From the Logical Square to Blanché’s Hexagon: Formalization, Applicability and the Idea of the Normative Structure of Thought

Abstract

The square of opposition and many other geometrical logical figures have increasingly proven to be applicable to different fields of knowledge. This paper seeks to show how Blanche generalizes the classical theory of oppositions of propositions and extends it to the structure of opposition of concepts. Furthermore, it considers how Blanche restructures the Apuleian square by transforming it into a hexagon. After presenting G. Kalinowski’s formalization of Blanche’s hexagonal theory, an illustration of its applicability to mathematics, to modal logic, and to the logic of norms is depicted. The paper concludes by criticizing Blanche’s claim according to which, his logical hexagon can be considered as the objective basis of the structure of the organisation of concepts, and as the formal structure of thought in general. It is maintained that within the frame of diagrammatic reasoning Blanche’s hexagon keeps its privileged place as a “nice” and useful tool, but not necessarily as a norm of thought.