Logical Geometry and its Applications.

The main goal of the project is to develop a systematic and formal perspective on the Aristotelian diagrams (such as the well-known square of oppositions). These diagrams have been used extensively by philosophers, logicians and linguists to explain or illustrate the phenomena they are interested in (such as necessity and obligation). There exists a vast body of results about these concrete uses of Aristotelian diagrams (historical case studies, concrete decorations of the square, concrete extensions of the square, etc.). The project builds upon these results, but also pushes significantly beyond the current state of the art. In earlier work, the Aristotelian diagrams mainly played a secondary or auxiliary role, viz. illustrating some other philosophical notion. In contrast, in this project, the Aristotelian relations and diagrams *themselves* will be the primary objects of investigation. For example, I will (i) develop a formal account of the information levels of the Aristotelian relations, and (ii) investigate whether these relations should be seen as 'absolute' (all or nothing) or as 'graded' relations. I will argue extensively that these formal theories are philosophically well-motivated, and use them to obtain new insights about Aristotelian diagrams. Given the widespread use of Aristotelian diagrams throughout philosophy, the insights obtained in this project will not only be relevant for specialists in this particular area, but also for philosophers in general.