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Hypercomputation

Minds and Machines 12 (4):461-502 (2002)

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  1. The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
  • Symbol Grounding in Computational Systems: A Paradox of Intentions.Vincent C. Müller - 2009 - Minds and Machines 19 (4):529-541.
    The paper presents a paradoxical feature of computational systems that suggests that computationalism cannot explain symbol grounding. If the mind is a digital computer, as computationalism claims, then it can be computing either over meaningful symbols or over meaningless symbols. If it is computing over meaningful symbols its functioning presupposes the existence of meaningful symbols in the system, i.e. it implies semantic nativism. If the mind is computing over meaningless symbols, no intentional cognitive processes are available prior to symbol grounding. (...)
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  • Autonomous Systems and the Place of Biology Among Sciences. Perspectives for an Epistemology of Complex Systems.Leonardo Bich - 2021 - In Gianfranco Minati (ed.), Multiplicity and Interdisciplinarity. Essays in Honor of Eliano Pessa. Springer. pp. 41-57.
    This paper discusses the epistemic status of biology from the standpoint of the systemic approach to living systems based on the notion of biological autonomy. This approach aims to provide an understanding of the distinctive character of biological systems and this paper analyses its theoretical and epistemological dimensions. The paper argues that, considered from this perspective, biological systems are examples of emergent phenomena, that the biological domain exhibits special features with respect to other domains, and that biology as a discipline (...)
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  • What is a Computer? A Survey.William J. Rapaport - 2018 - Minds and Machines 28 (3):385-426.
    A critical survey of some attempts to define ‘computer’, beginning with some informal ones, then critically evaluating those of three philosophers, and concluding with an examination of whether the brain and the universe are computers.
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  • 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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  • Computing Mechanisms.Gualtiero Piccinini - 2007 - Philosophy of Science 74 (4):501-526.
    This paper offers an account of what it is for a physical system to be a computing mechanism—a system that performs computations. A computing mechanism is a mechanism whose function is to generate output strings from input strings and (possibly) internal states, in accordance with a general rule that applies to all relevant strings and depends on the input strings and (possibly) internal states for its application. This account is motivated by reasons endogenous to the philosophy of computing, namely, doing (...)
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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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  • Continuities and Discontinuities Between Humans, Intelligent Machines, and Other Entities.Johnny Hartz Søraker - 2014 - Philosophy and Technology 27 (1):31-46.
    When it comes to the question of what kind of moral claim an intelligent or autonomous machine might have, one way to answer this is by way of comparison with humans: Is there a fundamental difference between humans and other entities? If so, on what basis, and what are the implications for science and ethics? This question is inherently imprecise, however, because it presupposes that we can readily determine what it means for two types of entities to be sufficiently different—what (...)
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  • Theoriegeleitete Bestimmung von Objektmengen und Beobachtungsintervallen am Beispiel des Halleyschen Kometen.Ulrich Gähde - 2012 - Philosophia Naturalis 49 (2):207-224.
    The starting point of the following considerations is a case study concerning the discovery of Halley's comet and the theoretical description of its path. It is shown that the set of objects involved in that system and the time interval during which their paths are observed are determined in a theory dependent way – thereby making use of the very theory later used for that system's theoretical description. Metatheoretical consequences this fact has with respect to the structuralist view of empirical (...)
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  • 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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  • Biological Hypercomputation: A New Research Problem in Complexity Theory.Carlos E. Maldonado & Nelson A. Gómez Cruz - 2015 - Complexity 20 (4):8-18.
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  • Using AI Methods to Evaluate a Minimal Model for Perception.Chris Fields & Robert Prentner - 2019 - Open Philosophy 2 (1):503-524.
    The relationship between philosophy and research on artificial intelligence has been difficult since its beginning, with mutual misunderstanding and sometimes even hostility. By contrast, we show how an approach informed by both philosophy and AI can be productive. After reviewing some popular frameworks for computation and learning, we apply the AI methodology of “build it and see” to tackle the philosophical and psychological problem of characterizing perception as distinct from sensation. Our model comprises a network of very simple, but interacting (...)
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  • Philosophy of Computer Science: An Introductory Course.William J. Rapaport - 2005 - Teaching Philosophy 28 (4):319-341.
    There are many branches of philosophy called “the philosophy of X,” where X = disciplines ranging from history to physics. The philosophy of artificial intelligence has a long history, and there are many courses and texts with that title. Surprisingly, the philosophy of computer science is not nearly as well-developed. This article proposes topics that might constitute the philosophy of computer science and describes a course covering those topics, along with suggested readings and assignments.
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  • Computers Are Syntax All the Way Down: Reply to Bozşahin.William J. Rapaport - 2019 - Minds and Machines 29 (2):227-237.
    A response to a recent critique by Cem Bozşahin of the theory of syntactic semantics as it applies to Helen Keller, and some applications of the theory to the philosophy of computer science.
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  • Significance of Models of Computation, From Turing Model to Natural Computation.Gordana Dodig-Crnkovic - 2011 - Minds and Machines 21 (2):301-322.
    The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and (...)
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  • Positive affirmation of non-algorithmic information processing.Carlos Eduardo Maldonado - 2017 - Cinta de Moebio 60:279-285.
    : One of the most compelling problems in science consists in understanding how living systems process information. After all, the way they process information defines their capacities to learning and adaptation. There is an increasing consensus in that living systems are not machines in any sense. Biological hypercomputation is the concept coined that expresses that living beings process information non-algorithmically. This paper aims at proving a positive understanding of “non-algorithmic” processes. Many arguments are brought that support the claim. This foster, (...)
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  • The Logic of Searle’s Chinese Room Argument.Robert I. Damper - 2006 - Minds and Machines 16 (2):163-183.
    John Searle’s Chinese room argument is a celebrated thought experiment designed to refute the hypothesis, popular among artificial intelligence scientists and philosophers of mind, that “the appropriately programmed computer really is a mind”. Since its publication in 1980, the CRA has evoked an enormous amount of debate about its implications for machine intelligence, the functionalist philosophy of mind, theories of consciousness, etc. Although the general consensus among commentators is that the CRA is flawed, and not withstanding the popularity of the (...)
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  • Physical Computation: How General Are Gandy’s Principles for Mechanisms?B. Jack Copeland & Oron Shagrir - 2007 - 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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  • 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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  • Computational Modeling Vs. Computational Explanation: Is Everything a Turing Machine, and Does It Matter to the Philosophy of Mind?Gualtiero Piccinini - 2007 - Australasian Journal of Philosophy 85 (1):93 – 115.
    According to pancomputationalism, everything is a computing system. In this paper, I distinguish between different varieties of pancomputationalism. I find that although some varieties are more plausible than others, only the strongest variety is relevant to the philosophy of mind, but only the most trivial varieties are true. As a side effect of this exercise, I offer a clarified distinction between computational modelling and computational explanation.<br><br>.
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  • Can Machines Think? An Old Question Reformulated.Achim Hoffmann - 2010 - Minds and Machines 20 (2):203-212.
    This paper revisits the often debated question Can machines think? It is argued that the usual identification of machines with the notion of algorithm has been both counter-intuitive and counter-productive. This is based on the fact that the notion of algorithm just requires an algorithm to contain a finite but arbitrary number of rules. It is argued that intuitively people tend to think of an algorithm to have a rather limited number of rules. The paper will further propose a modification (...)
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  • Quantum Algorithms: Philosophical Lessons.Amit Hagar - 2007 - Minds and Machines 17 (2):233-247.
    I discuss the philosophical implications that the rising new science of quantum computing may have on the philosophy of computer science. While quantum algorithms leave the notion of Turing-Computability intact, they may re-describe the abstract space of computational complexity theory hence militate against the autonomous character of some of the concepts and categories of computer science.
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  • The Interactive Nature of Computing: Refuting the Strong Church–Turing Thesis. [REVIEW]Dina Goldin & Peter Wegner - 2008 - 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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  • Turing-, Human- and Physical Computability: An Unasked Question. [REVIEW]Eli Dresner - 2008 - Minds and Machines 18 (3):349-355.
    In recent years it has been convincingly argued that the Church-Turing thesis concerns the bounds of human computability: The thesis was presented and justified as formally delineating the class of functions that can be computed by a human carrying out an algorithm. Thus the Thesis needs to be distinguished from the so-called Physical Church-Turing thesis, according to which all physically computable functions are Turing computable. The latter is often claimed to be false, or, if true, contingently so. On all accounts, (...)
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  • How to Make a Meaningful Comparison of Models: The Church–Turing Thesis Over the Reals.Maël Pégny - 2016 - Minds and Machines 26 (4):359-388.
    It is commonly believed that there is no equivalent of the Church–Turing thesis for computation over the reals. In particular, computational models on this domain do not exhibit the convergence of formalisms that supports this thesis in the case of integer computation. In the light of recent philosophical developments on the different meanings of the Church–Turing thesis, and recent technical results on analog computation, I will show that this current belief confounds two distinct issues, namely the extension of the notion (...)
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  • Practical Intractability: A Critique of the Hypercomputation Movement. [REVIEW]Aran Nayebi - 2014 - Minds and Machines 24 (3):275-305.
    For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to demonstrate this, these arguments lack the generality to be a satisfactory justification against the construction of any information-processing machine that computes beyond the universal Turing machine. To this end, I present a more (...)
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  • Quantum Hypercomputability?Amit Hagar & Alexandre Korolev - 2006 - Minds and Machines 16 (1):87-93.
    A recent proposal to solve the halting problem with the quantum adiabatic algorithm is criticized and found wanting. Contrary to other physical hypercomputers, where one believes that a physical process “computes” a (recursive-theoretic) non-computable function simply because one believes the physical theory that presumably governs or describes such process, believing the theory (i.e., quantum mechanics) in the case of the quantum adiabatic “hypercomputer” is tantamount to acknowledging that the hypercomputer cannot perform its task.
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  • Computers Aren’T Syntax All the Way Down or Content All the Way Up.Cem Bozşahin - 2018 - Minds and Machines 28 (3):543-567.
    This paper argues that the idea of a computer is unique. Calculators and analog computers are not different ideas about computers, and nature does not compute by itself. Computers, once clearly defined in all their terms and mechanisms, rather than enumerated by behavioral examples, can be more than instrumental tools in science, and more than source of analogies and taxonomies in philosophy. They can help us understand semantic content and its relation to form. This can be achieved because they have (...)
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  • Should Computability Be Epistemic? A Logical and Physical Point of View.Florent Franchette - 2016 - Philosophies 1 (1):15--27.
    Although the formalizations of computability provided in the 1930s have proven to be equivalent, two different accounts of computability may be distinguished regarding computability as an epistemic concept. While computability, according to the epistemic account, should be based on epistemic constraints related to the capacities of human computers, the non-epistemic account considers computability as based on manipulations of symbols that require no human capacities other than the capacity of manipulating symbols according to a set of rules. In this paper, I (...)
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  • Signs of the Times: Mind, Evolution, and the Twilight of Postmodernity.Charles J. Lumsden - 2011 - Semiotica 2011 (183):59-76.
    The creative imagination changes itself and the world in ways we cannot anticipate. This restless creativity gathers not just refutable facts; it hunts self-transforming revelations, semiotic prizes acclaimed and defended in the realms of inner awareness and political power. So doing, it eludes final description in any one set of signs. This means, I argue here, that sign systems must themselves give chase. Texts of this kind will not be the fixed embalmed arrays of signs and symbols that have sustained (...)
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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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  • On the Possibilities of Hypercomputing Supertasks.Vincent C. Müller - 2011 - 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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  • Do Accelerating Turing Machines Compute the Uncomputable?B. Jack Copeland & Oron Shagrir - 2011 - Minds and Machines 21 (2):221-239.
    Accelerating Turing machines have attracted much attention in the last decade or so. They have been described as “the work-horse of hypercomputation”. But do they really compute beyond the “Turing limit”—e.g., compute the halting function? We argue that the answer depends on what you mean by an accelerating Turing machine, on what you mean by computation, and even on what you mean by a Turing machine. We show first that in the current literature the term “accelerating Turing machine” is used (...)
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  • Quantum Computing.Amit Hagar & Michael Cuffaro - 2019 - Stanford Encyclopedia of Philosophy.
    Combining physics, mathematics and computer science, quantum computing and its sister discipline of quantum information have developed in the past few decades from visionary ideas to two of the most fascinating areas of quantum theory. General interest and excitement in quantum computing was initially triggered by Peter Shor (1994) who showed how a quantum algorithm could exponentially “speed-up” classical computation and factor large numbers into primes far more efficiently than any (known) classical algorithm. Shor’s algorithm was soon followed by several (...)
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  • Gretchenfragen an den Naturalisten.Gerhard Vollmer - 2012 - Philosophia Naturalis 49 (2):239-291.
    A philosophical position may be characterized in different ways. Here we try to say how the naturalist answers certain . The questions come from very different areas; the spectrum of subjects is therefore quite mixed. There are, however, aspects of order: We start with (questions about) abstract subjects like logic, mathematics, metaphysics, then turn to problems of realism. And since in general naturalists are realists, the following questions on truth, laws of nature, origin of the universe, cosmology, evolution, body-mind-problem, freedom (...)
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  • Computation in Cognitive Science: It is Not All About Turing-Equivalent Computation.Kenneth Aizawa - 2010 - Studies in History and Philosophy of Science Part A 41 (3):227-236.
    It is sometimes suggested that the history of computation in cognitive science is one in which the formal apparatus of Turing-equivalent computation, or effective computability, was exported from mathematical logic to ever wider areas of cognitive science and its environs. This paper, however, indicates some respects in which this suggestion is inaccurate. Computability theory has not been focused exclusively on Turing-equivalent computation. Many essential features of Turing-equivalent computation are not captured in definitions of computation as symbol manipulation. Turing-equivalent computation did (...)
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  • Quantum Hypercomputation—Hype or Computation?Amit Hagar & Alex Korolev - 2007 - Philosophy of Science 74 (3):347-363.
    A recent attempt to compute a (recursion‐theoretic) noncomputable function using the quantum adiabatic algorithm is criticized and found wanting. Quantum algorithms may outperform classical algorithms in some cases, but so far they retain the classical (recursion‐theoretic) notion of computability. A speculation is then offered as to where the putative power of quantum computers may come from.
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  • Computation, Hypercomputation, and Physical Science.Konstantine Arkoudas - 2008 - Journal of Applied Logic 6 (4):461-475.
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  • Computational Complexity and Human Decision-Making.Peter Bossaerts & Carsten Murawski - 2017 - Trends in Cognitive Sciences 21 (12):917-929.
  • Recursive Analysis of Singular Ordinary Differential Equations.Peter Buser & Bruno Scarpellini - 2010 - Annals of Pure and Applied Logic 162 (1):20-35.
    We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the recursively enumerable sets using Fourier coefficients of recursive analytic functions that are generated by differential equations and elementary operations.
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  • Undecidability Through Fourier Series.Peter Buser & Bruno Scarpellini - 2016 - Annals of Pure and Applied Logic 167 (7):507-524.