The Hole Argument, take n

Dougherty, John (2020): The Hole Argument, take n. In: Foundations of Physics, Vol. 50, No. 4: pp. 330-347

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.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science
• Subjects: 100 Philosophy and Psychology > 100 Philosophy
• ISSN: 0015-9018
• Language: English