David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
In B. J. Copeland, C. Posy & O. Shagrir (eds.), Computability: Turing, Gödel, Church, and Beyond. MIT Press (2013)
Traditionally, many writers, following Kleene (1952), thought of the Church-Turing thesis as unprovable by its nature but having various strong arguments in its favor, including Turing’s analysis of human computation. More recently, the beauty, power, and obvious fundamental importance of this analysis, what Turing (1936) calls “argument I,” has led some writers to give an almost exclusive emphasis on this argument as the unique justification for the Church-Turing thesis. In this chapter I advocate an alternative justification, essentially presupposed by Turing himself in what he calls “argument II.” The idea is that computation is a special form of mathematical deduction. Assuming the steps of the deduction can be stated in a first order language, the Church-Turing thesis follows as a special case of Gödel’s completeness theorem (first order algorithm theorem). I propose this idea as an alternative foundation for the Church-Turing thesis, both for human and machine computation. Clearly the relevant assumptions are justified for computations presently known. Other issues, such as the significance of Gödel’s 1931 Theorem IX for the Entscheidungsproblem, are discussed along the way.
|Keywords||Church-Turing Thesis Gödel’s completeness theorem Entscheidungsproblem|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
David Israel (2002). Reflections on Gödel's and Gandy's Reflections on Turing's Thesis. Minds and Machines 12 (2):181-201.
Michael Rescorla (2007). Church's Thesis and the Conceptual Analysis of Computability. Notre Dame Journal of Formal Logic 48 (2):253-280.
Eli Dresner (2008). Turing-, Human- and Physical Computability: An Unasked Question. [REVIEW] Minds and Machines 18 (3):349-355.
Carol E. Cleland (1993). Is the Church-Turing Thesis True? Minds and Machines 3 (3):283-312.
Itamar Pitowsky (2002). Quantum Speed-Up of Computations. Proceedings of the Philosophy of Science Association 2002 (3):S168-S177.
John T. Kearns (1997). Thinking Machines: Some Fundamental Confusions. [REVIEW] Minds and Machines 7 (2):269-87.
Nachum Dershowitz & Yuri Gurevich (2008). A Natural Axiomatization of Computability and Proof of Church's Thesis. Bulletin of Symbolic Logic 14 (3):299-350.
Tim Button (2009). SAD Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
B. Jack Copeland (2008). The Church-Turing Thesis. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.
Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.
Added to index2010-06-18
Total downloads83 ( #18,047 of 1,167,998 )
Recent downloads (6 months)30 ( #6,048 of 1,167,998 )
How can I increase my downloads?