An Arithmetization of Logical Oppositions

In Jean-Yves Béziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Basel, Switzerland: Birkhäuser. pp. 215-237 (2016)
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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.

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Fabien Schang
Université de Lorraine (PhD)

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References found in this work

Sur l'opposition des concepts.Robert Blanche - 1953 - Theoria 19 (3):89-130.
Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
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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