牛津通识读本：戈德尔定理 Godels Theorem: A Very Short Introduction

基本信息

Series:Very Short Introductions

Format:Paperback / softback 160 pages, 2

Publisher:Oxford University Press

Imprint:Oxford University Press

ISBN:9780192847850

Published:24 Nov 2022

Weight:136g

Dimensions:112 x 173 x 10 (mm)

Pub. Country:United Kingdom

Country of Origin:GB

Tariff Codes:49019900

页面参数仅供参考，具体以实物为准

书籍简介

库尔特-戈德尔（Kurt Goedel）在近一个世纪前发表了定理，表明任何公理化都不能确定有关算术的全部真理，而且只能确定真理。该定理挑战了关于数学性质的普遍预设，因此具有相当大的数学意义，同时也提出了各种深刻的哲学问题。戈德尔定理自此确立了自己作为一个里程碑式的智力成就，对今天的数学思想产生了深刻的影响。

戈德尔和他的定理已经吸引了一些崇拜者，尽管他的定理经常被误解。这本《极简介绍》将该定理置于其知识和历史背景中，并解释了关键概念以及对其实际内容的常见误解。A.W. 摩尔对该定理进行了清晰的陈述，提出了两个证明，每个证明都有一些关于其内容的独特之处。摩尔还讨论了该定理的重要的哲学含义。

特别是，摩尔谈到了一个问题，即该定理是否表明人类的思维具有超越任何可能的计算机的数学能力

关于该系列： 《极简介绍》系列包含了几乎所有学科领域的数百种书。这些口袋大小的书籍是快速掌握新学科的方式。我们的专家作者将事实、分析、观点、新想法和热情结合起来，使有趣和具有挑战性的主题具有很强的可读性。

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 profoundimpact 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 theoremshows the human mind to have mathematical powers beyond those of any possible computerABOUT 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.

作者简介

A.W. Moore是牛津大学的哲学教授和牛津大学圣休斯学院的哲学补习研究员。他曾在牛津大学学院和剑桥大学国王学院担任教学和研究职务。他与Lucy O'Brien共同担任《心灵》杂志的编辑。2016年，他在英国广播公司撰写并主持了《无限的历史》系列节目。

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.