David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 48 (2):253-280 (2007)
Church's thesis asserts that a number-theoretic function is intuitively computable if and only if it is recursive. A related thesis asserts that Turing's work yields a conceptual analysis of the intuitive notion of numerical computability. I endorse Church's thesis, but I argue against the related thesis. I argue that purported conceptual analyses based upon Turing's work involve a subtle but persistent circularity. Turing machines manipulate syntactic entities. To specify which number-theoretic function a Turing machine computes, we must correlate these syntactic entities with numbers. I argue that, in providing this correlation, we must demand that the correlation itself be computable. Otherwise, the Turing machine will compute uncomputable functions. But if we presuppose the intuitive notion of a computable relation between syntactic entities and numbers, then our analysis of computability is circular.
|Keywords||Church's thesis computation Turing machines|
|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
B. Jack Copeland & Diane Proudfoot (2010). Deviant Encodings and Turing's Analysis of Computability. Studies in History and Philosophy of Science Part A 41 (3):247-252.
Michael Rescorla (2012). Copeland and Proudfoot on Computability. Studies in History and Philosophy of Science Part A 43 (1):199-202.
Similar books and articles
Nachum Dershowitz & Yuri Gurevich (2008). A Natural Axiomatization of Computability and Proof of Church's Thesis. Bulletin of Symbolic Logic 14 (3):299-350.
B. Jack Copeland (2008). The Church-Turing Thesis. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.
Oron Shagrir & Itamar Pitowsky (2003). Physical Hypercomputation and the Church–Turing Thesis. Minds and Machines 13 (1):87-101.
Robert I. Soare (1996). Computability and Recursion. Bulletin of Symbolic Logic 2 (3):284-321.
John T. Kearns (1997). Thinking Machines: Some Fundamental Confusions. [REVIEW] Minds and Machines 7 (2):269-87.
Tim Button (2009). SAD Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
Leon Horsten (1995). The Church-Turing Thesis and Effective Mundane Procedures. Minds and Machines 5 (1):1-8.
Eli Dresner (2008). Turing-, Human- and Physical Computability: An Unasked Question. [REVIEW] Minds and Machines 18 (3):349-355.
Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.
Carol E. Cleland (1993). Is the Church-Turing Thesis True? Minds and Machines 3 (3):283-312.
Added to index2009-03-18
Total downloads84 ( #14,739 of 1,098,987 )
Recent downloads (6 months)14 ( #11,832 of 1,098,987 )
How can I increase my downloads?