Journal Article

Against <i>Pointillisme</i> about Mechanics

Jeremy Butterfield

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 57, issue 4, pages 709-753
Published in print December 2006 | ISSN: 0007-0882
Published online November 2006 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axl026
Against Pointillisme about Mechanics

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This paper forms part of a wider campaign: to deny pointillisme, 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 concept of velocity in classical mechanics; especially against proposals by Tooley, Robinson and Lewis. A companion paper argues against pointillisme about (chrono)-geometry, as proposed by Bricker. To avoid technicalities, I conduct the argument almost entirely in the context of “Newtonian” ideas about space and time, and the classical mechanics of point-particles, i.e. extensionless particles moving in a void. But both the debate and my arguments carry over to relativistic physics.

Introduction

The wider campaign

2.1 Connecting physics and metaphysics

        2.1.1 Avoiding controversy about the intrinsic–extrinsic distinction

        2.1.2 Distinction from three mathematical distinctions

2.2 Classical mechanics is not pointilliste, and can be perdurantist

        2.2.1 Two versions of pointillisme

        2.2.2 Two common claims

        2.2.3 My contrary claims

2.3 In more detail

        2.3.1 Four violations of pointillisme

        2.3.2 For perdurantism

Velocity as intrinsic?

3.1 Can properties represented by vectors be intrinsic to a point?

3.2 Orthodox velocity is extrinsic but local

        3.2.1 A question and a debate

        3.2.2 The verdict

3.3 Against intrinsic velocity

        3.3.1 A common view—and a common problem

        3.3.2 Tooley's proposal and his arguments

        3.3.3 Tooley's further discussion

Shadow velocities”: Lewis and Robinson

4.1 The proposal

4.2 Criticism: the vector field remains unspecified

4.3 Avoiding the presupposition of persistence, using Hilbert's ε symbol

4.4 Comparison with Robinson and Lewis

Journal Article.  19134 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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