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
No citations found.
Similar books and articles
Joseph S. Alper & Mark Bridger (1997). Mathematics, Models and Zeno's Paradoxes. Synthese 110 (1):143-166.
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.
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.
Nicholas Huggett (forthcoming). Zeno's Paradoxes. The Stanford Encyclopedia of Philosophy, Edward N. Zalta (Ed.).
Adolf Grünbaum (1970). Modern Science and Zeno's Paradoxes of Motion. In Wesley C. Salmon (ed.), Zeno’s Paradoxes. Bobbs-Merrill 200--250.
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
Brad Weslake (2006). Time. In Martin Cohen (ed.), Essentials of Philosophy and Ethics. Hodder Arnold
Added to index2010-08-31
Total downloads8 ( #405,910 of 1,911,680 )
Recent downloads (6 months)2 ( #322,162 of 1,911,680 )
How can I increase my downloads?