摘要/Abstract

本文基于以下哲学观点开展讨论：反对唯心主义，接收辩证唯物主义，在这样的大前提下讨论“有限无限问题”。本文基于黑格尔的辩证无限观，对实无限思想进行了全面的批判。自黑格尔辩证无限思想科学地解释了微积分中的极限概念之后，由无穷小量矛盾引起的第二次数学危机得到了彻底的解决，然而数学界并没有吸取历史上的经验教训，一直坚持唯心主义的实无限思想与方法论，这种思想最终给数学带来了第三次危机。在本文最后，基于辩证唯物主义无限观，作者对概括原则、最大序数悖论进行了分析，指出概括原则本质是一种实无限思想，只有将概括原则限定在潜

This paper discusses the problem of finity and infinity based on the philosophical perspectives of opposing idealism and receiving dialectical materialism. Based on Hegel's dialectical infinity view, this paper makes a comprehensive criticism of the thought of actual infinity. After Hegel's dialectical infinite thought scientifically explained the limit concept in calculus, the Second Mathematical Crisis caused by the contradiction of infinitesimal quantity was solved thoroughly. However, the mathematics world has not learned the experience and lessons in history, has always adhered to the idealist thought and methodology of actual infinity, this thought finally brought the third crisis to mathematics. At the end of this paper, based on the infinite view of dialectical materialism, the author analyzes the Principle of Comprehension and the Paradox of Maximum Ordinal Number, and points out that the essence of the Principle of Comprehension is a kind of actual infinity thought. Only by limiting the Principle of Comprehension to a potential infinity can we solve the Third Mathematical Crisis completely.