The persistent challenge of formulating ontic structuralism in a rigorous manner, which prioritizes structures over the entities they contain, calls for a transformation of traditional logical frameworks. I argue that Univalent Foundations (UF), which feature the axiom that all isomorphic structures are identical, offer such a foundation and are more attractive than other proposed structuralist frameworks. Furthermore, I delve into the significance in the case of the hole argument and, very briefly, the nature of symmetries.

The hole argument concludes that substantivalism about spacetime entails the radical indeterminism of the general theory of relativity (GR). In this paper, I amend and defend a response to the hole argument first proposed by Butterfield (1989) that relies on the idea of counterpart substantivalism. My amendment clarifies and develops the metaphysical presuppositions of counterpart substantivalism and its relation to various definitions of determinism. My defence consists of two claims. First, contra Weatherall (2018) and others: the hole argument is not (...) a blunder resulting from a mistaken view on how mathematical physics works, and requires a developed (meta)metaphysical response. Second, contra Melia (1999) and others: one can be content with a notion of determinism for GR which is not sensitive to merely haecceitistic differences. (shrink)

This special issue of Foundations of Physics collects together articles representing some recent new perspectives on the hole argument in the history and philosophy of physics. Our task here is to introduce those new perspectives.

Ladyman and Presnell have recently argued that the Hole argument is naturally resolved when spacetime is represented within homotopy type theory rather than set theory. The core idea behind their proposal is that the argument does not confront us with any indeterminism, since the set-theoretically different representations of spacetime involved in the argument are homotopy type-theoretically identical. In this article, we will offer a new resolution based on ZFC set theory to the argument. It neither relies on a constructive-intuitionistic form (...) of mathematics, as used by Ladyman and Presnell, nor is foundationally problematic, such as the existing set-theoretic suggestions. (shrink)