From Zeno ad infinitum: Iterative Reasonings in Early Greek Philosophy
Pierrot Seban
Abstract:This 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 dif… Show more
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