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The Hole Argument, take n

  • John DoughertyEmail author
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  1. Special Issue : Hole Argument

Abstract

I apply homotopy type theory (HoTT) to the hole argument as formulated by Earman and Norton. I argue that HoTT gives a precise sense in which diffeomorphism-related Lorentzian manifolds represent the same spacetime, undermining Earman and Norton’s verificationist dilemma and common formulations of the hole argument. However, adopting this account does not alleviate worries about determinism: general relativity formulated on Lorentzian manifolds is indeterministic using this standard of sameness and the natural formalization of determinism in HoTT. Fixing this indeterminism results in a more faithful mathematical representation of general relativity as used by physicists. It also gives a substantive notion of general covariance.

Keywords

Homotopy type theory General relativity Hole argument General covariance 
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Notes

Acknowledgements

An early version of this paper was presented at IPP 2015 and received helpful feedback from the audience. Thanks, too, to Craig Callender, Kathleen Connelly, Nat Jacobs, Chip Sebens, Sebastian Speitel, Anncy Thresher, and Christian Wüthrich for extensive feedback and discussion since then.

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Authors and Affiliations

  1. 1.Munich Center for Mathematical PhilosophyLMU MunichMunichGermany

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