Paradox

SISYPHUS’S ROCK AND ZENO’S PARADOXES 47number is infinite. For between any two things, there mustbe a third thing. If there are two separate things, some thirdthing must separate them. This third thing must itself beseparated from its neighbors. Since there must be a furtherseparator whenever one separator is postulated, the numberof things is infinite.Many witnesses to Zeno’s reductio ad absurdum argumentsbelieved he was showing off his debating skill. First,Zeno would prove one side of the case and then, in aturnabout, prove the other side. Thus the couplet by Timonof Philius: “Also the two-edged tongue of mighty Zeno,who, / Say what one would, could argue it untrue.” ButZeno does not think that everyone can be refuted. Parmenides,for one, cannot be refuted.Unlike Parmenides, Zeno does not offer direct argumentsin favor of a particular truth. He always proceedsindirectly, reducing the competing doctrines to absurdity.Socrates tries to make sense of Zeno’s book (from whichZeno has just read aloud):“Zeno, what do you mean by this? If existing things are amany, you say, then they must be both like and unlike.But this is impossible, since unlike things cannot be likeor like things unlike. That’s what you are saying, isn’t it?”“Just so,” Zeno replied.“Then if it is impossible for unlike things to be like,and for like things to be unlike, then it is impossible forthings to be a many; for if there were a many, impossibleconsequences would follow. Is that the purpose of yourargument—to maintain against all comers that therecannot be a many? And do you regard each of yourarguments as proof of this, so that in your view the