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Fletcher, Samuel C. (2020): On Representational Capacities, with an Application to General Relativity. In: Foundations of Physics, Vol. 50, No. 4: pp. 228-249
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Abstract

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 (Nous, 2017. 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.