On Representational Capacities, with an Application to General Relativity

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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.

Original languageEnglish (US)
Pages (from-to)228-249
Number of pages22
JournalFoundations of Physics
Issue number4
StatePublished - Apr 1 2020

Bibliographical note

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.


  • Abstraction
  • General relativity
  • Hole argument
  • Isomorphism
  • Models in science
  • Representation
  • Units


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