On Representational Capacities, with an Application to General Relativity

Recent work on the hole argument in general relativity by Weatherall (Br J Philos Sci 69(2):329–350, 2018) has drawn attention to the neglected concept of (mathematical) models’ representational capacities. I argue for several theses about the structure of these capacities, including that they should be understood not as many-to-one relations from models to the world, but in general as many-to-many relations constrained by the models’ isomorphisms. I then compare these ideas with a recent argument by Belot (Noûs, 2017. https://doi.org/10.1111/nous.12200) for the claim that some isometries “generate new possibilities” in general relativity. Philosophical orthodoxy, by contrast, denies this. Properly understanding the role of representational capacities, I argue, reveals how Belot’s rejection of orthodoxy does not go far enough, and makes better sense of our practices in theorizing about spacetime.