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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 and, on a more abstract level, the Aristotelian geometry. We then introduce two new logical geometries, 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
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DOI 10.1007/s10849-014-9207-y
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References found in this work BETA

A Natural History of Negation.Laurence Horn - 1989 - University of Chicago Press.
Meaning and Necessity.Rudolf Carnap - 1947 - University of Chicago Press.
First-Order Modal Logic.Roderic A. Girle, Melvin Fitting & Richard L. Mendelsohn - 2002 - Bulletin of Symbolic Logic 8 (3):429.
Dynamic Logic.Lenore D. Zuck & David Harel - 1989 - Journal of Symbolic Logic 54 (4):1480.

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Citations of this work BETA

Metalogical Decorations of Logical Diagrams.Lorenz6 Demey & Hans5 Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
An Arithmetization of Logical Oppositions.Fabien Schang - 2016 - In Jean-Yves Beziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Bâle, Suisse: pp. 215-237.
Using Syllogistics to Teach Metalogic.Lorenz6 Demey - 2017 - Metaphilosophy 48 (4):575-590.

View all 16 citations / Add more citations

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