The Pythagoreans: For the first half of the Twentieth century, the majority reading—following Tannery (1885)—of Zeno held that his arguments were directed against a technical doctrine of the Pythagoreans. According to this reading they held that all things were composed of elements that had the properties of a unit number, a geometric point and a physical atom: this kind of position would fit with their doctrine that reality is fundamentally mathematical. However, in the middle of the century a series of commentators (Vlastos, 1967, summarizes the argument and contains references) forcefully argued that Zeno’s target was instead a common sense understanding of plurality and motion—one grounded in familiar geometrical notions—and indeed that the doctrine was not a major part of Pythagorean thought. We have implicitly assumed that these arguments are correct in our readings of the paradoxes. That said, Tannery’s interpretation still has its defenders (see e.g., Matson 2001).