Results for 'Computability'

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  1. The fortieth annual lecture series 1999-2000.Brain Computations & an Inevitable Conflict - 2000 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 31:199-200.
  2. Randomness and Recursive Enumerability.Siam J. Comput - unknown
    One recursively enumerable real α dominates another one β if there are nondecreasing recursive sequences of rational numbers (a[n] : n ∈ ω) approximating α and (b[n] : n ∈ ω) approximating β and a positive constant C such that for all n, C(α − a[n]) ≥ (β − b[n]). See [R. M. Solovay, Draft of a Paper (or Series of Papers) on Chaitin’s Work, manuscript, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, 1974, p. 215] and [G. J. (...)
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  3.  11
    A Model for Proustian Decay.Computer Lars - 2024 - Nordic Journal of Aesthetics 33 (67).
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  4.  10
    Computer Science Logic: 11th International Workshop, CSL'97, Annual Conference of the EACSL, Aarhus, Denmark, August 23-29, 1997, Selected Papers.M. Nielsen, Wolfgang Thomas & European Association for Computer Science Logic - 1998 - Springer Verlag.
    This book constitutes the strictly refereed post-workshop proceedings of the 11th International Workshop on Computer Science Logic, CSL '97, held as the 1997 Annual Conference of the European Association on Computer Science Logic, EACSL, in Aarhus, Denmark, in August 1997. The volume presents 26 revised full papers selected after two rounds of refereeing from initially 92 submissions; also included are four invited papers. The book addresses all current aspects of computer science logics and its applications and thus presents the state (...)
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  5. The general problem of the primitive was finally solved in 1912 by A. Den-joy. But his integration process was more complicated than that of Lebesgue. Denjoy's basic idea was to first calculate the definite integral∫ b. [REVIEW]How to Compute Antiderivatives - 1995 - Bulletin of Symbolic Logic 1 (3).
     
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  6. Paul M. kjeldergaard.Pittsburgh Computations Centers - 1968 - In T. Dixon & Deryck Horton, Verbal Behavior and General Behavior Theory. Prentice-Hall.
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  7.  22
    Hector freytes, Antonio ledda, Giuseppe sergioli and.Roberto Giuntini & Probabilistic Logics in Quantum Computation - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler, New Challenges to Philosophy of Science. Springer Verlag. pp. 49.
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  8. Section 2. Model Theory.Va Vardanyan, On Provability Resembling Computability, Proving Aa Voronkov & Constructive Logic - 1989 - In Jens Erik Fenstad, Ivan Timofeevich Frolov & Risto Hilpinen, Logic, methodology, and philosophy of science VIII: proceedings of the Eighth International Congress of Logic, Methodology, and Philosophy of Science, Moscow, 1987. New York, NY, U.S.A.: Sole distributors for the U.S.A. and Canada, Elsevier Science.
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  9.  11
    Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning about Knowledge: March 19-22, 1988, Monterey, California.Joseph Y. Halpern, International Business Machines Corporation, American Association of Artificial Intelligence, United States & Association for Computing Machinery - 1986
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  10.  12
    A logical formalisation of false belief tasks.R. Velázquez-Quesada A. Institute for Logic Anthia Solaki Fernando, Computation Language, Netherlandsb Netherlands Organization for Applied Scientific Research, Media Studies Netherlandsc Information Science & Norway - forthcoming - Journal of Applied Non-Classical Logics:1-51.
    Theory of Mind (ToM), the cognitive capacity to attribute internal mental states to oneself and others, is a crucial component of social skills. Its formal study has become important, witness recent research on reasoning and information update by intelligent agents, and some proposals for its formal modelling have put forward settings based on Epistemic Logic (EL). Still, due to intrinsic idealisations, it is questionable whether EL can be used to model the high-order cognition of ‘real’ agents. This manuscript proposes a (...)
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  11.  4
    Adventures in Gödel Incompleteness.Harvey M. Friedman Mathematics, Philosophy, Computer Science Emeritus, Columbus, Oh & Usa - forthcoming - History and Philosophy of Logic:1-14.
    Begin discussing various forms of G1 put into the form: If a first order theory satisfies one or more adequacy conditions then it has one or more wildness properties. We continue with the new ‘no interpretation’ forms of G2, which are fundamentally model theoretic formulations. We also give corresponding model theoretic characterizations of the consistency statement Con(T) for finitely axiomatized T. We present the known proof of the 1-Con form by G2 by transparent diagonalization and discuss attempts to do so (...)
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  12. Computability and recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
    We consider the informal concept of "computability" or "effective calculability" and two of the formalisms commonly used to define it, "(Turing) computability" and "(general) recursiveness". We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory, and its connection to other related areas. (...)
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  13.  5
    Intentional identity revisited.Ahti Pietarinen A. School of Cognitive, Computing Sciences, Falmer, Brighton, BN1 9QH & Uk - 2010 - Nordic Journal of Philosophical Logic 6 (2):147-188.
    The problem of intentional identity, as originally offered by Peter Geach, says that there can be an anaphoric link between an indefinite term and a pronoun across a sentential boundary and across propositional attitude contexts, where the actual existence of an individual for the indefinite term is not presupposed. In this paper, a semantic resolution to this elusive puzzle is suggested, based on a new quantified intensional logic and game-theoretic semantics (GTS) of imperfect information. This constellation leads to an expressive (...)
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  14. An Introduction to Lorenzen's ‘Algebraic and Logistic Investigations on Free Lattices’ (1951).Thierry Coquand Henri Lombardi Stefan Neuwirth A. Computer Science - forthcoming - History and Philosophy of Logic:1-21.
    Lorenzen's article has immediately been recognised as a landmark in the history of infinitary proof theory. We propose a translation and this introduction in order to publicise its approach and method of proof, without any ordinal assignment. It is best known for providing a constructive proof of consistency for ramified type theory without axiom of reducibility by showing that it is a part of a trivially consistent ‘inductive calculus’ that describes our knowledge of arithmetic without detour; the proof resorts only (...)
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  15. Computability, Notation, and de re Knowledge of Numbers.Stewart Shapiro, Eric Snyder & Richard Samuels - 2022 - Philosophies 1 (7):20.
    Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between (...)
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  16. Computability theory and differential geometry.Robert I. Soare - 2004 - Bulletin of Symbolic Logic 10 (4):457-486.
    Let M be a smooth, compact manifold of dimension n ≥ 5 and sectional curvature | K | ≤ 1. Let Met (M) = Riem(M)/Diff(M) be the space of Riemannian metrics on M modulo isometries. Nabutovsky and Weinberger studied the connected components of sublevel sets (and local minima) for certain functions on Met (M) such as the diameter. They showed that for every Turing machine T e , e ∈ ω, there is a sequence (uniformly effective in e) of homology (...)
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  17.  56
    Computability Theory: An Introduction to Recursion Theory.Herbert B. Enderton - 2010 - Academic Press.
    Machine generated contents note: 1. The Computability Concept;2. General Recursive Functions;3. Programs and Machines;4. Recursive Enumerability;5. Connections to Logic;6. Degrees of Unsolvability;7. Polynomial-Time Computability;Appendix: Mathspeak;Appendix: Countability;Appendix: Decadic Notation;.
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  18.  35
    Computability and the game of cops and robbers on graphs.Rachel D. Stahl - 2022 - Archive for Mathematical Logic 61 (3):373-397.
    Several results about the game of cops and robbers on infinite graphs are analyzed from the perspective of computability theory. Computable robber-win graphs are constructed with the property that no computable robber strategy is a winning strategy, and such that for an arbitrary computable ordinal \, any winning strategy has complexity at least \}\). Symmetrically, computable cop-win graphs are constructed with the property that no computable cop strategy is a winning strategy. Locally finite infinite trees and graphs are explored. (...)
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  19. (1 other version)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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  20.  68
    Computing and Experiments: A Methodological View on the Debate on the Scientific Nature of Computing.Viola Schiaffonati & Mario Verdicchio - 2014 - Philosophy and Technology 27 (3):359-376.
    The question about the scientific nature of computing has been widely debated with no universal consensus reached about its disciplinary status. Positions vary from acknowledging computing as the science of computers to defining it as a synthetic engineering discipline. In this paper, we aim at discussing the nature of computing from a methodological perspective. We consider, in particular, the nature and role of experiments in this field, whether they can be considered close to the traditional experimental scientific method or, instead, (...)
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  21. Computability and physical theories.Robert Geroch & James B. Hartle - 1986 - Foundations of Physics 16 (6):533-550.
    The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature—one based on the issue of whether or not the physically measurable numbers predicted by the theory are computable in the mathematical sense. Applying this formulation to one approach to a quantum theory of gravity, there are found indications that there may exist no such (...)
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  22. Computational Modeling in Cognitive Science: A Manifesto for Change.Caspar Addyman & Robert M. French - 2012 - Topics in Cognitive Science 4 (3):332-341.
    Computational modeling has long been one of the traditional pillars of cognitive science. Unfortunately, the computer models of cognition being developed today have not kept up with the enormous changes that have taken place in computer technology and, especially, in human-computer interfaces. For all intents and purposes, modeling is still done today as it was 25, or even 35, years ago. Everyone still programs in his or her own favorite programming language, source code is rarely made available, accessibility of models (...)
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  23.  32
    Quantum Computation and Quantum Information.Michael A. Nielsen & Isaac L. Chuang - 2000 - Cambridge University Press.
    First-ever comprehensive introduction to the major new subject of quantum computing and quantum information.
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  24. Computability Results Used in Differential Geometry.Barbara F. Csima & Robert I. Soare - 2006 - Journal of Symbolic Logic 71 (4):1394 - 1410.
    Topologists Nabutovsky and Weinberger discovered how to embed computably enumerable (c.e.) sets into the geometry of Riemannian metrics modulo diffeomorphisms. They used the complexity of the settling times of the c.e. sets to exhibit a much greater complexity of the depth and density of local minima for the diameter function than previously imagined. Their results depended on the existence of certain sequences of c.e. sets, constructed at their request by Csima and Soare, whose settling times had the necessary dominating properties. (...)
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  25. Computability, Complexity and Languages.Martin Davies, Ron Segal & Elaine Weyuker - 1994 - Academic Press.
     
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  26. Computability theory and literary competence.Mark Silcox & Jon Cogburn - 2006 - British Journal of Aesthetics 46 (4):369-386.
    criticism defend the idea that an individual reader's understanding of a text can be a factor in determining the meaning of what is written in that text, and hence must play a part in determining the very identity conditions of works of literary art. We examine some accounts that have been given of the type of readerly ‘competence’ that a reader must have in order for her responses to a text to play this sort of constitutive role. We argue that (...)
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  27.  96
    Computability, consciousness, and algorithms.Robert Wilensky - 1990 - Behavioral and Brain Sciences 13 (4):690-691.
  28. (1 other version)Computability and λ-definability.A. M. Turing - 1937 - Journal of Symbolic Logic 2 (4):153-163.
  29.  78
    Computability: Computable Functions, Logic, and the Foundations of Mathematics.Richard L. Epstein - 2004
    This book is dedicated to a classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient (...)
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  30.  18
    On notions of computability-theoretic reduction between Π21 principles.Denis R. Hirschfeldt & Carl G. Jockusch - 2016 - Journal of Mathematical Logic 16 (1):1650002.
    Several notions of computability-theoretic reducibility between [Formula: see text] principles have been studied. This paper contributes to the program of analyzing the behavior of versions of Ramsey’s Theorem and related principles under these notions. Among other results, we show that for each [Formula: see text], there is an instance of RT[Formula: see text] all of whose solutions have PA degree over [Formula: see text] and use this to show that König’s Lemma lies strictly between RT[Formula: see text] and RT[Formula: (...)
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  31.  60
    Physical Computation: A Mechanistic Account.Gualtiero Piccinini - 2015 - Oxford, GB: Oxford University Press UK.
    Gualtiero Piccinini articulates and defends a mechanistic account of concrete, or physical, computation. A physical system is a computing system just in case it is a mechanism one of whose functions is to manipulate vehicles based solely on differences between different portions of the vehicles according to a rule defined over the vehicles. Physical Computation discusses previous accounts of computation and argues that the mechanistic account is better. Many kinds of computation are explicated, such as digital vs. analog, serial vs. (...)
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  32. Computability Theory.Barry Cooper - 2010 - Journal of the Indian Council of Philosophical Research 27 (1).
     
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  33.  74
    The veblen functions for computability theorists.Alberto Marcone & Antonio Montalbán - 2011 - Journal of Symbolic Logic 76 (2):575 - 602.
    We study the computability-theoretic complexity and proof-theoretic strength of the following statements: (1) "If X is a well-ordering, then so is ε X ", and (2) "If X is a well-ordering, then so is φ(α, X)", where α is a fixed computable ordinal and φ represents the two-placed Veblen function. For the former statement, we show that ω iterations of the Turing jump are necessary in the proof and that the statement is equivalent to ${\mathrm{A}\mathrm{C}\mathrm{A}}_{0}^{+}$ over RCA₀. To prove (...)
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  34.  60
    Computability of Recursive Functions.J. C. Shepherdson & H. E. Sturgis - 1967 - Journal of Symbolic Logic 32 (1):122-123.
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  35.  42
    Computability. Computable Functions, Logic, and the Foundations of Mathematics.Richard L. Epstein & Walter A. Carnielli - 2002 - Bulletin of Symbolic Logic 8 (1):101-104.
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  36.  46
    Towards applied theories based on computability logic.Giorgi Japaridze - 2010 - Journal of Symbolic Logic 75 (2):565-601.
    Computability logic (CL) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally been. Formulas in it represent computational problems, "truth" means existence of an algorithmic solution, and proofs encode such solutions. Within the line of research devoted to finding axiomatizations for ever more expressive fragments of CL, the present paper introduces a new deductive system CL12 and proves its soundness and (...)
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  37.  99
    Computational complexity of some Ramsey quantifiers in finite models.Marcin Mostowski & Jakub Szymanik - 2007 - Bulletin of Symbolic Logic 13:281--282.
    The problem of computational complexity of semantics for some natural language constructions – considered in [M. Mostowski, D. Wojtyniak 2004] – motivates an interest in complexity of Ramsey quantifiers in finite models. In general a sentence with a Ramsey quantifier R of the following form Rx, yH(x, y) is interpreted as ∃A(A is big relatively to the universe ∧A2 ⊆ H). In the paper cited the problem of the complexity of the Hintikka sentence is reduced to the problem of computational (...)
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  38.  32
    (1 other version)Computability, Proof, and Open-Texture.Stewart Shapiro - 2006 - In Adam Olszewski, Jan Wolenski & Robert Janusz, Church's Thesis After 70 Years. Ontos Verlag. pp. 420-455.
  39. Counterpossibles in Science: The Case of Relative Computability.Matthias Jenny - 2018 - Noûs 52 (3):530-560.
    I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, (...)
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  40. A natural axiomatization of computability and proof of Church’s thesis.Nachum Dershowitz & Yuri Gurevich - 2008 - Bulletin of Symbolic Logic 14 (3):299-350.
    Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of (...)
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  41. Quantum computation in brain microtubules.Stuart R. Hameroff - 2002 - Physical Review E 65 (6):1869--1896.
    Proposals for quantum computation rely on superposed states implementing multiple computations simultaneously, in parallel, according to quantum linear superposition (e.g., Benioff, 1982; Feynman, 1986; Deutsch, 1985, Deutsch and Josza, 1992). In principle, quantum computation is capable of specific applications beyond the reach of classical computing (e.g., Shor, 1994). A number of technological systems aimed at realizing these proposals have been suggested and are being evaluated as possible substrates for quantum computers (e.g. trapped ions, electron spins, quantum dots, nuclear spins, etc., (...)
     
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  42. Extending Ourselves: Computational Science, Empiricism, and Scientific Method.Paul Humphreys - 2004 - New York, US: Oxford University Press.
    Computational methods such as computer simulations, Monte Carlo methods, and agent-based modeling have become the dominant techniques in many areas of science. Extending Ourselves contains the first systematic philosophical account of these new methods, and how they require a different approach to scientific method. Paul Humphreys draws a parallel between the ways in which such computational methods have enhanced our abilities to mathematically model the world, and the more familiar ways in which scientific instruments have expanded our access to the (...)
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  43. Randomness and computability: Open questions.Joseph S. Miller & André Nies - 2006 - Bulletin of Symbolic Logic 12 (3):390-410.
    It is time for a new paper about open questions in the currently very active area of randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 [1]. All the question in it have been solved, except for one: is KL-randomness different from Martin-Löf randomness? This question is discussed in Section 6.Not all the questions are necessarily hard—some simply have not been tried seriously. When we think a question is a major one, and therefore likely to be (...)
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  44.  52
    Introduction to computability logic.Giorgi Japaridze - 2003 - Annals of Pure and Applied Logic 123 (1-3):1-99.
    This work is an attempt to lay foundations for a theory of interactive computation and bring logic and theory of computing closer together. It semantically introduces a logic of computability and sets a program for studying various aspects of that logic. The intuitive notion of computational problems is formalized as a certain new, procedural-rule-free sort of games between the machine and the environment, and computability is understood as existence of an interactive Turing machine that wins the game against (...)
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  45.  27
    Degrees of randomized computability.Rupert Hölzl & Christopher P. Porter - 2022 - Bulletin of Symbolic Logic 28 (1):27-70.
    In this survey we discuss work of Levin and V’yugin on collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. More precisely, Levin and V’yugin introduced an ordering on collections of sequences that are closed under Turing equivalence. Roughly speaking, given two such collections $\mathcal {A}$ and $\mathcal {B}$, $\mathcal {A}$ is below $\mathcal {B}$ in this ordering if $\mathcal {A}\setminus \mathcal {B}$ is negligible. The degree structure associated (...)
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  46. A computational foundation for the study of cognition.David Chalmers - 2011 - Journal of Cognitive Science 12 (4):323-357.
    Computation is central to the foundations of modern cognitive science, but its role is controversial. Questions about computation abound: What is it for a physical system to implement a computation? Is computation sufficient for thought? What is the role of computation in a theory of cognition? What is the relation between different sorts of computational theory, such as connectionism and symbolic computation? In this paper I develop a systematic framework that addresses all of these questions. Justifying the role of computation (...)
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  47. Computation, Information, Cognition: The Nexus and the Liminal.f.Gordana Dodig Crnkovic & Susan Stuart (eds.) - 2007 - Cambridge Scholars Press.
    Written by world-leading experts, this book draws together a number of important strands in contemporary approaches to the philosophical and scientific questions that emerge when dealing with the issues of computing, information, cognition and the conceptual issues that arise at their intersections. It discovers and develops the connections at the borders and in the interstices of disciplines and debates. This volume presents a range of essays that deal with the currently vigorous concerns of the philosophy of information, ontology creation and (...)
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  48. Godel on computability.W. Sieg - 2006 - Philosophia Mathematica 14 (2):189-207.
    The identification of an informal concept of ‘effective calculability’ with a rigorous mathematical notion like ‘recursiveness’ or ‘Turing computability’ is still viewed as problematic, and I think rightly so. I analyze three different and conflicting perspectives Gödel articulated in the three decades from 1934 to 1964. The significant shifts in Gödel's position underline the difficulties of the methodological issues surrounding the Church-Turing Thesis.
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  49. Computability: Gödel, Turing, Church, and beyond.B. J. Copeland, C. Posy & O. Shagrir (eds.) - 2013 - MIT Press.
  50.  33
    The dependence of computability on numerical notations.Ethan Brauer - 2021 - Synthese 198 (11):10485-10511.
    Which function is computed by a Turing machine will depend on how the symbols it manipulates are interpreted. Further, by invoking bizarre systems of notation it is easy to define Turing machines that compute textbook examples of uncomputable functions, such as the solution to the decision problem for first-order logic. Thus, the distinction between computable and uncomputable functions depends on the system of notation used. This raises the question: which systems of notation are the relevant ones for determining whether a (...)
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