Aristotelian Diagrams as Logic Diagrams

Recently, diagrams are more seen as logical systems. Curiously, Aristotelian diagrams, such as the square of opposition, have mostly been excluded from this. In this paper we challenge this prejudice and show that Aristotelian diagrams can be considered as proper logic diagrams that can be used to draw inferences. We do so by describing a logical system of Aristotelian diagrams: we provide a diagrammatic vocabulary and syntax, a set of axioms and (transformation) rules, and a formal semantics. We show how this diagrammatic logic system can be used to make inferences and argue that the crucial step here is to not only consider finished diagrams, but also unfinished diagrams; it is in the process of (re)constructing the diagram that the reasoning steps are made. We finish the paper by commenting on the soundness and completeness of the system.