Computability: Turing, Gödel, Church, and Beyond

Computability: Turing, Gödel, Church, and Beyond


In the Nineteen Thirties a sequence of seminal works released through Alan Turing, Kurt Gödel, Alonzo Church, and others verified the theoretical foundation for computability. This paintings, advancing special characterizations of potent, algorithmic computability, was once the end result of extensive investigations into the foundations of arithmetic. within the many years given that, the speculation of computability has moved to the heart of discussions in philosophy, computing device technological know-how, and cognitive technological know-how. during this quantity, exceptional desktop scientists, mathematicians, logicians, and philosophers contemplate the conceptual foundations of computability in mild of our glossy knowing. 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 disguise newer technical advancements, together with computability over the reals, Gödel's impression on mathematical common sense and on recursion concept and the influence of labor through 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

Show sample text content

Download sample