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Journal of Logic, Language and Information

, Volume 23, Issue 4, pp 527–565 | Cite as

Logical Geometries and Information in the Square of Oppositions

  • Hans Smessaert
  • Lorenz Demey
Article

Abstract

The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams (such as the square) and, on a more abstract level, the Aristotelian geometry (a set of logical relations). We then introduce two new logical geometries (and their corresponding diagrams), and develop a formal, well-motivated account of their informativity. This enables us to show that the square is strictly more informative than many of the more complex diagrams.

Keywords

Square of oppositions Logical geometry Logical diagram Opposition Implication Information as range  Unconnectedness 

Notes

Acknowledgments

Earlier versions of this paper were presented at Trends in Logic XI (Bochum, June 3–5 2012) and CLMPS 14 (Nancy, July 19–26 2011); we would like to thank the audiences of these talks for their helpful remarks and suggestions. We would also like to thank Dany Jaspers, Alessio Moretti, Fabien Schang, Margaux Smets and three anonymous referees for their extensive feedback on earlier versions of this paper. The second author is financially supported by a Ph.D. fellowship of the Research Foundation–Flanders (FWO).

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Authors and Affiliations

  1. 1.Department of LinguisticsKU LeuvenLeuvenBelgium
  2. 2.Center for Logic and Analytic PhilosophyKU LeuvenLeuvenBelgium

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