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From Zeno ad infinitum: Iterative Reasonings in Early Greek Philosophy

From Zeno ad infinitum: Iterative Reasonings in Early Greek Philosophy AbstractThis paper considers some aspects of the early conception and use of the infinite in ancient Greece, in the spirit of recent results in the history of ancient mathematics. It follows aspects of the practice of reasoning ad infinitum from the extant corpus of and about Zeno of Elea up to early Hellenistic examples in Aristotle and Euclid. Starting with the idea of ‘reasoning from indefinite iteration’, based on the metalogical recognition of the unachievability of an inference process, it identifies several different classes of more or less sophisticated arguments that make use of this idea, and examines the logical devices and notions required for their acceptance in the philosophical practice. Those include ‘Infinite regress’ properly speaking, where Non-Contradiction is used in the formation of indirect infinitary arguments. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Rhizomata de Gruyter

From Zeno ad infinitum: Iterative Reasonings in Early Greek Philosophy

Seban, Pierrot
Rhizomata , Volume 11 (1): 22 – Aug 30, 2023
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References (5)

Publisher
de Gruyter
Copyright
© 2023 Walter de Gruyter GmbH, Berlin/Boston
ISSN
2196-5110
eISSN
2196-5110
DOI
10.1515/rhiz-2023-0002
Publisher site
See Article on Publisher Site

Abstract

AbstractThis paper considers some aspects of the early conception and use of the infinite in ancient Greece, in the spirit of recent results in the history of ancient mathematics. It follows aspects of the practice of reasoning ad infinitum from the extant corpus of and about Zeno of Elea up to early Hellenistic examples in Aristotle and Euclid. Starting with the idea of ‘reasoning from indefinite iteration’, based on the metalogical recognition of the unachievability of an inference process, it identifies several different classes of more or less sophisticated arguments that make use of this idea, and examines the logical devices and notions required for their acceptance in the philosophical practice. Those include ‘Infinite regress’ properly speaking, where Non-Contradiction is used in the formation of indirect infinitary arguments.

Journal

Rhizomata – de Gruyter

Published: Aug 30, 2023

Keywords: Infinite Regress; Zeno of Elea; Parmenides; Ancient Logic; Infinity

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