Let us consider the two subarguments, in reverse order. First are there ‘always others between the things that are’? (In modern terminology, why must objects always be ‘densely’ ordered?) Suppose that we had imagined a collection of ten apples lined up; then there is indeed another apple between the sixth and eighth, but there is none between the seventh and eighth! On the assumption that Zeno is not simply confused, what does he have in mind? The texts do not say, but here are two possibilities: first, one might hold that for any pair of physical objects (two apples say) to be two distinct objects and not just one (a ‘double-apple’) there must be a third between them, physically separating them, even if it is just air. And one might think that for these three to be distinct, there must be two more objects separating them, and so on (this view presupposes that their being made of different substances is not sufficient to render them distinct). So perhaps Zeno is arguing against plurality given a certain conception of physical distinctness. But second, one might also hold that any body has parts that can be densely ordered. Of course 1/2s, 1/4s, 1/8s and so on of apples are not dense—such parts may be adjacent—but there may be sufficiently small parts—call them ‘point-parts’—that are. Indeed, if between any two point-parts there lies a finite distance, and if point-parts can be arbitrarily close, then they are dense; a third lies at the half-way point of any two. In particular, familiar geometric points are like this, and hence are dense. So perhaps Zeno is offering an argument regarding the divisibility of bodies. Either way, Zeno’s assumption of denseness requires some further assumption about the plurality in question, and correspondingly focusses the target of his paradox. 