### Abstract

Original language | English |
---|---|

Article number | 1 |

Pages (from-to) | 1-25 |

Number of pages | 25 |

Journal | Journal of Pure and Applied Mathematics: Advances and Applications |

Volume | 14 |

Issue number | 1 |

Publication status | Published - Nov 2015 |

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### Keywords

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

### Cite this

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**A ‘Minimal’ Set Theoretical Interpretation of Zeno’s Paradox of ‘Achilles and Tortoise’ .** / Chailos, George.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A ‘Minimal’ Set Theoretical Interpretation of Zeno’s Paradox of ‘Achilles and Tortoise’ .

AU - Chailos, George

PY - 2015/11

Y1 - 2015/11

N2 - 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.

AB - 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.

KW - Logic paradoxes,

KW - Axiomatic Set Theory

KW - Philosophy of Mathematics

M3 - Article

VL - 14

SP - 1

EP - 25

JO - Journal of Pure and Applied Mathematics: Advances and Applications

JF - Journal of Pure and Applied Mathematics: Advances and Applications

SN - 0974-9381

IS - 1

M1 - 1

ER -