Space Physical Theory Hermitian Operator Local Observer Analytical Apparatus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Yvon Gauthier
    • 1
  1. 1.University of MontrealMontrealCanada

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