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Title: The Paradoxes of Zeno
Author: Thomson, R. A.
Awarding Body: University of Strathclyde
Current Institution: University of Strathclyde
Date of Award: 1985
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In the Introduction it is shown that there are scientific theories ,which are real world examples of Zeno's Paradoxes. The Paradoxes are therefore not to be dismissed as frivolous. An analysis of what "paradox" is sets out the subsequent strategy of the thesis. Part One is an historical examination of Pythagoras, Heraclitus and Parmenides which places Zeno and the Paradoxes in context, showing why he was led to formulate them and how they work. Part Two is a grouping and analysis of refutations based on mathematics, logic and science. These refutations which utilize the theory of geometric progressions are shown to fail because the limit of an infinite series is not part of that series. Refutations based on the Cantor-Russell analysis of the continuum are seen to refute the Paradoxes of Plurality but to be harmless against the Paradoxes of Motion. It is shown that the Achilles Paradox can, through the use of elementary Relativity Theory, be reduced to the Stadium Paradox. Part Three deals with attempts to refute Zeno, (a) by using circumlocution of the problems as a strategy, and (b) through an analysis of the terms "motion" and "infinite". This section describes a convincing refutation of the first version of the Stadium Paradox. Part Four is concerned with refutations based on metaphysical theories of the working of the intellect with regard to motion and perception, and intellectual analysis of the space-time continuum. These are shown to provide a refutation of the Paradox of the Flying Arrow. Part Five contains an explanation of the problems in mathematics uncovered by Zeno through his Paradoxes and a refutation, based on non-standard analysis of the infinitesimal, of the second version of the Stadium Paradox and the Paradox of the Moving Rows. An Appendix contains an hypothetical reconstruction of Zeno's lost Paradoxes of Time.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Literature