Church's Thesis After 70 Years

Adam Olszewski, Jan Wolenski, Robert Janusz, Adam Olszewski, Jan Wolenski, Robert Janusz

• Publisher: De Gruyter
• Year: 2013
• Print ISBN: 9783110324945
• eBook ISBN: 9783110325461
• Edition: 1
• Topic: Philosophy
• Subtopic: Language in Philosophy

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.

Table of contents

• Preface
• Darren Abramson¤Church’s Thesis and Philosophy of Mind
• Andreas Blass, Yuri Gurevich¤Algorithms: A Quest for Absolute Definitions
• Douglas S. Bridges¤Church’s Thesis and Bishop’s Constructivism
• Selmer Bringsjord, Konstantine Arkoudas¤On the Provability, Veracity, and AI-Relevance of the Church–Turing Thesis
• Carol E. Cleland¤The Church–Turing Thesis. A Last Vestige of a Failed Mathematical Program
• B. Jack Copeland¤Turing’s Thesis
• Hartmut Fitz¤Church’s Thesis and Physical Computation
• Janet Folina¤Church’s Thesis and the Variety of Mathematical Justifications
• Andrew Hodges¤Did Church and Turing Have a Thesis about Machines?
• Leon Horsten¤Formalizing Church’s Thesis
• Stanislaw Krajewski¤Remarks on Church’s Thesis and Gödel’s Theorem
• Charles McCarty¤Thesis and Variations
• Elliott Mendelson¤On the Impossibility of Proving the “Hard-Half” of Church’s Thesis
• Roman Murawski, Jan Wolenski¤The Status of Church’s Thesis
• Jerzy Mycka¤Analog Computation and Church’s Thesis
• Piergiorgio Odifreddi¤Kreisel’s Church
• Adam Olszewski¤Church’s Thesis as Formulated by Church — An Interpretation
• Oron Shagrir¤Gö del on Turing on Computability
• Stewart Shapiro¤Computability, Proof, and Open-Texture
• Wilfried Sieg¤Step by Recursive Step: Church’s Analysis of Effective Calculability
• Karl Svozil¤Physics and Metaphysics Look at Computation
• David Turner¤Church’s Thesis and Functional Programming
• Index