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  1. Functionalism, Computationalism, and Mental Contents.Gualtiero Piccinini - 2004 - Canadian Journal of Philosophy 34 (3):375-410.
    Some philosophers have conflated functionalism and computationalism. I reconstruct how this came about and uncover two assumptions that made the conflation possible. They are the assumptions that (i) psychological functional analyses are computational descriptions and (ii) everything may be described as performing computations. I argue that, if we want to improve our understanding of both the metaphysics of mental states and the functional relations between them, we should reject these assumptions. # 2004 Elsevier Ltd. All rights reserved.
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  • Physical Hypercomputation and the Church–Turing Thesis.Oron Shagrir & Itamar Pitowsky - 2003 - 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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  • Accelerating Turing Machines.B. Jack Copeland - 2002 - Minds and Machines 12 (2):281-300.
    Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of contains n consecutive 7s, for any n; solve the Turing-machine halting problem; and decide the predicate calculus. Are accelerating Turing machines, then, logically impossible devices? I argue that they are not. There are implications concerning the nature of effective procedures and the theoretical limits of computability. Contrary (...)
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  • Building Infinite Machines.E. B. Davies - 2001 - British Journal for the Philosophy of Science 52 (4):671-682.
    We describe in some detail how to build an infinite computing machine within a continuous Newtonian universe. The relevance of our construction to the Church-Turing thesis and the Platonist-Intuitionist debate about the nature of mathematics is also discussed.
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  • Quantum Hypercomputation.Tien D. Kieu - 2002 - Minds and Machines 12 (4):541-561.
    We explore the possibility of using quantum mechanical principles for hypercomputation through the consideration of a quantum algorithm for computing the Turing halting problem. The mathematical noncomputability is compensated by the measurability of the values of quantum observables and of the probability distributions for these values. Some previous no-go claims against quantum hypercomputation are then reviewed in the light of this new positive proposal.
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  • 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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  • The Diagonal Method and Hypercomputation.Toby Ord & Tien D. Kieu - 2005 - British Journal for the Philosophy of Science 56 (1):147-156.
    The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation which claim to be able to solve the halting problem for Turing machines. We show that such arguments are flawed—a contradiction only occurs if a type of machine can compute its own diagonal function. We then demonstrate why such a situation (...)
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  • Turing's O-Machines, Searle, Penrose and the Brain.B. J. Copeland - 1998 - Analysis 58 (2):128-138.
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  • The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics.Roger Penrose - 1999 - Oxford University Press.
    In his bestselling work of popular science, Sir Roger Penrose takes us on a fascinating roller-coaster ride through the basic principles of physics, cosmology, mathematics, and philosophy to show that human thinking can never be emulated by a machine.
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  • Narrow Versus Wide Mechanism: Including a Re-Examination of Turing’s Views on the Mind-Machine Issue.B. Jack Copeland - 2000 - Journal of Philosophy 97 (1):5-32.
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  • 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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  • Computers Ltd: What They Really Can't Do.David Harel - 2003 - Oxford University Press.
    In Computers Ltd, David Harel, best-selling author of Algorithmics, explains and illustrates one of the most fundamental, yet under-exposed facets of computers - their inherent limitations. Looking at the bad news that is proven, lasting, and robust, discussing limitations that no amounts of hardware, software, talents, or resources can overcome, the book presents a disturbing and provocative view of computing at the start of the 21st century.
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  • Infinite Pains: The Trouble with Supertasks.John Earman & John Norton - 1996 - In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell. pp. 11--271.
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  • Infinite Time Turing Machines.Joel David Hamkins - 2002 - Minds and Machines 12 (4):567-604.
    Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.
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  • The Broad Conception of Computation.Jack Copeland - 1997 - 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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  • What Turing Did After He Invented the Universal Turing Machine.B. Jack Copeland & Diane Proudfoot - 2000 - Journal of Logic, Language and Information 9 (4):491-509.
    Alan Turing anticipated many areas of current research incomputer and cognitive science. This article outlines his contributionsto Artificial Intelligence, connectionism, hypercomputation, andArtificial Life, and also describes Turing's pioneering role in thedevelopment of electronic stored-program digital computers. It locatesthe origins of Artificial Intelligence in postwar Britain. It examinesthe intellectual connections between the work of Turing and ofWittgenstein in respect of their views on cognition, on machineintelligence, and on the relation between provability and truth. Wecriticise widespread and influential misunderstandings of theChurch–Turing thesis (...)
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  • Tasks and Supertasks.James Thomson - 1954 - Analysis 15 (1):1--13.
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  • Hypercomputation.B. Jack Copeland - 2002 - Minds and Machines 12 (4):461-502.
    A survey of the field of hypercomputation, including discussion of a variety of objections.
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  • Functionalism at Forty: A Critical Retrospective.Thomas Hofweber & Paul M. Churchland - 2005 - Journal of Philosophy 102 (1):33 - 50.
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  • A Brief Critique of Pure Hypercomputation.Paolo Cotogno - 2009 - Minds and Machines 19 (3):391-405.
    Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just on the absence of a definite value for some paradoxical construction; nature and quantity of computing resources are immaterial. The assumption that the halting problem is solved by oracles of higher Turing degree amounts just to postulation; infinite-time oracles are not actually solving paradoxes, but simply assigning them conventional values. Special values for non-terminating processes are likewise (...)
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  • The Universal Computer. The Road From Leibniz to Turing.Martin Davis - 2001 - Bulletin of Symbolic Logic 7 (1):65-66.
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  • So How Does the Mind Work?Steven Pinker - 2005 - Mind and Language 20 (1):1-38.
    In my book How the Mind Works, I defended the theory that the human mind is a naturally selected system of organs of computation. Jerry Fodor claims that 'the mind doesn't work that way'(in a book with that title) because (1) Turing Machines cannot duplicate humans' ability to perform abduction (inference to the best explanation); (2) though a massively modular system could succeed at abduction, such a system is implausible on other grounds; and (3) evolution adds nothing to our understanding (...)
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  • On the Possibility, or Otherwise, of Hypercomputation.Philip D. Welch - 2004 - British Journal for the Philosophy of Science 55 (4):739-746.
    We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal functions are not computable by any function of the class over which they diagonalise, there is no ?logical incomputability? in their being computed over a wider class. Hence this ?logical incomputability? regrettably cannot be used in his argument that no hypercomputation can compute the Halting problem. This seems to lead (...)
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  • Functionalism, Computationalism, & Mental States.Gualtiero Piccinini - 2004 - Studies in the History and Philosophy of Science 35 (4):811-833.
    Some philosophers have conflated functionalism and computationalism. I reconstruct how this came about and uncover two assumptions that made the conflation possible. They are the assumptions that (i) psychological functional analyses are computational descriptions and (ii) everything may be described as performing computations. I argue that, if we want to improve our understanding of both the metaphysics of mental states and the functional relations between them, we should reject these assumptions.
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  • Representation in Digital Systems.Vincent C. Müller - 2008 - In Adam Briggle, Katinka Waelbers & Brey Philip (eds.), Current Issues in Computing and Philosophy. IOS Press. pp. 116-121.
    Cognition is commonly taken to be computational manipulation of representations. These representations are assumed to be digital, but it is not usually specified what that means and what relevance it has for the theory. I propose a specification for being a digital state in a digital system, especially a digital computational system. The specification shows that identification of digital states requires functional directedness, either for someone or for the system of which it is a part. In the case or digital (...)
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  • Artificial Intelligence: A Philosophical Introduction.Jack Copeland - 1993 - Wiley-Blackwell.
    Presupposing no familiarity with the technical concepts of either philosophy or computing, this clear introduction reviews the progress made in AI since the inception of the field in 1956. Copeland goes on to analyze what those working in AI must achieve before they can claim to have built a thinking machine and appraises their prospects of succeeding. There are clear introductions to connectionism and to the language of thought hypothesis which weave together material from philosophy, artificial intelligence and neuroscience. John (...)
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  • The Mind Doesn't Work That Way: The Scope and Limits of Computational Psychology.Jerry A. Fodor - 2000 - MIT Press.
    Jerry Fodor argues against the widely held view that mental processes are largely computations, that the architecture of cognition is massively modular, and...
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  • Computability and Logic.G. S. Boolos & R. C. Jeffrey - 1977 - British Journal for the Philosophy of Science 28 (1):95-95.
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  • Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 2003 - Bulletin of Symbolic Logic 9 (4):520-521.
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  • The Emperor's New Mind.Roger Penrose - 1989 - Oxford University Press.
    Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever ...
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  • Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 2007 - Cambridge University Press.
    Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel’s incompleteness theorems, but also a large number of optional topics, from Turing’s theory of computability to Ramsey’s theorem. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a (...)
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  • Church's Thesis and Principles for Mechanisms.Robin Gandy - 1980 - In The Kleene Symposium. North-Holland. pp. 123--148.
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  • It From Qubit.David Deutsch - unknown
    Of John Wheeler’s ‘Really Big Questions’, the one on which the most progress has been made is It From Bit? – does information play a significant role at the foundations of physics? It is perhaps less ambitious than some of the other Questions, such as How Come Existence?, because it does not necessarily require a metaphysical answer. And unlike, say, Why The Quantum?, it does not require the discovery of new laws of nature: there was room for hope that it (...)
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  • The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics.Roger Penrose - 1990 - Science and Society 54 (4):484-487.
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  • Infinite Time Turing Machines.Joel Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
    We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. Every $\Pi^1_1$ set, for example, is decidable by such machines, and the semi-decidable sets form a portion of the $\Delta^1_2$ sets. Our oracle concept leads to a notion of relative computability for sets of reals and a rich degree structure, stratified by two natural jump operators.
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  • The Mind Doesn't Work That Way: The Scope and Limits of Computational Psychology.Jerry Fodor - 2001 - Philosophical Quarterly 51 (205):549-552.
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  • Functionalism at Forty.Paul M. Churchland - 2005 - Journal of Philosophy 102 (1):33 - 50.
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  • On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
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  • Computationalism: The Next Generation.Matthias Scheutz - 2002 - In Computationalism: New Directions. MIT Press. pp. 517-524.
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  • Philosophy and Computing: An Introduction.Luciano Floridi - 1999 - Routledge.
    _Philosophy and Computing_ explores each of the following areas of technology: the digital revolution; the computer; the Internet and the Web; CD-ROMs and Mulitmedia; databases, textbases, and hypertexts; Artificial Intelligence; the future of computing. Luciano Floridi shows us how the relationship between philosophy and computing provokes a wide range of philosophical questions: is there a philosophy of information? What can be achieved by a classic computer? How can we define complexity? What are the limits of quantam computers? Is the Internet (...)
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  • Tasks, Super-Tasks, and the Modern Eleatics.Paul Benacerraf - 1962 - Journal of Philosophy 59 (24):765-784.
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  • Infinite Time Turing Machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
    Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.
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  • An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
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  • Philosophie der Mathematik Und Naturwissenschaft.Hermann Weyl - 1927
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  • Computationalism: New Directions.Matthias Scheutz (ed.) - 2002 - MIT Press.
    A new computationalist view of the mind that takes into account real-world issues of embodiment, interaction, physical implementation, and semantics.
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