HAND BOOK OF THE FIRST WORLD CONGRESS ON THE SQUARE OF OPPOSITION www.square-of-opposition.org Montreux, Switzerland June 1-3, 2007 Edited by Jean-Yves Beziau´ and Gillman Payette Contents 1 First World Congress on the Square of Opposition 1 1.1 The Square : a Central Object for Thought . 1 1.2 Aim of the Congress . 1 1.3 Primary Organizers . 1 1.4 Supporting Organizers . 2 2 Abstracts of Invited Talks 3 Valentin Bazhanov: Non-Classical Stems from Classical: N.A. Vasiliev’s Approach to Logic and His Reassessment of the Square of Opposition 3 Sieghard Beller: Human Deontic Reasoning and the Deontic Square of Op- position . 3 Jean-Yves Beziau:´ The 0-corner of the Square of Opposition, Paraconsis- tent Logic and the Polyhedron of Opposition . 4 Ivana Bianchi and Ugo Savardi: Perceptual Contrariety . 4 Pascal Engel: Can there be an Epistemic Square of Opposition? . 5 Laurence R. Horn: Lexical Pragmatics and the Geometry of Opposition . 5 Saul Kripke: Doctrine of Distribution in “Traditional” and Modern Quan- tification Theory . 6 Alessio Moretti: The Crowdy Logical Zoo Inhabited by the Old Square of Oppositions and the Many Strange Visitors of it . 6 Terence Parsons: Some Things that are Right with the Traditional Square of Opposition . 8 Pieter Seuren: The Blessings of Undue Existential Import . 8 Hans Smessaert: On the 3D Visualization of Logical Relations . 10 Jan Wolenski:´ Applications of Squares of Oppositions and their General- izations in Philosophical Analysis . 10 3 Abstracts of Contributors 13 R. Lill Anjum and J. Arnt Myrstad: All Men are Animals, but what Does it Really Mean? . 13 Andres´ Badenes: ‘Not Possible’ and ‘Impossible’ at a Modal Square of Opposition in Aristotle’s De Interpretatione 13 . 14 Semir´ Badir: Le Carre´ Semiotique´ dans tous ses Etats´ . 16 Hanoch Ben-Yami: The Validity of the Square . 16 i ii Peter Bernhard: Visualizations of the Square of Opposition . 17 Francesco Berto: Strong Paraconsistency and the Intuition of Opposition . 18 Jean-Yves Beziau,´ Alexandre Costa-Leite and Gillman Payette: Imagina- tion and the Square of Opposition . 18 Arthur Bierman: On Emplacing . 19 Andres´ Bobenrieth: Contradiction, “Contraryness” and Inconsistency: Elu- cidation and Terminological Proposal . 20 Stefania Bonfiglioli: Aristotle’s Non-Logical Works and the Square of Op- positions in Semiotics . 20 Joseph Brenner: Applying the Square of Opposition to Reality . 20 Veronique´ Briere:` Words, Predications, Forms of Things and Forms of Sig- nified Items–Which Ontological-Semantic Foundations for the Square of Opposition? . 21 Edward Buckner: The Fourth Corner of the Square . 21 Juan M. Campos-Benıtez: The Medieval Modal Octagon and the S5 Lewis Modal System . 22 Wagner de Campos Sanz: The Inversion Principle and The Interpretation of The Square of Oppositions . 22 Ferdinando Cavaliere and Antonio Donnarumma: Fuzzy Syllogisms, Nu- merical Square, Triangle of Contraries, Inter-Bivalence - with an His- torical Appendix on the Quantification of the Predicates . 24 Christopher Dartnell, Dominique Luzeaux and Jean Sallantin: Aristotle’s Square in a Logic of Scientific Discovery . 25 Aimable-Andre Dufatanye: The Geometrical Logical Figures and the Ob- jective and Normative Structure of Thought . 25 Jean-Claude Dumoncel and Pierre Simonnet: From the Square to the Star: Etoile de Blanche,´ Carre´ Apuleen´ & Carre´ Latin . 26 George Englebretsen: The Square Squared . 26 Katarzyna Gan-Krzywoszyaska:´ On Existence and some Ontologies . 27 Luis Estrada–Gonzalez:´ Pseudo-Weak Logics and the Traditional Square of Opposition . 27 Paul M. Healey: Contradicting the Improbable . 27 Dany Jaspers: Peirce’s Dagger and Natural Logic . 28 Jan C. Joerden: Supererogation and the Deontological Decagon . 28 Yurii Khomskii: William of Sherwood, Singular Propositions and the Hexagon of Opposition . 30 Rainer Kivi: Extended square of opposition . 31 Holger Leuz: The Square of Opposition in Modal Logic and Modal Reasoning 32 Elena Lisanyuk: Aristotle’s Square of Oppositions and W.Ockham’s Razor . 32 Wolfgang Lenzen: Gottfried Ploucquet’s Attempts to Refute the Traditional “Square of Opposition” . 34 Dominique Luzeaux, Jean Sallantin and Christopher Dartnell: Logical and Categorical Extensions of Aristotle’s Square . 34 Jaap Maat: How to Fit Singular Propositions into the Square: The Solution of John Wallis (1616-1703) . 35 Teresa Marques: The Square of Opposition and the Paradoxes . 35 iii John N. Martin: Existential Commitment in the Cartesian Square of Oppo- sition . 36 Robert Marty: Square vs Triad . 36 Ingolf Max: Dimensions of Opposition: Representing the Square by Two- dimensional Operators, and Some Linguistic Applications . 37 Paul McNamara: From the Deontic Square to the Deontic Octoecagon and Beyond . 37 Fred Seymour Michael: Paraconsistency, Negation and the Double Square . 39 Jacques Moeschler: Why are There no Negative Particulars? Horn’s Con- jecture Revisited . 40 Uaininn O’Meadhra: A Newly Discovered Medieval Diagram of the ’Square’ on Gotland, Sweden . 41 Alex Orenstein: Saving the Square and Having it All . 41 Ernesto Perini-Santos: John Buridan on the Bearer of Logical Relations . 42 Jerzy Perzanowski: Classical Modal Logics of the Square of Oppositions . 42 Claudio Pizzi: Aristotle’s Cubes and Consequential Implication . 42 Maria Popova and Ivan Kasabov: Applications Of The Square of Opposi- tion in Language, Phonology and Semantics . 42 Jean Sallantin, Christophe Douy, Abdelkader Gouaich, Juan Carlos Mar- tinez, Denis Pierre, Antoine Seilles , Jean-Baptiste Soufron Jean-Philippe Cointet: A Logical Framework to Annotate Documents in a Virtual Agora . 43 Fabien Schang: Illocutionary Oppositions . 43 Luc Schneider: The Logic of the Ontological Square . 45 Peter Schroeder-Heister: Direct Negation in Proof-Theoretic Semantics and the Square of Opposition . 46 Sumanta Sarathi Sharma: Interpreting Squares of Opposition with the Help of Diagrams . 47 Fabrice Silpa: Square of Opposition in Terminist Logic A Study of Consis- tency of Discourse . 47 Jurgis¨ Skilters: Oppositions Within a Frame . 48 Mireille Staschok: Non-Traditional Squares of Predication and Quantification 48 Corina Stroßner¨ and Niko Strobach: A Blanche´ Star for Truth-Functional Paraconsistent One-Place Operators . 49 Janusz Sytnik - Czetwertynski:´ R. Boscovich’s Onto/Logical Square of Op- positions . 50 Sara L. Uckelman: Anselm’s Logic of Agency . 51 Rafal Urbaniak: Square of Opposition and Existential Assumptions of Syl- logistic . 51 Paulo A. S. Veloso and Sheila R. M. Veloso: On Computing Modality-Like Diagrams . 52 Karin Verelst: Deictical Roots of the Square . 52 Patrick Walsh: The Modal Square of Opposition Applied to the Ontological and Cosmological Arguments . 53 Mark Weinstein: Counter-Examples in Theory-Driven Inquiry . 53 Dag Westerstahl:˚ Basic Square Knowledge . 54 iv Jonathan Westphal: The Application of Vector Theory to Syllogistic Logic . 54 4 Artistic Program 57 4.1 Music: The Square of Jazz . 57 4.2 Movie: The Square of Salome´ ..................... 58 Sponsors 61 Notes 63 1 First World Congress on the Square of Opposition 1.1 The Square : a Central Object for Thought The square of opposition is a very famous theme related to Aristotelian logic dealing with the notions of opposition, negation, quantification and proposition. It has been continuously studied by people interested in logic, philosophy and Aristotle during two thousand years. Even Frege, one of the main founders of modern mathematical logic, uses it. During the 20th century the interest for the square of opposition has been extended to many areas, cognitive science ultimately. Some people have proposed to replace the square by a triangle, on the other hand the square has been generalized into more complex geometrical objects: hexagons, octagons and even polyhedra and multi-dimensional objects. 1.2 Aim of the Congress This will be the first international congress organized about the square of opposition. The square will be considered in its various aspects. There will be talks by the best specialists of the square, and this will be an interdisciplinary event gathering people from various fields: logic, philosophy, mathematics, psychology, linguistics, anthropology, semiotics. Visual and artistic representations of the square will also be presented. There will be a musical performance and a movie illustrating the square. The meeting will end by a final round square table where subalterned people will express their various contrarieties, subcontrarieties and contradictions. 1.3 Primary Organizers Jean-Yves Beziau,´ University of Neuchatel/Swissˆ National Science Founda- tion, Switzerland Michael Frauchiger, Open University and Lauener Foundation, Switzerland 1 2 Square of Opposition Katarzyna Gan-Krzywoszynska, Poznan University, Poland Alessio Moretti, University of Neuchatel/Universityˆ of Nice, Switzerland/France Gillman Payette, Dalhousie University/University of Calgary, Canada Fabien Schang, Archives Poincare/University´ of Nancy 2, France, France 1.4 Supporting Organizers Alexandre Costa-Leite, University of Neuchatel/ENS,ˆ Switzerland/France Catherine Duquaire, EBC, Lyon, France Joana Medeiros, TVR, Rio de Janeiro, Brazil 2 Abstracts of Invited Talks Non-Classical Stems from Classical: N.A. Vasiliev’s Approach to Logic and His Reassessment of the Square of Opposition VALENTIN BAZHANOV Ulaynovsk State University Russia [email protected] In XIX century the persistent (“dead”) opposition to Aristotelian logic may be no- ticed. Nicolai A. Vasiliev (1880 – 1940) perceived this opposition