The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Martin Davis (ed.)
Dover Publication (1965)
"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 Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Suitable for graduate and undergraduate courses. 1965 ed.
|Keywords||Gödel's theorem Unsolvability (Mathematical logic Recursive functions Turing machines Computable functions|
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|Call number||QA9.65.U53 2004|
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I. Alonzo Church, I Wish to Express Here My Gratitude to Various Members of the Department of Mathematics of Cornell University Who Obliged Me by Critically Reading Various Drafts of This Paper. Bibliography.
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Gualtiero Piccinini (2009). Computationalism in the Philosophy of Mind. Philosophy Compass 4 (3):515-532.
Stewart Shapiro (1980). On the Notion of Effectiveness. History and Philosophy of Logic 1 (1-2):209-230.
Stewart Shapiro (1983). Remarks on the Development of Computability. History and Philosophy of Logic 4 (1-2):203-220.
Alessandra Carbone & Franco Montagna (1990). Much Shorter Proofs: A Bimodal Investigation. Mathematical Logic Quarterly 36 (1):47-66.
Gilbert Harman (1983). Internally Represented Grammars. Behavioral and Brain Sciences 6 (3):408.
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