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Title: Metalogic, Metalanguage and Logical Geometry
Author(s): DEMEY, Lorenz
Journal: Logique et Analyse
Volume: 248    Date: 2019   
Pages: 453-478
DOI: 10.2143/LEA.248.0.3287325

Abstract :
Logical geometry studies Aristotelian diagrams (such as the square of opposition) as objects of independent interest. In the past few years, it has become increasingly clear that these diagrams are directly related to a number of metalogical and metalinguistic issues. The present paper has two interrelated aims. On the one hand, I provide a fully general and mathematically precise account of the Aristotelian relations, which takes into account their metalogical aspects, and explains how a single type of relations can hold between object-logical as well as between metalogical entities. On the other hand, I argue for the theoretical fruitfulness of this general approach to the Aristotelian relations, by showing how it enables a unified pragmatic account of certain linguistic phenomena, regardless of whether they occur at the object- or metalinguistic level. The paper thus fits within the larger project of constructing a bridge between logical geometry and metalogical and -linguistic considerations.

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