Die Unendlichkeit der Natur und der Einzeldinge - Husserls allseitig unendliches Erscheinungskontinuum und das Konzept des Kontinuums in der Philosophie der Mathematik

Abstract

The infinity of nature and the individual things - Husserl's infinite continuum of appearances and the concept of continuum in philosophy of mathematics

In contemporary philosophy, the world is increasingly identified with infinity and closed world views are suppressed. How deep is this infinity, what is its nature? To answer this question, the open infinity of Tengelyi, Husserl and Gabriel is contrasted with the absolute infinite described by Cantor and von Kues. It turns out that the open infinity is still something potential - similar to the Aristotelian infinity of possible division - because it is thought to be incomplete. This potential infinity is problematic because limitations arise that require a background against which the finite can exist. Therefore, here Husserl's conception of the open infinity of the Eidos will be combined with insights from contemporary philosophy of mathematics about the nature of infinity in order to show that the openness of the infinity of the world has nothing potential or incomplete. Contingency and time are inseparable combined to space and must, thus, be considered as actually infinite as space. Compared to the description of the absolute infinite by von Kues and Cantor, this results in an actual infinite, linear continuum that can be identified with this absolute infinite in which possibilities, past and future always exist intertwined.

Keywords: Infinity, continuum, philosophy of mathematics, metaphysics, ontology, Husserl, Eidos