Olszewski / Wolenski / Janusz Church's Thesis After 70 Years

1. Auflage 2013
ISBN: 978-3-11-032546-1
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Deutsch, Englisch, Band 1, 551 Seiten

Reihe: Ontos Mathematical Logic

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.

Autoren/Hrsg.

Olszewski, Adam

Wolenski, Jan

Janusz, Robert

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Geisteswissenschaften Philosophie Geschichte der Westlichen Philosophie Westliche Philosophie: 20./21. Jahrhundert

Inhaltsverzeichnis

1;Preface;7
2;Darren Abramson¤Church’s Thesis and Philosophy of Mind;9
3;Andreas Blass, Yuri Gurevich¤Algorithms: A Quest for Absolute Definitions;24
4;Douglas S. Bridges¤Church’s Thesis and Bishop’s Constructivism;58
5;Selmer Bringsjord, Konstantine Arkoudas¤On the Provability, Veracity, and AI-Relevance of the Church–Turing Thesis;66
6;Carol E. Cleland¤The Church–Turing Thesis. A Last Vestige of a Failed Mathematical Program;119
7;B. Jack Copeland¤Turing’s Thesis;147
8;Hartmut Fitz¤Church’s Thesis and Physical Computation;175
9;Janet Folina¤Church’s Thesis and the Variety of Mathematical Justifications;220
10;Andrew Hodges¤Did Church and Turing Have a Thesis about Machines?;242
11;Leon Horsten¤Formalizing Church’s Thesis;253
12;Stanis aw Krajewski¤Remarks on Church’s Thesis and Gödel’s

Theorem;269
13;Charles McCarty¤Thesis and Variations;281
14;Elliott Mendelson¤On the Impossibility of Proving the “Hard-Half” of Church’s Thesis;304
15;Roman Murawski, Jan Wolenski¤The Status of Church’s Thesis;310
16;Jerzy Mycka¤Analog Computation and Church’s Thesis;331
17;Piergiorgio Odifreddi¤Kreisel’s Church;353
18;Adam Olszewski¤Church’s Thesis as Formulated by Church — An Interpretation;383
19;Oron Shagrir¤Gö
del on Turing on Computability;393
20;Stewart Shapiro¤Computability, Proof, and Open-Texture;420
21;Wilfried Sieg¤Step by Recursive Step: Church’s Analysis of Effective Calculability;456
22;Karl Svozil¤Physics and Metaphysics Look at Computation;491
23;David Turner¤Church’s Thesis and Functional Programming;518
24;Index;545