David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Bulletin of Symbolic Logic 3 (2):154-180 (1997)
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
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References found in this work BETA
Emil L. Post (1936). Finite Combinatory Processes-Formulation. Journal of Symbolic Logic 1 (3):103-105.
Alonzo Church (1936). A Note on the Entscheidungsproblem. Journal of Symbolic Logic 1 (1):40-41.
Daniele Mundici & Wilfried Seig (1995). Paper Machines. Philosophia Mathematica 3 (1):5-30.
Elliott Mendelson (1990). Second Thoughts About Church's Thesis and Mathematical Proofs. Journal of Philosophy 87 (5):225.
Jozéf Pepis (1938). Ein Verfahren der Mathematischen Logik. Journal of Symbolic Logic 3 (2):61-76.
Citations of this work BETA
Eli Dresner (2008). Turing-, Human- and Physical Computability: An Unasked Question. [REVIEW] Minds and Machines 18 (3):349-355.
Kumiko Tanaka-Ishii & Yuichiro Ishii (2008). Sign and the Lambda-Term. Semiotica 2008 (169):197-220.
Enrique Alonso & Maria Manzano (2005). Diagonalisation and Church's Thesis: Kleene's Homework. History and Philosophy of Logic 26 (2):93-113.
Charles Parsons (1999). 1999 Spring Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 5 (4):479-484.
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