Computability Computability Computability Turing, Gödel, Church, and Beyond Turing, Gödel, Church, and Beyond Edited by B

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Computability Computability Computability Turing, Gödel, Church, and Beyond Turing, Gödel, Church, and Beyond Edited by B

computer science/philosophy Computability Computability Computability turing, Gödel, Church, and beyond turing, Gödel, Church, and beyond edited by b. Jack Copeland, Carl J. posy, and oron Shagrir edited by b. Jack Copeland, Carl J. posy, and oron Shagrir Copeland, b. Jack Copeland is professor of philosophy at the ContributorS in the 1930s a series of seminal works published by university of Canterbury, new Zealand, and Director Scott aaronson, Dorit aharonov, b. Jack Copeland, martin Davis, Solomon Feferman, Saul alan turing, Kurt Gödel, alonzo Church, and others of the turing archive for the History of Computing. Kripke, Carl J. posy, Hilary putnam, oron Shagrir, Stewart Shapiro, Wilfried Sieg, robert established the theoretical basis for computability. p Carl J. posy is professor of philosophy and member irving Soare, umesh V. Vazirani editors and Shagrir, osy, this work, advancing precise characterizations of ef- of the Centers for the Study of rationality and for lan- fective, algorithmic computability, was the culmina- guage, logic, and Cognition at the Hebrew university tion of intensive investigations into the foundations of Jerusalem. oron Shagrir is professor of philoso- of mathematics. in the decades since, the theory of phy and Former Chair of the Cognitive Science De- computability has moved to the center of discussions partment at the Hebrew university of Jerusalem. He in philosophy, computer science, and cognitive sci- is currently the vice rector of the Hebrew university. ence. in this volume, distinguished computer scien- tists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by turing, Gödel, and Church, including the Church- turing thesis and Gödel’s response to Church’s and turing’s proposals. other chapters cover more recent the MIT press technical developments, including computability over Cover images massachusetts institute of technology the reals, Gödel’s influence on mathematical logic alan turing (left): King’s College. Kurt Gödel (middle): From Cambridge, massachusetts 02142 and on recursion theory and the impact of work by http://mitpress.mit.edu the Kurt Gödel papers, the Shelby White and leon levy turing and Emil post on our theoretical understand- archives Center, institute for advanced Study, princeton, ing of online and interactive computing; and others nJ, uSa, on deposit at princeton university. alonzo Church 978-0-262-01899-9 relate computability and complexity to issues in the (right): alonzo Church papers, manuscripts Division, 9 0 0 0 0 Department of rare books and Special Collections, prince- philosophy of mind, the philosophy of science, and ton university library. all images used with permission. 9 780262 018999 the philosophy of mathematics..

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