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  1. Using Syllogistics to Teach Metalogic.Lorenz Demey - 2017 - Metaphilosophy 48 (4):575-590.
    This article describes a specific pedagogical context for an advanced logic course and presents a strategy that might facilitate students’ transition from the object-theoretical to the metatheoretical perspective on logic. The pedagogical context consists of philosophy students who in general have had little training in logic, except for a thorough introduction to syllogistics. The teaching strategy tries to exploit this knowledge of syllogistics, by emphasizing the analogies between ideas from metalogic and ideas from syllogistics, such as existential import, the distinction (...)
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  • 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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  • Morphisms Between Aristotelian Diagrams.Alexander De Klerck, Leander Vignero & Lorenz Demey - forthcoming - Logica Universalis:1-35.
    In logical geometry, Aristotelian diagrams are studied in a precise and systematic way. Although there has recently been a good amount of progress in logical geometry, it is still unknown which underlying mathematical framework is best suited for formalizing the study of these diagrams. Hence, in this paper, the main aim is to formulate such a framework, using the powerful language of category theory. We build multiple categories, which all have Aristotelian diagrams as their objects, while having different kinds of (...)
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  • 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.
    The paper examines Schopenhauer’s complex diagrams from the Berlin Lectures of the 1820 s, which show certain partitions of classes. Drawing upon ideas and techniques from logical geometry, we show that Schopenhauer’s partition diagrams systematically give rise to a special type of Aristotelian diagrams, viz. (strong) α -structures.
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