A Note on Zeno's Arrow

Abstract

The paradox, I conjecture, had the following form: (1) Anything that is occupying a space just its own size is at rest. (2) A moving arrow, while it is moving, is moving in the present. (3) But in the present the arrow is occupying a space just its own size. (4) Therefore, in the present the arrow is at rest. (5) Therefore a moving arrow, while it is moving, is at rest. Two items about the reconstruction deserve mention. First, I have interpreted the phrase 'is against what is equal' (xtTo T61L'oov) as 'is occupying a space just its own size'. The Greeks notoriously had difficulty working out a conception of space and the interpretation, I think, preserves the sense of the Greek while sparing us its artificial ring. Second, the phrase, 'in the now' (EV -v viv) is probably Aristotelian.2 But it does, I shall argue, capture a concept crucial to Zeno's argument which has been overlooked by modem commentators: the concept of the present instant. Commentators tend to interpret Zeno as saying that in a moment the arrow occupies a space its own size.3 And yet much of the strength of the paradox and of Aristotle's response depends on the fact that the moment of travel with which Zeno is concerned is the present moment.4