The Set Theory and the Description of Infinity: the Nature of Infinity Perceived from Metaphysics and Ontology

Abstract

Infinity is possibly one of the most complicated conceptions confronting mathematics and philosophy. People could always conceive it via intuition, but find it hard to describe in the logical realm. In the 19th century, German mathematician Cantor proposed the set theory, for the first time, people could use mathematical tools to explain the nature of infinity. However, such an explanation still lies on the axiomatic foundation, which does not directly fit our intuition about infinity. Therefore, this study will attempt to establish a 'bridge' between the infinity that fits intuition and the infinity that is described by set theory, hence arguing why the set theory could describe infinity universally in the senses of metaphysics and ontology.