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Models and Ontologies in Mathematics and Physics by Barry Smith

Barry Smith presented Models and Ontologies in Mathematics and Physics at the Ontology Summit 2025 on 12 February 2025. In the paper https://arxiv.org/abs/2305.01560 Jobst Landgrebe and I outline the beginnings of on ontology of physics and mathematics from a BFO (= commonsensical) perspective. I will sketch how the ontologies of classical and modern physics relate to the ontology of common sense and of mathematics. In brief, classical physics inherits the common-sense view of nature, and uses mathematics to formalise our natural understanding of the causes and effects we observe in time and space when we select subsystems of nature for modelling. But in modern physics, we do not extend the realm of common sense by augmenting our knowledge of what is going on in nature. Rather, we have measurements that we do not understand, so we know nothing about the ontology of what we measure. We help ourselves by using entities from mathematics, which we do understand ontologically.