No categorial support for radical ontic structural realism

TL;DR

This paper critically examines radical ontic structural realism (ROSR) and argues that category theory does not provide a better framework for ROSR than set theory, challenging recent defenses of ROSR using category-theoretic reformulations.

Contribution

The paper refutes the claim that category theory better supports ROSR, showing it does not offer a more hospitable environment than set theory for ROSR's ontological commitments.

Findings

Category theory does not better support ROSR than set theory.

Application of category theory to quantum field theory and relativity does not imply object-free structures.

Category theory offers little comfort to ROSR.

Abstract

Radical ontic structural realism (ROSR) asserts an ontological commitment to 'free-standing' physical structures understood solely in terms of fundamental relations, without any recourse to relata which stand in these relations. Bain (2011) has recently defended ROSR against the common charge of incoherence by arguing that a reformulation of fundamental physical theories in category-theoretic terms (rather than the usual set-theoretic ones) offers a coherent and precise articulation of the commitments accepted by ROSR. In this essay, we argue that category theory does not offer a more hospitable environment to ROSR than set theory. We also show that the application of category-theoretic tools to topological quantum field theory and to algebraic generalisations of general relativity do not warrant the claim that these theories describe 'object-free' structures. We conclude that category theory offers little if any comfort to ROSR.