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)

In this paper, I revisit Frege's theory of sense and reference in the constructive setting of the meaning explanations of type theory, extending and sharpening a program–value analysis of sense and reference proposed by Martin-Löf building on previous work of Dummett. I propose a computational identity criterion for senses and argue that it validates what I see as the most plausible interpretation of Frege's equipollence principle for both sentences and singular terms. Before doing so, I examine Frege's implementation of his (...) theory of sense and reference in the logical framework of Grundgesetze, his doctrine of truth values, and views on sameness of sense as equipollence of assertions. (shrink)