Logica Universalis

, Volume 6, Issue 1–2, pp 45–67

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


DOI: 10.1007/s11787-012-0040-2

Cite this article as:
Dufatanye, AA. Log. Univers. (2012) 6: 45. doi:10.1007/s11787-012-0040-2


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 Blanché generalizes the classical theory of oppositions of propositions and extends it to the structure of opposition of concepts. Furthermore, it considers how Blanché restructures the Apuleian square by transforming it into a hexagon. After presenting G. Kalinowski’s formalization of Blanché’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 Blanché’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 Blanché’s hexagon keeps its privileged place as a “nice” and useful tool, but not necessarily as a norm of thought.

Mathematics Subject Classification (2010)

Primary 03A10 Secondary 03B05 03B45 


Apuleian square Blanché’s hexagon formalization hexagon of modalities norm of thought intellectual structures principle of non-contradiction diagrammatic reasoning 

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Ecole Normale Supérieure de LyonLyon Cedex 07France

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