The Square of Opposition: A Cornerstone of Thought

Editors:

ISBN: 978-3-319-45061-2 (Print) 978-3-319-45062-9 (Online)

Table of contents (20 chapters)

  1. Front Matter

    Pages i-vi

  2. Introduction

    1. Front Matter

      Pages 1-1

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      Chapter

      Pages 3-12

      The Square of Opposition: A Cornerstone of Thought

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      Chapter

      Pages 13-17

      Welcome Address to the Participants of the IV International Congress on: The Square of Opposition Vatican City, PUL, May 5–9, 2014

  3. Historical Perspectives on the Square

    1. Front Matter

      Pages 19-19

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      Chapter

      Pages 21-34

      The Proto-exposition of Aristotelian Categorical Logic

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      Chapter

      Pages 35-52

      The Modal Octagon and John Buridan’s Modal Ontology

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      Chapter

      Pages 53-78

      From Aristotle’s Square of Opposition to the “Tri-unity’s Concordance”: Cusanus’ Non-classical Reasoning

  4. Reinterpretations of the Square

    1. Front Matter

      Pages 79-79

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      Chapter

      Pages 81-103

      Symmetric Properties of the Syllogistic System Inherited from the Square of Opposition

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      Chapter

      Pages 105-117

      The Square of Opposition Interpreted with a Decidable Modal Logic

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      Chapter

      Pages 119-142

      Two Standard and Two Modal Squares of Opposition

  5. Philosophical Perspectives on the Square

    1. Front Matter

      Pages 143-143

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      Chapter

      Pages 145-167

      The Many Faces of Inconsistency

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      Chapter

      Pages 169-178

      Aristotle, Frege and “Second Nature”

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      Chapter

      Pages 179-193

      There Is No Cube of Opposition

  6. Theoretical Investigations on the Square

    1. Front Matter

      Pages 195-195

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      Chapter

      Pages 197-214

      The Unreasonable Effectiveness of Bitstrings in Logical Geometry

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      Chapter

      Pages 215-237

      An Arithmetization of Logical Oppositions

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      Chapter

      Pages 239-250

      Groups, Not Squares: Exorcizing a Fetish

  7. Expansions and Variations of the Square

    1. Front Matter

      Pages 251-251

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      Chapter

      Pages 253-272

      From the Square to Octahedra

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      Chapter

      Pages 273-290

      Iconic and Dynamic Models to Represent “Distinctive” Predicates: The Octagonal Prism and the Complex Tetrahedron of Opposition

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      Chapter

      Pages 291-303

      The Exact Intuitionistic Meaning of the Square of Opposition

  8. Applications of the Square

    1. Front Matter

      Pages 305-305

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      Chapter

      Pages 307-313

      The Ontological Modal Collapse as a Collapse of the Square of Opposition

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      Chapter

      Pages 315-324

      Fuzzy Eubouliatic Logic: A Fuzzy Version of Anderson’s Logic of Prudence

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      Chapter

      Pages 325-337

      Why Care beyond the Square? Classical and Extended Shapes of Oppositions in Their Application to “Introspective Disputes”