A partial defense of algebraic relationalism

TL;DR

This paper defends algebraicism as a genuine relationalist view that explains physical fields through structural relations without relying on a spacetime manifold, challenging the view that it is equivalent to substantivalism.

Contribution

It critiques the standard algebraicism that equates to substantivalism and offers alternative algebraic models that better embody relationalism with conceptual benefits.

Findings

Standard algebraicism is considered equivalent to substantivalism.

Alternative algebraic models better implement relationalism.

These models have conceptual advantages over traditional substantivalism.

Abstract

I defend algebraicism, according to which physical fields can be understood in terms of their structural relations without reference to a spacetime manifold, as a genuine relationalist view against the conventional wisdom that it is equivalent to substantivalism, according to which spacetime exists fundamentally. I criticize the standard version of algebraicism that is considered equivalent to substantivalism. Furthermore, I present alternative examples of algebraicism that better implement relationalism with their conceptual advantages over substantivalism or its standard algebraic counterpart.