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viernes, 18 de mayo de 2012

Around and Beyond the Square of Opposition Jean-Yves Béziau and Dale Jacquette


2012DOI: 10.1007/978-3-0348-0379-3


Series Editor
Jean-Yves Béziau (Federal University of Rio de Janeiro and Brazilian Research Council,
Rio de Janeiro, Brazil)
Editorial Board Members
Hajnal Andréka (Hungarian Academy of Sciences, Budapest, Hungary)
Mark Burgin (University of California, Los Angeles, USA)
Razvan Diaconescu ˘ (Romanian Academy, Bucharest, Romania)
Josep Maria Font (University of Barcelona, Barcelona, Spain)
Andreas Herzig (Centre National de la Recherche Scientifique, Toulouse, France)
Arnold Koslow (City University of New York, New York, USA)
Jui-Lin Lee (National Formosa University, Huwei Township, Taiwan)
Larissa Maksimova (Russian Academy of Sciences, Novosibirsk, Russia)
Grzegorz Malinowski (University of Łód´z, Łód´z, Poland)
Darko Sarenac (Colorado State University, Fort Collins, USA)
Peter Schröder-Heister (University Tübingen, Tübingen, Germany)
Vladimir Vasyukov (Russian Academy of Sciences, Moscow, Russia)

Preface
The theory of inferences and oppositions among categorical propositions, based on Aristotelian term logic, is pictured in a striking square diagram. The graphic representation
of contradictories, contraries, subcontraries and subalterns intended as a foundation for
syllogistic logic can be understood and applied in many different ways with interesting
implications for various disciplines, notably including epistemology, linguistics, mathematics, psychology. The square can also be generalized in other two-dimensional and
multi-dimensional graphic depictions of logical and other relations, extending in breath
and depth the original Aristotelian theory. The square of opposition is accordingly a very
attractive theme which has persisted down through the centuries with no signs of disappearing or even diminishing in fascination. For the last 10 years, there has been a new
growing interest for the square due to new discoveries and challenging interpretations.
This book presents a collection of previously unpublished papers by well-regarded specialists on the theory and interpretation of the concept and application of the square of
opposition from all over the world. We thank all the authors who have contributed a paper
to this book, and the referees who have analyzed, commented on, and made invaluable
recommendations for improving the essays.
Jean-Yves Béziau
Dale Jacquette

Contents

Part I Historical and Critical Aspects of the Square
The New Rising of the Square of Opposition . . . . . . . . . . . . . . . . . . .  3
Jean-Yves Béziau
Logical Oppositions in Arabic Logic: Avicenna and Averroes . . . . . . . . . .  21
Saloua Chatti
Boethius on the Square of Opposition . . . . . . . . . . . . . . . . . . . . . . .  41
Manuel Correia
Leibniz, Modal Logic and Possible World Semantics: The Apulean Square as
a Procrustean Bed for His Modal Metaphysics . . . . . . . . . . . . . . . .  53
Jean-Pascal Alcantara
Thinking Outside the Square of Opposition Box . . . . . . . . . . . . . . . . .  73
Dale Jacquette
John Buridan’s Theory of Consequence and His Octagons of Opposition . . .  93
Stephen Read
Why the Fregean “Square of Opposition” Matters for Epistemology . . . . . .  111
Raffaela Giovagnoli
Part II Philosophical Discussion Around the Square of Opposition
Two Concepts of Opposition, Multiple Squares . . . . . . . . . . . . . . . . . .  119
John T. Kearns
Does a Leaking O-Corner Save the Square? . . . . . . . . . . . . . . . . . . . .  129
Pieter A.M. Seuren
The Right Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  139
Hartley Slater
Oppositions and Opposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  147
Fabien Schang
viiviii Contents
Pluralism in Logic: The Square of Opposition, Leibniz’ Principle of Sufficient
Reason and Markov’s Principle . . . . . . . . . . . . . . . . . . . . . . . .  175
Antonino Drago
Part III The Square of Opposition and Non-classical Logics
The Square of Opposition in Orthomodular Logic . . . . . . . . . . . . . . . .  193
H. Freytes, C. de Ronde, and G. Domenech
No Group of Opposition for Constructive Logics: The Intuitionistic and
Linear Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  201
Baptiste Mélès
The Square of Opposition and Generalized Quantifiers . . . . . . . . . . . . .  219
Duilio D’Alfonso
Privations, Negations and the Square: Basic Elements of a Logic of Privations 229
Stamatios Gerogiorgakis
Fuzzy Syllogisms, Numerical Square, Triangle of Contraries, Inter-bivalence . 241
Ferdinando Cavaliere
Part IV Constructions Generalizing the Square of Opposition
General Patterns of Opposition Squares and 2n-gons . . . . . . . . . . . . . . .  263
Ka-fat Chow
The Cube Generalizing Aristotle’s Square in Logic of Determination of
Objects (LDO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  277
Jean-Pierre Desclés and Anca Pascu
Hypercubes of Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  293
Thierry Libert
Part V Applications of the Square of Opposition
How to Square Knowledge and Belief . . . . . . . . . . . . . . . . . . . . . . .  305
Wolfgang Lenzen
Structures of Oppositions in Public Announcement Logic . . . . . . . . . . . .  313
Lorenz Demey
Logical Opposition and Collective Decisions . . . . . . . . . . . . . . . . . . . .  341
Srecko Kova ´ cˇ
A Metamathematical Model for A/O Opposition in Scientific Inquiry . . . . .  357
Mark WeinsteinContributors
Jean-Pascal Alcantara Centre Georges Chevrier-UMR 5605, Université de Bourgogne,
Dijon, France
Jean-Yves Béziau CNPq – Brazilian Research Council, UFRJ – University of Brazil,
Rio de Janeiro, Brazil
Ferdinando Cavaliere Cesenatico, FC, Italy
Saloua Chatti Department of Philosophy, Faculté des Sciences Humaines et Sociales,
University of Tunis, Tunis, Tunisia
Ka-fat Chow The Hong Kong Polytechnic University, Hong Kong, China
Manuel Correia Facultad de Filosofía, Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
Duilio D’Alfonso University of Calabria, Arcavacata di Rende, CS, Italy
C. de Ronde Departamento de Filosofía “Dr. A Korn”, Universidad de Buenos AiresCONICET, Buenos Aires, Argentina; Center Leo Apostel and Foundations of the Exact
Sciences, Vrije Universiteit Brussel, Brussels, Belgium
Lorenz Demey Center for Logic and Analytical Philosophy, Institute of Philosophy, KU
Leuven – University of Leuven, Leuven, Belgium
Jean-Pierre Desclés LaLIC (Langues, Logiques, Informatique et Cognition), Université
de Paris Sorbonne, Paris, France
G. Domenech Instituto de Astronomía y Física del Espacio, Buenos Aires, Argentina
Antonino Drago University of Pisa, Pisa, Italy
H. Freytes Universita degli Studi di Cagliari, Cagliari, Italy; Instituto Argentino de
Matemática, Buenos Aires, Argentina
Stamatios Gerogiorgakis University of Erfurt, Erfurt, Germany
Raffaela Giovagnoli Pontifical Lateran University, Vatican City, Italy
Dale Jacquette University of Bern, Bern, Switzerland
ixx Contributors
John T. Kearns Department of Philosophy and Center for Cognitive Science, University
at Buffalo, the State University of New York, Buffalo, NY, USA
Srecko Kova ´ cˇ Institute of Philosophy, Zagreb, Croatia
Wolfgang Lenzen Dept. of Philosophy, University of Osnabrueck, Osnabrueck, Germany
Thierry Libert Département de mathématiques, Université Libre de Bruxelles (U.L.B.),
Brussels, Belgium
Baptiste Mélès Université Blaise Pascal, Clermont-Ferrand, France
Anca Pascu LaLIC, Université de Bretagne Occidentale Brest, Brest Cedex 03, France
Stephen Read Department of Philosophy, University of St Andrews, St Andrews, Scotland, UK
Fabien Schang LHSP Henri Poincaré (UMR7117), Université de Lorraine, Nancy,
France
Pieter A.M. Seuren Max Planck Institute for Psycholinguistics, Nijmegen, The Netherlands
Hartley Slater University of Western Australia, Crawley, WA, Australia
Mark Weinstein Department of Educational Foundations, Montclair State University,
Upper Montclair, NJ, USA



2 comentarios:

  1. This series is devoted to the universal approach to logic and the development of a general
    theory of logics. It covers topics such as global set-ups for fundamental theorems of
    logic and frameworks for the study of logics, in particular logical matrices, Kripke
    structures, combination of logics, categorical logic, abstract proof theory, consequence
    operators, and algebraic logic. It includes also books with historical and philosophical
    discussions about the nature and scope of logic. Three types of books will appear in the
    series: graduate textbooks, research monographs, and volumes with contributed papers.

    ResponderEliminar
  2. Una buena noticia para los que se interesan en Universal Logic !

    ResponderEliminar

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