Against Pointillisme: A Call to Arms
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.
KeywordsClassical Mechanic Spatial Point Spacetime Region Traction Vector Extrinsic Property
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I am very grateful to audiences in Cambridge, Melbourne, and at the ESF conference in Zeist, and to A. Caulton,W. Myrvold, M.Wilson and the editor, for helpful conversations and comments. I thank O. Gonzalo, A. Stuart and Cambridge University Press, for permission to reproduce Figures 1 to 3 from A First Course in Continuum Mechanics, copyright 2008.
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