Bulletin of Symbolic Logic 3 (2):154-180 (1997)
|Abstract||Alonzo Church's mathematical work on computability and undecidability is well-known indeed, and we seem to have an excellent understanding of the context in which it arose. The approach Church took to the underlying conceptual issues, by contrast, is less well understood. Why, for example, was "Church's Thesis" put forward publicly only in April 1935, when it had been formulated already in February/March 1934? Why did Church choose to formulate it then in terms of Gödel's general recursiveness, not his own λ -definability as he had done in 1934? A number of letters were exchanged between Church and Paul Bernays during the period from December 1934 to August 1937; they throw light on critical developments in Princeton during that period and reveal novel aspects of Church's distinctive contribution to the analysis of the informal notion of effective calculability. In particular, they allow me to give informed, though still tentative answers to the questions I raised; the character of my answers is reflected by an alternative title for this paper, Why Church needed Gödel's recursiveness for his Thesis. In Section 5, I contrast Church's analysis with that of Alan Turing and explore, in the very last section, an analogy with Dedekind's investigation of continuity|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Janet Folina (1998). Church's Thesis: Prelude to a Proof. Philosophia Mathematica 6 (3):302-323.
R. Urbaniak (2011). How Not To Use the Church-Turing Thesis Against Platonism. Philosophia Mathematica 19 (1):74-89.
B. Jack Copeland (2008). The Church-Turing Thesis. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.
Carol E. Cleland (1993). Is the Church-Turing Thesis True? Minds and Machines 3 (3):283-312.
Saul A. Kripke (forthcoming). Another Approach: The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Completeness Theorem. In B. J. Copeland, C. Posy & O. Shagrir (eds.), Computability: Gödel, Turing, Church, and beyond. MIT Press.
Michael Rescorla (2007). Church's Thesis and the Conceptual Analysis of Computability. Notre Dame Journal of Formal Logic 48 (2):253-280.
Tim Button (2009). Sad Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
Robert I. Soare (1996). Computability and Recursion. Bulletin of Symbolic Logic 2 (3):284-321.
Henning Theißen (2011). Witness and Service to the World. Discovering Protestant Church Renewal in Europe. Neue Zeitschrift für Systematische Theologie Und Religionsphilosophie 53 (2).
Added to index2009-01-28
Total downloads9 ( #115,524 of 556,909 )
Recent downloads (6 months)1 ( #64,931 of 556,909 )
How can I increase my downloads?