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Duality in Logic and Language

Internet Encyclopedia of Philosophy (2016)

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  1. Between Square and Hexagon in Oresme's Livre du Ciel Et du Monde.Lorenz Demey - 2019 - History and Philosophy of Logic 41 (1):36-47.
    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 (...)
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  • Boolean Considerations on John Buridan's Octagons of Opposition.Lorenz Demey - 2018 - History and Philosophy of Logic 40 (2):116-134.
    This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then (...)
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  • No-Right and its Correlative.Andrew Halpin - 2021 - American Journal of Jurisprudence 65 (2):147-166.
    : This article aims to dispel the confusion over no-right by drawing attention to three straightforward points, and by examining a neglected source of complexity. The former embrace the practical significance of a no-right within Hohfeld’s scheme; the important difference between the practical significance of a normative position and the theoretical status of the concept representing it; and, the relationship between logical duals and contradictories when applied to normative positions. The complexity is associated with liberty as the correlative of no-right, (...)
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