Second, revised edition of the first collection of articles around the topic of universal logic Starting point of interdisciplinary research in the fields of, e. g., logic, linguistic, philosophy, mathematics, computer science Includes supplementary material: sn. pub/extras
The theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various epistemology, linguistics, mathematics, sociology, physics. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original Aristotelian theory. The square of opposition from its origin in antiquity to the present day continues to exert a profound impact on the development of deductive logic. Since 10 years there is a new growing interest for the square due to recent discoveries and challenging interpretations. This book presents a collection of previously unpublished papers by high level specialists on the square from all over the world.
The present book discusses all aspects of paraconsistent logic, including the latest findings, and its various systems. It includes papers by leading international researchers, which address the subject in many different ways: development of abstract paraconsistent systems and new theorems about them; studies of the connections between these systems and other non-classical logics, such as non-monotonic, many-valued, relevant, paracomplete and fuzzy logics; philosophical interpretations of these constructions; and applications to other sciences, in particular quantum physics and mathematics. Reasoning with contradictions is the challenge of paraconsistent logic. The book will be of interest to graduate students and researchers working in mathematical logic, computer science, philosophical logic, linguistics and physics.
The square of opposition is a diagram related to a theory of opposi-tions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantifi-cation, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has recently become a topic of intense interest due to the development of a general geometry of opposition (polygons and polyhedra) with many applications. A congress on the square with an interdisciplinary character has been organized on a regular basis (Montreux 2007, Corsica 2010, Beirut 2012, Vatican 2014, Rapa Nui 2016). The volume at hand is a sequel to two successful books: The Square of Opposition - A General Framework of Cognition, ed. by J.-Y. Béziau & G. Payette, as well as Around and beyond the Square of Oppo-sition, ed. by J.-Y. Béziau & D. Jacquette, and, like those, a collection of selected peer-reviewed papers. The idea of this new volume is to maintain a good equilibrium between history, technical developments and applications. The volume is likely to attract a wide spectrum of readers, mathematicians, philosophers, linguists, psychologists and computer scientists, who may range from undergraduate students to advanced researchers.
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.