ABSTRACT
INrecentdecadesstudentsofmathematics,philosophyandthe classicshaveagainandagainraisedtheirvoices1tovindicatethe seriousimportanceofZeno'sparadoxesofmotion(Vorsokr. 2 29A25-82=Lee,Jnos19-36),notevenexcludingtheStadium. Nolongercantheproblemimpliedintheparadoxesbedisposed ofbysimplypointingoutthattimeandspaceareequallydivisible. Thequestionwhichisatthebottomofallfourofthemisfar moreprofound.Itconcernsthefundamentalstructureofcontinua,andthecognateproblemofthenatureoftheinfiniteand itsrelationshiptothefinite;4or,toquoteBrochard:'Laquestion estdesavoircomment...cetteseriededivisions,pardefinition inepuisable,peutetreepuisee...'(p.9).Furthermore,ithas beenshownthatAristotle,whencriticizingtheparadoxes,was notconcernedconscientiouslytoadjusthisobjectionstothat whichthehistoricalZenohadtriedtoprove,orratherdisprove.s ForAristotle,Zeno'sdeductionswerenothingbutsingleitems intheimmensewealthofgivenmaterialofwhichhecouldtake advantagetoclarifyhisownviews.Ifitisthusestablishedthat Zeno'ssyllogismsmustnotnecessarilybecondemnedasafutile playofdialectics6andthatAristotle'scensurefailstodoZeno justice,aroadseemstobeopentoafullrehabilitationand,per-
*[ThisarticlewasoriginallypublishedinEnglishintheAmericanjournal ofPhilosophyfor1942.Arevisedversion,inGerman,waspublishedinthe author'sWegeundFormenfriJhgriechischenDenkens(Beck,1955;zndedition, 196o).Intheversionthatfollows,theoriginalEnglishhasbeensomewhat revised,andadditionshavebeenmade(markedbybrackets[...],bythe editors),tobringthearticleintouniformitywiththelatestGermanversion.]
ZE:-.JOOFELEA'sATTACKSONPLURALITY
haps,glorification.Buttherestillremainsroomfordoubt.How adequatelydidtherealZenoactuallydealwiththeproblemshe hadinhand?Andhowsincerewasheaboutthem?Thesequestionscannot,forobviousreasons,beconclusivelyansweredfor thefourparadoxesofmotionwhichhavecomedowntousonly intheformwhichAristotleorhiscommentators?gavethem.We havetolookrathertothefoursfragmentspreservedintheir originalwording(Vorsokr.B1-4).Sincetheylikewisedealwith aspectsoftheidenticalproblem,theproblemofthecontinuum, theyarelikelytoyieldinferencesofamoregeneralnature.And itmightproveworthwhiletodetermine,asaccuratelyascanbe done,preciselywhatZenosaidinhisownwords,andhowhe saidit.
