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Zeno, Aristotle, the Racetrack and the Achilles: a historical and philosophical investigation

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Title
Zeno, Aristotle, the Racetrack and the Achilles: a historical and philosophical investigation
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Allen
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Benjamin William
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Benjamin William Allen
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Robert
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Robert Bolton
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chair
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Peter
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Advisory Committee
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Peter Klein
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Zimmerman
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Dean
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Advisory Committee
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Dean Zimmerman
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Pellegrin
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Pierre
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Advisory Committee
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Pierre Pellegrin
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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theses
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2008
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2008-10
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English
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electronic
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vii, 334 pages
Abstract
I reconstruct the original versions of Zeno's Racetrack and Achilles paradoxes, along with Aristotle's responses thereto. Along the way I consider some of the consequences for modern analyses of the paradoxes.
It turns out that the Racetrack and the Achilles were oral two-party question-and-answer dialectical paradoxes. One consequence is that the arguments needed to be comprehensible to the average person, and did not employ theses or concepts familiar only to philosophical specialists. I rely on this fact in reconstructing the original dialectical versions of the paradoxes. I show that both paradoxes rely for their success on forcing the dialectical answerer to reflect on his own potentially unending experience of imagination, and show that this renders the most popular contemporary critique of each paradox unworkable in an ancient dialectical context.
In responding to the Racetrack, Aristotle seeks to replace the answerer's first-person experience with something more objective, a visible diagram. He then argues that the Racetrack involves an equivocation, an equivocation resulting from the fact that one and the same visible diagram can be interpreted in two ways. He frames his charge of equivocation in standard dialectical fashion, but his use of a diagram is his own innovation.
While first employing his response to the Racetrack to construct a response to the somewhat different Achilles paradox, Aristotle later proceeds to offer a revised critique of the Racetrack itself. His revised critique is heavily influenced by his reaction to a variant pre-Aristotelian version of the paradox, a version involving counting. This leads him to reflect on the possibility of mentally experiencing an infinite collection. He also reflects on his earlier diagrammatic methodology, and on the conditions that individuate points, especially halfway-points. He concludes that points which are individuated in diagrams need not represent points that are individuated in reality. His revised critique of the Racetrack hinges on the distinction between actual points and potential points, and I show that this critique maintains the dialectical form of its predecessor, while constituting a reflection on the potentially misleading nature of diagrams.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 327-333).
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Topic
Philosophy
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Topic
Dialectic
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Topic
Paradox
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Name
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Zeno, of Elea
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Aristotle
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Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17425
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ETD_1175
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Identifier (type = doi)
doi:10.7282/T3NC61K3
Genre (authority = ExL-Esploro)
ETD doctoral
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Open
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Benjamin Allen
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Affiliation
Rutgers University. Graduate School - New Brunswick
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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