Models, Theories, and Structures: Thirty Years on

By Newton C. A. DA COSTA, Steven French. Philosophia Scientiæ, 2000

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Modelling and representing: An artefactual approach to model-based representation (2011, background): “…agreement among philosophers of science that models give us knowledge because they represent some real-world “target systems” (e.g., Bailer-Jones 2003; da Costa and French 2000; French and Ladyman 1999; Frigg 2002; Morrison and Morgan 1999; Suárez 1999; Giere 2004; Contessa 2007, Maki forthcoming).”
How do models give us knowledge? The case of Carnot’s ideal heat engine (2011, background): “…between a model and its target system is analysed in terms of morphisms of various kinds: The suggested morphisms include isomorphism (e.g. van Fraassen 1980, Suppe 1974), partial isomorphism (e.g. da Costa and French 2000, French and Ladyman 1999) and homomorphism (Bartels 2006, Ambrosio 2007).”