On Hegel’s View of Dialectical Infinity

Abstract

It is well known that the problem of finity and infinity is the basic problem of mathematics, and it is also the basic problem of Philosophy. From the perspective of philosophy and mathematics, this paper comprehensively reviews and analyzes Hegel’s view of dialectical infinity, introduces Engels’discussion on infinity, deeply analyzes the characteristics of the thought of actual infinity, and points out: Hegel’s thought of real infinity is completely different from the thought of actual infinity, the Being of infinity (objective infinity) is not equal to the completed infinity (subjective infinity), the mathematical limit is a real infinity, and real infinity is the inner law of infinite things and truth; the view of actual infinity views the objective material world from the viewpoint of static rather than motion, denying the contradiction between finity and infinity, so it is actually a downright idealist. In this paper, the author puts forward the Infinite Exchange Paradox, which strongly questions the idea of actual infinity in Hilbert Hotel Problem, and points out the internal irreconcilable contradiction in the idea of actual infinity. At the same time, we made a detailed comparison of Hegel’s view of infinity and the view of mathematical infinity, and on this basis, the author gives a complete definition of the view of dialectical infinity: abandoning the wrong aspects of the potential infinity and actual infinity, and actively absorbing correct aspects of both, that is, not only to recognize the existence and knowability of infinite objectivity, but also to admit the imcompletion of infinite process. The reexcavation of Hegel’s view of dialectical infinity and the criticism of the actual infinity thought aim to find possible philosophical solutions for Russell’s Paradox and the problem of Continuum Hypothesis.