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  1. added 2018-03-05
    Universality, Invariance, and the Foundations of Computational Complexity in the Light of the Quantum Computer.Michael E. Cuffaro - 2018 - In Sven Ove Hansson (ed.), Technology and Mathematics: Philosophical and Historical Investigations. Springer. pp. 253-282.
    Computational complexity theory is a branch of computer science dedicated to classifying computational problems in terms of their difficulty. While computability theory tells us what we can compute in principle, complexity theory informs us regarding our practical limits. In this chapter I argue that the science of \emph{quantum computing} illuminates complexity theory by emphasising that its fundamental concepts are not model-independent, but that this does not, as some suggest, force us to radically revise the foundations of the theory. For model-independence (...)
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  2. added 2018-02-17
    Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
    A version of the Church-Turing Thesis states that every effectively realizable physical system can be simulated by Turing Machines (‘Thesis P’). In this formulation the Thesis appears to be an empirical hypothesis, subject to physical falsification. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. The conclusions are that these models reduce to supertasks, i.e. infinite computation, and that even supertasks are no solution for recursive incomputability. This yields that the realization (...)
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  3. added 2017-12-14
    Wittgensteins Diagonal-Argument: Eine Variation auf Cantor und Turing.Juliet Floyd - forthcoming - In Joachim Bromand & Bastian Reichert (eds.), Wittgenstein und die Philosophie der Mathematik. Münster: Mentis Verlag. pp. 167-197.
    A German translation with 2017 postscript of Floyd, Juliet. 2012. "Wittgenstein's Diagonal Argument: A Variation on Cantor and Turing." In Epistemology versus Ontology, Logic, Epistemology: Essays in Honor of Per Martin-Löf, edited by P. Dybjer, S. Lindström, E. Palmgren and G. Sundholm, 25-44. Dordrecht: Springer Science+Business Media. An analysis of philosophical aspects of Turing's diagonal argument in his (136) "On computable numbers, with an application to the Entscheidungsproblem" in relation to Wittgenstein's writings on Turing and Cantor.
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  4. added 2017-11-27
    The Turing Guide.Jack Copeland, Jonathan Bowen, Robin Wilson & Mark Sprevak (eds.) - 2017 - Oxford: Oxford University Press.
  5. added 2017-02-12
    Thesis Eleven – 25 Years On.Peter Beilharz - 2006 - Thesis Eleven 85 (1):6-7.
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  6. added 2017-02-08
    Closing the Circle: An Analysis of Emil Post's Early Work.Liesbeth De Mol - 2006 - Bulletin of Symbolic Logic 12 (2):267 - 289.
    In 1931 Kurt Gödel published his incompleteness results, and some years later Church and Turing showed that the decision problem for certain systems of symbolic logic has a negative solution. However, already in 1921 the young logician Emil Post worked on similar problems which resulted in what he called an "anticipation" of these results. For several reasons though he did not submit these results to a journal until 1941. This failure 'to be the first', did not discourage him: his contributions (...)
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  7. added 2017-02-03
    Computers Don't Follow Instructions.Stevan Harnad - unknown
    Harnad accepts the picture of computation as formalism, so that any implementation of a program - thats any implementation - is as good as any other; in fact, in considering claims about the properties of computations, the nature of the implementing system - the interpreter - is invisible. Let me refer to this idea as 'Computationalism'. Almost all the criticism, claimed refutation by Searle's argument, and sharp contrasting of this idea with others, rests on the absoluteness of this separation between (...)
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  8. added 2017-02-02
    Hypercomputation: Computing More Than the Turing Machine.Toby Ord - unknown
    In this report I provide an introduction to the burgeoning field of hypercomputation – the study of machines that can compute more than Turing machines. I take an extensive survey of many of the key concepts in the field, tying together the disparate ideas and presenting them in a structure which allows comparisons of the many approaches and results. To this I add several new results and draw out some interesting consequences of hypercomputation for several different disciplines.
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  9. added 2017-02-02
    An Analysis of the Criteria for Evaluating Adequate Theories of Computation.Nir Fresco - 2008 - Minds and Machines 18 (3):379-401.
    This paper deals with the question: What are the criteria that an adequate theory of computation has to meet? 1. Smith's answer: it has to meet the empirical criterion (i.e. doing justice to computational practice), the conceptual criterion (i.e. explaining all the underlying concepts) and the cognitive criterion (i.e. providing solid grounds for computationalism). 2. Piccinini's answer: it has to meet the objectivity criterion (i.e. identifying computation as a matter of fact), the explanation criterion (i.e. explaining the computer's behaviour), the (...)
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  10. added 2017-01-30
    The Physical Church-Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
    This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. (...)
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  11. added 2017-01-29
    Church's Thesis and its Epistemological Status.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:123-134.
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  12. added 2017-01-29
    Gary R. Collins, "Psychology Series for Church Leaders". Vol. II. "Effective Counselling". [REVIEW]William J. Nessel - 1973 - The Thomist 37 (1):262.
  13. added 2017-01-28
    On the Interpretation of Church's Thesis.P. Cotogno - 1992 - Epistemologia 15 (2):315-350.
    Church's Thesis states the equivalence of computable functions and recursive functions. This can be interpreted as a definition, as an explanation, as an axiom, and as a proposition of mechanistic philosophy. A number of arguments and objections, including a pair of counterexamples based on Gödel's Incompleteness Theorem, allow to conclude that Church's Thesis can be reasonably taken both as a definition and as an axiom, somewhat less convincingly as an explanation, but hardly as a mechanistic proposition.
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  14. added 2017-01-26
    A Note on Ramsey Theorems and Turing Jumps.Lorenzo Carlucci & Konrad Zdanowski - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 89--95.
  15. added 2017-01-26
    Analog Computation and Church's Thesis.Jerzy Mycka - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 1--331.
  16. added 2017-01-26
    Remarks on Church's Thesis and GOdel's Theorem.Stanisław Krajewski - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 1--269.
  17. added 2017-01-22
    Non-Turing Computations Via Malament-Hogarth Space-Times.Gábor Etesi & István Németi - 2002 - International Journal of Theoretical Physics 41:341--70.
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  18. added 2017-01-21
    Observability of Turing Machines: A Refinement of the Theory of Computation.Yaroslav Sergeyev & Alfredo Garro - 2010 - Informatica 21 (3):425–454.
    The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the relativity of mathematical languages used to describe the Turing machines. A deep investigation is performed on the interrelations between mechanical computations and their mathematical descriptions emerging when a human (the researcher) starts to describe a Turing machine (the object of the study) by (...)
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  19. added 2017-01-21
    An Abstract Model For Parallel Computations: Gandy’s Thesis.Wilfried Sieg & John Byrnes - 1999 - The Monist 82 (1):150-164.
    Wilfried Sieg and John Byrnes. AnModel for Parallel Computation: Gandy's Thesis.
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  20. added 2017-01-15
    Les Deux Formes de la Thèse de Church-Turing Et L’Épistémologie du Calcul.Maël Pégny - 2012 - Philosophia Scientae 16:39-67.
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  21. added 2017-01-14
    A Quantum-Information-Theoretic Complement to a General-Relativistic Implementation of a Beyond-Turing Computer.Christian Wuthrich - 2015 - Synthese 192 (7):1989-2008.
    There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istvan Nemeti and Gyula David have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this (...)
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  22. added 2017-01-14
    Church’s Thesis and the Variety of Mathematical Justifications.Janet Folina - unknown
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  23. added 2017-01-12
    Review of Computability: Turing, Gödel, Church, and Beyond. [REVIEW]Andrew Arana - 2015 - Notre Dame Philosophical Reviews 3 (20).
  24. added 2016-12-08
    Computationalism, The Church–Turing Thesis, and the Church–Turing Fallacy.Gualtiero Piccinini - 2007 - Synthese 154 (1):97-120.
    The Church–Turing Thesis (CTT) is often employed in arguments for computationalism. I scrutinize the most prominent of such arguments in light of recent work on CTT and argue that they are unsound. Although CTT does nothing to support computationalism, it is not irrelevant to it. By eliminating misunderstandings about the relationship between CTT and computationalism, we deepen our appreciation of computationalism as an empirical hypothesis.
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  25. added 2016-12-08
    Effective Computation by Humans and Machines.Shagrir Oron - 2002 - Minds and Machines 12 (2):221-240.
    There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. According to this account, to which I refer as the Gandy–Sieg account, Turing and Church aimed to characterize the functions that can be computed by a human computer. In addition, Turing provided a highly convincing argument (...)
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  26. added 2016-09-26
    The Church-Turing Thesis and Hyper-Computation.O. Shagrir & I. Pitowsky - forthcoming - Minds and Machines.
  27. added 2016-08-07
    Carnap, Turing and Wittgenstein : Contrasting Notions of Analysis.Juliet Floyd - 2012 - In Pierre Wagner (ed.), Carnap's Ideal of Explication and Naturalism. Palgrave-Macmillan.
  28. added 2016-01-31
    What is a Digital State?Vincent C. Müller - 2013 - In Mark J. Bishop & Yasemin Erden (eds.), The Scandal of Computation - What is Computation? - AISB Convention 2013. AISB. pp. 11-16.
    There is much discussion about whether the human mind is a computer, whether the human brain could be emulated on a computer, and whether at all physical entities are computers (pancomputationalism). These discussions, and others, require criteria for what is digital. I propose that a state is digital if and only if it is a token of a type that serves a particular function - typically a representational function for the system. This proposal is made on a syntactic level, assuming (...)
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  29. added 2016-01-31
    20 Years After The Embodied Mind - Why is Cognitivism Alive and Kicking?Vincent C. Müller - 2013 - In Blay Whitby & Joel Parthmore (eds.), Re-Conceptualizing Mental "Illness": The View from Enactivist Philosophy and Cognitive Science - AISB Convention 2013. AISB. pp. 47-49.
    I want to suggest that the major influence of classical arguments for embodiment like "The Embodied Mind" by Varela, Thomson & Rosch (1991) has been a changing of positions rather than a refutation: Cognitivism has found ways to retreat and regroup at positions that have better fortification, especially when it concerns theses about artificial intelligence or artificial cognitive systems. For example: a) Agent-based cognitivism' that understands humans as taking in representations of the world, doing rule-based processing and then acting on (...)
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  30. added 2015-11-13
    The Physical Church Thesis and Physical Computational Complexity.Itamar Pitowski - 1990 - Iyyun 39:81-99.
  31. added 2015-06-27
    Quantum Computing.Amit Hagar & Michael Cuffaro - 2015 - Stanford Encyclopedia of Philosophy.
    Combining physics, mathematics and computer science, quantum computing has developed in the past two decades from a visionary idea to one of the most fascinating areas of quantum mechanics. The recent excitement in this lively and speculative domain of research was triggered by Peter Shor (1994) who showed how a quantum algorithm could exponentially "speed up" classical computation and factor large numbers into primes much more rapidly (at least in terms of the number of computational steps involved) than any known (...)
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  32. added 2015-04-05
    Reflections on Mechanism.Guglielmo Tamburrini - 1988 - Dissertation, Columbia University
    For a general formulation of the undecidability and incompleteness theorems one has to characterize precisely the notion of formal system. Such a characterization is provided by the proposal to identify the intuitive concept of effectively calculable function with that of partial recursive function. A proper understanding of this identification, which is known under the name of "Church's thesis", is crucial for a philosophical assessment of these metamathematical results. The undecidability and incompleteness theorems suggest one major but certainly not the only (...)
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  33. added 2015-04-05
    Church's Thesis and Philosophy.William John Thomas - 1972 - Dissertation, Case Western Reserve University
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  34. added 2015-04-05
    The Church and Usury. Thesis, St. Patrick's Coll., Maynooth.Patrick Cleary - 1914
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  35. added 2015-03-24
    B. Jack Copeland, Carl J. Posy, and Oron Shagrir, Eds, Computability: Turing, Gödel, Church, and Beyond. Cambridge, Mass.: MIT Press, 2013. ISBN 978-0-262-01899-9. Pp. X + 362. [REVIEW]Roy T. Cook - 2014 - Philosophia Mathematica 22 (3):412-413.
  36. added 2015-03-24
    The Church-Turing Thesis: Its Nature and Status.Antony Galton - 1996 - In P. J. R. Millican & A. Clark (eds.), Machines and Thought: The Legacy of Alan Turing, Volume 1. Clarendon Press.
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  37. added 2015-03-23
    Is Turing's Thesis the Consequence of a More General Physical Principle?Matthew P. Szudzik - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 714--722.
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  38. added 2015-03-23
    Church's Thesis as Formulated by Church—An Interpretation.Adam Olszewski - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 1--383.
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  39. added 2015-03-23
    Church's Thesis and Bishop's Constructivism.Douglas S. Bridges - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 1--58.
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  40. added 2015-03-23
    Formalizing Church's Thesis.Leon Horsten - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 1--253.
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  41. added 2015-03-23
    Church's Thesis as an Empirical Hypothesis.Sven Ove Hansson - 1985 - International Logic Review 16:96-101.
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  42. added 2015-03-23
    Doubts About Some Standard Arguments for Church's Thesis.William J. Thomas - 1973 - In Radu J. Bogdan & Ilkka Niiniluoto (eds.), Logic, Language, and Probability. Boston: D. Reidel Pub. Co.. pp. 55--62.
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  43. added 2015-03-21
    A Note on the Theorems of Church‐Turing and Trachtenbrot.Michael Deutsch - 1994 - Mathematical Logic Quarterly 40 (3):422-424.
    We sketch proofs of the theorems of Church-Turing and Trachtenbrot using a semi-monomorphic axiomatization.
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  44. added 2015-03-20
    Les deux formes de la thèse de Church-Turing et l'épistémologie du calcul.Maël Pégny - 2012 - Philosophia Scientiæ 16 (16-3):39-67.
    La thèse de Church-Turing stipule que toute fonction calculable est calculable par une machine de Turing. En distinguant, à la suite de nombreux auteurs, une forme algorithmique de la thèse de Church-Turing portant sur les fonctions calculables par un algorithme d’une forme empirique de cette même thèse, portant sur les fonctions calculables par une machine, il devient possible de poser une nouvelle question : les limites empiriques du calcul sont-elles identiques aux limites des algorithmes ? Ou existe-t-il un moyen empirique (...)
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  45. added 2015-03-20
    Cleland on Church's Thesis and the Limits of Computation.Clayton Peterson & François Lepage - 2012 - Philosophia Scientiæ 16 (16-3):69-85.
    Cet article se veut une critique de la thèse défendue par [Cleland 1993], laquelle soutient que la thèse de Church doit être rejetée puisque les limites du calcul dépendent de la structure physique du monde. Dans un premier temps, nous offrons un (très) bref aperçu de la thèse de Church puis nous présentons l argument de Cleland. Par la suite, nous proposons une analyse critique de son argument, ce qui nous amènera à faire quelques distinctions conceptuelles par rapport aux notions (...)
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  46. added 2015-03-19
    Some Notes on Church's Thesis and the Theory of Games.Luca Anderlini - 1990 - Theory and Decision 29 (1):19-52.
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  47. added 2015-03-18
    Church's Thesis After 70 Years.Peter Smith - unknown
    In the section ‘Further reading’, I listed a book that arrived on my desk just as I was sending IGT off to the press, namely Church’s Thesis after 70 Years edited by Adam Olszewski et al. On the basis of a quick glance, I warned that the twenty two essays in the book did seem to be of ‘variable quality’. But actually, things turn out to be a bit worse than that: the collection really isn’t very good at all! After (...)
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  48. added 2015-03-18
    Squeezing Church's Thesis Again.Peter Smith - unknown
    In the very last chapter of my Introduction to Gödel Theorems, I rashly claimed that there is a sense in which we can informally prove Church’s Thesis. This sort of claim isn’t novel to me: but it certainly is still very much the minority line. So maybe it is worth rehearsing some of the arguments again. Even if I don’t substantially add to the arguments in the book, it might help to approach things in a different order, with some different (...)
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  49. added 2015-03-18
    Church's Thesis After Seventy Years.A. Olszewski, J. Wole'nski & R. Janusz (eds.) - 2006 - Ontos Verlag.
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  50. added 2015-03-18
    Church's Thesis After 70 Years.Adam Olszewski, Jan Wolenski & Robert Janusz (eds.) - 2006 - Ontos Verlag.
1 — 50 / 97