Abstract: Recent trends in this literature can be broadly characterised by the way they begin either from the mathematics or the metaphysics. I take Weatherall (2018) as the primary example of the mathematical approach, in which he argues that if one is only to reflect on the correct use of the mathematics, one can block or undermine the hole argument. For the metaphysical approach, I focus on a line of argument I identify in Pooley and Read (2021) in which they claim that arguments from mathematical practice fail to eliminate the relevant space of metaphysical possibilities. Specifically, they maintain that the hole diffeomorphic manifolds can represent haecceitistically different spacetimes. In response to these trends, the primary aims of this research are twofold: first, I articulate a structuralist account of scientific representation, building on Van Fraassen's structuralist empiricism (2008), that answers the demarcation problems posed by Frigg and Nguyen (2022); second, I aim to use this account to diagnose the reasons for, and provide solutions to, the recent impasse in the voluminous literature on the hole argument. While I am sympathetic to the arguments from mathematical practice, I argue that without a structuralist account of scientific representation Pooley and Read’s counterargument cannot be defused. While I am conceding this point, however, I am doing so in a minimal way: no such representation can meet the criteria of being a scientific representation. Further, if the points p and p' in the hole argument are to represent different events in spacetime, it is merely by means of stipulation. If, as I argue, scientific representation is to be understood structurally, for a manifold to be considered a model of a spacetime, it needs to include a representation relation, understood as some variety of structural mapping. Moreover, an isomorphism acting on a model would also need to have a corresponding transformation on the representation relation, which is at least sensitive to the strongest notion of structure in the manifold being considered. I conclude that, while mathematical practice alone fails to exclude the possibility of the hole diffeomorphic models representing haecceitistic differences, a structuralist account of scientific representation excludes the possibility of these classifying as scientific representations.
The PoP-Grunch (Philosophy of Physics Graduate Lunch) is a weekly informal seminar in which graduate students in Philosophy of Physics present their work in progress.
Philosophy of Physics Graduate Lunch Seminar Convenor: Eleanor March, Bryan Cheng and Paolo Faglia
