Against Pointillisme about Geometry

TL;DR

This paper challenges the doctrine of pointillisme, which claims that fundamental properties are defined at points in space or spacetime, by arguing against its application to the structure of space and spacetime itself.

Contribution

It provides a philosophical argument against pointillisme about space and spacetime, extending the critique beyond mechanics to the fundamental structure of the universe.

Findings

Argues against pointillisme about space and spacetime structure

Supports the critique within Newtonian, relativistic, and quantum physics contexts

Engages with existing philosophical debates on intrinsic properties

Abstract

This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or point-sized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts. More specifically, this paper argues against pointillisme about the structure of space and-or spacetime itself, especially a paper by Bricker (1993). A companion paper argues against pointillisme in mechanics, especially about velocity; it focusses on Tooley, Robinson and Lewis. To avoid technicalities, I conduct the argument almost entirely in the context of ``Newtonian'' ideas about space and time. But both the debate and my arguments carry over to relativistic, and even quantum, physics.