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Chapter 3 - Archytas

Published online by Cambridge University Press:  05 May 2014

Malcolm Schofield
Affiliation:
University of Cambridge
Carl A. Huffman
Affiliation:
DePauw University, Indiana
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Summary

Introduction

Archytas, a citizen of Tarentum on the Adriatic coast of southern Italy, and a contemporary of Plato, is a significant figure in the history of ancient Greek science. After pioneering work in geometry by Hippocrates of Chios in the later decades of the fifth century BC, Archytas was one of the three or four major contributors to the history of Greek mathematics – in his case geometry and harmonic theory in particular – before Euclid. Detailed discussion of his work in these fields will be found in Chapters 8 and 9. He is in fact the first and only Pythagorean who can be credibly associated with significant technical achievements in mathematics. He was also, as it happens, a considerable figure in politics, who held the office of General probably for seven consecutive years, at a time when there is reason to think that a democratically governed Tarentum was an especially flourishing power in the region.

Was Archytas also a philosopher? He is credited by Aristotle's pupil Eudemus, ordinarily regarded as a reliable witness for this period of Greek thought, with a celebrated argument for the infinite extent of the universe, best known from the version in Lucretius. According to the Aristotelian commentator Simplicius, Eudemus said he used to put the question (A24): “If I arrived at the extremity of the heaven, could I extend my hand or staff into what is outside, or not?” It would be odd to suppose that that would not be possible. But if we suppose it would, and conclude that the boundary must therefore in fact lie further beyond, we then face the same question about what would happen if I tried to extend hand or staff into what is outside that boundary. And so on ad infinitum. So if I can always reach beyond any putative limit, the conclusion can only be that the beyond is in fact unlimited. Therefore, Eudemus’ testimony shows that Archytas certainly philosophized.

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Publisher: Cambridge University Press
Print publication year: 2014

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  • Archytas
  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book: A History of Pythagoreanism
  • Online publication: 05 May 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139028172.004
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  • Archytas
  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book: A History of Pythagoreanism
  • Online publication: 05 May 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139028172.004
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Archytas
  • Edited by Carl A. Huffman, DePauw University, Indiana
  • Book: A History of Pythagoreanism
  • Online publication: 05 May 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139028172.004
Available formats
×