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.

中文翻译：

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Hole 论证，取 n

我将同伦类型理论 (HoTT) 应用于由 Earman 和 Norton 制定的空洞论证。我认为 HoTT 给出了一个精确的意义，其中与微分同胚相关的洛伦兹流形代表相同的时空，破坏了厄曼和诺顿的验证主义困境和空穴论证的常见公式。然而，采用这种解释并不能减轻对决定论的担忧：在洛伦兹流形上制定的广义相对论使用这种相同标准和 HoTT 中决定论的自然形式化是不确定的。解决这种不确定性导致了物理学家使用的广义相对论的更忠实的数学表示。它还给出了一般协方差的实质性概念。