Description
Book SynopsisIn 1931 Kurt Godel 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. The authors provide an explanation of the main ideas and broad implications of Godel's discovery.
Trade ReviewA little masterpiece of exegesis. * Nature *
An excellent nontechnical account of the substance of Gödel's celebrated paper. -- American Mathematical Society
Table of ContentsContents 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
