Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: Chailos George
Pages: [1] - [25]
Received Date: June 7, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jpamaa_7100121511
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.
logic paradoxes, axiomatic set theory, philosophy of mathematics.
