Hegel’s Concept of True Infinity

Hegel’s dialectical method, constituting the foundation of his philosophical system, remains subject to diverse interpretations. It is generally assumed that, while, based on Hegelian philosophy, the understanding ( Verstand ) fixes contradictions as something independent and final, reason ( Vernunft ) dialectically sublates these contradictions by revealing their inner interconnection and transition into one another. However, the question remains as to how exactly, according to Hegel, this transition takes place. This article examines the fundamental problem in Hegel’s philosophy, the relationship between understanding and reason, by analysing Hegel’s treatment of the relationship between finitude and infinity. This analysis results in the concept of true infinity and proves to be an application and model interpretation of the sequence of what Hegel calls the moments of the logical domain: (a) “the abstract side or that of the understanding”, (b) “the dialectical or negatively rational side”, and (c) “the speculative or positively rational side”. These moments are the stages in which the insight into what is truly actual must unfold. They define the concept and the specific form of argumentation of Hegel’s philosophy. Insight into what is the truly actual arises from the critique of the way in which the ordinary, pre-philosophical consciousness, or what Hegel calls the understanding, conceives the concepts of the finite and the infinite. The understanding comprehends them, on the one hand, as separate and mutually exclusive spheres and, on the other, in such a way that one must go beyond the sphere of the finite to the infinite as the genuinely true and permanent. Since the infinite is conceived as the limit of the finite, the infinite in turn appears as something finite, beyond which the understanding seeks to go; that to which the understanding goes out is only the infinite again, which, however, is only the limit of the finite, beyond which the understanding again seeks to go out. In this way the understanding is driven out into an infinite progress. Hegel’s analysis reveals the conceptual deficit of the understanding, which consists in the inability to grasp the true connection between the concepts of the finite and the infinite under the guidance of the special concept of a self-referential negation, which defines the logical structure of the concept of true infinity.