Church's Thesis After 70 Years / / ed. by Adam Olszewski, Jan Wolenski, Robert Janusz.

• Superior document: Title is part of eBook package: De Gruyter DGBA Backlist Complete English Language 2000-2014 PART1
• MitwirkendeR: Abramson, Darren,; Arkoudas, Konstantine,; Blass, Andreas,; Bridges, Douglas S.,; Bringsjord, Selmer,; Cleland, Carol E.,; Copeland, B. Jack,; Fitz, Hartmut,; Folina, Janet,; Gurevich, Yuri,; Hodges, Andrew,; Horsten, Leon,; Krajewski, Stanisław,; McCarty, Charles,; Mendelson, Elliott,; Murawski, Roman,; Mycka, Jerzy,; Odifreddi, Piergiorgio,; Olszewski, Adam,; Shagrir, Oron,; Shapiro, Stewart,; Sieg, Wilfried,; Svozil, Karl,; Turner, David,; Wolenski, Jan,
• HerausgeberIn: Janusz, Robert,; Olszewski, Adam,; Wolenski, Jan,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2013]; ©2006
• Year of Publication: 2013
• Language: English
• Series: Ontos Mathematical Logic , 1
• Physical Description: 1 online resource (551 p.)

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

Frontmatter -- Contents -- Preface -- Church’s Thesis and Philosophy of Mind -- Algorithms: A Quest for Absolute Definitions -- Church’s Thesis and Bishop’s Constructivism -- On the Provability, Veracity, and AI-Relevance of the Church–Turing Thesis -- The Church–Turing Thesis. A Last Vestige of a Failed Mathematical Program -- Turing’s Thesis -- Church’s Thesis and Physical Computation -- Church’s Thesis and the Variety of Mathematical Justifications -- Did Church and Turing Have a Thesis about Machines? -- Formalizing Church’s Thesis -- Remarks on Church’s Thesis and Gödel’s Theorem -- Thesis and Variations -- On the Impossibility of Proving the “Hard-Half” of Church’s Thesis -- The Status of Church’s Thesis -- Analog Computation and Church’s Thesis -- Kreisel’s Church -- Church’s Thesis as Formulated by Church — An Interpretation -- Gödel on Turing on Computability -- Computability, Proof, and Open-Texture -- Step by Recursive Step: Church’s Analysis of Effective Calculability -- Physics and Metaphysics Look at Computation -- Church’s Thesis and Functional Programming -- Index