The Concept of Infinity under German Idealism and Modern Set Theory

Abstract

The purpose of this paper is to compare and analyse the concepts of infinity in German idealism and Modern set theory. The fisrt part of this paper analyses Kant and Hegels views on mathematical infinity, where Kant suggests a notion of potential infinity constructed by means of intuition, while Hegel that of actual infinity. The second part illustrates the characteristics of Cantorian transfinite sets and both the progress it has made and the limitations. Following the two main parts, not only a clear contrast between the notions of infinity under German idealism and Cantorian set theory can be made but their close link can also be shown. By analysing perspectives of Freges logicism, Hilberts formalism, Brouwers intuitionism, and Badious comments, it is clear German idealism has lost its mainstream position in understanding the mathematical concept of infinity. However, the concept of infinity in German idealism can be supplied as a powerful facilitator for philosophers and mathematicians to understand this concept in the realm of mathematics.