What Scientific Theories Could Not Be (Halvorson)

Occasionally, the issue of the model-theoretic, or "semantic", view of scientific theories has been mentioned here on M-Phi. I've spent ages arguing that this view is mistaken. My objections have always been that first a model $\mathcal{A}$ (or, a collection $\Sigma$ of models) is not a truth-bearer, whereas a scientific theory must be a truth bearer: otherwise one simply assumes instrumentalism from the start, which is cheating. But, second, if one tries to remedy this by saying that a collection $\Sigma$ of models is "true" if and only if some $\mathcal{A} \in \Sigma$ represents the world, then the notion of a "structure representing the world" has never been either defined precisely or explicated coherently. And, third, if one tries to do this in the most obvious way, then one is led very quickly to a Newman problem: a structure $\mathcal{A}$ represents the world just if the world is large enough. This is because the world isn't, or isn't obviously, a structure in the usual mathematical sense. And fourth, there is a non-obvious way to remedy the Newman problem, which involves defining the notion of an interpretation of a structure, but it, in effect, reintroduces the notion of an interpreted language, $(\mathcal{L}, \mathcal{I})$--precisely the thing the advocates of the "semantic view" insisted should be avoided! (Interesting, is it not, that advocates of a so-called "semantic" view should reject the concept of an interpretation: perhaps the central concept of semantics.) Some of these objections have also been made by others (e.g., Anjan Chakravartty in 2001 and Roman Frigg in 2006).

The philosopher of physics Hans Halvorson (Princeton) now has a very interesting preprint on the Pittsburgh PhilSci archive called "What Scientific Theories Could Not Be", which I believe is forthcoming in Philosophy of Science. Halvorson raises several further objections against the semantic view of theories. In particular, it argues that by identifying a theory with a collection of models and analysing equivalence in terms of isomorphisms between models, the view gets theoretical equivalences wrong. It's very stimulating paper and I recommend it for anyone interested in this important topic within General Philosophy of Science.