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A Consistent Conception of The Extended Linear Continuum as an Aggregate of Unextended Elements

Published online by Cambridge University Press:  14 March 2022

Adolf Grünbaum
Adolf Grünbaum*
Affiliation:
Lehigh University
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Extract

It is a commonplace in the analytic geometry of physical space-time that an extended straight line segment, having positive length, is treated as “consisting of” unextended points, each of which has zero length. Analogously, time intervals of positive duration are resolved into instants, each of which has zero duration.

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Type
Research Article
Information
Philosophy of Science , Volume 19 , Issue 4 , October 1952 , pp. 288 - 306
Copyright
Copyright © 1952, The Williams & Wilkins Company

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Footnotes

∗

This paper is based on part of a dissertation presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Yale University, and written during the tenure of a pre-doctoral fellowship from the American Council of Learned Societies for 1948–1950.

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