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Chris Isham [7]Christopher J. Isham [2]
  1. Jeremy Butterfield & Chris Isham, A Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations.
    We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth-value to a proposition that the value of a quantity lies in a certain set D of real numbers. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectrum (we call these interval valuations). There are two main (...)
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  2. Jeremy Butterfield & Chris Isham (2001). Physics Meets Philosophy at the Panck Scale. Cambridge University Press.
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  3. Jeremy Butterfield & Chris Isham (2001). Spacetime and the Philosophical Challenge of Quantum Gravity. In 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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  4. John Hamilton, Chris Isham & Jeremy Butterfield, A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category.
    We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann algebras as a base category (Section 2); and the relation of our generalized valuations to (i) the assignment to quantities of intervals of real numbers, and (ii) the idea of a subobject of the coarse-graining presheaf (Section 3).
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  5. Jeremy Butterfield & Chris Isham, A Topos Perspective on the Kochen-Specker Theorem: II. Conceptual Aspects, and Classical Analogues.
    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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  6. Jeremy Butterfield & Chris Isham (1999). On the Emergence of Time in Quantum Gravity. In , The Arguments of Time. Published for the British Academy by Oxford University Press. 111--168.
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  7. Chris Isham & Jeremy Butterfield, A Topos Perspective on the Kochen-Specker Theorem: I. Quantum States as Generalised Valuations.
    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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  8. Christopher J. Isham (1988). Creation of the Universe as a Quantum Process. In Robert J. Russell, William R. Stoeger & George V. Coyne (eds.), Physics, Philosophy, and Theology: A Common Quest for Understanding. University of Notre Dame Press [Distributor]. 375--408.
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