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Profile: Mark Hogarth (Cambridge University)
  1.  36
    Deciding Arithmetic Using SAD Computers.Mark Hogarth - 2004 - British Journal for the Philosophy of Science 55 (4):681-691.
    Presented here is a new result concerning the computational power of so-called SADn computers, a class of Turing-machine-based computers that can perform some non-Turing computable feats by utilising the geometry of a particular kind of general relativistic spacetime. It is shown that SADn can decide n-quantifier arithmetic but not (n+1)-quantifier arithmetic, a result that reveals how neatly the SADn family maps into the Kleene arithmetical hierarchy. Introduction Axiomatising computers The power of SAD computers Remarks regarding the concept of computability.
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  2. The Definability of Objective Becoming in Minkowski Spacetime.Rob Clifton & Mark Hogarth - 1995 - Synthese 103 (3):355 - 387.
    In his recent article On Relativity Theory and Openness of the Future (1991), Howard Stein proves not only that one can define an objective becoming relation in Minkowski spacetime, but that there is only one possible definition available if one accepts certain natural assumptions about what it is for becoming to occur and for it to be objective. Stein uses the definition supplied by his proof to refute an argument due to Rietdijk (1966, 1976), Putnam (1967) and Maxwell (1985, 1988) (...)
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  3.  42
    Non-Turing Computers and Non-Turing Computability.Mark Hogarth - 1994 - Psa 1994:126--138.
    A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...)
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  4. Does General Relativity Allow an Observer to View an Eternity in a Finite Time?Mark Hogarth - 1992 - Foundations Of Physics Letters 5:173--181.
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  5.  89
    A Remark Concerning Prediction and Spacetime Singularities.Mark Hogarth - 1997 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (1):63-71.
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  6.  16
    Predicting the Future in Relativistic Spacetimes.Mark Hogarth - 1993 - Studies in History and Philosophy of Science Part A 24 (5):721-739.
  7.  5
    Time, Space and Philosophy.Robert Clifton & Mark Hogarth - 1993 - Philosophical Books 34 (2):123-125.
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    A Remark Concerning Prediction and Spacetime Singularities.Mark Hogarth - 1997 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (1):63-71.
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  9. Spacetime.Jeremy Butterfield, Mark Hogarth & Gordon Belot (eds.) - 1996 - Dartmouth Pub. Co..
  10. A New Problem for Rule Following.Mark Hogarth - forthcoming - Journal of Applied Mathematics and Computation.
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  11. Non-Turing Computers Are the New Non-Euclidean Geometries.Mark Hogarth - forthcoming - International Journal of Unconventional Computing:1--15.
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  12. Non-Turing Computers and Non-Turing Computability.Mark Hogarth - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:126-138.
    A true Turing machine requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime, but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar to our world. But curiously enough-and this is (...)
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  13. Predictability, Computability and Spacetime.Mark Hogarth - 1996 - Dissertation, Cambridge University
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  14. Predicting the Future in Relativistic Spacetimes.Mark Hogarth - 1993 - Studies in History and Philosophy of Science Part A 24 (5):721-739.
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