Around and Beyond the Square of Opposition

Editors:

ISBN: 978-3-0348-0378-6 (Print) 978-3-0348-0379-3 (Online)

Table of contents (24 chapters)

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  1. Front Matter

    Pages I-X

  2. Historical and Critical Aspects of the Square

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 3-19

      The New Rising of the Square of Opposition

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      Book Chapter

      Pages 21-40

      Logical Oppositions in Arabic Logic: Avicenna and Averroes

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      Book Chapter

      Pages 41-52

      Boethius on the Square of Opposition

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      Book Chapter

      Pages 53-71

      Leibniz, Modal Logic and Possible World Semantics: The Apulean Square as a Procrustean Bed for His Modal Metaphysics

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      Book Chapter

      Pages 73-92

      Thinking Outside the Square of Opposition Box

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      Book Chapter

      Pages 93-110

      John Buridan’s Theory of Consequence and His Octagons of Opposition

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      Book Chapter

      Pages 111-116

      Why the Fregean “Square of Opposition” Matters for Epistemology

  3. Philosophical Discussion around the Square of Opposition

    1. Front Matter

      Pages 117-117

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      Book Chapter

      Pages 119-127

      Two Concepts of Opposition, Multiple Squares

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      Book Chapter

      Pages 129-138

      Does a Leaking O-Corner Save the Square?

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      Book Chapter

      Pages 139-145

      The Right Square

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      Book Chapter

      Pages 147-173

      Oppositions and Opposites

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      Book Chapter

      Pages 175-189

      Pluralism in Logic: The Square of Opposition, Leibniz’ Principle of Sufficient Reason and Markov’s Principle

  4. The Square of Opposition and Non-Clasical Logics

    1. Front Matter

      Pages 191-191

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      Book Chapter

      Pages 193-200

      The Square of Opposition in Orthomodular Logic

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      Book Chapter

      Pages 201-217

      No Group of Opposition for Constructive Logics: The Intuitionistic and Linear Cases

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      Book Chapter

      Pages 219-227

      The Square of Opposition and Generalized Quantifiers

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      Book Chapter

      Pages 229-239

      Privations, Negations and the Square: Basic Elements of a Logic of Privations

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      Book Chapter

      Pages 241-260

      Fuzzy Syllogisms, Numerical Square, Triangle of Contraries, Inter-bivalence

  5. Constructions Generalizing the Square of Opposition

    1. Front Matter

      Pages 261-261

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      Book Chapter

      Pages 263-275

      General Patterns of Opposition Squares and 2n-gons

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      Book Chapter

      Pages 277-291

      The Cube Generalizing Aristotle’s Square in Logic of Determination of Objects (LDO)

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      Book Chapter

      Pages 293-301

      Hypercubes of Duality

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