The Square of Opposition: A Cornerstone of Thought

Part I. Introduction

1. The Square of Opposition: A Cornerstone of Thought
Jean-Yves Béziau, Gianfranco Basti

2. Welcome Address to the Participants of the IV International Congress on: The Square of Opposition Vatican City, PUL, May 5–9, 2014
Monsignor Enrico Dal Covolo

Part II. Historical Perspectives on the Square

3. The Proto-exposition of Aristotelian Categorical Logic
Manuel Correia

4. The Modal Octagon and John Buridan’s Modal Ontology
Spencer Johnston

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

Part III. Reinterpretations of the Square

6. Symmetric Properties of the Syllogistic System Inherited from the Square of Opposition
Bora İ Kumova

7. The Square of Opposition Interpreted with a Decidable Modal Logic
Paul Weingartner

8. Two Standard and Two Modal Squares of Opposition
Jiří Raclavský

Part IV. Philosophical Perspectives on the Square

9. The Many Faces of Inconsistency
Bobenrieth M. Andrés

10. Aristotle, Frege and “Second Nature”
Raffaela Giovagnoli, Philip Larrey

11. There Is No Cube of Opposition
Jean-Yves Béziau

Part V. Theoretical Investigations on the Square

12. The Unreasonable Effectiveness of Bitstrings in Logical Geometry
Hans Smessaert, Lorenz Demey

13. An Arithmetization of Logical Oppositions
Fabien Schang

14. Groups, Not Squares: Exorcizing a Fetish
Walter Carnielli

Part VI. Expansions and Variations of the Square

15. From the Square to Octahedra
José David García-Cruz

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

17. The Exact Intuitionistic Meaning of the Square of Opposition
Joseph Vidal-Rosset

Part VII. Applications of the Square

18. The Ontological Modal Collapse as a Collapse of the Square of Opposition
Christoph Benzmüller, Bruno Woltzenlogel Paleo

19. Fuzzy Eubouliatic Logic: A Fuzzy Version of Anderson’s Logic of Prudence
Gert-Jan C. Lokhorst

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

Keywords: Philosophy, Logic, Philosophy of Mathematics, Mathematical Logic and Foundations