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Philosophia Mathematica Advance Access published online on November 5, 2009
Philosophia Mathematica, doi:10.1093/philmat/nkp017
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© The Author [2009]. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Whitehead and Russell on Points{dagger}

David Bostock*

* Merton College, Oxford OX1 4JD, England. judith.kirby{at}admin.merton.ox.ac.uk

This paper considers the attempts put forward by A.N. Whitehead and by Bertrand Russell to ‘construct’ points (and temporal instants) from what they regard as the more basic concept of extended ‘regions’. It is shown how what they each say themselves will not do, and how it should be filled out and amended so that the ‘construction’ may be regarded as successful. Finally there is a brief discussion of whether this ‘construction’ is worth pursuing, or whether it is better—as in today’s mathematics—to prefer a ‘construction’ that goes the other way round, i.e., to view a region as a set of points.

{dagger} I take ‘points’ to include ‘points of time’, i.e., instants.


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