Against Pointillisme: A Call to Arms

Abstract

This paper forms part of a wider campaign: to deny pointillisme. That is the octrine that a physical theory’s fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or pointsized objects located there; so that properties of spatial or spatiotemporal regions and their material contents are determined by the point-by-point facts.

Elsewhere, I argued against pointillisme about chrono-geometry, and about velocity in classical mechanics. In both cases, attention focussed on temporal extrinsicality: i.e. on what an ascription of a property implies about other times. Therefore, I also discussed the metaphysical debate whether persistence should be understood as endurance or perdurance.

In this paper, I focus instead on spatial extrinsicality: i.e. on what an ascription of a property implies about other places. The main idea will be that the classical mechanics of continuous media (solids or fluids) involves a good deal of spatial extrinsicality—which seems not to have been noticed by philosophers, even those who have no inclination to pointillisme.

I begin by describing my wider campaign. Then I present some elementary aspects of stress, strain and elasticity—emphasising the kinds of spatial extrinsicality they each involve.

I conduct the discussion entirely in the context of “Newtonian” ideas about space and time. But my arguments carry over to relativistic physics.