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  1. Darren Abramson (2011). Philosophy of Mind Is (in Part) Philosophy of Computer Science. Minds and Machines 21 (2):203-219.
    In this paper I argue that whether or not a computer can be built that passes the Turing test is a central question in the philosophy of mind. Then I show that the possibility of building such a computer depends on open questions in the philosophy of computer science: the physical Church-Turing thesis and the extended Church-Turing thesis. I use the link between the issues identified in philosophy of mind and philosophy of computer science to respond to a prominent argument (...)
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  2. Tom Addis, Jan Townsend Addis, Dave Billinge, David Gooding & Bart-Floris Visscher (2008). The Abductive Loop: Tracking Irrational Sets. [REVIEW] Foundations of Science 13 (1):5-16.
    We argue from the Church-Turing thesis (Kleene Mathematical logic. New York: Wiley 1967) that a program can be considered as equivalent to a formal language similar to predicate calculus where predicates can be taken as functions. We can relate such a calculus to Wittgenstein’s first major work, the Tractatus, and use the Tractatus and its theses as a model of the formal classical definition of a computer program. However, Wittgenstein found flaws in his initial great work and he explored these (...)
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  3. Enrique Alonso (1999). Ingenio E Industria. Guía de Referencia Sobre la Tesis de Turing-Church (Inventiveness and Skili. Reference Guide on Church-Turing Thesis). Theoria 14 (2):249-273.
    La Teoría de la Computación es un campo especialmente rico para la indagación filosófica. EI debate sobre el mecanicismo y la discusión en torno a los fundamentos de la matemática son tópicos que estan directamente asociados a la Teoria de la Computación desde su misma creación como disciplina independiente. La Tesis de Turing-Church constituye uno de los resultados mas característicos en este campo estando, además, lleno de consecuencias filosóficas. En este ensayo se ofrece una guía de referencia útil a aquellos (...)
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  4. Luca Anderlini (1990). Some Notes on Church's Thesis and the Theory of Games. Theory and Decision 29 (1):19-52.
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  5. Jonathan Berg & Charles Chihara (1975). Church's Thesis Misconstrued. Philosophical Studies 28 (5):357 - 362.
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  6. Robert Black (2000). Proving Church's Thesis. Philosophia Mathematica 8 (3):244--58.
    Arguments to the effect that Church's thesis is intrinsically unprovable because proof cannot relate an informal, intuitive concept to a mathematically defined one are unconvincing, since other 'theses' of this kind have indeed been proved, and Church's thesis has been proved in one direction. However, though evidence for the truth of the thesis in the other direction is overwhelming, it does not yet amount to proof.
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  7. G. Lee Bowie (1973). An Argument Against Church's Thesis. Journal of Philosophy 70 (3):66-76.
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  8. Douglas S. Bridges (2006). Church's Thesis and Bishop's Constructivism. In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. 1--58.
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  9. Selmer Bringsjord, In Defense of the Unprovability of the Church-Turing Thesis.
    One of us has previously argued that the Church-Turing Thesis (CTT), contra Elliot Mendelson, is not provable, and is — light of the mind’s capacity for effortless hypercomputation — moreover false (e.g., [13]). But a new, more serious challenge has appeared on the scene: an attempt by Smith [28] to prove CTT. His case is a clever “squeezing argument” that makes crucial use of Kolmogorov-Uspenskii (KU) machines. The plan for the present paper is as follows. After covering some necessary preliminaries (...)
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  10. Selmer Bringsjord & Konstantine Arkoudas (2006). On the Provability, Veracity, and AI-Relevance of the Church-Turing Thesis. In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. 68-118.
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  11. Tim Button (2009). Hyperloops Do Not Threaten the Notion of an Effective Procedure. Lecture Notes in Computer Science 5635:68-78.
    This paper develops my (BJPS 2009) criticisms of the philosophical significance of a certain sort of infinitary computational process, a hyperloop. I start by considering whether hyperloops suggest that "effectively computable" is vague (in some sense). I then consider and criticise two arguments by Hogarth, who maintains that hyperloops undermine the very idea of effective computability. I conclude that hyperloops, on their own, cannot threaten the notion of an effective procedure.
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  12. Tim Button (2009). SAD Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
    Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version (...)
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  13. Patrick Cleary (1914). The Church and Usury. Thesis, St. Patrick's Coll., Maynooth.
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  14. Carol Cleland (2006). The Church-Turing Thesis: A Last Vestige of a Failed Mathematical Program. In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. 119-146.
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  15. Carol E. Cleland (1995). Effective Procedures and Computable Functions. Minds and Machines 5 (1):9-23.
    Horsten and Roelants have raised a number of important questions about my analysis of effective procedures and my evaluation of the Church-Turing thesis. They suggest that, on my account, effective procedures cannot enter the mathematical world because they have a built-in component of causality, and, hence, that my arguments against the Church-Turing thesis miss the mark. Unfortunately, however, their reasoning is based upon a number of misunderstandings. Effective mundane procedures do not, on my view, provide an analysis of ourgeneral concept (...)
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  16. Carol E. Cleland (1993). Is the Church-Turing Thesis True? Minds and Machines 3 (3):283-312.
    The Church-Turing thesis makes a bold claim about the theoretical limits to computation. It is based upon independent analyses of the general notion of an effective procedure proposed by Alan Turing and Alonzo Church in the 1930''s. As originally construed, the thesis applied only to the number theoretic functions; it amounted to the claim that there were no number theoretic functions which couldn''t be computed by a Turing machine but could be computed by means of some other kind of effective (...)
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  17. Roy T. Cook (2014). 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] Philosophia Mathematica 22 (3):412-413.
  18. B. J. Copeland, C. Posy & O. Shagrir (eds.) (forthcoming). Computability: Gödel, Turing, Church, and Beyond. MIT Press.
  19. B. Jack Copeland (2008). The Church-Turing Thesis. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.
    There are various equivalent formulations of the Church-Turing thesis. A common one is that every effective computation can be carried out by a Turing machine. The Church-Turing thesis is often misunderstood, particularly in recent writing in the philosophy of mind.
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  20. B. Jack Copeland & Oron Shagrir (2007). Physical Computation: How General Are Gandy's Principles for Mechanisms? [REVIEW] Minds and Machines 17 (2):217-231.
    What are the limits of physical computation? In his ‘Church’s Thesis and Principles for Mechanisms’, Turing’s student Robin Gandy proved that any machine satisfying four idealised physical ‘principles’ is equivalent to some Turing machine. Gandy’s four principles in effect define a class of computing machines (‘Gandy machines’). Our question is: What is the relationship of this class to the class of all (ideal) physical computing machines? Gandy himself suggests that the relationship is identity. We do not share this view. We (...)
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  21. Jack Copeland (1997). The Broad Conception of Computation. American Behavioral Scientist 40 (6):690-716.
    A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine - a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the 'Church-Turing thesis', is the claim that the class of functions that can be computed by machines is identical to the class of functions that can be computed by (...)
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  22. Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. 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 defined by Turing Machines (‘Thesis P’); in this formulation the Thesis appears an empirical, more than a logico-mathematical, proposition. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. These models depend on infinite computation, explicitly or implicitly, and appear physically implausible; moreover, even if infinite computation were realizable, the Halting Problem would not be affected. Therefore, Thesis (...)
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  23. Michael Deutsch (1994). A Note on the Theorems of Church‐Turing and Trachtenbrot. 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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  24. Steven Ericsson-Zenith (forthcoming). Explaining Experience In Nature: The Foundations Of Logic And Apprehension. Institute for Advanced Science & Engineering.
    At its core this book is concerned with logic and computation with respect to the mathematical characterization of sentient biophysical structure and its behavior. -/- Three related theories are presented: The first of these provides an explanation of how sentient individuals come to be in the world. The second describes how these individuals operate. And the third proposes a method for reasoning about the behavior of individuals in groups. -/- These theories are based upon a new explanation of experience in (...)
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  25. Janet Folina (1998). Church's Thesis: Prelude to a Proof. Philosophia Mathematica 6 (3):302-323.
    This paper defends the traditional conception of Church's Thesis , as unprovable but true, against a group of arguments by Gandy, Mendelson, Shapiro and Sieg. The arguments here considered urge that CT is provable or proved. This paper argues, first, that contra-Mendelson, CT does connect a mathematically precise concept with an intuitive notion . Second, the various ‘proofs’ of CT fail to undermine the traditional conception of CT as unprovable. Either they do not conform to the sense of proof imbedded (...)
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  26. Antony Galton (1996). The Church-Turing Thesis: Its Nature and Status. In P. J. R. Millican & A. Clark (eds.), Machines and Thought: The Legacy of Alan Turing, Volume 1. Clarendon Press.
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  27. Robin Gandy (1980). Church's Thesis and Principles for Mechanisms. In The Kleene Symposium. North-Holland. 123--148.
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  28. Dina Goldin & Peter Wegner (2008). The Interactive Nature of Computing: Refuting the Strong Church–Turing Thesis. [REVIEW] Minds and Machines 18 (1):17-38.
    The classical view of computing positions computation as a closed-box transformation of inputs (rational numbers or finite strings) to outputs. According to the interactive view of computing, computation is an ongoing interactive process rather than a function-based transformation of an input to an output. Specifically, communication with the outside world happens during the computation, not before or after it. This approach radically changes our understanding of what is computation and how it is modeled. The acceptance of interaction as a new (...)
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  29. Yuri Gurevich (2012). What is an Algorithm. Lecture Notes in Computer Science.
  30. Amit Hagar & Giuseppe Sergioli (2015). Counting Steps: A Finitist Interpretation of Objective Probability in Physics. Epistemologia 37 (2):262-275.
    We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) from a physical state to another, and (3) the size of the set of time--complexity functions that are compatible with the physical (...)
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  31. Sven Ove Hansson (1985). Church's Thesis as an Empirical Hypothesis. International Logic Review 16:96-101.
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  32. Leon Horsten (2006). Formalizing Church's Thesis. In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. 1--253.
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  33. Leon Horsten (1995). The Church-Turing Thesis and Effective Mundane Procedures. Minds and Machines 5 (1):1-8.
    We critically discuss Cleland''s analysis of effective procedures as mundane effective procedures. She argues that Turing machines cannot carry out mundane procedures, since Turing machines are abstract entities and therefore cannot generate the causal processes that are generated by mundane procedures. We argue that if Turing machines cannot enter the physical world, then it is hard to see how Cleland''s mundane procedures can enter the world of numbers. Hence her arguments against versions of the Church-Turing thesis for number theoretic functions (...)
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  34. David Israel (2002). Reflections on Gödel's and Gandy's Reflections on Turing's Thesis. Minds and Machines 12 (2):181-201.
    We sketch the historical and conceptual context of Turing's analysis of algorithmic or mechanical computation. We then discuss two responses to that analysis, by Gödel and by Gandy, both of which raise, though in very different ways. The possibility of computation procedures that cannot be reduced to the basic procedures into which Turing decomposed computation. Along the way, we touch on some of Cleland's views.
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  35. László Kalmár (1957). An Argument Against the Plausibility of Church's Thesis. In A. Heyting (ed.), ¸ Iteheyting:Cim. Amsterdam, North-Holland Pub. Co.. 72--80.
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  36. John T. Kearns (1997). Thinking Machines: Some Fundamental Confusions. [REVIEW] Minds and Machines 7 (2):269-87.
    This paper explores Church's Thesis and related claims madeby Turing. Church's Thesis concerns computable numerical functions, whileTuring's claims concern both procedures for manipulating uninterpreted marksand machines that generate the results that these procedures would yield. Itis argued that Turing's claims are true, and that they support (the truth of)Church's Thesis. It is further argued that the truth of Turing's and Church'sTheses has no interesting consequences for human cognition or cognitiveabilities. The Theses don't even mean that computers can do as much (...)
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  37. Saul A. Kripke (2013). The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Completeness Theorem. In B. J. Copeland, C. Posy & O. Shagrir (eds.), Computability: Turing, Gödel, Church, and Beyond. MIT Press.
    Traditionally, many writers, following Kleene (1952), thought of the Church-Turing thesis as unprovable by its nature but having various strong arguments in its favor, including Turing’s analysis of human computation. More recently, the beauty, power, and obvious fundamental importance of this analysis, what Turing (1936) calls “argument I,” has led some writers to give an almost exclusive emphasis on this argument as the unique justification for the Church-Turing thesis. In this chapter I advocate an alternative justification, essentially presupposed by Turing (...)
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  38. Vincent C. Müller (2011). On the Possibilities of Hypercomputing Supertasks. Minds and Machines 21 (1):83-96.
    This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such (...)
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  39. Wayne C. Myrvold (1997). The Decision Problem for Entanglement. In Robert S. Cohen, Michael Horne & John Stachel (eds.), Potentiality, Entanglement, and Passion-at-a-Distance: Quantum Mechanical Studies for Abner Shimony. Kluwer Academic Publishers. 177--190.
  40. Wayne C. Myrvold (1995). Computability in Quantum Mechanics. In Werner De Pauli-Schimanovich, Eckehart Köhler & Friedrich Stadler (eds.), Vienna Circle Institute Yearbook. Kluwer Academic Publishers. 33-46.
    In this paper, the issues of computability and constructivity in the mathematics of physics are discussed. The sorts of questions to be addressed are those which might be expressed, roughly, as: Are the mathematical foundations of our current theories unavoidably non-constructive: or, Are the laws of physics computable?
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  41. A. Olszewski, J. Wole'nski & R. Janusz (eds.) (2006). Church's Thesis After Seventy Years. Ontos Verlag.
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  42. Adam Olszewski (2006). Church's Thesis as Formulated by Church—An Interpretation. In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. 1--383.
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  43. Adam Olszewski, Jan Wolenski & Robert Janusz (eds.) (2007). Church's Thesis After 70 Years. Ontos Verlag.
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  44. Martina Orlandi (forthcoming). On the Notion of Computability - We Don't Really Need to Define It. Dialectic, Special Issue on Science and Mathematics.
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  45. Maël Pégny (2012). Les deux formes de la thèse de Church-Turing et l'épistémologie du calcul. Philosophia Scientiæ. Travaux d'Histoire Et de Philosophie des Sciences 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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  46. Clayton Peterson & François Lepage (2012). Cleland on Church's Thesis and the Limits of Computation. Philosophia Scientiæ. Travaux d'Histoire Et de Philosophie des Sciences 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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  47. Gualtiero Piccinini (2011). The Physical Church–Turing Thesis: Modest or Bold? 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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  48. Gualtiero Piccinini (2007). Computationalism, the Church–Turing Thesis, and the Church–Turing Fallacy. 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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  49. Itamar Pitowsky (2003). Physical Hypercomputation and the Church–Turing Thesis. Minds and Machines 13 (1):87-101.
    We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy’s thesis.
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  50. Michael Rescorla (2007). Church's Thesis and the Conceptual Analysis of Computability. Notre Dame Journal of Formal Logic 48 (2):253-280.
    Church's thesis asserts that a number-theoretic function is intuitively computable if and only if it is recursive. A related thesis asserts that Turing's work yields a conceptual analysis of the intuitive notion of numerical computability. I endorse Church's thesis, but I argue against the related thesis. I argue that purported conceptual analyses based upon Turing's work involve a subtle but persistent circularity. Turing machines manipulate syntactic entities. To specify which number-theoretic function a Turing machine computes, we must correlate these syntactic (...)
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