A ‘Minimal’ Set Theoretical Interpretation of Zeno’s Paradox of ‘Achilles and Tortoise’ .

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Abstract

In this article we analyze Zeno's paradox of " Achilles and Tortoise " using exclusively the theory of infinite sets. In contrast with spatiotemporal based attempts for resolution of the paradox, our interpretation and resolution entails only set theory without making any assumptions on the spatiotemporal structure, since in our opinion Zeno's paradoxes are purely logical paradoxes. This is in accordance to the Eleatic thought, which discarded the " reality " composed by the senses. In particular, we propose a resolution of the paradox from a minimal subset of the set theoretical axioms ZFC that is in concord with the mathematics developed in Pythagorean and Eleatic Schools, based on discrete structures.
Original languageEnglish
Article number1
Pages (from-to)1-25
Number of pages25
JournalJournal of Pure and Applied Mathematics: Advances and Applications
Volume14
Issue number1
Publication statusPublished - Nov 2015

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Achilles
Tortoise
Paradox
Zeno
Mathematics
Eleatic School
Logical Paradoxes
Concord
Set Theory
Thought
Pythagorean School

Keywords

  • Logic paradoxes,
  • Axiomatic Set Theory
  • Philosophy of Mathematics

Cite this

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