Augustus De Morgan's unpublished octagon of opposition
type: Item
instance of: scholarly article
title: Augustus De Morgan's unpublished octagon of opposition
DOI: 10.1007/978-3-030-90823-2_7
author: Anna-Sophie Heinemann
author: Lorenz Demey
publication date: 2024-09-09T00:00:00Z
review text: In this paper, the authors will argue that one of De Morgan's unpublished diagrams, which occurs several times throughout his manuscripts, is an example of the type of so-called KJ octagons.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].
reviewed by: C. Pereira da Silva
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B65
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 7909179
zbMATH Keywords: syllogistics
zbMATH Keywords: logical notation
zbMATH Keywords: logical geometry
zbMATH Keywords: square of opposition
zbMATH Keywords: Keynes-Johnson octagon
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7909179