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  1. Systems of Logic Based on Ordinals.Alan Mathison Turing - 1939 - London: Printed by C.F. Hodgson & Son.
  • The Rediscovery of the Mind.John R. Searle - 1992 - MIT Press.
    The title of The Rediscovery of the Mind suggests the question "When was the mind lost?" Since most people may not be aware that it ever was lost, we must also then ask "Who lost it?" It was lost, of course, only by philosophers, by certain philosophers. This passed unnoticed by society at large. The "rediscovery" is also likely to pass unnoticed. But has the mind been rediscovered by the same philosophers who "lost" it? Probably not. John Searle is an (...)
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  • Tasks and Supertasks.James Thomson - 1954 - Analysis 15 (1):1--13.
  • Minds, Brains, and Programs.John Searle - 1980 - Behavioral and Brain Sciences 3 (3):417-57.
    What psychological and philosophical significance should we attach to recent efforts at computer simulations of human cognitive capacities? In answering this question, I find it useful to distinguish what I will call "strong" AI from "weak" or "cautious" AI. According to weak AI, the principal value of the computer in the study of the mind is that it gives us a very powerful tool. For example, it enables us to formulate and test hypotheses in a more rigorous and precise fashion. (...)
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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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  • Tasks, Super-Tasks, and the Modern Eleatics.Paul Benacerraf - 1962 - Journal of Philosophy 59 (24):765-784.
  • Philosophie der Mathematik Und Naturwissenschaft.Hermann Weyl - 1927 - De Gruyter Oldenbourg.
    Hermann Weyls "Philosophie der Mathematik und Naturwissenschaft" erschien erstmals 1928 als Beitrag zu dem von A. Bäumler und M. Schröter herausgegebenen "Handbuch der Philosophie". Die amerikanische Ausgabe, auf der die deutsche Übersetzung von Gottlob Kirschmer beruht, erschien 1949 bei Princeton University Press. Das nunmehr bereits in der 8. Auflage vorliegende Werk ist längst auch in Deutschland zum Standardwerk geworden.
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  • Creativity, the Turing Test, and the (Better) Lovelace Test.Selmer Bringsjord, P. Bello & David A. Ferrucci - 2001 - Minds and Machines 11 (1):3-27.
    The Turing Test is claimed by many to be a way to test for the presence, in computers, of such ``deep'' phenomena as thought and consciousness. Unfortunately, attempts to build computational systems able to pass TT have devolved into shallow symbol manipulation designed to, by hook or by crook, trick. The human creators of such systems know all too well that they have merely tried to fool those people who interact with their systems into believing that these systems really have (...)
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  • Super Turing-Machines.B. Jack Copeland - 1998 - Complexity 4 (1):30-32.
  • A Logical Calculus of the Ideas Immanent in Nervous Activity.Warren S. McCulloch & Walter Pitts - 1943 - The Bulletin of Mathematical Biophysics 5 (4):115-133.
    Because of the “all-or-none” character of nervous activity, neural events and the relations among them can be treated by means of propositional logic. It is found that the behavior of every net can be described in these terms, with the addition of more complicated logical means for nets containing circles; and that for any logical expression satisfying certain conditions, one can find a net behaving in the fashion it describes. It is shown that many particular choices among possible neurophysiological assumptions (...)
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  • Effective Procedures and Computable Functions.Carole E. Cleland - 1995 - 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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  • Is the Church-Turing Thesis True?Carol E. Cleland - 1993 - 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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  • Mirror Notation: Symbol Manipulation Without Inscription Manipulation.Roy A. Sorensen - 1999 - Journal of Philosophical Logic 28 (2):141-164.
    Stereotypically, computation involves intrinsic changes to the medium of representation: writing new symbols, erasing old symbols, turning gears, flipping switches, sliding abacus beads. Perspectival computation leaves the original inscriptions untouched. The problem solver obtains the output by merely alters his orientation toward the input. There is no rewriting or copying of the input inscriptions; the output inscriptions are numerically identical to the input inscriptions. This suggests a loophole through some of the computational limits apparently imposed by physics. There can be (...)
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  • Beyond the Universal Turing Machine.B. Jack Copeland & Richard Sylvan - 1999 - Australasian Journal of Philosophy 77 (1):46-66.
  • On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
  • The Paradox of Temporal Process.R. M. Blake - 1926 - Journal of Philosophy 23 (24):645-654.
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  • Our Knowledge of the external World as a field of scientific method in Philosophy.Bertrand Russell - 1914 - Revue Philosophique de la France Et de l'Etranger 81:306-308.
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  • Mr.~Black on Temporal Paradoxes.Richard Taylor - 1951 - Analysis 12 (2):38--44.
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  • Achilles and the Tortoise.J. M. Hinton & C. B. Martin - 1953 - Analysis 14 (3):56 - 68.
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  • Limiting Recursion.E. Mark Gold - 1965 - Journal of Symbolic Logic 30 (1):28-48.
    A class of problems is called decidable if there is an algorithm which will give the answer to any problem of the class after a finite length of time. The purpose of this paper is to discuss the classes of problems that can be solved by infinitely long decision procedures in the following sense: An algorithm is given which, for any problem of the class, generates an infinitely long sequence of guesses. The problem will be said to be solved in (...)
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  • The Sum of an Infinite Series.J. Watling - 1952 - Analysis 13 (2):39--46.
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  • Trial and Error Predicates and the Solution to a Problem of Mostowski.Hilary Putnam - 1965 - Journal of Symbolic Logic 30 (1):49-57.
  • Achilles and the Tortoise.Max Black - 1950 - Analysis 11 (5):91.
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  • A Note on the Entscheidungsproblem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (1):40-41.
  • Achilles and the Tortoise.Max Black - 1950 - In Wesley C. Salmon (ed.), Analysis. Bobbs-Merrill. pp. 67-81.
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  • Finitism in Mathematics (I).Alice Ambrose - 1935 - Mind 44 (174):186-203.
  • Finitism in Mathematics (II.).Alice Ambrose - 1935 - Mind 44 (175):317-340.
  • A Logical Calculus of the Ideas Immanent in Nervous Activity.Warren S. Mcculloch & Walter Pitts - 1943 - Journal of Symbolic Logic 9 (2):49-50.
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  • Non-Turing Computers and Non-Turing Computability.Mark Hogarth - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:126-138.
    A true Turing machine requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime, but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar to our world. But curiously enough-and this is (...)
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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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  • Non-Turing Computers and Non-Turing Computability.Mark Hogarth - 1994 - Psa 1994:126--138.
    A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...)
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  • Does General Relativity Allow an Observer to View an Eternity in a Finite Time?Mark Hogarth - 1992 - Foundations Of Physics Letters 5:173--181.
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