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Groups, Not Squares: Exorcizing a Fetish

  • Walter Carnielli
Chapter
Part of the Studies in Universal Logic book series (SUL)

Abstract

I argue that the celebrated Square of Opposition is just a shadow of a much deeper relationship on duality, complementarity, opposition and quaternality expressed by algebraic means, and that any serious attempt to make sense of squares and cubes of opposition must take into account the theory of finite groups. By defining a group as triadic if all its elements, other than the identity, have order 3, I show that a natural notion of triality group acting on three-valued structures emerges, generalizing the intuitions of duality and quaternality.

Keywords

Boolean groups Group theory Square of opposition Triadic groups 

Mathematics Subject Classification (2000)

Primary 03A05 Secondary 05C25 

Notes

Acknowledgements

I acknowledge support from FAPESP Thematic Project LogCons 2010/51038-0, Brazil and from the National Council for Scientific and Technological Development (CNPq), Brazil. I am thankful to the five anonymous referees who have read, commented and criticized this paper.

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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Centre for Logic, Epistemology and the History of Science, CLE and Department of PhilosophyState University of Campinas - UnicampSPBrazil

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