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 | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,653 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesNicholas Huggett (forthcoming). Zeno's Paradoxes. The Stanford Encyclopedia of Philosophy, Edward N. Zalta (Ed.).
Peter Lynds (forthcoming). Zeno's Paradoxes: A Timely Solution. PhilSci Archive.
William I. McLaughlin (1998). Thomson's Lamp is Dysfunctional. Synthese 116 (3):281-301.
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 & Sylvia L. Miller (1992). An Epistemological Use of Nonstandard Analysis to Answer Zeno's Objections Against Motion. Synthese 92 (3):371 - 384.
Craig Harrison (1996). The Three Arrows of Zeno. Synthese 107 (2):271 - 292.
Gary Mar & Paul St Denis (1999). What the Liar Taught Achilles. Journal of Philosophical Logic 28 (1):29-46.
Alba Papa-Grimaldi (1996). Why Mathematical Solutions of Zeno's Paradoxes Miss the Point: Zeno's One and Many Relation and Parmenides' Prohibition. The Review of Metaphysics 50 (2):299 - 314.
Joseph S. Alper & Mark Bridger (1997). Mathematics, Models and Zeno's Paradoxes. Synthese 110 (1):143-166.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads36 ( #32,948 of 548,984 )Recent downloads (6 months)1 ( #63,327 of 548,984 )How can I increase my downloads? |
My notes
Discussion
