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Why Mathematical Solutions of Zeno’s Paradoxes Miss The Point: Zeno’s One and Many Relation and Parmenides’ Prohibition.

Papa-Grimaldi, Alba (1996) Why Mathematical Solutions of Zeno’s Paradoxes Miss The Point: Zeno’s One and Many Relation and Parmenides’ Prohibition. UNSPECIFIED.

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    Abstract

    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


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    Item Type: Other
    Keywords: parmenides, zeno, mathematics, infinitesimals, infinity, eleatics, zeno's arrow, stadium, achilles, indeterminate forms
    Subjects: General Issues > History of Philosophy of Science
    General Issues > Theory Change
    General Issues > Realism/Anti-realism
    Depositing User: Dr Alba Papa-Grimaldi
    Date Deposited: 18 May 2005
    Last Modified: 07 Oct 2010 11:13
    Item ID: 2304
    Public Domain: No
    URI: http://philsci-archive.pitt.edu/id/eprint/2304

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