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 Aristotles ontological square, logical oppositions in Avicennas hypothetical logic, and the power of the square of opposition to solve theological problems regarding predestination and theodicy. Other topics covered include:Hegels opposition to diagramsDe Morgans unpublished octagon of opposition turnstile figures of oppositioninstitutional model-theoretic treatment of oppositionsLacans four formulas of sexuationthe theory of oppositional poly-simplexesThe Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts.

The Square of opposition: Past, Present and Future.- Division of Entities and Foundations of Reality: Aristotles Ontological Square.- Logical Oppositions in Avicennas Hypothetical Logic.- Incommensurability and Inapplicability of the Squares of Opposition.- The square of opposition as a framework for Stephen Langtons theological solutions.- The limits of the square - Hegels opposition to diagrams in its historical context.- Augustus De Morgans Unpublished Octagon of Opposition.- A Bitstring Semantic for Calculus CL.- Logical Diagrams, Visualization Criteria, and Boolean Algebras.- Turnstile Figures of Opposition.- The Naturalness of Jacques Lacan's Logic.- On Modal Opposition within some Modal Discussive Logics.- On the Transformations of the Square of Opposition from the point of view of Institution Model Theory.- Color-Coded Epistemic Modes in a Jungian Hexagon of Opposition.- Many-valued logical hexagons in a 3-oppositional trisimplex.- Tri-Simplicial Contradiction: the Pascalian 3D Simplex and its Oppositional Tri-Segment.