The power of the hexagon

Logica Universalis 6 (1-2):1-43 (2012)

Authors
Jean-Yves Beziau
Universidade Federal do Rio de Janeiro
Abstract
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
Keywords Hexagon of opposition  square of opposition  contradiction  negation  quantification  possibility  modal logic  deontic logic  conceptual analysis  structuralism  truth  a priori
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DOI 10.1007/s11787-012-0046-9
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References found in this work BETA

Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
A Natural History of Negation.Laurence Horn - 1989 - University of Chicago Press.
On the 3d Visualisation of Logical Relations.Hans Smessaert - 2009 - Logica Universalis 3 (2):303-332.

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Citations of this work BETA

Metalogical Decorations of Logical Diagrams.Lorenz Demey & Hans Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
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