An Arithmetization of Logical Oppositions

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