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Classifying Forms: Abstract Logics as Formal Ontologies
The paper focuses on the model-theoretic approach to logical structures developed by Jean-Yves Béziau within the framework of his Logica Universalis project. Firstly, it proposes an interpretation of model-theoretical abstract logics as classifications of isomorphism types, i.e., abstract structures. The isomorphism property is considered a meta-constraint on classes of structures rather than a criterion for demarcating logical from non-logical terms. Secondly, the paper adopts a model-theoretic interpretation of Husserlian manifolds as classes of models corresponding to theories, thereby treating abstract logics as formal ontologies. Finally, it introduces a dichotomy between substantial and dynamic formality to generalize the concept of logicality as invariance.