『ゲ－デルは何を証明したか』（原書）刊行５０周年記念版<br>Gödel's Proof

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『ゲ－デルは何を証明したか』（原書）刊行５０周年記念版
Gödel's Proof

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  • 製本 Hardcover:ハードカバー版／ページ数 160 p.
  • 言語 ENG
  • 商品コード 9780814758168
  • DDC分類 511.3

基本説明

邦訳：1999年・白揚社。
New in paperback. Hardcover was published in 2002. Marking the fiftieth anniversary of the original publication of Gödel's Proof, New York University Press is proud to publish this special anniversary edition of one of its bestselling books, with a new introduction by Douglas R. Hofstadter. First published in 1958 and in print continuously since then in 10 languages, this seminal work offers every educated person the chance to understand a previously difficult and inaccessible subject.

Full Description

An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic

In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."

However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.

New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

Contents

Contents Foreword to the New Edition by Douglas R. Hofstadter ix Acknowledgments xxiii i Introduction 1 ii The Problem of Consistency 7 iii Absolute Proofs of Consistency 25 iv The Systematic Codification of Formal Logic 37 v An Example of a Successful Absolute Proof of Consistency 45 vi The Idea of Mapping and Its Use in Mathematics 57 vii Godel's Proofs 68 a Godel numbering 68 b The arithmetization of meta-mathematics 80 c The heart of Godel's argument 92 viii Concluding Reflections 109 Appendix: Notes 114 Brief Bibliography 125 Index 127