Godel's Proof

by James R. Newman, Ernest Nagel

Overview

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."
 

Product Details

ISBN-13:	9788828374282
Publisher:	Digital Deen Publications
Publication date:	08/13/2018
Sold by:	StreetLib SRL
Format:	eBook
File size:	306 KB

About the Author

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 Gödel, Escher, Bach: An Eternal Golden Braid.

Table of 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

What People are Saying About This

From the Publisher

"A little masterpiece of exegesis."

-Nature,

"An excellent non-technical account of the substance of Gödel's celebrated paper."

-Bulletin of the American Mathematical Society

Editorial Reviews

"A little masterpiece of exegesis."

-Nature

"An excellent nontechnical account of the substance of Gödel's celebrated paper."

-American Mathematical Society

From the Publisher