Very Short Introductions: Brilliant, Sharp, Inspiring
Kurt Goedel 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. Goedel's Theorem has since established itself as a landmark intellectual achievement, having a profound impact on today's mathematical ideas. Goedel 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 distinctive 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.
Rezensionen / Stimmen
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 *
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Höhe: 168 mm
Breite: 112 mm
Dicke: 15 mm
Gewicht
ISBN-13
978-0-19-284785-0 (9780192847850)
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Schweitzer Klassifikation
A.W. Moore is Professor of Philosophy at the University of Oxford and Tutorial Fellow in Philosophy at St Hugh's College, Oxford. He has held teaching and research positions at University College, Oxford, and King's College, Cambridge. He is joint editor, with Lucy O'Brien, of the journal Mind. In 2016 he wrote and presented the series A History of the Infinite on BBC Radio 4.
Autor*in
Tutorial Fellow at St Hugh's College, and Professor of Philosophy at the University of Oxford
1: What is Goedels theorem?
2: The appeal and demands of axiomatization
3: Historical background
4: The key concepts involved in Goedel's theorem
5: The diagonal proof of Goedel's theorem
6: A second proof of Goedel's theorem, and a proof of Goedel's second theorem
7: Hilbert's programme, the human mind, and computers
8: Making sense in and of mathematics
