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The Exoteric Square of Opposition

The Sixth World Congress on the Square of Opposition

  • Conference proceedings
  • © 2022

Overview

Editors:
  1. Jean-Yves Beziau

    1. Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

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  2. Ioannis Vandoulakis

    1. The Hellenic Open University, Patras, Greece

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  • Highlights new research related to the square of opposition
  • Examines the theory of the square of opposition through an interdisciplinary lens
  • Explores the past, present, and future of the field

Part of the book series: Studies in Universal Logic (SUL)

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Table of contents (16 papers)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. The Square of Opposition: Past, Present, and Future

    • Jean-Yves Beziau, Ioannis Vandoulakis
    Pages 1-14

  3. Division of Entities and Foundations of Reality: Aristotle’s Ontological Square

    • Gianluigi Segalerba
    Pages 15-52

  4. Logical Oppositions in Avicenna’s Hypothetical Logic

    • Saloua Chatti
    Pages 53-88

  5. Incommensurability and Inapplicability of the Squares of Opposition

    • Sumanta Sarathi Sharma
    Pages 89-107

  6. The Square of Opposition as a Framework for Stephen Langton’s Theological Solutions

    • Marcin Trepczyński
    Pages 109-121

  7. The Limits of the Square: Hegel’s Opposition to Diagrams in Its Historical Context

    • Valentin Pluder
    Pages 123-139

  8. Augustus De Morgan’s Unpublished Octagon of Opposition

    • Anna-Sophie Heinemann, Lorenz Demey
    Pages 141-169

  9. A Bitstring Semantics for Calculus CL

    • Jens Lemanski, Fabien Schang
    Pages 171-193

  10. Logical Diagrams, Visualization Criteria, and Boolean Algebras

    • Roland Bolz
    Pages 195-224

  11. Turnstile Figures of Opposition

    • Jean-Yves Beziau
    Pages 225-240

  12. The Naturalness of Jacques Lacan’s Logic

    • Hubert Martin Schüler
    Pages 241-257

  13. On Modal Opposition Within Some Modal Discussive Logics

    • Krystyna Mruczek-Nasieniewska, Marek Nasieniewski
    Pages 259-275

  14. On the Transformations of the Square of Opposition from the Point of View of Institution Model Theory

    • Yiannis Kiouvrekis, Petros Stefaneas, Ioannis Vandoulakis
    Pages 277-301

  15. Color-Coded Epistemic Modes in a Jungian Hexagon of Opposition

    • Julio Michael Stern
    Pages 303-332

  16. Many-Valued Logical Hexagons in a 3-Oppositional Trisimplex

    • Régis Angot-Pellissier
    Pages 333-345

  17. Tri-simplicial Contradiction: The “Pascalian 3D Simplex” for the Oppositional Tri-segment

    • Alessio Moretti
    Pages 347-479
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Keywords

About this book

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of opposition to solve theological problems regarding predestination and theodicy. Other topics covered include:
  • Hegel’s opposition to diagrams
  • De Morgan’s unpublished octagon of opposition 
  • turnstile figures of opposition
  • institutional model-theoretic treatment of oppositions
  • Lacan’s four formulas of sexuation
  • the theory of oppositional poly-simplexes

The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts.

Editors and Affiliations

  • Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    Jean-Yves Beziau

  • The Hellenic Open University, Patras, Greece

    Ioannis Vandoulakis

Bibliographic Information

  • Book Title: The Exoteric Square of Opposition

  • Book Subtitle: The Sixth World Congress on the Square of Opposition

  • Editors: Jean-Yves Beziau, Ioannis Vandoulakis

  • Series Title: Studies in Universal Logic

  • DOI: https://doi.org/10.1007/978-3-030-90823-2

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-030-90822-5Published: 24 August 2022

  • Softcover ISBN: 978-3-030-90825-6Published: 25 August 2023

  • eBook ISBN: 978-3-030-90823-2Published: 23 August 2022

  • Series ISSN: 2297-0282

  • Series E-ISSN: 2297-0290

  • Edition Number: 1

  • Number of Pages: X, 479

  • Number of Illustrations: 106 b/w illustrations, 193 illustrations in colour

  • Topics: Mathematical Logic and Foundations, Philosophy, general, Logic, Philosophy, general

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