Omar Mahmutović
The logical hexagon of opposition is the minimal structure that explicates the entire network of oppositional relations between logical propositions. As such, it represents the continuation and completion of the project initiated by Aristotle through the combinatorics of judgments according to quality and quantity, a conceptual sequence formally expressed by the logical square. While the square registers four relations, it leaves unarticulated the situations in which both contrary assertions are false or both subcontrary assertions are true. The hexagon explicates these precise instances by introducing the Y and U nodes, thereby closing the oppositional structure. The thesis of this article affirms that the logical hexagon constitutes an essential explication of the square itself. Through a detailed analysis of the development of logical geometry, it becomes clear that the hexagon articulates and fully illuminates the internal structure that the square contains in an implicit form. This analysis allows the fundamental relations of the square to be conceived within a broader and more coherent framework. In this manner, the logical hexagon as a construction serves as a necessary conceptual clarification and illustration of the geometric representation of logical relations.