There Is No Cube of Opposition

  • Jean-Yves BéziauEmail author
Part of the Studies in Universal Logic book series (SUL)


The theory of opposition has been famously crystallized in a square. One of the most common generalizations of the square is a cube of opposition. We show here that there is no cube such that each of its faces is a square of opposition. We discuss the question of generalization and present two other generalizations of the theory of opposition to the third dimension: one based on Blanché’s hexagon of opposition, the other on the square of contrariety.


Cube of opposition Generalization Hexagon of opposition n-Opposition Square of opposition 

Mathematics Subject Classification (2000)

Primary 03A05; Secondary 00A30; 03B45 03B53 03B22 03B50. 



Thanks to Catherine Chantilly and Robert Purdy for discussion and comments.


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Brazilian Research CouncilUniversity of BrazilRio de JaneiroBrazil

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