We argue that several apparently distinct responses to the hole argument, all invoking formal or mathematical considerations, should be viewed as a unified “mathematical response.” We then consider and rebut two prominent critiques of the mathematical response before reflecting on what is ultimately at issue in this literature.
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Bradley, C., & Weatherall, J. O. (2022). Mathematical Responses to the Hole Argument: Then and Now. Philosophy of Science, 89(5), 1223–1232. https://doi.org/10.1017/psa.2022.58