Die absolute Unendlichkeit des Raumzeit-Kontinuums als grundlegende Fundamentalontologie

Abstract

The absolute infinity of the space-time-continuum as fundamental ontology

In his fundamental ontology, Heidegger describes the extent - extensio - in space and time as the most fundamental commonality of being and entity and, moreover, the mutual dependence, i.e. the connection between space and time, as the time-space. In the present article, the space-time (the time-space) is confirmed as the most fundamental property of being and entity, and its nature is identified as continuous. Thereafter, the nature of the continuum and its power (in mathematics: its cardinality) are examined in order to determine being in its essence and thus the fundamental ontological foundation of being and entity. This investigation is carried out by analyzing the construction of contemporary mathematics on set theory and three axioms related to it. In conclusion, Heidegger's fundamental ontology is updated, based on his own revision, by including these findings about the nature and power of the continuum.

Keywords: fundamental ontology, absolute infinity, space and time, philosophy of mathematics, set theory