クルト・ゲーデル(1906-1978年）は約100年前、どのような数学体系も不完全であるとする有名な定理を発表し、数学の本質に関する一般的な前提を覆し、大きな関心を集めました。本書は今日では数学の考え方に大きな影響を与える画期的な知的業績として確立された定理を、知的・歴史的文脈に位置づけ、重要な概念を説明し、実際に述べられている内容に対する一般的な誤解を解きほぐします。この定理は哲学的にもさまざまな深い問題を提起しましたが、この定理が果たして機械に対する人間の優越性を示すものであるかどうかという問題も取り上げ、論じます。
 

• 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

    
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. Adrian 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