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Computability: Turing, Gödel, Church, and Beyond

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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

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Detail Information

Series Title

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Call Number

004 COM

Publisher

Cambridge, Massachusetts : The MIT Press., 2013

Collation

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Language

English

ISBN/ISSN

9780262312677

Classification

004

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

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Subject(s)

Computer

Specific Detail Info

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Statement of Responsibility

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

Other Information

Cataloger

Khusnun

Source

https://direct.mit.edu/books/edited-volume/3387/ComputabilityTuring-Godel-Church-and-Beyond

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Digital Object Identifier (DOI)

https://doi.org/10.7551/mitpress/8009.001.0001

Journal Volume

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Journal Issue

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