Why Mathematical Solutions of Zeno's Paradoxes Miss the Point: Zeno's One and Many Relation and Parmenides' Prohibition
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
Review of Metaphysics 50 (2):299 - 314 (1996)
MATHEMATICAL RESOLUTIONS OF ZENO’s PARADOXES of motion have been offered on a regular basis since the paradoxes were first formulated. In this paper I will argue that such mathematical “solutions” miss, and always will miss, the point of Zeno’s arguments. I do not think that any mathematical solution can provide the much sought after answers to any of the paradoxes of Zeno. In fact all mathematical attempts to resolve these paradoxes share a common feature, a feature that makes them consistently miss the fundamental point which is Zeno’s concern for the one-many relation, or it would be better to say, lack of relation. This takes us back to the ancient dispute between the Eleatic school and the Pluralists. The first, following Parmenide’s teaching, claimed that only the One or identical can be thought and is therefore real, the second held that the Many of becoming is rational and real.1 I will show that these mathematical “solutions” do not actually touch Zeno’s argument and make no metaphysical contribution to the problem of understanding what is motion against immobility, or multiplicity against identity, which was Zeno’s challenge. I would like to point out at this stage that my contention.
|Keywords||No keywords specified (fix it)|
|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
Alba Papa-Grimaldi (2007). The Presumption of Movement. Axiomathes 17 (2):137-154.
Alba Papa-Grimaldi (2008). Temporal Relations Vs. Logical Reduction: A Phenomenal Theory of Causality. [REVIEW] Axiomathes 18 (3):339-358.
Similar books and articles
Gary Mar & Paul St Denis (1999). What the Liar Taught Achilles. Journal of Philosophical Logic 28 (1):29-46.
Jeanne Peijnenburg & David Atkinson (2010). Lamps, Cubes, Balls and Walls: Zeno Problems and Solutions. Philosophical Studies 150 (1):49 - 59.
Adolf Grünbaum (1970). Modern Science and Zeno's Paradoxes of Motion. In Wesley C. Salmon (ed.), Zeno’s Paradoxes. Bobbs-Merrill 200--250.
Wesley C. Salmon (ed.) (1970). Zeno's Paradoxes. Bobbs-Merrill.
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
Phil Hopkins (2006). Zeno's Boêtheia Tôi Logôi. Epoché: A Journal for the History of Philosophy 11 (1):1-25.
Nicholas Huggett (forthcoming). Zeno's Paradoxes. The Stanford Encyclopedia of Philosophy, Edward N. Zalta (Ed.).
Adolf Grünbaum (1955). Modern Science and the Refutation of the Paradoxes of Zeno. In Wesley C. Salmon (ed.), Zeno’s Paradoxes. Bobbs-Merrill 164--175.
Added to index2009-01-28
Total downloads122 ( #33,085 of 1,934,364 )
Recent downloads (6 months)23 ( #28,419 of 1,934,364 )
How can I increase my downloads?