Dialectical Infinity and the Third Mathematical Crisis —On the Fundamental Error of Actual Infinity

Zhang Hong

doi:10.22158/jrph.v3n2p73

Abstract

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 Maximum Ordinal Paradox, 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.

Highlights

This paper discusses the problem of finity and infinity based on the philosophical perspectives of opposing idealism and receiving dialectical materialism
As for Hegel’s dialectical view of infinity, we conclude as follows: The mutual stipulation of finite things makes up infinity, infinity is the unity of bad infinity and real infinity, and it is a free self Being; Real infinity cannot be separated from bad infinity, Being-for-self is inseparable from Being-in-itself
It is in the negative of the quantity at the same time did not find the quality of things from the negative, but the quality of things with a negative, or even to the opposite of finite being, become an abstraction, artificially cut off contact between the infinite and finite, let oneself fall into nihilism, let oneself become an other that has no inner relation with the infinite process, that is to say, actual infinity and infinite process are entirely different things

Summary

Introduction

This paper discusses the problem of finity and infinity based on the philosophical perspectives of opposing idealism and receiving dialectical materialism. At the end of this paper, based on the infinite view of dialectical materialism, the author analyzes the Principle of Comprehension and the Maximum Ordinal Paradox, and points out that the essence of the Principle of Comprehension is a kind of actual infinity thought.

Results

Conclusion