Daniel J Singer
The Problem of Scientific Modeling
represent, and associating a theory of springs with all possible springs does not appear to be any more structure-centric than associating the theory with the set of propositions that describe all possible springs, as in the “received” view. So, for structural realists, the use of Godfrey-Smith’s type of models undermines the appeal of the semantic approach compared to the “received” view. In order to make the semantic view useful to the structural realist, models must be stipulated in a structure-centric manner. The most familiar way to do this is with the Tarskian set-theoretic approach favored by Suppes. Here the structure of the theory can be associated with the relations defined explicitly in the model. Alternatively, the state-space view, which takes a model to be a set of states along with transition rules, is the most prominent contender. Here, the theory structure can be associated with the transition rules or some manipulation of them. For the purposes of this essay, although I occasionally make reference to models as state-spaces or Hilbert spaces with transition rules, my arguments are generalizable to any abstract-model representation. It is necessary only that theory models be structure-centric abstract semantic objects to avoid the structural realist’s objection to Godfrey-Smith’s view. I will use “theory model” to mean an abstract structure-centric model of a theory, and I will take an abstract-model semantic view to be the view that a scientific theory is a collection of theory models.
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Modeling with the Semantic Approach
As we saw above, the structural realist requires the use of abstract models to exploit the semantic view of theories, and I will show that the abstract-model semantic view is incompatible with an adequate account of the practice of modeling in science. In this and the next sections, I will describe some past approaches to dealing with modeling and resemblance in the abstract-model semantic view, but I will show that none of these accounts is sufficient. Then in Section 5, I will provide an argument that no such account can be given. In the end, since scientific modeling plays such an central role in scientific practice, any acceptable complete philosophy of science should admit of an account of scientific modeling, so I will conclude that the structural realist must either forgo the abstract-model semantic view or adjust the semantic view to include a type of model interpretation that is counter to the original thesis of the semantic view. But first, let’s look at the role of models in science. Much of science is consumed with the use of scientific models. Take, for example, the Lotka-Volterra model of predator-prey interaction, the Bohr model of the atom, or equilibrium models in economics. Generally, scientific modeling has the following form: there 5