Augustus De Morgan's unpublished octagon of opposition (Q6600388)

In this paper, the authors will argue that one of De Morgan's unpublished diagrams, which occurs several times throughout his manuscripts, is an example of the type of so-called KJ octagons. Throughout the twentieth century, this type of diagram has been studied extensively in philosophical logic, and in recent years even in computer science. Consequently, its logical and diagrammatic properties are now well-understood. Historically speaking, it has long been assumed that this type of octagon was studied for the first time by John Neville Keynes and William E. Johnson around the turn of the twentieth century (1894--1921); hence the term KJ octagon. However, the manuscript findings presented in this paper clearly show that this type of octagon was already known by De Morgan, some five decades earlier than Keynes and Johnson. \N\NThe paper is organized as follows. In Section 2, the authors present the manuscript findings and provide a transcription of the relevant sections of De Morgan's handwritten notes. In Section 3, they discuss some key aspects of De Morgan's logic, which will help us make sense of the diagrams in his manuscripts. With these prerequisites in place, the authors then show in Section 4 that De Morgan's octagon belongs to the type of KJ octagons, and briefly discusses the significance of this result for the historiography of logical diagrams. Finally, Section 5 wraps things up and suggests some questions for future research.\N\NFor the entire collection see [Zbl 1515.03010].