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An Arithmetization of Logical Oppositions

  • Fabien Schang
Chapter
Part of the Studies in Universal Logic book series (SUL)

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. To finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.

Keywords

k-base system Bitstring Chasles’ relation Opposite Opposition Question-answer semantics Vectors 

Mathematics Subject Classification

Primary 03B35 Secondary 03B05 03B65 

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia

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