Alan Turing's Systems of Logic

Erscheinungsjahr 2012
ISBN: 978-0-691-15574-6
Verlag: Princeton University Press

Buch, Englisch, 160 Seiten, Format (B × H): 181 mm x 261 mm, Gewicht: 509 g

Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912-1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene--were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. Though less well known than his other work, Turing's 1938 Princeton PhD thesis, "Systems of Logic Based on Ordinals," which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. This book presents a facsimile of the original typescript of the thesis along with essays by Andrew Appel and Solomon Feferman that explain its still-unfolding significance. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal--a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.

Autoren/Hrsg.

Appel, Andrew W.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik EDV | Informatik EDV & Informatik Allgemein EDV & Informatik: Geschichte

Inhaltsverzeichnis

List of Plates ix

Foreword by Douglas Hofstadter xi

Preface to the 2012 Centenary edition xv

PART ONE: THE LOGICAL

1 Esprit de Corps to 13 February 1930 1

2 The Spirit of Truth to 14 April 1936 46

3 New Men to 3 September 1939 111

4 The Relay Race to 10 November 1942 160

BRIDGE PASSAGE to 1 April 1943 242

PART TWO: THE PHYSICAL

5 Running Up to 2 September 1945 259

6 Mercury Delayed to 2 October 1948 314

7 The Greenwood Tree to 7 February 1952 390

8 On the Beach to 7 June 1954 456

Postscript 529

Author's Note 530

Notes 541

Acknowledgements 569

Index 570

Über Autor(innen)

Appel, Andrew W.
Andrew W. Appel is the Eugene Higgins Professor and Chairman of the Department of Computer Science at Princeton University.