David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 14 (2):189-207 (2006)
The identification of an informal concept of ‘effective calculability’ with a rigorous mathematical notion like ‘recursiveness’ or ‘Turing computability’ is still viewed as problematic, and I think rightly so. I analyze three different and conflicting perspectives Gödel articulated in the three decades from 1934 to 1964. The significant shifts in Gödel's position underline the difficulties of the methodological issues surrounding the Church-Turing Thesis.
|Keywords||No keywords specified (fix it)|
|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
Gualtiero Piccinini (2011). The Physical Church–Turing Thesis: Modest or Bold? British Journal for the Philosophy of Science 62 (4):733 - 769.
G. Piccinini (2011). The Physical Church-Turing Thesis: Modest or Bold? British Journal for the Philosophy of Science 62 (4):733-769.
P. Cassou-Nogues (2009). Gödel's Introduction to Logic in 1939. History and Philosophy of Logic 30 (1):69-90.
Rossella Lupacchini (2014). Hilbert's Axiomatics as ‘Symbolic Form’? Perspectives on Science 22 (1):1-34.
Similar books and articles
Wilfried Sieg (1997). Step by Recursive Step: Church's Analysis of Effective Calculability. Bulletin of Symbolic Logic 3 (2):154-180.
Saul A. Kripke (2013). The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Completeness Theorem. In B. J. Copeland, C. Posy & O. Shagrir (eds.), Computability: Turing, Gödel, Church, and Beyond. MIT Press
Stewart Shapiro (1983). Remarks on the Development of Computability. History and Philosophy of Logic 4 (1-2):203-220.
Robert I. Soare (1996). Computability and Recursion. Bulletin of Symbolic Logic 2 (3):284-321.
George Boolos, John Burgess, Richard P. & C. Jeffrey (2007). Computability and Logic. Cambridge University Press.
B. J. Copeland, C. Posy & O. Shagrir (eds.) (forthcoming). Computability: Gödel, Turing, Church, and Beyond. MIT Press.
Oron Shagrir (2002). Effective Computation by Humans and Machines. Minds and Machines 12 (2):221-240.
Peter Koepke (2005). Turing Computations on Ordinals. Bulletin of Symbolic Logic 11 (3):377-397.
Nachum Dershowitz & Yuri Gurevich (2008). A Natural Axiomatization of Computability and Proof of Church's Thesis. Bulletin of Symbolic Logic 14 (3):299-350.
Wilfried Sieg (2005). Only Two Letters: The Correspondence Between Herbrand and Gödel. Bulletin of Symbolic Logic 11 (2):172-184.
J. J. C. Smart (1961). Godel's Theorem, Church's Theorem, and Mechanism. Synthese 13 (June):105-10.
Robert F. Hadley (2008). Consistency, Turing Computability and Gödel's First Incompleteness Theorem. Minds and Machines 18 (1):1-15.
Neil Thompson (2012). Arithmetic Proof and Open Sentences. Philosophy Study 2 (1):43-50.
Added to index2010-08-24
Total downloads26 ( #183,016 of 1,941,049 )
Recent downloads (6 months)4 ( #225,914 of 1,941,049 )
How can I increase my downloads?