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Everywhere and EverywhenAdventures in Physics and Philosophy$
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Nick Huggett

Print publication date: 2010

Print ISBN-13: 9780195379518

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780195379518.001.0001

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Zeno's Arrow Paradox

Zeno's Arrow Paradox

(p.27) 3 Zeno's Arrow Paradox
Everywhere and Everywhen

Nick Huggett (Contributor Webpage)

Oxford University Press

This pair of chapters discuss Zeno's paradoxes and some of their modern descendants: the ‘dichotomy’, the ‘arrow’, and the ‘supertasks’ of Thompson's lamp and Bernadete. These paradoxes arise from the inifinite divisibility of time and space. For instance, the dichotomy considers dividing a journey into two stages, and then the second stage into half, and the second half of that into half, and so on to infinity: every stage takes a finite time, so shouldn't the whole journey take infinitely long, never to be completed? The problems are challenges to the mathematical description of the world: for instance, the number of metres comprising a journey. The paradoxes reveal confusions in the mathematical nature of infinity, and its application by physics to the world. The chapter explains how a proper understanding of infinity resolves the paradoxes, and demonstrates how these philosophical questions were crucial to the development of mathematical physics.

Keywords:   Zeno, paradox, dichotomy paradox, supertask, arrow paradox, motion, Thompson Lamp, Bernadete, mathematical physics

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