Synthese 192 (5):1315-1335 (2015)

Authors
Patrick Reeder
Kenyon College
Abstract
I offer a novel solution to Zeno’s paradox of The Arrow by introducing nilpotent infinitesimal lengths of time. Nilpotents are nonzero numbers that yield zero when multiplied by themselves a certain number of times. Zeno’s Arrow goes like this: during the present, a flying arrow is moving in virtue of its being in flight. However, if the present is a single point in time, then the arrow is frozen in place during that time. Therefore, the arrow is both moving and at rest. In “Zeno’s Arrow, Divisible Infinitesimals, and Chrysippus,” White suggests using an infinitesimal value as the length of the present. Contra Zeno, this allows the arrow to be moving in the present, rather than frozen in place. In this paper, I follow the basic outline of White’s solution but argue that his solution suffers from arbitrariness and a related theoretical artificiality in relation to the system of infinitesimals he invokes, viz. in relation to the hyperreal infinitesimals of nonstandard analysis. After arguing that any solution to the paradox must satisfy certain theoretical requirements, I examine White’s solution alongside two nilpotent solutions. One of these solutions is inspired by F.W. Lawvere’s Smooth Infinitesimal Analysis and the other is inspired by Paolo Giordano’s ring of Fermat Reals. I argue that Giordano’s nilpotents supply the best answer to Zeno’s paradox
Keywords Zeno  Infinitesimal  Nonstandard analysis  Nilpotent infinitesimals
Categories No categories specified
(categorize this paper)
ISBN(s)
DOI 10.1007/s11229-014-0620-1
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,231
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Taming of the True.Neil Tennant - 1997 - Oxford, England: Oxford University Press.
The Last Word.Thomas Nagel - 1997 - Oxford: Oxford University Press.

View all 17 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Another Note on Zeno's Arrow.Ofra Magidor - 2008 - Phronesis 53 (4-5):359-372.
Zeno's Arrow, Newton's Mechanics, and Bell's Inequalities.Leonard Angel - 2002 - British Journal for the Philosophy of Science 53 (2):161-182.
Another Look at Some of Zeno's Paradoxes.Flash Qfiasco - 1980 - Canadian Journal of Philosophy 10 (1):119 - 130.
Zeno’s Boêtheia Tôi Logôi: Thought Problems About Problems for Thought.Phil Hopkins - 2006 - Epoché: A Journal for the History of Philosophy 11 (1):1-25.
The Universal Arrow of Time.Oleg Kupervasser, Hrvoje Nikolić & Vinko Zlatić - 2012 - Foundations of Physics 42 (9):1165-1185.
Time and Zeno's Arrow.V. C. Chappell - 1962 - Journal of Philosophy 59 (8):197-213.

Analytics

Added to PP index
2015-01-11

Total views
63 ( #171,345 of 2,455,387 )

Recent downloads (6 months)
1 ( #449,037 of 2,455,387 )

How can I increase my downloads?

Downloads

My notes