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  1. On Formally Undecidable Propositions of Principia Mathematica and Related Systems.Kurt Gödel - 1931 - New York, NY, USA: Basic Books.
    First English translation of revolutionary paper that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
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  • Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes.Kurt Gödel - 1958 - Dialectica 12 (3):280.
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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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  • The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions.Martin Davis (ed.) - 1965 - Hewlett, NY, USA: Dover Publication.
    "A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by (...)
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  • (1 other version)A note on the entscheidungsproblem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (1):40-41.
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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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  • (1 other version)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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  • Some Definitional Suggestions for Automata Theory.Dana Scott - 1975 - Journal of Symbolic Logic 40 (4):615-616.
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  • Remarks before the Princeton Bicentennial Conference on Problems in Mathematics.Kurt Gödel - 1990 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Kurt Gödel: Collected Works Vol. Ii. Oxford University Press. pp. 150--153.
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  • Mechanical procedures and mathematical experience.Wilfried Sieg - 1994 - In Alexander George (ed.), Mathematics and mind. New York: Oxford University Press. pp. 71--117.
    Wilfred Sieg. Mechanical Procedures and Mathematical Experience.
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  • On the Foundations of Logic and Arithmetic.David Hilbert - 1905 - The Monist 15 (3):338-352.
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  • The Foundations of Mathematics.David Hilbert - 1927 - In ¸ Itevanheijenoort1967. Harvard University Press.
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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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  • Some Remarks on the Undecidability Results.Kurt Gödel - 1990 - In Solomon Feferman, John Dawson & Stephen Kleene (eds.), Kurt Gödel: Collected Works Vol. Ii. Oxford University Press. pp. 305--306.
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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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  • (1 other version)From Frege to Gödel.Jean van Heijenoort - 1968 - Philosophy of Science 35 (1):72-72.
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  • Recipes, algorithms, and programs.Carol E. Cleland - 2001 - Minds and Machines 11 (2):219-237.
    In the technical literature of computer science, the concept of an effective procedure is closely associated with the notion of an instruction that precisely specifies an action. Turing machine instructions are held up as providing paragons of instructions that "precisely describe" or "well define" the actions they prescribe. Numerical algorithms and computer programs are judged effective just insofar as they are thought to be translatable into Turing machine programs. Nontechnical procedures (e.g., recipes, methods) are summarily dismissed as ineffective on the (...)
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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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