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The Church-Turing Thesis: Consensus and Opposition

  • Conference paper
Logical Approaches to Computational Barriers (CiE 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3988))

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Abstract

Many years ago, I wrote [7]:

It is truly remarkable (Gödel ...speaks of a kind of miracle) that it has proved possible to give a precise mathematical characterization of the class of processes that can be carried out by purely machanical means. It is in fact the possibility of such a characterization that underlies the ubiquitous applicability of digital computers. In addition it has made it possible to prove the algorithmic unsolvability of important problems, has provided a key tool in mathematical logic, has made available an array of fundamental models in theoretical computer science, and has been the basis of a rich new branch of mathemtics.

A few years later I wrote [8]:

The subject ...is Alan Turing’s discovery of the universal (or all-purpose) digital computer as a mathematical abstraction. ...We will try to show how this very abstract work helped to lead Turing and John von Neumann to the modern concept of the electronic computer.

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Author information

Authors and Affiliations

  1. Mathematics Dept., University of California, Berkeley, CA, 94720, USA

    Martin Davis

Authors
  1. Martin Davis
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Swansea University, Singleton Park, SA2 8PP, Swansea, United Kingdom

    Arnold Beckmann

  2. Department of Computer Science, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK

    Ulrich Berger

  3. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, Amsterdam, TV, The Netherlands

    Benedikt Löwe

  4. School of Physical Sciences, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, United Kingdom

    John V. Tucker

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© 2006 Springer-Verlag Berlin Heidelberg

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Davis, M. (2006). The Church-Turing Thesis: Consensus and Opposition. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_13

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  • DOI: https://doi.org/10.1007/11780342_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35466-6

  • Online ISBN: 978-3-540-35468-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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