Gödel's Theorem - A Very Short Introduction

When Kurt Gödel published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, it had a profound impact on mathematical ideas and philosophical thought. Adrian Moore places the theorem in its intellectual and historical context, explaining the key concepts and misunderstandings.

Very Short Introductions: Brilliant, Sharp, Inspiring

Kurt Gödel first published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing but the truth concerning arithmetic, nearly a century ago. The theorem challenged prevalent presuppositions about the nature of mathematics and was consequently of considerable mathematical interest, while also raising various deep philosophical questions. Gödel's Theorem has since established itself as a landmark intellectual achievement, having a profound impact on today's mathematical ideas. Gödel and his theorem have attracted something of a cult following, though his theorem is often misunderstood.

This Very Short Introduction places the theorem in its intellectual and historical context, and explains the key concepts as well as common misunderstandings of what it actually states. A. W. Moore provides a clear statement of the theorem, presenting two proofs, each of which has something d istinctive to teach about its content. Moore also discusses the most important philosophical implications of the theorem. In particular, Moore addresses the famous question of whether the theorem shows the human mind to have mathematical powers beyond those of any possible computer

ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Inhaltsverzeichnis:

1: What is Gödels theorem?
2: The appeal and demands of axiomatization
3: Historical background
4: The key concepts involved in Gödel's theorem
5: The diagonal proof of Gödel's theorem
6: A second proof of Gödel's theorem, and a proof of Gödel's second theorem
7: Hilbert's programme, the human mind, and computers
8: Making sense in and of mathematics

Rezension:

This is a concisely written book, and the ideas are subtle, so I suspect that many laymen will find some of this material a bit demanding. On the whole, though, it seems reasonably accessible....A bibliography (short, but annotated) is also a useful feature of this book. All in all, this seems like another good entry in the interesting Very Short Introduction series. Mark Hunacek, Mathematical Gazette