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This article argues for a representational semantic conception (RSC) of scientific theories, which respects the bare claim of any semantic view, namely, that theories can be characterized as sets of models. RSC must be sharply distinguished from structural versions that assume a further identity of ‘models’ and ‘structures’, which we reject. The practice turn in the recent philosophical literature suggests instead that modeling must be understood in a deflationary spirit, in terms of the diverse representational practices in the sciences. These insights are applied to some mathematical models, thus showing that the mathematical sciences are not in principle counterexamples to RSC.
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