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Jean-Yves Béziau & Stamatios Gerogiorgakis

New Dimensions of the Square of Opposition


ISBN: 978-3-88405-112-2

Price: €118.00 (including 7 % tax)


Price: € 118.00 (incl. 7 % MwSt.) Print
Price: € 118.00 (incl. 19 % MwSt.) eBook

Series: Analytica 
414 pp., Index, Abstracts, Authors’ short Biographies, Library Binding            
Munich 2017
ISBN 978-3-88405-112-2 Print
ISBN 978-3-88405-733-9  E-Book

The square of opposition is a diagram related to a theory of oppositions 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 quantification, 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 Opposition, 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, mathe-maticians, philosophers, linguists, psychologists and computer scientists, who may range from undergraduate students to advanced researchers.                                                    
The Editors: 
Jean-Yves Beziau is Professor of Logic at the department of philosophy of the Federal University of Rio de Janeiro and titular member of the Brazilian Academy of Philosophy. He has a PhD in Philosophy and a PhD in Mathematical logic and renewed the studies on the square of opposition organizing also world events on 13 this topic.
Stamatios Gerogiorgakis (PhD LMU Munich, Dr. phil. habil. University of Erfurt) is 'Privatdozent' at the University of Erfurt. His work ranges from the history of logic to the philosophy of religion and from metaphysics to semantical paradoxes.He blogs at:  www.philori.de                                                   
Table of Contents
 Jean-Yves Béziau / Stamatios Gerogiorgakis
 The Many Dimensions of the Square of Opposition                                                        
 Introduction 9

 1    Historical and Critical Aspects of the Square
  
 Paul J.E. Dekker
 Heraclitean Oppositions                                                19

 Juliette Lemaire 
 Is Aristotle the Father of the Square of Opposition? 33
  
 Stamatios Gerogiorgakis
 A Vindication of a secundum-quid-et-simpliciter  Solution of the Paradox of Epimenides by Way  of Mereological Hexagons  71

 Enrique Alvarez and Manuel Correia
 Conversion and Opposition:  Traditional and Theoretical Formulations 87   

 Régis Angot-Pellissier
 Taoist Logical Hexagon. The Philosophical  Meaning  of 3-opposition
 and  Weak 2-opposition
 in Cosmology 107

 2   The Square of Opposition and Non-Classical Logics
  
 Ka-fat Chow
 Opposition Inferences and Generalized  Quantifiers 155

 Claudio Pizzi
 Contingency Logics 
 and Modal Squares of Opposition 201

 Christan de Ronde, Hector Freytes and  Graciela Domenech
 Quantum Mechanics and the Interpretation of the Orthomodular Square of Opposition 221

 Luca Tranchini and Michae1 Arndt
 A Constructive View of the Square of Oppositions 241


 Fatemah Ayatollah Zadeh Shirazi 
 2n-polygon of Opposition and 2n-tuples Satisfying It  275

 3   Applications of the Square of Opposition

 François Nicolas
The Hexagon of Opposition in Music 299

 Jean-Yves Béziau 
Opposition and Order  321
Jonas R. Becker Arenhart and Décio Krause
Oppositions and Quantum Mechanics:   Superposition and Identity        337 

 Katarzyna Gan-Krzywoszyńska 
and Piotr Leśniewski
An Erotetic Hexagon: 
Oppositions  as a Basis for the Logic of Questions         355

 Fabio Tfouni
Interdiction and Silence: A Traditional 
Reading of the Square of Opposition                              377

 Index                                                                                 391
Abstracts / Authors’ Short Biographies                  399     



 


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