Le Poidevin, R. (2004) Space, supervenience and substantivalism. Analysis, 64 (283). pp. 191198. ISSN 00032638

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Abstract
[FIRST PARAGRAPH]
Consider a straight line on a flat surface running from point A to C and passing though B. Suppose the distance AB to be four inches, and the distance BC to be six inches. We can infer that the distance AC is ten inches. Of all geometrical inferences, this is surely one of the simplest. Of course, things are a little more complicated if the surface is not flat. If A, B and C are points on a sphere, then the shortest distance between A and C may be smaller (it may even be zero). We can make our inference immune from concerns about nonEuclidean spaces, however, by qualifying it as follows: if AB = n, and BC = m, then, in the direction A⇒B⇒C, the distance AC is n + m. This is apparently entirely trivial. But trivial truths can hide significant ontological ones. Let us translate our mathematical example to the physical world, and suppose A, B and C to be points, still in a straight line, but now at the centre of gravity of three physical objects:
Item Type:  Article 

Copyright, Publisher and Additional Information:  © 2004 Blackwell Publishing. This is an author produced version of a paper published in Analysis. Uploaded in accordance with the publisher's selfarchiving policy. 
Institution:  The University of Leeds 
Academic Units:  The University of Leeds > Faculty of Arts (Leeds) > School of Humanities (Leeds) > School of Philosophy (Leeds) The University of Leeds > Faculty of Arts (Leeds) > School of Philosophy, Religion and History of Science (Leeds) > School of Philosophy (Leeds) 
Depositing User:  Leeds Philosophy Department 
Date Deposited:  02 Nov 2007 18:28 
Last Modified:  08 Feb 2013 17:04 
Published Version:  http://dx.doi.org/10.1111/j.00032638.2004.00484.x 
Status:  Published 
Publisher:  Blackwell Publishing 
Refereed:  Yes 
Identification Number:  10.1111/j.00032638.2004.00484.x 
Related URLs:  
URI:  http://eprints.whiterose.ac.uk/id/eprint/3244 