Computability: Turing, Gödel, Church, and Beyond (MIT Press) by B. Jack Copeland,Carl J. Posy,Oron Shagrir

By B. Jack Copeland,Carl J. Posy,Oron Shagrir

In the Thirties a sequence of seminal works released by way of Alan Turing, Kurt Gödel, Alonzo Church, and others verified the theoretical foundation for computability. This paintings, advancing detailed characterizations of potent, algorithmic computability, used to be the end result of extensive investigations into the rules of arithmetic. within the many years given that, the idea of computability has moved to the heart of discussions in philosophy, desktop technology, and cognitive technological know-how. during this quantity, distinct computing device scientists, mathematicians, logicians, and philosophers examine the conceptual foundations of computability in mild of our smooth realizing. a few chapters concentrate on the pioneering paintings via Turing, Gödel, and Church, together with the Church-Turing thesis and Gödel's reaction to Church's and Turing's proposals. different chapters hide more moderen technical advancements, together with computability over the reals, Gödel's effect on mathematical good judgment and on recursion concept and the impression of labor by way of Turing and Emil publish on our theoretical knowing of on-line and interactive computing; and others relate computability and complexity to matters within the philosophy of brain, the philosophy of technology, and the philosophy of arithmetic. Contributors:Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani

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