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. 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 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
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