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# Godel's Theorem: A Very Short Introduction

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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

Συγγραφέας: Moore A.W.
Εκδότης: OXFORD UNIVERSITY PRESS
Σελίδες: 152
ISBN: 9780192847850
Εξώφυλλο: Μαλακό Εξώφυλλο
Αριθμός Έκδοσης: 1
Έτος έκδοσης: 2022

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

A.W. Moore is Professor of Philosophy and Lecturer in Philosophy at the University of Oxford, UK, and Tutorial Fellow of St Hugh’s College, Oxford. 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.