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  1. The Problem of Hidden Variables in Quantum Mechanics.Simon Kochen & E. P. Specker - 1967 - Journal of Mathematics and Mechanics 17:59--87.
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  • A topos perspective on the kochen-Specker theorem: I. Quantum states as generalised valuations.Chris Isham & Jeremy Butterfield - unknown
    Any attempt to construct a realist interpretation of quantum theory founders on the Kochen-Specker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context (...)
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  • Spacetime and the philosophical challenge of quantum gravity.Jeremy Butterfield & Chris Isham - 2001 - In Jeremy Butterfield & Chris Isham (eds.), Physics Meets Philosophy at the Panck Scale. Cambridge University Press.
    We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in quantum (...)
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  • A topos perspective on the kochen-Specker theorem: II. Conceptual aspects, and classical analogues.Jeremy Butterfield & Chris Isham - unknown
    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 (...)
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