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Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of a effectively computable function defined in natural numbers with the notion of a recursive function. Despite of the many efforts of prominent scientists, Church's Thesis has never been falsified. There exists a vast literature concerning the thesis. The aim of the book is to provide one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming.
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Darren Abramson
Church’s Thesis and Philosophy of Mind . . . . . . 9
Andreas Blass, Yuri Gurevich
Algorithms: A Quest for Absolute Definitions . . 24
Douglas S. Bridges
Church’s Thesis and Bishop’s Constructivism . . . 58
Selmer Bringsjord, Konstantine Arkoudas
On the Provability, Veracity, and AI-Relevance
of the Church–Turing Thesis . . . . . . . . . . . . . 66
Carol E. Cleland
The Church–Turing Thesis. A Last Vestige of
a Failed Mathematical Program . . . . . . . . . . . 119
B. Jack Copeland
Turing’s Thesis . . . . . . . . . . . . . . . . . . . . . . . 147
Hartmut Fitz
Church’s Thesis and Physical Computation . . . . . 175
Janet Folina
Church’s Thesis and the Variety of
Mathematical Justifications . . . . . . . . . . . . . . 220
Andrew Hodges
Did Church and Turing Have a Thesis about
Machines? . . . . . . . . . . . . . . . . . . . . . . . . . . 242
Leon Horsten
Formalizing Church’s Thesis . . . . . . . . . . . . . . 253
Stanis³aw Krajewski
Remarks on Church’s Thesis and G¨odel’s
Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
6 Contents
Charles McCarty
Thesis and Variations . . . . . . . . . . . . . . . . . . . 281
Elliott Mendelson
On the Impossibility of Proving the
“Hard-Half” of Church’s Thesis . . . . . . . . . . . 304
Roman Murawski, Jan Wolenski
The Status of Church’s Thesis . . . . . . . . . . . . . 310
Jerzy Mycka
Analog Computation and Church’s Thesis . . . . . 331
Piergiorgio Odifreddi
Kreisel’s Church . . . . . . . . . . . . . . . . . . . . . . 353
Adam Olszewski
Church’s Thesis as Formulated by Church —
An Interpretation . . . . . . . . . . . . . . . . . . . . . 383
Oron Shagrir
G¨odel on Turing on Computability . . . . . . . . . . 393
Stewart Shapiro
Computability, Proof, and Open-Texture . . . . . 420
Wilfried Sieg
Step by Recursive Step: Church’s Analysis of
Effective Calculability . . . . . . . . . . . . . . . . . 456
Karl Svozil
Physics and Metaphysics Look at Computation . . 491
David Turner
Church’s Thesis and Functional Programming . . 518
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545
Mathematical Logic Volume 1
eBook for Adobe Reader, ISBN 3-938793-03-1
551 pages, 22,50 Euro. Single licence for Windows, Mac, Unix and Mobile! Special conditions for libraries.
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