Ontology and the mathematization of the scientific enterprise

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Krause, Décio; Arenhart, Jonas R. B.; da Costa, Newton C. A.
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preprint description
In this basically expository paper we discuss the role of logic and mathematics in researches concerning the ontology of scientific theories, and we consider the particular case of quantum mechanics. We argue that systems of logic in general, and classical logic in particular, may contribute substantially with the ontology of any theory that has this logic in its base. In the case of quantum mechanics, however, from the point of view of philosophical discussions concerning identity and individuality, those contributions may not be welcome for a specific interpretation, and an alternative system of logic perhaps could be used instead of a classical system. In this sense, we argue that the logic and ontology of a scientific theory may be seen as mutually influencing each other. On the one hand, logic contributes to shape the general features of the ontology of a theory; on the other hand, the theory also puts constraints on the possible understanding of ontology and, respectively, on possible systems of logic that may be the underlying logic of the theory.