Step by recursive step: Church's analysis of effective calculability

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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DOI 10.2307/421012
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References found in this work BETA
A Note on the Entscheidungsproblem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (1):40-41.
Finite Combinatory Processes-Formulation.Emil L. Post - 1936 - Journal of Symbolic Logic 1 (3):103-105.
Paper Machines.Daniele Mundici & Wilfried Seig - 1995 - Philosophia Mathematica 3 (1):5-30.
Ein Verfahren der Mathematischen Logik.Jozéf Pepis - 1938 - Journal of Symbolic Logic 3 (2):61-76.

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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.
Sign and the Lambda-Term.Kumiko Tanaka-Ishii & Yuichiro Ishii - 2008 - Semiotica 2008 (169):197-220.
Diagonalisation and Church's Thesis: Kleene's Homework.Enrique Alonso & Maria Manzano - 2005 - History and Philosophy of Logic 26 (2):93-113.
1999 Spring Meeting of the Association for Symbolic Logic.Charles Parsons - 1999 - Bulletin of Symbolic Logic 5 (4):479-484.

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