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.