History and Philosophy of Logic 41 (1):36-47 (2019)

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Abstract
In logic, Aristotelian diagrams are almost always assumed to be closed under negation, and are thus highly symmetric in nature. In linguistics, by contrast, these diagrams are used to study lexicalization, which is notoriously not closed under negation, thus yielding more asymmetric diagrams. This paper studies the interplay between logical symmetry and linguistic asymmetry in Aristotelian diagrams. I discuss two major symmetric Aristotelian diagrams, viz. the square and the hexagon of opposition, and show how linguistic considerations yield various asymmetric versions of these diagrams. I then discuss a pentagon of opposition, which occupies an uneasy position between the square and the hexagon. Although this pentagon belongs neither to the symmetric realm of logic nor to the asymmetric realm of linguistics, it occurs several times in the literature. The oldest known occurrence can be found in the cosmological work of the 14th-century author Nicole Oresme.
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DOI 10.1080/01445340.2019.1647485
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References found in this work BETA

A Natural History of Negation.Laurence Horn - 1989 - University of Chicago Press.
The Development of Logic.William Calvert Kneale & Martha Kneale - 1962 - Oxford, England: Clarendon Press.
A Natural History of Negation.Jon Barwise & Laurence R. Horn - 1991 - Journal of Symbolic Logic 56 (3):1103.
The Development of Logic.William Kneale & Martha Kneale - 1962 - Studia Logica 15:308-310.
A Natural History of Negation.Laurence R. Horn - 1991 - Philosophy and Rhetoric 24 (2):164-168.

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