华东师范大学学报(哲学社会科学版) ›› 2002, Vol. 34 ›› Issue (4): 30-36.doi: 10.16382/j.cnki.1000-5579.2002.04.007

• 哲学 政治 • 上一篇    下一篇

论数学哲学中的直觉主义思想

冯棉   

  • 收稿日期:2002-02-27 出版日期:2002-07-01 发布日期:2025-12-11

On the Intuitionistic Thought in Mathematical Philosophy

Mian FENG   

  • Received:2002-02-27 Online:2002-07-01 Published:2025-12-11

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摘要：

数学哲学中的直觉主义学派高度重视直觉和个人的创造性思维在科学实践中的作用, 这具有积极的意义; 它对排中律和间接证明方法有效性的质疑, 揭示了经典逻辑只具有相对的真理性; 它所倡导的构造性和能行性的研究方法, 促进了人工智能和计算机科学的发展。但是, 对直觉功能的过分夸大则并不足取。

关键词: 直觉主义, 排中律, 悖论, 逻辑主义, 形式主义, 间接证明, 构造性

Abstract:

This paper discusses the intuitionistic theory and thought in mathematical philosophy. Intuitionism highly values intuition and personal creative thinking in scientific practice. This is a positive viewpoint. Intuitionism questions the validity of law of excluded middle and the vaildity of indirect proof, and it indicates that classical logic is only a relative truth. Intuitionism stands for constructive and effective methods. These methods promote development of artificial intelligence and computer science. However, an excessive exaggeration of intuitive function is wrong.

Key words: intuitionism, law of excluded middle, paradox, logicism, formalism, indirect proof, constructive