Abstract
How should one remove “excess structure” from a physical theory? Dewar (2019) presents two ways to undertake such a task: first, one could move to a reduced version of the theory, where one defines the models of the theory only in terms of structure that is invariant under the symmetries of the theory. Second, one could move to a sophisticated version of the theory, where symmetry-related models of a theory are isomorphic. Dewar argues that despite these alternatives attributing the same structure to the world, the sophisticated version can have explanatory benefits over the reduced version. Here, I consider a different argument that might be considered in favour of the sophisticated view: the differences between isomorphic models in a sophisticated theory can have representational significance. Thus, a reduced version of a theory may be unable to distinguish physical situations that can be distinguished in the sophisticated version of the theory. That isomorphic models can be used to represent distinct situations has been argued before (for instance, Belot (2018); Fletcher (2018); Roberts (2020)). However, these arguments do not directly show that the reduced version of a theory is unable to represent such situations. Indeed, if the reduced version of a theory posits the same structure as the sophisticated alternative, how can the sophisticated version represent a greater number of physical possibilities? I will argue that this tension can be resolved by considering more carefully the ways that isomorphic models can be used to represent distinct situations. This will provide support for the claim that the sophisticated version of a theory can be representationally advantageous to its reduced version, without rejecting the claim that the sophisticated and reduced version of a theory ascribe the same structure. In particular, I will argue that the sense in which isomorphic models can represent distinct situations is that one has the freedom to define additional structure within the models of the theory that can be used to represent a physical standard of comparison. It is the ability to define this additional structure that may be lacking in the reduced version of the theory, since one may not have the same representational freedom within the models of the reduced theory. I will use this argument to make a more general claim: the language that one uses to define the models of a theory is not always merely a conventional choice. One may choose one way of representing the models of a theory because it provides one with the resources to define additional structure that plays a physical role, even though this structure is not part of the structure of the theory. I suggest that more attention should therefore be paid to the role that model theory plays in determining which version of a theory should be adopted.
