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Gödel's Theorem: A Very Short Introduction

A. W. Moore

24 November 2022

ISBN: 9780192847850

152 pages
Paperback
174x111mm

Very Short Introductions

Price: £8.99

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.

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Description

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.

  • Places Gödel's famous theorem in its intellectual and historical context, while explaining the key concepts
  • Gives two proofs of the theorem
  • Considers common misunderstandings associated with the theorem
  • Discusses the theorem's most important philosophical implications
  • Part of the Very Short Introductions series - over ten million copies sold worldwide

About the Author(s)

A. W. Moore, Tutorial Fellow at St Hugh's College, and Professor of Philosophy at the University of Oxford

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.

Table of Contents

    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