Part 1. Historical and Critical Aspects of the Square -- The New Rising of the Square of Opposition / Jean-Yves Béziau -- Logical Oppositions in Arabic Logic: Avicenna and Averroes / Saloua Chatti -- Boethius on the Square of Opposition / Manuel Correia -- Leibniz, Modal Logic and Possible World Semantics: The Apulean Square as a Procrustean Bed for His Modal Metaphysics / Jean-Pascal Alcantara -- Thinking Outside the Square of Opposition Box / Dale Jacquette -- John Buridan’s Theory of Consequence and His Octagons of Opposition / Stephen Read -- Why the Fregean "Square of Opposition" Matters for Epistemology / Raffaela Giovagnoli -- Part 2. Philosophical Discussion around the Square of Opposition -- Two Concepts of Opposition, Multiple Squares / John T. Kearns -- Does a Leaking O-Corner Save the Square? / Pieter A. M. Seuren -- The Right Square / Hartley Slater -- Oppositions and Opposites / Fabien Schang -- Pluralism in Logic: The Square of Opposition, Leibniz’ Principle of Sufficient Reason and Markov’s Principle / Antonino Drago
Part 3. The Square of Opposition and Non-Clasical Logics -- The Square of Opposition in Orthomodular Logic / H. Freytes, C. de Ronde and G. Domenech -- No Group of Opposition for Constructive Logics: The Intuitionistic and Linear Cases / Baptiste Méles -- The Square of Opposition and Generalized Quantifiers / Duilio D’Alfonso -- Privations, Negations and the Square: Basic Elements of a Logic of Privations / Stamatios Gerogiorgakis -- Fuzzy Syllogisms, Numerical Square, Triangle of Contraries, Inter-bivalence / Ferdinando Cavaliere -- Part 4. Constructions Generalizing the Square of Opposition -- General Patterns of Opposition Squares and 2n-gons / Ka-fat Chow -- The Cube Generalizing Aristotle’s Square in Logic of Determination of Objects (LDO) / Jean-Pierre Desclés and Anca Pascu -- Hypercubes of Duality / Thierry Libert -- Part 5. Applications of the Square of Opposition -- How to Square Knowledge and Belief / Wolfgang Lenzen -- Structures of Oppositions in Public Announcement Logic / Lorenz Demey -- Logical Opposition and Collective Decisions / Srećko Kovač -- A Metamathematical Model for A/O Opposition in Scientific Inquiry / Mark Weinstein
"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 fields: 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 is a very attractive theme which has been going through centuries without evaporating. 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 of the square from all over the world." -- Publisher’s website.