Chapter

Zeno's Paradox of Measure

Brian Skyrms

in From Zeno to Arbitrage

Published in print November 2012 | ISBN: 9780199652808
Published online January 2013 | e-ISBN: 9780191745829 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199652808.003.0002
Zeno's Paradox of Measure

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Zeno’s paradox of measure is less well known that his other paradoxes, but it stands at the center of them. The paradoxes of motion can all be seen as blocking various escape routes from the basic paradox of measure. Although the paradox, as a paradox, has been resolved by the modern theory of measure and integral, the basic logic of Zeno’s argument reappears in various forms in modern proofs of the existence of non-measurable sets. In a different setting, these considerations arise in contemporary discussions of subjective probability

Keywords: Zeno; measure; infinitesimal; non-measurable set; measure algebra

Chapter.  14427 words. 

Subjects: Philosophy of Science

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