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John von Neumann on mathematical and axiomatic physics

In Giovanni Boniolo, Paolo Budinich & Majda Trobok (eds.), The Role of Mathematics in Physical Sciences: Interdisciplinary and Philosophical Aspects. Dordrecht, Netherlands: Springer. pp. 43-54 (2005)

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  1. Einstein's Dissatisfaction with Nonrelativistic Quantum Mechanics and Relativistic Quantum Field Theory.Miklós Rédei - 2010 - Philosophy of Science 77 (5):1042-1057.
    It is argued that in his critique of standard nonrelativistic quantum mechanics Einstein formulated three requirements as necessary for a physical theory to be compatible with the field-theorectical paradigm, and it is shown that local, relativistic, algebraic quantum field theory typically satisfies those criteria-although, there are still open questions concerning the status of operational separability of quantum systems localized in space like separated space-time regions. It is concluded that local algebraic quantum field theory can be viewed as a research program (...)
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  • Von Neumann's Methodology of Science: From Incompleteness Theorems to Later foundational Reflections.Giambattista Formica - 2010 - Perspectives on Science 18 (4):480-499.
    In spite of the many efforts made to clarify von Neumann’s methodology of science, one crucial point seems to have been disregarded in recent literature: his closeness to Hilbert’s spirit. In this paper I shall claim that the scientific methodology adopted by von Neumann in his later foundational reflections originates in the attempt to revaluate Hilbert’s axiomatics in the light of Gödel’s incompleteness theorems. Indeed, axiomatics continues to be pursued by the Hungarian mathematician in the spirit of Hilbert’s school. I (...)
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