Paradox

52 A BRIEF HISTORY OF THE PARADOXups does not mean Achilles actually caught up infinitelymany times. Similarly, the flight of an arrow can be analyzedinto an unlimited number of subflights. Whenever we divideits flight into n parts we could have divided it into n + 1 parts.But this does not mean that the flight of the arrow is acollection of actual subflights.ZENO’S ARGUMENT AGAINST PLACEParmenides had already presented an argument againstplace. Common sense distinguishes between an object and theroom it occupies. After all, an object can move from its placeand another object can take its place. Indeed, the object cansimply vacate the area, leaving an empty place. Since theobject is what is and the place is what is not, Parmenides’objections to nonexistent things bear down on places.One reply to Parmenides is that places are not mere nothings.The stalls in a stable are places but only come into beingwith the creation of the stable. Zeno’s rejoinder is that if placesexist and everything that exists has a place, then each place willhave a place. There will be an infinite hierarchy of places.In A Room of One’s Own, the egalitarian Virginia Woolfargues that everyone should have their own room. Zenoshows us that Woolf can ill afford to extend the franchise torooms themselves.ZENO AND THE MILLET SEEDZeno amplified Parmenides’ case against the senses by allegingperceptual inconsistencies. In a dialogue with Protagoras,