Mathematics, models and Zeno's paradoxes

Synthese 110 (1):143-166 (1997)
Abstract
A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
Categories (categorize this paper)
DOI 10.1023/A:1004967023017
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 28,191
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
What the Liar Taught Achilles.Gary Mar & Paul St Denis - 1999 - Journal of Philosophical Logic 28 (1):29-46.
The Three Arrows of Zeno.Craig Harrison - 1996 - Synthese 107 (2):271 - 292.
Zeno's Paradoxes: A Timely Solution.Peter Lynds - forthcoming - PhilSci Archive.
Zeno's Paradoxes.Nicholas Huggett - forthcoming - The Stanford Encyclopedia of Philosophy, Edward N. Zalta (Ed.).
Modern Science and Zeno's Paradoxes of Motion.Adolf Grünbaum - 1970 - In Wesley C. Salmon (ed.), Zeno’s Paradoxes. Bobbs-Merrill. pp. 200--250.
Time.Brad Weslake - 2006 - In Martin Cohen (ed.), Essentials of Philosophy and Ethics. Hodder Arnold.

Monthly downloads

Added to index

2009-01-28

Total downloads

100 ( #51,002 of 2,172,657 )

Recent downloads (6 months)

1 ( #325,028 of 2,172,657 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums