[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content
Springer Nature Link
Log in

The Church-Turing thesis and effective mundane procedures

  • Critical Exchange
  • Published:
Minds and Machines Aims and scope Submit manuscript

Abstract

We critically discuss Cleland's analysis of effective procedures as ‘mundane effective procedures’. She argues that Turing machines cannot carry out mundane procedures, since Turing machines are abstract entities and therefore cannot generate the causal processes that are generated by mundane procedures. We argue that if Turing machines cannot enter the physical world, then it is hard to see how Cleland's “mundane procedures” can enter the world of numbers. Hence her arguments against versions of the Church-Turing thesis for number theoretic functions miss the mark.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Cleland, C. (1993), ‘Is the Church-Turing Thesis True?’Minds and Machines 3, pp. 283–312.

    Google Scholar 

  • Earman, J. (1986),A Primer on Determinism, Dordrecht, Reidel.

    Google Scholar 

  • Friedman, H. (1971), ‘Algorithmic Procedures, Generalized Turning Algorithms, and Elementary Recursion Theory’, in R. Gandy and C. Yates, eds.,Logic Colloquium '69, Amsterdam: North-Holland.

    Google Scholar 

  • Gandy, R. (1980), ‘Church's Thesis and Principles for Mechanics’, in J. Barwise, H.J. Keisler, and K. Kunen, eds.,The Kleene Symposium, Amsterdam: North-Holland, pp. 123–148.

    Google Scholar 

  • Grzegorczyk, A. (1957), ‘On the Definitions of Computable Real Continuous Functions’,Fundamenta Mathematica 44, pp. 61–71.

    Google Scholar 

  • Penrose, R. (1989),The Emperor's New Mind. Concerning Computers, Minds, and the Laws of Physics, London: Vintage.

    Google Scholar 

  • Turing, A. (1936–1937), ‘On Computable Numbers with an Application to the Entscheidungsproblem’,Proceedings of the London Mathematical Society. Ser. 2, 42, pp. 230–265.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Logic and Philosophy of Science, Department of Philosophy, University of Leuven, Kardinaal Mercierplein 2, B-3000, Leuven, Belgium

    Leon Horsten & Herman Roelants

Authors
  1. Leon Horsten
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Herman Roelants
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The first author is a postdoctoral researcher of the Belgian National Fund for Scientific Research. The financial support of this organization is gratefully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Horsten, L., Roelants, H. The Church-Turing thesis and effective mundane procedures. Mind Mach 5, 1–8 (1995). https://doi.org/10.1007/BF00974186

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00974186

Key words

Search

Navigation