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79Deciding arithmetic using SAD computersBritish Journal for the Philosophy of Science 55 (4): 681-691. 2004.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 pow…Read more
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Non-Turing Computers and Non-Turing ComputabilityPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994 126-138. 1994.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 the main point of this paper…Read more
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3Does General Relativity Allow an Observer to View an Eternity in a Finite Time?Foundations Of Physics Letters 5 173--181. 1992.
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74Non-Turing Computers and Non-Turing ComputabilityPsa 1994 126--138. 1994.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 our world. But curiously …Read more
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15Spacetime (edited book)Dartmouth Pub. Co.. 1996.This collection of articles on the theme of space and time covers such broad topics as the philosophy of spacetime, spacetime structure, spacetime ontology, the epistemology of geometry, and general relativity.
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37Predicting the future in relativistic spacetimesStudies in History and Philosophy of Science Part A 24 (5): 721-739. 1993.
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108A remark concerning prediction and spacetime singularitiesStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 28 (1): 63-71. 1997.
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Non-Turing Computers are the New Non-Euclidean GeometriesInternational Journal of Unconventional Computing 1--15. forthcoming.
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209The definability of objective becoming in Minkowski spacetimeSynthese 103 (3). 1995.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) that Minkows…Read more
Cambridge, United Kingdom of Great Britain and Northern Ireland
Areas of Interest
Philosophy of Mathematics |
Philosophy of Physical Science |