Computability Turing, Gödel, Church, and

Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments.

In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, 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 technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics.

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

B. Jack Copeland is Professor of Philosophy at the University of Canterbury, New Zealand, Director of the Turing Archive for the History of Computing, and Honorary Research Professor of Philosophy at the University of Queensland, Australia.

Carl J. Posy is Professor of Philosophy and Member of the Centers for the Study of Rationality and for Language, Logic, and Cognition at the Hebrew University of Jerusalem.

Oron Shagrir is Professor of Philosophy and Former Chair of the Cognitive Science Department at the Hebrew University of Jerusalem. He is currently the vice rector of the Hebrew University.

B. Jack Copeland is Professor of Philosophy at the University of Canterbury, New Zealand, Director of the Turing Archive for the History of Computing, and Honorary Research Professor of Philosophy at the University of Queensland, Australia.

Carl J. Posy is Professor of Philosophy and Member of the Centers for the Study of Rationality and for Language, Logic, and Cognition at the Hebrew University of Jerusalem.

Oron Shagrir is Professor of Philosophy and Former Chair of the Cognitive Science Department at the Hebrew University of Jerusalem. He is currently the vice rector of the Hebrew University.

B. Jack Copeland is Professor of Philosophy at the University of Canterbury, New Zealand, Director of the Turing Archive for the History of Computing, and Honorary Research Professor of Philosophy at the University of Queensland, Australia.

Oron Shagrir is Professor of Philosophy and Former Chair of the Cognitive Science Department at the Hebrew University of Jerusalem. He is currently the vice rector of the Hebrew University.

Carl J. Posy is Professor of Philosophy and Member of the Centers for the Study of Rationality and for Language, Logic, and Cognition at the Hebrew University of Jerusalem.

Hilary Putnam was Walter Beverly Pearson Professor of Mathematical Logic at Harvard University.

Umesh Vazirani is Roger A. Strauch Professor in the Electrical Engineering and Computer Sciences Department at the University of California, Berkeley.

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Computability Turing, Gödel, Church, and Beyond

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