Bulletin of Symbolic Logic 3 (2):154-180 (1997)

Authors
Wilfried Sieg
Carnegie Mellon University
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)
Categories (categorize this paper)
DOI 10.2307/421012
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,903
Through your library

References found in this work BETA

On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
A Note on the Entscheidungsproblem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (1):40-41.
Introduction to Mathematical Logic.S. C. Kleene - 1956 - Journal of Symbolic Logic 23 (3):362-362.

View all 22 references / Add more references

Citations of this work BETA

The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
Alan Turing and the Mathematical Objection.Gualtiero Piccinini - 2003 - Minds and Machines 13 (1):23-48.
The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
Gödel’s Philosophical Challenge.Wilfried Sieg - 2020 - Studia Semiotyczne 34 (1):57-80.
Proving Church's Thesis.Robert Black - 2000 - Philosophia Mathematica 8 (3):244--58.

View all 20 citations / Add more citations

Similar books and articles

Church's Thesis: Prelude to a Proof.Janet Folina - 1998 - Philosophia Mathematica 6 (3):302-323.
Witness and Service to the World. Discovering Protestant Church Renewal in Europe.Henning Theißen - 2011 - Neue Zeitschrift für Systematicsche Theologie Und Religionsphilosophie 53 (2):225-239.
Computability and Recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
SAD Computers and Two Versions of the Church–Turing Thesis.Tim Button - 2009 - British Journal for the Philosophy of Science 60 (4):765-792.
Church's Thesis and the Conceptual Analysis of Computability.Michael Rescorla - 2007 - Notre Dame Journal of Formal Logic 48 (2):253-280.
Is the Church-Turing Thesis True?Carol E. Cleland - 1993 - Minds and Machines 3 (3):283-312.
The Church-Turing Thesis.B. Jack Copeland - 2008 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.
How Not To Use the Church-Turing Thesis Against Platonism.R. Urbaniak - 2011 - Philosophia Mathematica 19 (1):74-89.

Analytics

Added to PP index
2009-01-28

Total views
49 ( #208,996 of 2,426,535 )

Recent downloads (6 months)
1 ( #541,589 of 2,426,535 )

How can I increase my downloads?

Downloads

My notes