Logica Universalis

, Volume 6, Issue 1–2, pp 1–43 | Cite as

The Power of the Hexagon

  • Jean-Yves BéziauEmail author


The hexagon of opposition is an improvement of the square of opposition due to Robert Blanché. After a short presentation of the square and its various interpretations, we discuss two important problems related with the square: the problem of the I-corner and the problem of the O-corner. The meaning of the notion described by the I-corner does not correspond to the name used for it. In the case of the O-corner, the problem is not a wrong-name problem but a no-name problem and it is not clear what is the intuitive notion corresponding to it. We explain then that the triangle of contrariety proposed by different people such as Vasiliev and Jespersen solves these problems, but that we don’t need to reject the square. It can be reconstructed from this triangle of contrariety, by considering a dual triangle of subcontrariety. This is the main idea of Blanché’s hexagon. We then give different examples of hexagons to show how this framework can be useful to conceptual analysis in many different fields such as economy, music, semiotics, identity theory, philosophy, metalogic and the metatheory of the hexagon itself. We finish by discussing the abstract structure of the hexagon and by showing how we can swing from sense to non-sense thinking with the hexagon.

Mathematics Subject Classification

Primary 03B22 Secondary 03A05 03B44 03B45 00A30 


Hexagon of opposition square of opposition contradiction negation quantification possibility modal logic deontic logic conceptual analysis structuralism truth a priori 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.CNPq-Brazilian Research CouncilUniversity of Brazil, Rio de Janeiro (UFRJ)Rio de JaneiroBrazil

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