Univalence and Ontic Structuralism

TL;DR

This paper advocates for using Univalent Foundations to rigorously implement ontic structuralism, emphasizing the identity of isomorphic structures and addressing related philosophical issues.

Contribution

It introduces Univalent Foundations as a promising logical framework for ontic structuralism, highlighting its advantages over other approaches.

Findings

UF treats isomorphic structures as identical, aligning with structuralist principles

UF provides a rigorous basis for addressing the hole argument

Brief discussion on symmetries in the context of UF

Abstract

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.