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The Routledge Companion to Ancient

James Warren, Frisbee Sheffield

Parmenides, Zeno, and Melissus

Publication details https://www.routledgehandbooks.com/doi/10.4324/9781315871363.ch3 Stephen Makin Published online on: 20 Dec 2013

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The publisher does not give any warranty express or implied or make any representation that the contents be complete or accurate or up to date. The publisher shall not be liable for an loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 ing “theunshakenheartof well-rounded ”hasbeenpreserved,quitedeliberately, We arefortunatethatagood dealofthesecondpartParmenides’poem,concern- three seePalmer2009:Chapter5.) 1982: 234–237;onParmenidesandMelissusseePalmer2004;foratreatmentofall defender ofParmenides;forcriticaldiscussionseeSolmsen accepted. (SeePlato’sParmenides this accountoftherelationbetweenParmenides,ZenoandMelissusisnotuniversally originally setoutbyParmenides.Iwillacceptthisframeworkinwhatfollows,although views which,whilefundamentallyParmenidean,differedinsomedetailsfromthose of hand.MelissusdevelopedParmenides’thoughtbyarguing,ofteninfreshways,for those whothoughtParmenides’ideassufficientlyabsurdthattheycouldberejectedout tive setofviewsaboutthenaturereality.Zenowasadefender,inthatheattacked nides wasaninnovator,inthatheofferedpositiveargumentsforanovelandprovoca- the threecanbetakenasrepresentativeofadistinctphilosophicalstrategy.Parme- on anopaquesetofviewsenunciatedbytheearliestthree,Parmenides.Each the GreekislandofSamos).Theconnectionbetweenthemisgenerallytakentoturn Elea insouthernItaly,thehomecityofbothParmenidesandZeno(Melissuscamefrom together byscholars.Theyaresometimesreferredtocollectivelyasthe Parmenides, ZenoandMelissus,philosophersofthefifthcentury perspective: dess whoofferstoteachhimboththetruenatureofreality andamorefamiliarmortal tion whichsetsthestructureforpoemasawhole: Parmenidesapproachesagod- Parmenides’ poemisconventionallydividedintothree parts. Firstthereisanintroduc- have tobeassuredly,pervading allthingsthroughout. But nonethelessyoushalllearnthesethingstoo,how what isbelievedwould rounded truth,andtheopinionsofmortals,inwhichthere isnotruereliance. It isproperthatyoushouldlearnallthings,boththeunshaken heartofwell- PARMENIDES, ZENO, AND MELISSUS Parmenides I:theargumentstructure DK 28B1.28–32(translations throughoutasinKRS) Stephen Makin 126b–129a forthesourceofviewZenoasa 3

1971, Vlastos1975,Barnes bc, areoftengrouped ,after Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 at than Simplicius(thefirsttwolinesarequotedtwice,withsomevariations,byPlato This shortpassageisoneofthefewParmenideanfragmentspreservedbyasourceother ofrealitythanperceptionandcommonsense: philosophical thinking.Thisistheideathatthought nature ofthought,DK28B10–12,16–19). include referencetotheheavenlybodies,animalreproduction,embryologyand been alengthyandquitedetailedaccountofthenaturalworld(thesurvivingfragments general outlookhastoaccommodatethefactthathedidofferwhatseemshave part ofParmenides’poem,otherthantonotethatanyinterpretation this account(seeCurd1998:Chapter3foradiscussion).Iwillsaynomoreabout survived. ThereisconsiderabledisagreementastoParmenides’purposeinproviding nature ofreality(thisisthelengthyfragmentreproducedasDK28B8). tion inwhichParmenidesarguesforastrikingandhighlyrevisionaryaccountofthe amongst thepassagesSimpliciusquotesarefortynineconsecutivelinesofargumenta- century by Simplicius,aNeoplatonistphilosopherandcommentatoronAristotleofthesixth : not- from understandingthetruenatureofrealityissomesort oferrorconcerningbeing (“judge byreason”).Andfourth, on Parmenides’claimsbythinkingthroughthearguments heoffersintheirsupport against beingguidedby“habit,bornofmuchexperience”). Third,weshoulddecide simply onthegroundsthattheyaregreatlyatoddswithcommonoutlook(hewarns tion,” thatis,ofordinaryhumanopinion).Second,hewarnsagainstrejectinghisviews sense, andarehighlycontentious(hiswholeargumentisa“strife-encompassedrefuta- Parmenides iswellawarethattheviewsheoffersareverymuchatoddswithcommon ad). WecanextractthefollowingfourpointsconcerningParmenides’procedure.First, Parmenides’ positiveviewsaredrivenbyaninsightwhichisattheveryheartof Far lessofthethirdpartpoem,anaccount“theopinionsmortals”has How couldthoughtestablishthenatureofreality?The goddessoffersParmenidesa passed refutationspokenbyme. ear andatonguefullofmeaninglesssound:judgebyreasonthestrife-encom- much ,forceyoudownthisway,bymakinguseanaimlesseyeor must holdbackyourthoughtfromthiswayofenquiry,norlethabit,born For nevershallthisbeforciblymaintained,thatthingsarenotare,butyou indicate it. cernible track:foryoucould notknowwhatisnot—thatcannotbedone—nor that itisneedful[it]not be,thatIdeclaretoyouisanaltogetherindis- of (forsheattends uponTruth);theother,that[it]isnotand of. Theone,that[it]isanditimpossiblefor nottobe,isthepath Come nowandIwilltellyou…theonlywaysofenquiry thataretobethought ad. Hehadaccesstothepoem,butrecognizedthatcopieswererare.Included (“never shallthisbeforciblymaintained,thatthings arenotare”). 237a and258d;therestbySextusEmpiricuswritinginsecondcentury PARMENIDES, ZENO,ANDMELISSUS Parmenides thinksthatwhatpreventsmostpeople 35 is amorereliableguidetothetrue DK 28B7 DK 28B2 and Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 rumph,” isthat“tree”asound somehowrelatedtosomethingintheworld,whereas between asignificantbitof language,suchas“tree,”andamerenoise,“har- which theyhold.Further, it maywellseemplausiblethatoneimportantdifference verb “[it]isnot”? and describingtheworldwhilelimitingthemselvestousing onlyformsofthenegative ruled out,sincesurelyno-one(outsideaphilosopher’sfantasy) wouldtryinvestigating second asapossiblewayofenquiry?Andwhatwouldit matterifthesecondwaywere cernible track.”Twoquestionsimmediatelyarise.Why doesParmenidesruleoutthe path ofPersuasion(forsheattendsuponTruth)”;thesecondway“isanaltogetherindis- far moreemphasisonthereferencestonecessityandimpossibility.) of theforbiddenpositive“[it]is.”(SeePalmer2009foraninterpretationwhichplaces elephants inGreecebuttherecouldhavebeen–thefinalitalicizedtermisaninstance mutandis is forbidden negative“[it]isnot.”Soyouwillineffectbelimitedtomentioningonlywhat there arefishintheseabutneednot those whichinvolve“[it]isnot,”thenyouwillnotbeabletoclaim,forexample,that going tofollowthefirstway,limitingyourselfclaimsinvolving“[it]is”andabjuring the twowayswouldalsoincludesomereferencetonecessityandimpossibility.Ifyouare animals andthattherearenodragons. tive verb“[it]isnot”:forexample,thatsandnotnourishing,sheepareflying claims abouttheworldonlytothosewhichcanbeexpressedusingformsofnega- distant countries.BycontrastifyoufollowParmenides’secondwaywilllimityour example, thatwateriswet,therearefishintheseaandelephants onlytothosewhichcanbeexpressedusingformsofthepositiveverb“[it]is”:for it islike.IfyoufollowParmenides’firstwaythenwilllimityourclaimsaboutthe 1974). Supposeyoustartinvestigatingtheworldaroundyou,tryingtoestablishwhat the outset.Itispreferabletounderstandtwo“waysofenquiry”asfollows(seeFurth mislead bythisintothinkingthatParmenideshasadeterminatesubjectinviewfrom as providedbytheparenthesized[it]inpassagequoted,butitisimportantnotbe by thenegationofsameword,oukestin.Englishrequiresasubjectfortheseverbs, estin, thethirdpersonsingularpresentindicativeofverbtobe;coresecond two startingpoints.ThecoreofthefirstpointisgivenbyasingleGreekword an accountofthenaturethatworld.Therearetwowaysenquirybecausethere off fromsomestartingpointalonganinvestigativeenquiryintotheworld,resultingin ? Thealternativesaredescribedas“waysofenquiry.”imageisthatsetting of whichisdescribedas“indiscernible.”Butwhatmoresensecanwemakethepas- This isclearinoutline:therearetwoalternatives,oneofwhichleadstotruthand Knowing of .Anengagingway in toParmenides’thoughtisthefollowing(cf.Owen1960). 28 B6,B7).Wehaveherethe drivingthoughtbehindParmenidesaccountofthenature “you couldnotknowwhatisnot—thatcannotbedone—nor indicateit”(seealsoDK Parmenides sayssomethingexplicitlyaboutthefirstquestion inthequotedpassage: and hastobe(thatis,what“is…isimpossiblenotbe”).Likewisemutatis Parmenides thinksonlyoneofthesewaysenquiryiscoherent:thefirstway“the Given justthisminimalcharacterization,wecanseewhyParmenides’descriptionof if youfollowthesecondway:willnotbeabletoclaimthatthereareno and indicating seem toberelations,andtherefore torequirerelata Parmenides II:waysofenquiry STEPHEN MAKIN 36 have been—theitalicizedtermsimportthe between

Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 two waysofenquiry: way, andlaterinthepoemParmenidessaysexplicitlythatheiseffectivelyrulingout Accepting Parmenides’stricturesagainstthesecondwayplayshavocwiththisthird too cold,butothershavenosnow,andarenotimpassableinthewintermonths…” the north,someareveryhighandsnowcappedevenwhenweatherhereisnot out claimslike“therearemountainstothenorth,butnonesouth.Ofthosein tive “[it]is”and those forms.Humanenquirymoretypicallyfollowsathirdway,using arise whenusingformsofthenegativeverb“[it]isnot.”Ofcourse,no-oneuses The pointofintroducingthesecondwayistofocusourmindsonproblemswhich world whilelimitingthemselvestousingonlyformsofthenegativeverb“[it]isnot”? way ofenquirywereruledout,sinceno-oneeverdoesgoaroundinvestigatingthe verb form“[it]is.” dragons.” ThenIhave,contrarytothestricturesofsecondway,usedpositive second way.SupposeIsay“therearenogiantreptiliandragons,but to expressanytruthcorrelatedwiththatfalsehoodwithoutstrayingfromParmenides’ “there arenodragons”couldbesignificant,itwouldfalse.Butwillimpossible pictures orstory-beasts,ratherthangiantreptilianfire-breathers.Inthatcase,while For tomakethatmoveisjustallowafterallthereare world for“dragon”toconnectwith:drawings,children’sstoriesorideasinthehead. dragons, then“dragon”willbeamerenoise,justlike“harrumph.” saying “therearenodragons.”HowcouldwhatIhavesaidbetrue?Iftherereally non-existents couldbeknownorindicated.Suppose,followingthesecondway,Itry being significant,ratherthanamerenoise.)Butgivenallthat,itisveryhardtoseehow in theworld;butpointhereisjustthatitsdoingsopartiallyconstitutiveof difficult—question howhumanbeingscanmanagetoget“tree”relatesomething “harrumph” ismerelyasoundproducedbythroatclearing.(Itanother—andvery the natureofreality. which Parmenidesmentioned, asbeingtheonlycoherentwaytopursueenquiry into itself onlyofthepositiveform “[it]is”;andthattakesusrightbacktothefirst way of thenegative“[it]isnot,” however,leavesuswithawayofenquirywhichcanavail “[it] isnot”ifittobeapermissible wayofenquiry.Purgingthethirdany uses way “onwhichmortalswander”—needs tobepurgedoftheproblematicnegativeform from Parmenides’rejectionofthesecondwayleadsus to seethatthethirdway—the is not”ratherthanthatitusesonly What isproblematicaboutParmenides’secondwaythat ituses Now recallthesecondquestionabove.WhywoulditmatterifParmenides’ Of courseParmenideswillbeunmovedifsomeonepointsoutthere taken bythemallisbackwardturning. believe thattobeandnotarethesame same;andthepath are carriedalong,deafandblindatonce,dazed,undiscriminating hordes,who headed; forhelplessnessguidesthewanderingthoughtintheir breasts, andthey I holdyouback,butthenfromthatonwhichmortalswanderknowingnothing,two isnot.Ibidyouponderthat,forthisthefirstwayofenquiryfromwhich What istheretobesaidandthoughtmustneedsbe:foritbeing,but the negative“[it]isnot.”Investigationofworldtypicallychurns PARMENIDES, ZENO,ANDMELISSUS that form.Incaseapplyingthelessonslearned 37 DK 28B6(emphasesadded) dragons, butthattheyare the negativeform“[it] are there arestory- both things inthe the posi- only Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 side, equallybalancedinevery directionfromthecenter”?)Themostimportantthing there isafurthestlimit,it is perfected,likethebulkofaballwell-roundedonevery figurative ways(howliterally arewetotaketheclaimatDK28B8.42–44that“since form ofwritingisnotconducive toclarity,andhesometimeswritesinwhatseem like DK 28B8iscertaintobecontentious. Parmenidesisbreakingnewground,hispoetic my laterremarksonMelissus). 1979, Curd1991forcriticismoftheorthodoxviewParmenides asamonist;seealso , andclaimingthatrealityisbothundifferentiated andunique(butseeBarnes is” DK28B8.25)—indeed,manyhavetakenParmenides tobedefendingaformof but overthereisnodog(“Soitallcontinuous:forwhatdrawsnearto what there canbeanygenuinevarietyintheworld:forexample, thatoverherethereisadog earlier mustnotbehereanymore(seeDK28B8.26–28).Oragain,itishardto seethat where previouslytherewerenobrownleaves,andthegreenleaveswhichhere If theleavesaretohaveturnedfromgreenbrown,there mustbebrownleavesnow anything changingeither.Changeinvolvestherebeing somethingnewintheworld. related reasons—goingoutofexistence,thenwewillnotbeabletotalksensiblyabout Further, ifwecannottalksensiblyaboutsomethingcomingintoexistence,or—for of temporaryexistentwithwhichwearemostfamiliar:dogs,oaktrees,mountains. of enquiryintotheworldwillrevealthattruenaturerealityexcludestype a formoftheprohibitednegative“[it]isnot.”Sofollowingonlypermissibleway a thingnow,butearlierontherewasnotanysuchthing.Buttheitalicizedwordsare suppose thatsomethinghascomeintoexistencethenwearesayingthereissuch We aredebarredfromsayingofanythingthatithascomeintoexistence.Forifwe reality. negative verbform“[it]isnot”woulddeliverstrikingconclusionsaboutthenatureof can, however,appreciateinacoupleofcaseshowParmenideanrenunciationthe and insomecasesitisunclearpreciselyforwhatpositionParmenidesarguing.We It isnotpossibletolookindetailatallofParmenides’.Manyareopaque, will champion enquiry re-appearsatthestart,andisfollowedbyanoutlineofaccountParmenides served inthehistoryofwesternphilosophy.Theimageasinglepermissibleway and difficultargumentation:theearliestblockofsustainedphilosophicalargumentpre- Parmenides offershisownviewofthenaturerealityinforty-ninelinesdense The interpretationandexplicationofanyparticularargument inthelongfragment that itisnot allow youtosaynorthinkfromnotbeing:foritisbesaidthought For whatbirthwillyouseekforit?Howandwhencediditgrow?Ishallnot single kindandunshakenperfect very manysigns,thatbeinguncreatedandimperishableitis,wholeofa There stillremainsjustoneaccountofaway,thatitis.Onthiswaythereare Parmenides III:thenatureofreality STEPHEN MAKIN 38 DK 28B8.6–9 DK 28B8.1–4 Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 ( example: iftherearemanythings,thenthesamethings arebothlikeandunlike Zeno’s argumentsconcernedplurality,andhadacommon form.Platogivesjustone ing pagesofPlato’sdialogueParmenides 210b22–27.) this structure. hard (althoughnotimpossible) toforcetheZenonianargumentsaboutmotion into unlikely, though,thatallZeno’s argumentswereofthissingleform,sinceitwould be small, indeedofnosizeatall, andlarge,indeedofunlimitedsize(DK29B1,B2). It is over aZenonianargument thatiftherearemanythingsthentheymustbeboth are bothlimitedandunlimited (DK29B3).Simpliciusalsomovesbackandforth words” Simpliciusreportstheargumentthatifthereare manythingsthesame Simplicius providestwoargumentsofthistype.Claiming toquote“Zeno’sownvery 25, andanargumentabouttheexistenceofplaceat reports aSorites-typeargumentconcerningperceptible soundat associated withZenowhicharenotobviouslytiedtoParmenides’views.( most directlytoParmenides.Butoneshouldnotethatthereareotherarguments concentrate onZeno’sargumentsconcerningpluralityandmotion,sincetheserelate but theevidenceisthatZenowroteagooddealmorethanhasbeenpreserved.Iwill was thecasewithParmenides,SimpliciusdoesreproducesomeofZeno’sownwords, ibility andcontinuityofspacetime,sohefeelsnoneedtoquoteZeno.As arguments insofarastheyraiseissuesofindependentinterestforhimaboutthedivis- adapted toapplychangemoregenerally—isAristotle.Heisconcernedwiththe he can.(ForthisviewofZenoseeBarnes1982:231–237.) equally betreatedasafreewheelingparadox-monger,outtoraiseproblemsforanyone Parmenides’ ideasandarguments;inthatcaseitwillbeunsurprisingZenocould and challengeour course, ifthatisZeno’spurposethenwewouldexpecthisargumentstoconnectwith by shakingtheconfidenceweallfeelinbasicfeaturesofourfamiliarworldview.Of to beobvious,andtheParmenideanalternativeabsurd. what theyarelikeandinwhereare;there things whichcomeintoandgooutofexistence;thereare fidence thatthefamiliarcommonsenseviewofthingsgetsbasicscorrect.There but onemightthinkthatthereisnoneed no varietyintheworldseemsridiculous.ThereismuchParmenidestodisentangle, really he achievedatsuchanearlystageinthehistoryofwesternphilosophy.Butideathat issues ofphilosophicalimportance.Andwecanadmiretheargumentativerigorwhich of realityseriously.Wecanrecognizethathisconcernsabout“whatisnot”pointto Most peoplecominguponParmenides’poemwouldnotbeinclinedtotakehisaccount thatonecannotspeakorthinkofwhatisnot. to takefromthisbriefsurveyofParmenides’workforthepresent,though,isdriving Parmenides Our mainevidenceforZenoasadefenderofParmenidean monismistheopen- Our earliestsourceforZeno’sargumentsaboutmotion—someofwhichcouldbe Zeno ofEleasoughttoredressthedialecticalbalancesomewhatinParmenides’favor there is,forexample,nocomingintoandgoingoutofexistence,change, 127e–128a). Noancientexplicationofthis commonsense outlook,ratherthanmakeanyexplicitreferenceto Zeno I:thepurposeofhisarguments PARMENIDES, ZENO,ANDMELISSUS to disentangleitinorderpreserveourcon- 39 (126a–130a). AccordingtoPlato’sreport, lots things whichchange,bothin of suchthings.Allthisseems hassurvived,but 4.1, 209a23–25and4.3, Physics 7.5, 250a19– are Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 The issueappearstobethenumber According toSimpliciusthefollowingareZeno’sownwords: whenever Itrytofocusdownonjust about theflowerbedandsand.ItlooksasifZenohasawayofaddinganextrathing between themtoo—forexamplesomesand–thenZenowillaskthesamequestion tion aboutthegardenhedgeandflowerbed.IfIanswerthatthereissomethingelse from oneanother:aflowerbedinbetweenthem.ButZenowillnowaskthesameques- two the worldcontains:mygardenhedgeandlawn.WhyamIconfidentthattheyare extra itemstotheworldatwill.Takejusttwoofhugevarietythingswethink have beenmoreorfewer;butinfact,therearethis the morefamiliar“limited/finite”and“unlimited/infinite”).Presumablytherecould apeira number (“justasmanythereare”;thecontrastbetweenGreek suggests thislineofthought:Howevermanythereare,aresurelya that therearelotsofthingsintheworld.Howmany?Thefirstlimbargument bits thanjellyfishare).However itwould,bycontrast,beverysurprisingtosuppose that is harderthanchina)andhuman capacities(humansarebetteratbreakingthings into of sand).Thereasonsliein abouttheconstitutionofdifferentmaterials(diamond planks) andotherthingswhich resistoureffortsatdivision(lumpsofdiamond,grains there aresomethingsinthe worldwhichwecanbreakintobits(chinaplates,wooden divisibility whichunderliethisintuition.Thereisnothing surprisinginrecognizingthat of thefactthatitissurprisinglydifficulttohandleviews aboutspatialextensionand the argumentspreservedinZenonianmaterialatDK 29B1andB2takeadvantage may seemintuitivelyobviousthattheworldcontainsa plurality ofdifferentthings.But things. Nowsincecommonexperiencepresentsmewith anarrayofthingsinspace,it it willturnoutthatany“single”thingwecaretothink ofisjustacollectionother ments aboutplurality:theideathatoncewestartconsidering theworldasaplurality indeterminate orunlimitedplurality. things Ithinktheworldcontains:ifcontains a pluralityofthingsthenitisan next tooneanother,sothatagainhehasawayofadding extraitemstothebunchof and hedge),ratherthanastwothings:aright-sideleft-sidelawnpushedrightup things. ForthenZenocanaskwhyIcountmylawnasjust questions bysayingthattheredoesn’thavetobeanythingwhichseparatesdistinct contain. Further,Iamnobetteroffinmycommonsenseoutlookiftrytostopthese The secondlimboftheargument,however,suggestsaZenonianrecipeforadding There isalineofthoughtatworkherewhichalsofeatures inotherZenonianargu- things? Anappealingansweristhattheresomethingelsewhichseparatesthem And thusthethingsthatareunlimited(apeira). always othersbetweenthethingsthatare,andagainthose. Iftherearemanythings,thethingsthatunlimited;for will belimited(peperasmena). and neithermorenorlessthanthat.Butiftheyareasmanyare, If therearemanythings,itisnecessarythatjustastheyare, is aswellcapturedbythetranslations“determinate”and“indeterminate” Zeno II:argumentsaboutplurality STEPHEN MAKIN of thingswhichthereare.Commonsensetellsus two 40 of thethingswhichIsupposeworldto many—a determinatenumber. one of apairthings(lawn peperasmena DK 29B3 determinate and Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 it arrivesatthegoal”(Physics on thegroundthatwhich isinlocomotionmustarriveatthehalf-waystagebefore mary oftheDichotomyisterse; hereportsthatit:“assertsthenon-existenceofmotion Dichotomy, theAchilles, FlyingArrowandtheMovingRows. Aristotle reportsfourZenonian argumentsconcerningmotion,commonlyknownas the some extendedthingsintheworldhave nitude couldn’texist,forsincetheywouldadd with magnitude.InfactZenoreliesonthislastpointtoarguethatthingswithoutmag- Adding togethertwo(ormore)thingswithnomagnitudewillnotproducesomething posed ofthingswithnosizeevercometocontainextendedsuchasmytable? nitude” (DK29B1.10–12). are manythings,itisnecessarythatthey…small…;soasnottohavemag- B2.19–20). ThatgivesZenoonelimboftheargumentheisdeveloping:“Thusifthere “It hasnomagnitudesinceeachofthemanyissameasitselfandone”(DK29 would havetobeunextended,withoutanymagnitudeatall.AsSimpliciusreportsit: is itselfacollectionofbits,thenanyunitarybitfromwhichcomposed a plurality,thenwhatisitpluralityof?Ontheonehand,ifeverythingthatextended world isapluralityofdifferentthings.Hepushesthefollowingquestion.If of smallerbitsgivesout? things don’t.Whyshoulditbeatonesizeratherthananotherthatthemere bits itwilllookobjectionablyarbitrarytosupposethatneverthelesssomeextended original. Forsinceitseemsplaintocommonsensethatsomeextendedthingsdo natural tothinkthatevery the Platoniccharacterization. manipulated theZenonianmaterialavailabletohimin ordertobringitintolinewith large astobeunlimited”(DK29B1.10–12). it isnecessarythattheyarebothsmallandlarge;so asnottohavemagnitude,so ment togeneratewhatlookslikeafatalcontradiction: “Thus iftherearemanythings, unsatisfactory initsownright,butZenocancombineitwiththefirstlimbofhisargu- things whichmakeuptheworldisinfinitelylarge.Andnotonlythatconclusionalso size, thentheresultisgoingtobeinfinitelylarge,sothatitnowseemseachof ... Howeverifoneaddstogetheraninfinitenumberofbitseachwhichhasequal quarters, andmorethanjusteighteighths,Nnthsforanyyoulike equal sizedbits,sinceitwillhavemorebitsthanjusttwohalves,andfour not beabletobreakitintoallthebitshas):indeedwillhaveaninfinitenumberof with magnitudewillhaveaninfinitenumberofbits(although,asnotedearlier,we with magnitudehasbitswhichthemselveshavemagnitude,itappearsthatanything of Zeno’soverallargument.Iftheyhavemagnitude,howbigarethey?Sinceanything to makeuptheworlddo B2.8–16). Butifwerespondbyinsistingthatofcoursethethingswhichgotogether The DichotomyandtheAchilles relyonessentiallythesameidea.Aristotle’ssum- Even asastand-aloneconclusionthislooksunsatisfactory.Howcouldworldcom- How doesZenoextractproblemsfromallthisforthecommonsenseideathat Here wehaveaconclusionoftheformwhichPlatoidentified atthebeginningofhis Parmenides (127e), althoughwecannotknowtowhatextentSimplicius has Zeno III:argumentsaboutmotion PARMENIDES, ZENO,ANDMELISSUS have magnitude,thenweopenourselvestothesecondlimb extended thinghasatleasttwobits,eachhalfthesizeof 6.9 239b11–13,DK29A25). smaller bits,whileothershavenone.Itisvery 41 nothing, theywouldbe nothing (DK29 possession have Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 vided adiagraminorderto clarify theargument(DK29A28). Alexander ofAphrodisias,an Aristoteliancommentatorofthethirdcentury : theMovingRows. only becauseitisthoughtbysometoberelevantanother ofZeno’sargumentsabout temporal (seeSorabji1983forathoroughtreatment). Imentiontheviewhere ceding section.)Thereisdebateamongscholarsaboutthe historyofthissortspatio- would alsoberelevanttotheZenonianargumentsabout pluralitydiscussedinthepre- periods oftime,andpresentingtheillusioncontinuity. (Anatomisttheorylikethis ous, butmorelikeanarrayofpixelsonacomputerscreenflashingandoffforfixed Physics and thenseveneighths,soon;AristotlementionsthisvariantoftheDichotomyat spatial atomcouldpass(sincefirsthalfofitwouldhavetopass,andthenthreequarters, temporal periodsthenZenocouldaskhowthetime atoms. Forifitremainedtruethateverytemporalperiodwerecomprisedoftwosmaller raised byvariantsoftheDichotomy,thisresponsewouldalsohavetoposittemporal are nodistancessmallerthanthespatialminimumD.Nowinordertoavoidproblems midway betweenthereanditsdestination.There is distanceDawayfromitsdestination,itwillnotbetruethathastogetapoint that therejustis strong formofspatialatomism,accordingtowhichthereisaminimaldistanceDsuch were denied,theargumentwouldloseitsbite.Denyingthatassumptiongeneratesa on theassumptionthatanydistancecomprisestwohalfdistances.If tion justone,whichperhapscomesmostimmediatelytomind.TheDichotomyrelies inSalmon1970;alsoSainsbury1988:5–24;Lowe2002:288–306).Iwillmen- which somethinghastomakeinordergetgoingfromAB. be aninfiniteseriesofthesemidwaypoints,andsoabeginninglesssub-journeys and Bithastoget¼ABmidwaybetweenA½AB,soon.Againthereseem start away ataslowerrate).Second,itisimpossibleforsimilarreasonsthatsomethingshould someone, ,movingquicklytowardsadestination,tortoise,whichis at itsdestination(theAchillesisessentiallythesameargument,exceptthatweconsider ofsub-journeyswhichsomethinghastomakeingoingfromABbeforeitarrives distances thentherewillbeaninfiniteseriesofthesemidwaypoints,andsoendless the point¾ABmidwaybetween½ABandB,soon.Ifanydistancecontainstwohalf- arriving atBitfirsthastoarrivethepoint½ABmidwaybetweenAandB;then something shouldfinish the problem(Aristotle’sbriefcharacterizationallowsforeither).First,itisimpossiblethat something shouldevercoveranyarbitrarydistanceA–B.Therearetwowaysofposing Once againAristotle’sreportishighlycompressed: A richvarietyofresponseshavebeenofferedtothisargument(seethecollection If somethingmovesthenitcoversadistanceindoingso.Butseemsimpossiblethat thinks itfollowsthathalfthe timeisequaltoitsdouble. of thestadium,othersfrom themiddle—atequalspeeds,inwhich[Zeno] equal bodiesinthestadiumfromoppositedirections—the onefromtheend The fourthargumentisthatconcerningequalbodies which movealongside covering the distance A–B. For before it gets to the point ½AB midway between A covering thedistanceA–B.Forbeforeitgetstopoint½ABmidwaybetweenA 8.8, 263a15–23).Onaviewlikethismotionwouldnotbesmoothandcontinu- no distancesmallerthanD.Sooncesomethinggetstoapointwhich covering the distance A–B. For before it finishes covering A–B by covering thedistanceA–B.ForbeforeitfinishesA–Bby STEPHEN MAKIN Physics 6.9,329b33–240a1=DK29 A28 42 is which somethingtakestocoverthe no suchmidwaypoint,sincethere ad, pro- Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 states theunwelcomeconclusionthatt totle identifies,is2t hardly beanappealingresponse todenythatB1everdoesmovefrombeingopposite C1 size as“halfanA”(ifthere werewewouldbebacktotheDichotomy).Andit answer isruledout,because sincetheAsareofatomicmagnitudetherejustisnosuch A,” sincetheAsarestationary, whiletheCsaremoving,relativetoBs.But that being oppositeC1to opposite C2?Thecommonsenseanswerwouldbe“half an embarrassing question:how manyAsdoesB1passinthetimetakenforittogetfrom the As,BsandCsareatomicbodies.Inthatcase relativityofvelocityforcesan in ordertoevadetheDichotomyargument(seeOwen1957 forthisapproach).Suppose is aimedattheviewmentionedearlier,whichadoptsa strong spatio-temporalatomism that whetherornotsomethingismovingreallya factaboutit. one thingmovesdependsonfactsaboutthemotionofother things,thenitmightseem moving thenitmustbeatsomevelocityorother. Butifthevelocityatwhich relativity ofvelocitycallsintoquestiontherealitymotion. Afterall,ifsomethingis thanonewhichisstationary.Thefirstpossibility isthatZenoarguingthe than beingmuddledabout,thefactthatsomethingmoves morerapidlypastamoving Moving Rows.Therearetwooptions.Accordingtoboth,Zenoistradingon,rather (namely t arrangements inFig.1and2representsboth namely 2t should taketwiceaslongforB1topassfouroftheCsitdoestwoAs: As. TheCsarethesamesizeasSo,givenassumptionAristotleidentifies,it from itsFig.1positionto2ist that assumption,thenitmayproceedasfollows.SupposethetimetakesB1tomove even ifoneofthosebodiesisstationaryandmoving.Iftheargumentdoesrelyon tion thatsomethingmovingtakesthesametimetopasstwobodiesofsize, who isdeeplyunimpressedbythisargument,saysthatZenoreliesonthefalseassump- from beingoppositeA2toA4). bodies changeoverthetimethatittakesB1togopasttwoofAs(thatis,move ing atequalspeedsinoppositedirections.Fig.1and2showhowthepositionsof The secondpossibilityisthatAristotlehasomittedacrucial :thattheargument Some commentators,however,havesoughtamorecharitableinterpretationofthe How dothesediagramssuggestthat“halfthetimeisequaltoitsdouble”?Aristotle, The As,BsandCsareequalsizedbodies.Asstationary,themov- ⇐ Fig. 2: B4B3B2B1⇒ ⇐ Fig. 1: ) . Butitisclearfromexaminingthediagramsthatintervalbetween and the timeittakesB1topassfourCs(which,givenassumptionAris- ). Thedeliberatelyparadoxical‘halfthetimeisequaltoitsdouble’ PARMENIDES, ZENO,ANDMELISSUS C1 C2C3 C4 B4 B3 B2 B1 A1 A2A3A4 A1 A2A3A4 = 2t C1 C2 C3 C4 43 . . DuringthattimeB1passestwoofthe the timeittakesB1topasstwoAs ⇒ Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 Arrow: the leftofC1(oppositeA2inFig.1)torightA42). to beingoppositeC2,sinceitwillthenbewhollyunclearhowB1couldhavegotfrom flaw: report ofZeno’sArrowargumentisfollowedimmediately byhisdiagnosisofitsmain that atleastitisn’tresteither. is notmoving:andthesituationseemsmore,ratherthanless,paradoxical ifwepointout unchallenged, Zenowillstillbeabletoconcludethatthroughout its“flight”thearrow contained withinaperiodoftimetowhatholdsthroughout theperiodoftimeremains that thearrowisnotmoving.So,ifinferencefromwhatholdsatanyarbitraryinstant arrow isneitherinmotionnoratrestaninstantthenanyarbitraryittrue sumably thisresponsebyitselfwouldnotsatisfyZenoanyway.Forifitistruethatan disadvantage oncethosenotionshadbeenexplicatedbyNewtonianscience,andpre- denial ofmotionandvelocityataninstantputAristotelianphysicsaconsiderable ). Thatresponsetotheargument,however,incursweightyconceptualcosts: time (becausebeingatrestinvolvesremaininginthesameplaceforsomeperiodof motion involvescoveringdistance),restwouldalsobepossibleonlyoveraperiodof (Physics hold, however,asAristotledid,thattheconceptsofmotionandrestarecorrelates at leasttwostrategieswhichcouldbeadoptedinrespondingtotheargument. conclusion isdrawnaboutthearrowduringitsentire“flight.”Consequentlytherewill the arrowatanyarbitraryinstantduringitsflight.Secondonbasisofthatclaima been firedandhittingthetarget,inwhichcase‘movingarrow’isreallyatrest. fired anditshittingthetarget.Soarrowisatresteveryinstantbetweenhaving what goesfortwelvenoonanyotherinstantwecaretopickbetweenitsbeing at rest(aswemightputit:itisin But surely,Zenowillsay,somethingoccupyingaspaceexactlyitsownsizeandshapeis noon. Attwelvenoonthearrowwilljustbeoccupyinganarrow-shapedareaofspace. early) afternoon.Considerhowitiswiththearrowatun-extendedinstanttwelve Imagine anarrowwhichisfiredinthe(verylate)morningandhitsitstarget twelve noonandtheoneafterit etc. Thetroubleisthatthere isno think ofperiodstime,such astheextendedlunchbreak,builtupfrominstants like The broadreferencehereis toAristotle’sgeneralanalysisofcontinuity.Wecannot The finalZenonianargumentaboutmotionreportedbyAristotleistheFlying So someresponseisrequiredtothesecondstageof argumentaswell.Aristotle’s According tothefirstpartofargument,arrowisatrestnoon.Onemight This argumentgoesintwomainstages.Firstaclaimisallegedtoholdconcerning a now,theflyingarrowisthereforemotionless it occupiesanequalspaceisatrest,andifthatwhichlocomotionalwaysin Zeno’s reasoning,however,isfallacious,whenhesaysthatifeverything other magnitudeiscomposed ofindivisibles. This isfalse;fortimenotcomposedofindivisiblenows anymorethan 6.3, 234a31–34):sincemotionispossibleonlyoveraperiodoftime(because that space).Sothearrowisatresttwelvenoon.But STEPHEN MAKIN 44 Physics 6.9,239b5–7=DK29A27 Physics 6.9,239b8–9 oneafterit . It’sobvi- Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 fragments preserved(once again) bySimpliciusareinaterse,plainprosestyle, and Eleatic outlookbeyondwhat ispresentedinParmenides’poem. but heisnomerefollower.We canidentifythreewaysinwhichMelissusdevelops the intriguingly—he alsohada considerable militaryreputationasanadmiral;DK30A3), 185b10–12). Melissusargues forabroadlyParmenideanviewofreality(although— ity. Aristotlejudgedhimamuchpoorerphilosopher than Parmenides( Melissus hastraditionallybeenthoughttheleastimpressive oftheParmenideantrin- which periods/lines/extended-itemsarebuiltup,thenwhyshould noon, weretheresuchaninstant).Butifinstants/points/indivisiblesaren’tblocksfrom he’s setoffatnoon—iftherewere,that’swherehewouldbethefirstinstantafter (recall theDichotomyargument:similarly,thereisnofirstplacerunneratafter could berecordedbyalessaccurateclock,showsveryclearlythatthere of aseriesmoreaccurateclocks,eachrecordinganinstantclosertotwelvenoonthan ously not12.01,sinceamoreaccurateclockcouldhavedisplayed12.005;andthinking particular useof“now”refersdependsonthetime that “now”referstothepresent of theFlyingArrowtradingonfollowingthreefacts:thatarrowsmovequickly, Parmenides’ claimsfromridicule of carefullytunedstatementshisarguments.IfZeno’spurposereallywastodefend ceding sectionofthischapter).ButitisequallylikelythatZenohadavariedrepertoire claims toreproduce“inZeno’sownverywords”(DK29B3;seediscussioninthepre- crisp statement,inthetersestyleoflimited/unlimitedargument,whichSimplicius now. WecannotknowhowZenooriginallystatedhisFlyingArrow.Maybehehada common Greekadverbnun:justasfamiliarandnuancedinitsusetheEnglish guage. OneofthewordswhichoccursinAristotle’sstatementZeno’sargumentis so on.Heiscreatingaphysics,andreliantforhisvocabularyonordinaryGreeklan- But Aristotleisbreakingnewgroundinhisthinkingaboutspace,time,motion,and a richvocabularyforpickingdifferentinstantsout—twelvenoon,12.00,12.0000,t dance ofwaysreferringtonon-extendedpointstime:wehavetheword the lensofAristotle’ssophisticatedanalysiscontinuity.Wemodernshaveanabun- being colored,sowithmoving. should anythingfollowaboutthegreenbushesandtreesIcansoobviouslysee?Aswith color? whatwouldbethedifferencebetweenpointswithdifferentcolours?);butwhy geometrical pointwithintheviewfrommywindowcouldpossiblyhaveacolor(which something’s periodofflightfromclaimsaboutanarbitraryinstant,saytwelvenoon.No changeless ing watchingarcherymightthinkitamusingtosayZeno:“somuchforParmenides’ by Aristotle’swonderfulanalysisofcontinuity(seeLear 1981,LePoidevin2002). remain difficultissuesraisedbyZeno’sFlyingArrowargument whicharenotresolved maneuvered intoanexasperatedoutburstof“allright,it’s notmoving going toinvitemoredifficultquestions,andisalltooeasy toseehowsomeonecouldbe one isnowstationaryinthetarget.Staringevenharder atthenextarrowfiredisjust the obviousreply—“yes,ofcourse”—Zenoisdoubtlessinapositiontosaythat,no,that First, Melissuswritesinastyle farmoreaccessiblethanthatofParmenides.The It isimportantnottofocusZeno’soriginalargumenttoosharplybyviewingitthrough then?” SupposeZenoshouldsay:“isthat PARMENIDES, ZENO,ANDMELISSUS then onecanimaginerhetoricallyeffectivestatements and that“now”refersindexically Melissus 45 of arrow movingnow?”Bythetimeof that particularuse).Anyonestand- (the timeto anything rightnow.”There is nosuchinstant follow about instant,and Physics which a 1.2, etc.

Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 we haveseen,Melissusdoes sometimesarguefairlystraightforwardlyforcentralclaims ward andaccessibleversion of Parmenides’‘weirdandwonderful’accountreality. As nothing, andnothingdoesnot exist,thenitisimpossibleforanythingtomove. space forthingstomoveinto, withMelissusarguingthatsinceemptyspacewould be Here wehaveanearlystatement oftheveryinfluentialideathatmotionrequiresempty Contrast thefollowingfromMelissus: of realityallowsfornochangeormotion.Buthispreciseargumentisdense: own argumentshadbeendifficultandallusive.Parmenidesthoughtthatthetruenature unlimitedness ofspace,orindifferentlyforeither). ticular passageswhetherMelissusisarguingfortheunlimitednessoftime,or both intimeandspace(seeDK30B2–4;however,itissometimesunclearpar- contrast, atleaststakesoutaclearview,holdingthatrealityisextendedwithoutlimit into auniquepresent,orastimeless(seeSchofield1970,Matten1986).Melissus,by It isutterlyopaquewhetherParmenidesthinkingofrealityaseternal,orcondensed more determinate.Parmenides’viewsontime,forexample,arenighimpenetrable: some scholarshavedatedtothesecondcenturyad(seeMansfeld1988). another isfoundinthepseudo-AristotelianOnMelissus,XenophanesandGorgias his thoughtinanextendeddeductivestructure:oneparaphraseisduetoSimplicius, we havetwoparaphrasesofMelissus’overalllineargument,bothwhichsetout Phys.111.15–16). InadditiontothepreservationofsomeoriginalMelissanmaterial, Simplicius saysthat“Melissuswroteinanarchaicstylebutnotunclearly”( It wouldbeamistake,though, tothinkthatMelissuspresentsjustamorestraightfor- Third, insomecasesMelissusoffersinnovativesupportforviewswhereParmenides’ Second, therearesomeareasinwhichMelissusmakesParmenides’ideasclearerand give way. what wasempty;butsincethereisnosuchthingasempty, ithasnowhereto point, butisfull.Forifthereweresuchathingasempty itwouldgivewayinto ing couldnotverywellexist.Nordoesitmove.Forcannot givewayatany And nothingofitisempty.Forwhatemptynothing. Well,whatisnoth- within thebondsofalimit,whichkeepsitinoneveryside. it liesonitsownandthusfixedwillremain.ForstrongNecessityholds true convictionhasthrustthemoff.Remainingthesameandinplace ceasing, sincecomingtobeandperishinghavewanderedveryfaraway, But changelesswithinthelimitsofgreatbondsitexistswithoutbeginningor into being,itisnot:norifevergoingtobeinthefuture. And howcouldwhatisbeinthefuture?Howitcometobe?Forifcame it neverwasnorwillbe,sinceisnow,alltogether,one,continuous STEPHEN MAKIN 46 DK 28B8.26–31 DK 28B8.19–20 DK 28B8.5–6 DK 30B7.7 which Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 2005). Melissus’ ownplainanddirectarguments(DK30B8;forfurtherdiscussionseeMakin of Zeno’sdiagnoseslogicaltroubleinthecommonsenseoutlook,andunpersuadedby than —despiteParmenides’insistencethatonejudgebyargument,intheface who persistedinplacingtheirconfidencetheevidenceofsenseperceptionrather hostility towhat-is-not,andamoreindirectargumentaimedatthoseofhisopponents a differencebetweenthedeductivelytransparentarguments,restingonParmenidean Finally thematerialpreservedbySimpliciussuggeststhatMelissushimselfrecognized argued thatwhatisrealincorporeal: and space,full,needtobebalancedagainstareportfromSimpliciusthatMelissus the seeminglystraightforwardMelissanclaimsthatwhatisrealunlimitedintime that whatisrealsuffersneitherpainnoranguish(DK30B7.4–5,16–23).Andeven ous ideasofhisown,whoseimportisnoteasytounderstand:heargues,forexample, in onewayandadifferentthingqualifieddifferently).Melissusalsointroducesmysteri- Lear, J.(1981),“ANoteonZeno’s Arrow”,Phronesis26:91–104 Le Poidevin,R.(2002),“Zeno’sArrow andtheSignificanceofPresent”,inC.Callander(ed.)Time, Furth, M.(1974),“ElementsofEleatic ”,inA.Mourelatos(ed.)ThePre-Socratics,GardenCity, Curd, P.(1998),TheLegacyofParmenides , Princeton,NJ:PrincetonUniversity Press Curd, P.(1991),“ParmenideanMonism”,Phronesis36:241–264 Barnes, J.(1982),ThePresocraticPhilosophers(revisedsinglevolumeedition),London:Routledge Barnes, J.(1979),“ParmenidesandtheEleaticOne”,ArchivfürGeschichtederPhilosophie 61:1–21 Cambridge UniversityPress,2010) Testimonies oftheMajorPresocraticseditedwithtranslationandcommentsbyDanielGraham(twovolumes, An alternativetoDiels-KranzisTheTextsofEarlyGreekPhilosophy:CompleteFragmentsandSelected Press, 1983)=KRS. The PresocraticPhilosophersbyG.S.Kirk,J.E.RavenandM.Schofield(2ndedition:Cambridge University The Diels-KranzvolumedoesnotincludeanyEnglishtranslation. I havereliedontheclassiccollection indicates afragment,“A”wouldindicatedoxographicalreport). “DK 28B2”aretoDiels-Kranz(thefirstnumberisthechapter:Parmenides, 29Zeno,30Melissus;“B” sokratiker The standardcollectionofPresocraticfragmentsandtestimoniaisthethreevolumeDieFragmentederVor- no variety,sincedifferencewouldleadtoplurality—therebe there weretwotheywouldlimitoneanother;thereforeDK30A5:whatisrealexhibits in bothtimeandspace;thereforeDK30B6:therecanonlybeonerealthing,sinceif that realityisauniqueandundifferentiatedwhole(DK30B2:whatrealunlimited monism. Bycontrast,thereisnosuchdebateaboutMelissus,whoarguesexplicitly there isscholarlydebateaboutthedepthandnatureofParmenides’commitmentto of Parmenides’poem.Othercases,however,arelessclear.Wehavenotedearlierthat Reality andExperience,Cambridge:CambridgeUniversity Press:57–72 NY: Anchor:241–70 But ifithadsolidity,wouldhaveparts,andbenolongerone.” says: “If,then,itwere,mustbeone;andbeingone,nothavebody. That [Melissus]wantswhatexiststobeincorporealhemakesclearwhen edited byH.DielsandW.Kranz(6thedition,Weidmann,Zurich,1952).Referencesintheform PARMENIDES, ZENO,ANDMELISSUS References andfurtherreading 47 one thing qualified DK 30B9 Downloaded By: 10.3.98.104 At: 07:17 27 Sep 2021; For: 9781315871363, chapter3, 10.4324/9781315871363.ch3 Vlastos, G(1975),“’sTestimonyConcerningZenoofElea”,JournalHellenicStudies95:136–163 Sorabji, R.(1983),Time,CreationandtheContinuum,London:Duckworth Solmsen, F.(1971),“TheTraditionaboutZenoofEleaRe-examined”,Phronesis16:116–141 Schofield, M.(1970),“DidParmenidesDiscoverEternity?”,ArchivfürGeschichtederPhilosophie52: Salmon, W.(1970),Zeno’sParadoxes,Indianapolis:Bobbs-Merrill;republishedHackett2001 Sainsbury, M.(1988),,Cambridge:CambridgeUniversityPress Palmer, J.(2009),ParmenidesandPresocraticPhilosophy,Oxford:OxfordUniversityPress Palmer, J.(2004),“MelissusandParmenides”,OxfordStudiesinAncientPhilosophy26:19–54 Owen, G.E.L.(1986),,ScienceandDialectic:CollectedPapersinGreekPhilosophy,ed.M.Nussbaum, Owen, G.E.L.(1960),“EleaticQuestions”,ClassicalQuarterly10:84–102;reprintedinOwen1986:3–26 Owen, G.E.L.(1957),“ZenoandtheMathematicians”,ProceedingsofAristotelianSociety58:199–222; Matthen, M.(1986),“ANoteonParmenidesDenialofPastandFuture”,Dialogue25:553–557 Mansfeld, J.(1988),“DeMelissoXenophaneGorgia:PyrrhonizingAristotelianism”,RheinischesMuseumder Makin, S.(2005),“MelissusandHisOpponents:TheArgumentofDK30B8”,Phronesis50:263–288 Lowe, E.J.(2002),ASurveyofMetaphysics,Oxford:OxfordUniversityPress TheancientcommentatorsonAristotle 45. Aristotle’sphilosophyofnature 22. Plato’s 15. LeucippusandDemocritus 5. AnaxagorasandEmpedoclesintheshadowofElea 4. TheworldofearlyGreekphilosophy 1. 113–135 London: Duckworth reprinted inOwen1986:45–61 Philologie 131:239–276 Related chapters STEPHEN MAKIN 48