ABSTRACT
What are models and what is their place in the edifice of science? We begin by distinguishing between two basic types of models: representational models and logical models. This allows us to explicate the role of models in the Received View, which sees models as alternative interpretations of a theory’s formalism, and discuss criticisms of this approach to models. We introduce set-theoretical structures and formal semantics, and we discuss what it means for two structures to be isomorphic. This paves the ground for a discussion of the limitations of first-order logic, focusing on Löwenheim-Skolem theorem and on Gödel’s first incompleteness theorem. We then ask what implications these limitations have for the Received View and point out that these limitations are not ipso facto arguments against the view.
