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“Geometry and Motion.” British Journal for the Philosophy of Science 51 (2000) 561-595 (50th Anniversary Issue).
Reprinted in P. Clark and K. Hawley (eds.), Philosophy of Science Today. Oxford University Press (2003), pp. 201-235.
(published version) [preprint]
Abstract. This paper discuss one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world. The focus is on motion and geometry in prerelativistic physics: beginning with a discussion of the topic’s historical roots and continuing with a review of the new approach to these issues which emerged about thirty years ago and an assessment of the current status of the debate. At the end of the paper some remarks are made concerning cognate questions in the relativistic context.
Notes. (1) In Section 4, I sloppily speak of rotating systems when I should speak of systems with non-vanishing angular momentum. This is a bad idea, for reasons that emerge in Brad Skow’s “Sklar’s Maneuver”: a system can of course have non-vanishing angular momentum even if each particle is moving inertially (so that one would not normally speak of rotation, which suggests acceleration); and it follows from this that invoking a primitive notion of absolute acceleration will not allow relationalists about motion to capture the full content of Newton’s theory. (2) I no longer think that the treatment of geometric possibility sketched in Section 5.1 is adequate: the approach of Manders does not mesh well with the approach I want to take to counting possibilities; and in any case, it is not clear that this approach can be extended to cover all of the cases required. (Thanks here to Caro Brighouse, Nick Huggett, and Brad Skow.)
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