Logical Geometries and Information in the Square of Oppositions

Journal of Logic, Language and Information 23 (4):527-565 (2014)
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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

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Citations of this work

Schopenhauer’s Partition Diagrams and Logical Geometry.Jens Lemanski & Lorenz Demey - 2021 - In A. Basu, G. Stapleton, S. Linker, C. Legg, E. Manalo & P. Viana (eds.), Diagrams 2021: Diagrammatic Representation and Inference. 93413 Cham, Deutschland: pp. 149-165.
Metalogical Decorations of Logical Diagrams.Lorenz Demey & Hans Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.
Epistemic Pluralism.Fabien Schang - 2017 - Logique Et Analyse 239 (60):337-353.

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References found in this work

Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
A Natural History of Negation.Laurence R. Horn - 1989 - University of Chicago Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
Logical Dynamics of Information and Interaction.Johan van Benthem - 2011 - New York: Cambridge University Press.

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