David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 110 (1):143-166 (1997)
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)|
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
No references found.
Citations of this work BETA
Vincent Ardourel (2015). A Discrete Solution for the Paradox of Achilles and the Tortoise. Synthese 192 (9):2843-2861.
Michael B. Burke (2000). The Impossibility of Superfeats. Southern Journal of Philosophy 38 (2):207-220.
Constantin Antonopoulos (2004). Moving Without Being Where You 'Re Not; a Non-Bivalent Way'. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 35 (2):235 - 259.
Constantin Antonopoulos (2003). The Tortoise is Faster. Southern Journal of Philosophy 41 (4):491-510.
Constantin Antonopoulos (2004). Moving Without Being Where You’Re Not; A Non-Bivalent Way. Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 35 (2):235-259.
Similar books and articles
Nicholas Huggett (forthcoming). Zeno's Paradoxes. The Stanford Encyclopedia of Philosophy, Edward N. Zalta (Ed.).
Alba Papa-Grimaldi (1996). Why Mathematical Solutions of Zeno's Paradoxes Miss the Point: Zeno's One and Many Relation and Parmenides' Prohibition. Review of Metaphysics 50 (2):299 - 314.
Gary Mar & Paul St Denis (1999). What the Liar Taught Achilles. Journal of Philosophical Logic 28 (1):29-46.
Craig Harrison (1996). The Three Arrows of Zeno. Synthese 107 (2):271 - 292.
William I. McLaughlin & Sylvia L. Miller (1992). An Epistemological Use of Nonstandard Analysis to Answer Zeno's Objections Against Motion. Synthese 92 (3):371 - 384.
Karin Verelst (2006). Zeno's Paradoxes. A Cardinal Problem. 1. On Zenonian Plurality. In J. Šķilters (ed.), Paradox: Logical, Cognitive and Communicative Aspects. Proceedings of the First International Symposium of Cognition, Logic and Communication,. University of Latvia Press
William I. McLaughlin (1998). Thomson's Lamp is Dysfunctional. Synthese 116 (3):281-301.
Peter Lynds (forthcoming). Zeno's Paradoxes: A Timely Solution. PhilSci Archive.
Joseph S. Alper & Mark Bridger (1997). Mathematics, Models and Zeno's Paradoxes. Synthese 110 (1):143-166.
Added to index2009-01-28
Total downloads58 ( #71,508 of 1,792,259 )
Recent downloads (6 months)5 ( #170,928 of 1,792,259 )
How can I increase my downloads?