ABSTRACT
ATsometimeinthefirsthalfofthefifthcenturyBC,Zenoinventedthesetofparadoxesonwhichhissuccessorshavesharpenedtheirwits.Thepuzzleshavecomedowntousinvarious versions,moreorlessincompleteandmoreorlessreflectingthe specialinterestsoflaterwriters.WhatwehaveleftofZeno'sbestknownworkcomes,onthemosthopefulview,tolessthantwo hundredwords.Still,thishasnotstoppedZeno'sadmirersfrom trying,withallduecaution,toreconstructtheprogrammeofall orsomeofhisarguments.Iwanttomakeonesuchprogramme plausibleandtoshowhow,ifIamright,thismakessomesolutionstothepuzzlesbesidethepoint.*
Mysecondinterestinthepaperisthis.Zeno,itiscommonly said,wasandwishedtobethebenefactorofGreekmathematics. ByhisdaythePythagoreanshadbroughtmathematicstoahigh levelofsophistication.Butthefoundationsoftheirsystemwere anestofconfusions,andZenowasouttoexposetheseconfusions. Onebeneficialresultofhisarguments(onthisfamiliaraccount) wastocompelmathematicianstodistinguisharithmeticfrom geometry.
