Abstract

Leibniz's theory of infinity contains many theoretically difficult aspects. Until today only some of them have been systematically studied by mathematicians and philosophers. For instance Leibniz didn't only discover some of the paradoxical properties of an infinite set: he also discovered that a classification of four kinds of infinity is possible and that their properties can be investigated. This article reconstructs this classification and these properties. The metaphysical implications in Leibniz's system and some of the possible developments of these theories in the modern philosophy of mathematics are also investigated