In Jean-Yves Beziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Bâle, Suisse: pp. 215-237 (2016)

Authors
Fabien Schang
Universidade Federal de Goiás (PhD)
Abstract
An arithmetic theory of oppositions is devised by comparing expressions, Boolean bitstrings, and integers. This leads to a set of correspondences between three domains of investigation, namely: logic, geometry, and arithmetic. The structural properties of each area are investigated in turn, before justifying the procedure as a whole. Io finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.
Keywords oppositions  k-base system  vectors  Chasles' relations  Yi King  hexagrams
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References found in this work BETA

Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
Sur l'opposition des concepts.Robert Blanche - 1953 - Theoria 19 (3):89-130.
On the 3d Visualisation of Logical Relations.Hans Smessaert - 2009 - Logica Universalis 3 (2):303-332.
“Setting” N-Opposition.Régis Pellissier - 2008 - Logica Universalis 2 (2):235-263.

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Citations of this work BETA

End of the Square?Fabien Schang - 2018 - South American Journal of Logic 4 (2):485-505.
Making Sense of History? Thinking About International Relations.Fabien Schang - 2014 - In Leonid Grinin, Ilya V. Ilyin & Andrey V. Korotayev (eds.), Globalistics and Globalization Studies. Aspects & Dimensions of Global Views. Volgograd, Oblast de Volgograd, Russie: pp. 50-60.

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Abstract Logic of Oppositions.Fabien Schang - 2012 - Logic and Logical Philosophy 21 (4):415--438.
Le problème de l'opposition dans la philosophie de Nietzsche.Wolfgang Müller-Lauter - 2006 - Revue Philosophique de la France Et de l'Etranger 196 (4):455 - 478.
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Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
The Geometry of Standard Deontic Logic.Alessio Moretti - 2009 - Logica Universalis 3 (1):19-57.
Oppositions and Opposites.Fabien Schang - 2012 - In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Bâle, Suisse: Birkhäuser. pp. 147--173.

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