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.

This paper is a critical response to Andreas Bartels' (2006) sophisticated defense of a structural account of scientific representation. We show that, contrary to Bartels' claim, homomorphism fails to account for the phenomenon of misrepresentation. Bartels claims that homomorphism is adequate in two respects. First, it is conceptually adequate, in the sense that it shows how representation differs from misrepresentation and non-representation. Second, if properly weakened, homomorphism is formally adequate to accommodate misrepresentation. We question both claims. First, we show that homomorphism is not the right condition to distinguish representation from misrepresentation and non-representation: a "representational mechanism" actually does all the work, and it is independent of homomorphism -as of any structural condition. Second, we test the claim of formal adequacy against three typical kinds of inaccurate representation in science which, by reference to a discussion of the notorious billiard ball model, we define as abstraction, pretence, and simulation. We first point out that Bartels equivocates between homomorphism and the stronger condition of epimorphism, and that the weakened form of homomorphism that Bartels puts forward is not a morphism at all. After providing a formal setting for abstraction, pretence and simulation, we show that for each morphism there is at least one form of inaccurate representation which is not accommodated. We conclude that Bartels' theory -while logically laying down the weakest structural requirements -is nonetheless formally inadequate in its own terms. This should shed serious doubts on the plausibility of any structural account of representation more generally.

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