Jill North argues that Hamiltonian mechanics provides the most spare -- and hence most accurate -- account of the structure of a classical world. We point out some difficulties for her argument, and raise some general points about attempts to minimize structural commitments.

According to the semantic view of scientific theories, theories are classes of models. I show that this view -- if taken seriously as a formal explication -- leads to absurdities. In particular, this view equates theories that are truly distinct, and it distinguishes theories that are truly equivalent. Furthermore, the semantic view lacks the resources to explicate interesting theoretical relations, such as embeddability of one theory into another. The untenability of the semantic view -- as currently formulated -- threatens to (...) undermine scientific structuralism. (shrink)

We are used to talking about the “structure” posited by a given theory of physics, such as the spacetime structure of relativity. What is “structure”? What does the mathematical structure used to formulate a theory tell us about the physical world according to the theory? What if there are different mathematical formulations of a given theory? Do different formulations posit different structures, or are they merely notational variants? I consider the case of Lagrangian and Hamiltonian classical mechanics. I argue that, (...) contrary to standard wisdom, these are not genuinely equivalent theories: they differ in statespace structure. I suggest that we should be realists about statespace structure. (shrink)