Relationalism about mechanics based on a minimalist ontology of matter

TL;DR

This paper explores a minimalist relationalist ontology of matter points and assesses two strategies for integrating it with classical mechanics, highlighting challenges in maintaining minimalism while reproducing standard predictions.

Contribution

It analyzes the compatibility of a minimalist relationalist ontology with classical mechanics and shows the difficulties in doing so without losing ontological simplicity.

Findings

Humean strategy interprets standard theories relationally without adding elements.

Relationalist theory strategy struggles to reproduce standard predictions minimally.

Maintaining a minimalist relationalist ontology is challenging with current approaches.

Abstract

This paper elaborates on relationalism about space and time as motivated by a minimalist ontology of the physical world: there are only matter points that are individuated by the distance relations among them, with these relations changing. We assess two strategies to combine this ontology with physics, using classical mechanics as example: the Humean strategy adopts the standard, non-relationalist physical theories as they stand and interprets their formal apparatus as the means of bookkeeping of the change of the distance relations instead of committing us to additional elements of the ontology. The alternative theory strategy seeks to combine the relationalist ontology with a relationalist physical theory that reproduces the predictions of the standard theory in the domain where these are empirically tested. We show that, as things stand, this strategy cannot be accomplished without compromising a minimalist relationalist ontology.