Ontology and Mathematics: Set Theory, Category Theory, and the Theory of Infinites in Being and Event, Logics of Worlds and The Immanence of Truths

Abstract

This paper examines the relationship between philosophy and its conditions. The affirmation “mathematics is ontology”, which I posited thirty years ago, has certain inconveniences. In this article, I present six varying possibilities for ontology. My own philosophical decision was to proclaim that being is a pure multiplicity, without the One and without any specific attribute such as “matter” or “spirit”. This movement of thought brought me to study the mathematical condition of philosophy and to search for a rigorous structuration of my speculative decision within the field of mathematics. However, my initial postulate that “Being is the multiplicity without the One” is not a mathematical but a philosophical statement. This paper concludes with a presentation of the relationship between mathematics and philosophy in Being and Event, Logics of Worlds, and The Immanence of Truths.