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A Topos Perspective on the Kochen-Specker Theorem: II. Conceptual Aspects, and Classical Analogues

Butterfield, Jeremy and Isham, Chris (1999) A Topos Perspective on the Kochen-Specker Theorem: II. Conceptual Aspects, and Classical Analogues. UNSPECIFIED.

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    Abstract

    In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; and in part mathematical---the valuation arises naturally in the topos theory of presheaves. This paper discusses the conceptual aspects of this proposal. We also undertake two other tasks. First, we explain how the proposed valuations could arise much more generally than just in quantum physics; in particular, they arise as naturally in classical physics. Second, we give another motivation for such valuations (that applies equally to classical and quantum physics). This arises from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition.


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    Item Type: Other
    Additional Information: Published in: International Journal of Theoretical Physics, volume 38, 1999, pages 827-859.
    Keywords: Kochen-Specker theorem; category theory; topos theory; partial truth
    Subjects: Specific Sciences > Physics > Classical Physics
    Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Jeremy Butterfield
    Date Deposited: 29 Aug 2004
    Last Modified: 07 Oct 2010 11:12
    Item ID: 1917
    Public Domain: No
    URI: http://philsci-archive.pitt.edu/id/eprint/1917

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