Gödel's Theorem
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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 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
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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.