The Square of Opposition ― A General Framework for Cognition

The square of opposition is a simple geometrical figure expressing some fundamental ideas about cognition. It is based on Aristotle’s philosophy and has been fascinating people for two thousand years. The three notions of opposition presented in the square can be applied to analyze and understand such diverse subjects as reasoning about mathematical objects, perceptions of reality, speech acts, moral reasoning and reasoning about possibility.
This book presents recent research papers dealing with the history and philosophy of the square, new diagrammatic and mathematical developments arising from it, and its applications to the fields of linguistics, psychology and argumentation.
It also includes a DVD composed of events from the first world congress on the square of opposition held in June 2007 in Montreux, featuring some of the speeches and presentations of the participants, like the professors Pascal Engel, Laurence Horn, Terence Parsons, Jan Wolenski. Further, the DVD contains extracts of a square jazz show which was composed and presented for this occasion and extracts of the movie «The Square of Salomé». The movie, which was produced for this event, is a remake of the famous biblical story using the square to display the relations between the main characters.

Jean-Yves Beziau is Professor at the Federal University of Rio de Janeiro, Brazil. He has a PhD in philosophy and a PhD in mathematical logic. He has worked in France, Poland, Brazil, Switzerland and USA (Stanford and UCLA). His main line of investigation is universal logic, a general theory of logical structures. He is Editor-in-Chief of the journal Logica Universalis.
Gillman Payette is a doctoral student at the University of Calgary, Alberta, Canada. His work is focused primarily on applications of logic in the social sciences, preservationist and paraconsistent logic, and the foundations of logical consequence. He is a Killam and Joseph-Armand Bombardier SSHRCC fellow.