Dougherty, John
(2020):
The Hole Argument, take n.
In: Foundations of Physics, Vol. 50, No. 4: pp. 330347

Full text not available from 'Open Access LMU'.
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 diffeomorphismrelated 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.