Scientific representation and perspective

Consider the aims of the following three influential philosophical views. The semantic view of theories aims to supply the proper form and content of scientific theories. Structural realism aspires to delimit the epistemology and ontology of science. Mathematical structuralism seeks to reveal the epistemological and ontological nature of – you guessed it – mathematical objects. Given their divergent aims they may seem like unlikely bedfellows, but the semantic view of theories, structural realism and mathematical structuralism share enough ground to be able to benefit or suffer from some of the same reasons. What unites the three views is the purely structural analysis of their respective subject matter. The semantic view sees theories as nothing more than families of models, i.e. sets of structures. Representation, according to this view, is a matter of establishing mappings between some models of the theory and target domains. Structural realism judges scientific knowledge and perhaps even ontology to be wholly structural. Mathematical structuralism proclaims that the objects of mathematics are specifiable only up to isomorphism.
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