The Mathematical Foundations of Logical Geometry

Aristotelian diagrams have been widely used throughout the history of philosophy and logic. Nowadays, they also have several applications in other disciplines. However, many of these applications suffer from substantial problems, often due to a lack of understanding of the intricate logical properties of these diagrams. Therefore, a theoretical investigation of Aristotelian diagrams is required (i.e. logical geometry). This doctoral project is part of the interdisciplinary STARTDIALOG project, in which the overarching goal is to develop a unified theory of Aristotelian diagrams. My specific project will focus on the mathematical foundations of logical geometry. This work will have two broad aspects. Firstly, I will study mathematical notions (i.e. possible morphisms, isomorphisms, automorphisms, etc.) that will allow us to study (classical) Aristotelian diagrams using the tools of category theory. Secondly, I will work towards a typology (i.e. classification) of these diagrams. This foundational work will benefit all researchers working with Aristotelian diagrams.