In 1931 Kurt G÷del 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. G÷del received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciencesperhaps 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 G÷del'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 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
'A little masterpiece of exegesis.'
'An excellent nontechnical account of the substance of GA¶del's celebrated paper.'
Ernest Nagel was John Dewey Professor of Philosophy at Columbia University. James R. Newman was the author of What is Science. Douglas R. Hofstadter is College of Arts and Sciences Professor of computer science and cognitive science at Indiana University and author of the Pulitzer-prize winning G÷del, Escher, Bach: An Eternal Golden Braid.