burnyeat - protagoras and self-refutation

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hilosophical Review

Protagoras and Self-Refutation in Plato's TheaetetusAuthor(s): M. F. BurnyeatSource: The Philosophical Review, Vol. 85, No. 2 (Apr., 1976), pp. 172-195Published by: Duke University Presson behalf of Philosophical ReviewStable URL: http://www.jstor.org/stable/2183729.

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The Philosophical eview,LXXXV, 2 (April 1976).

PROTAGORAS AND SELF-REFUTATION INPLATO'S THEAETETUSM. F. BURNYEATTIS paper is a sequel to an earlierone inwhich discussedanargument n Sextus Empiricus M 7.389-390) directedagainstthesophistProtagorasand his doctrinethat man is themeasure of allthings.1 extus nterprets rotagoras'famousproclamation Man isthemeasureofallthings" s the subjectivisthesis hat very ppear-ance whatsoever s true,and his argument s thatthe thesis s self-refuting ecause one of thethings hat ppears (is udged) tobe thecase is thatnotevery ppearance istrue: f, s thesubjectivist olds,everyappearance is true,but at the same time tappears thatnotevery ppearance istrue, hen tfollows hatnotevery ppearance istrue. The problemwas to discover how this argumentcould be

classified s aperitroper self-refutation. ysuggestionwasthat n acontextwhere itcan be presupposed thatsubjectivismmeetswithdisagreement, hesecondpremise s guaranteedto hold and we canargue straightforwardlyhat fsubjectivisms true, t s false. Such acontext, proposed,would be establishedbythe dialecticaldebatestowardwhichGreek ogicalreflections eretypicallyirected, nd itis thisdialectical ettingwhichprovidesthekey to Protagoras'self-refutation.But therealProtagorasdid nothold thesubjectivisthesis.As theearlierpaper explained,the more authentic nterpretationfPro-tagoras s thatgiven nPlato'sTheaetetus,ccordingtowhichhewasarelativist homaintained hat veryudgment s trueforinrelationto) the personwhose udgment it is; that s whatthe doctrinethatman is themeasureof all things riginally toodfor,notthe crudesubjectivismhatSextusrefutes. o it snatural oask howthechargeof self-refutationaresagainstthe subtlerrelativism fthesophist

himself.The question has both a philosophicaland a historical spect.FromPlatotoHusserlandJohnAnderson,philosophersofvariouspersuasionshave found it mportant o showthat Protagoras'doc-I "Protagoras nd Self-refutationn LaterGreekPhilosophy," hilosophicaleview,(1975), p. 44.

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PROTAGORAS AND SELF-REFUTATIONtrineof relative ruth s self-refuting,2nd itwould be satisfyingoknow whether the case can be made out. Historically, here is aproblem about Plato's venture at the task n the Theaetetus.extusclaimstoderive hisself-refutationrgumentfromPlato and beforehim fromDemocritus), nd what ooks like the identical rgumentto Sextus' is indeed presented in the Theaetetus s a triumphantoverturningof Protagoras' philosophy. Yet Protagoras in thatdialogue, as inthe best modern reconstructions f the sophist'sowndoctrine, s a strict elativistwhose position appears to invalidatethe verybasis of the argument.Both aspects of the question will concern us here. My aim is tooffer resolution of the historicalpuzzle which willalso help toclarify ome of the philosophical issues that cloud the notion ofrelativetruth.Here, to begin with, s the well-knownpassage in Plato's ownwords:

Secondly,t[theTruth hatProtagoras rote] as thismost xquisitefeature:3 nthe ubjectfhisownview, greeinghat veryoneudgeswhatsso,he forhispart Protagoras]resumablyoncedes obe truetheopinion f thosewhoudgetheopposite ohim nthat hey hinkthathe ismistaken.... Accordingly,e would oncede hathisownview s false, fhe agreesthat he opinionofthosewhothinkhimmistakens true Theaetetus71ab].On the face of it,the argument s as follows:If (A) every udgment is true,

and (B) itis udged that A) is false,then C) it is true that A) is falseand, consequently, D) (A) is false.Ifthis nalysis f the passage is correct, lato'sversion ftheperitropeof Protagoras speaks of judgments instead of appearances, butotherwise tdoes notdiffern any ogically mportant espectfromtheargument nSextus. Plato'sProtagoras,however,unlikeSextus',2 Edmund Husserl, Logical nvestigations,rans.byJ. N. Findlay London, 1970), I,138 ff.;John Anderson,"MarxistPhilosophy,"Australasianournal fPsychologyndPhilosophy1935); cited fromhisStudies nEmpirical hilosophySydney,1962), p. 294.Husserl's concern s to attackpsychologism n logic, Anderson'sto refute he notionof historically elativetruth dvocated in Engels' Anti-Diihring.

'E7rEila ... 'IXet, ontinuing rpwrov ev feTX.171a2), has therefore he samesubject as &KEZ (171a2-3) and 'loTat(171a4-5), viz.avT4qvVqv aX',a67avv ssEKvoa'iypatv from 170e9-17 a1.173



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M. F. BURNYEATdoes not hold that every udgment is true (period) but-verydifferently-that every udgment is true for the person whosejudgment t s.The differences crucial.Starting rom n adequatelyformulatedrelativism,(M) Every udgment is trueforthe person whose udgmentit is,and given(N) It is udged that M) is false,all that can be inferred s that(0) (M) is false-or "(M) is false" s true-for thepersonwho

judges it to be so.This establishesthat the Measure doctrine s false forProtagoras'opponents but notyetthat t is falsefor Protagorashimself;con-sequently,his relativismsnot so far shown to be self-refuting.isthesis hatevery udgment is true forthe person whose udgmentitis does not commithim to endorsingwhatever nyone thinks s trueforhimself s well as forthepersonwhothinks t;hence itdoes notrequirehimto concede the truth f his opponents' opinionthathe ismistaken.Or so it is generally hought.The position,then, s this: the argument as it standsin thetextappears to be an ignoratio lenchi, tarting ut froma subjectivistposition, A), whichProtagorasdid nothold, and recasting n therelativisticmould of M) yieldsonly the seeminglyharmless onclu-sion that the Measure doctrine s false forProtagoras' opponents.An impasse so obviously nsatisfactoryhould give us pause. Criticsfrom George Grote to GregoryVlastos have protestedat the waySocrates at the climacticmoment drops the relativizing ualifierswithwhich Protagoras specifies or whom a judgment is true, butfewhave thought t necessaryto wonder whyPlato should makeSocratesproceedinthisfashion nd none, to mymind,has convinc-ingly explained his foisting upon Protagoras the unrelativizedpremise A).Vlastoswrites:

Protagoras s veryfussy bout adding "for. .." after "true"or "is" or"real." .. . Even Plato himselfs not as carefulas he should be on this4 George Grote,Plato and the ther ompanions fSokrates3London, 1875), II, 347ff.; GregoryVlastos, Introductionto the Libraryof Liberal Arts Plato's Protagoras(Indianapolis and New York, 1956), p. xiv,n. 29; also W. G. Runciman,Plato'sLaterEpistemologyCambridge, 1962), p. 16, Kenneth M. Sayre,Plato's AnalyticMethod(Chicago and London, 1969), pp. 87-88.

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PROTAGORAS AND SELF-REFUTATIONpoint.While e puts n the for. ." almostnvariablyhile eportingrdescribingrotagoras' octrinenotonly t 170a,butat 152b,c, 58a,and allthrough 66c-167c, here herepetitionets lmost iresome,and then gain at 171e-172a; lsoatCrat. 85e-386d), e sometimesdrops t nthe ourse f rguinggainst rotagorase.g., n the exquis-ite" rgumentt 17 a),therebynadvertentlyitiatingis wnpolemic.

On reading this I want to ask: can we be satisfiedwith a simplediagnosis of inadvertence fPlato is so conscientious n reportingProtagoras'doctrine?How could he be blind to the omissionof thequalifiers rom key rgument gainst positionhe has so carefullydescribed?Runciman, n the otherhand, suggests hatPlato maybeconsciouslyoverstatinghis case. But what would be the pointofdeliberately verstating ne's case to theextentofmaking ta caseagainst a position quite other than itsofficial arget?The task of explanationbecomes harder still fwe attend to thecontext n which the self-refutationrgumentoccurs.This is at astagein the dialogue after heyouthful heaetetus has conceded aseries of objections(161c-164b) against the Protagoreandoctrine(more precisely, hey are objectionsto Theaetetus' definition fknowledge s perception, utthedialogue takesthisdefinitionobeequivalentto theProtagoreandoctrine, o thatobjectionsto eithertellagainst both; compare 164d with15 e-152a, 160de).These criti-cismshavingbeen discounted as verbal and superficial 164c), andProtagoras thoroughly defended against them (166a-168c),Theodorus is prevailed upon to replace Theaetetus as Socrates'interlocutor-in order that the distinguished mathematician'smaturity nd professional ense of rigor shall ensure more seriousand responsible reatment orthe deas of his friendProtagoras cf.162e, 168b-169d). n effect,hen,Socratesbeginsthe sectionwhichconcerns us with promiseto deal fairlynd ustlywithProtagoras

5Runciman, loc.cit.,relying n remarksmade at the conclusion of the argument(17 lcd) inwhich Socratesentertains he dea that Protagoras mightpop up with nanswer. The passage in question will be discussed in due course. It has helped totrigger thirdview, hat heomission f the qualifiers s deliberatebut ronic, ecentlyput forwardby Edward N. Lee, " 'Hoist with His Own Petard': Ironic and ComicElements in Plato's Critique of Protagoras Tht. 161-171)" in E. N. Lee, A. P. D.Mourelatos, R. M. Rorty eds.), Exegesis nd Argument,tudies n GreekPhilosophypresentedoGregorylastosPhronesis,upp.vol. I [1973] ); I discussLee's interpretationin nn. 6 and 23 below.175



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M. F. BURNYEAT(cf. 167e).6Not only that,but since for chronologicalreasons Pro-tagoras cannot be present to defendhis thesis n person,7Socratesoffers hefurtherafeguardthathe willuse Protagoras'own work oauthorize the admission he intends to elicit,rather than rely,asbefore,on the udgment of himself nd his interlocutor s to whatProtagoraswould or should be willing o admit 169de). The refuta-tion of Protagorasis to be derived directly romProtagoras'ownstatements, ogetherwiththe empiricalfact,whichProtagorascan-not credibly eny, hatother people think hatwhat Protagoras aysis false. The whole section is peppered with references to Pro-tagoras'book Truth nd its hesis hatman s the measure ofallthings(170c2, dl-2, d5, 170e9-171a 1, 17lb7,c6); twice ocrateseven makesa direct address to its defunctauthor, Protagorashimself 170a6,c2). And inembarking n thisprojectofrefuting rotagorasout ofhis own book Socrates opens witha perfectly air and responsiblestatement f the main thesis of that work:

He says, oeshe not, hatwhat eems oeachperson s so for hepersonto whomtseems?To which Theodorus replies, "Yes, he does say that" 170a).

6 Lee, op. cit., pp. 226-239, has done valuable service to the dialogue by callingattention o the deep irony hatpervades the peeches nwhich ocrates mpersonatesProtagoras demanding seriousand responsible dialecticaltreatment or his theory(162de, 168b), not long after ocrates has pointed out that, f Protagoras' account oftruthstaken seriously, ialectic r thetesting y rgument nd discussion f people'sviewsand theoriesbecomesa farce 16 le-162a). But thisdoes not annul the promiseto deal fairlywith rotagoras r make ronic he refutationwhich arries tout. On thecontrary, he irony s in thefact hat one such as Protagorasdemands, is promised,and finally as we shallsee) is given a refutation f unexceptionable eriousness.Thejoke is rather spoiled when Lee finds lements of irony n the refutationtself.Heclaimsthat,byomittinghequalifiers n whichProtagoras nsists, ocratesteachesanironic lesson about the conditionsfor assertinganything hatcan significantly ediscussed or denied. This suggestionwill concern us indue course n. 23 below)-Ithink toverdoes the rony nd fails o mend Socrates' ogic-but itshouldbe said atonce that Lee is open to the same damaging objection as Runciman: itought tobeProtagoraswho is attacked whether eriously r ironically), nd thisought to meanbeginning from M) ratherthan A). In fact, here s not a word in Lee's discussionabout the omission of the qualifier n premise (A) and how thattallieswiththe(admittedly ronic) palaver about securing ustice forProtagoras.Yet preciselywhatjustice involveshere is a man'sright obejudged by the viewshe reallyholds (168bcwith167e).

7The dramaticdate ofthedialogue is 399 B.C., well after hedeath of Protagoras.176



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PROTAGORAS AND SELF-REFUTATIONAfter such a beginning twould be nothing ess than perversedishonestywerePlato without eason to makeSocratesargue inthesequel ina waythatdepended for tsdamagingeffectn omissionoftherelativizing ualifiers. need hardly aythatperversedishonestyis not a charge to be leveled lightlygainst a philosopherof Plato'sstature nd integrity.ut theonlywayto forestallt stoworkoverthetext n thehope that a more detailedunderstandingof what sgoing on willpresentSocrates'reasoningin a new aspect.We can make a start y ooking nto themore immediate ontextof theself-refutationrgument,which smerely he ast na closelyknitsequence of three linked argumentsagainstProtagoras. Thesequence goes as follows.Either (1) Protagoras himself did notbelievetheTruth ewrote, nwhichcase, since no one else does, it snot (sc. the truth)foranybodyat all (170e7-170a1).8 Or (2) he didbelieve it,but themajority f people do not share his opinion, inwhichcase twothings ollow.First, a) the more the adherentsofhisTruth reoutnumberedbypeople whodo notbelieve t, hemore t snot (sc. the truth)than it is. "Necessarily,"repliesTheodorus, "atleast f t s tobe and not to be (sc.thetruth) ccordingas each personbelievesordoes not believe t" 17 a 1-5).Secondly, b) Protagoras scaught bytheperitropergument s quoted earlier 17 lab), and thisleads eventually o the same conclusionas argument 1)-namely,that his doctrine is not true for anybodyat all, not even for thesophisthimself171c5-7). It is (2) (b) thathas pre-empted he atten-tion; it is,of course,highlighted ySocrates as thereallyexquisiteone. But the neglectof itscompanion argumentshas meant that

criticshave overlooked the evidencetheseprovidethatPlato thinksProtagorasvulnerable to objectionswhich do notdepend on omis-sion of therelativizing ualifiers.For the firstrgumentof the triocertainly ses theappropriatequalifier, nd thesecond is not unam-biguouslyat fault in this respect. But before discussing the sig-nificance f thisevidence, we need a more formal tatement f thepositionagainst which the threearguments re directed.I quoted earlier theformulationWhat seemsto each person s sofortheperson to whom tseems" (170a). This lays tdown that forall personsx and all propositions )

8F. M. Cornford, lato'sTheory fKnowledgeLondon, 1935), p. 78, translates s ifthe conditional et Uiv KTX. were contrary o fact: "Supposing that not even hebelieved .. thenthisTruth .. would notbe true for nyone."The Greekdoes notpresent t as such there s no 'dv),but as one limbof a dilemma:whetherhe believedit or did notbelieve it, n eithercase it s not true foranybody.177



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M. F. BURNYEATP 1. If it seems to x thatp,9 then it is true forx thatp.P 1 is indeed Protagoras'major contribution o the extreme mpiri-cistepistemologywhich thedialogue elaborates out of Theaetetus'definition f knowledge s perception. t guaranteesthat,no matterhow "wild" and variable from the common-sensepoint of view) aperson's experience may be, the udgments he is led to will be trueforhim,givinghimcertainknowledgeof howthings re forhim. f,as Protagoras holds, all thingsare for each person exactly s theyappear to him, no one can be mistaken bout the reality hat con-fronts im,ofwhichhe is the soleauthoritativejudgemeasure).Butit s clear thatPlato also understandsProtagoras o make the furtherclaim thatnothing s true for person unless t eems tohimto be so,unless he believes t.In otherwords,the converse rule also holds:P2. If it is true forx thatp, then itseems tox thatp;which s equivalent toP3. If it does not seem tox thatp, then itis not trueforx thatp.That is to say,Protagorashas to defend the equivalence of"It seemstox thatp" and "It is trueforx thatp," not merely n implicationfromthe former o the latter.Protagoras ommits imself o the full quivalence when he claimsthat man (sc. each man) is the measure not only of whatis (sc. forhim), but also of what s not (sc. for him). At least, when Plato firstquotes theoriginaldictum nfull, Man is themeasure of all things,of thosethat re,that hey re,and of thosethat renot, hat hey renot,"he explains it in termsof the example of two people in the

wind,one of whom feelscold while the other does not; in whichsituationProtagoraswould have us believe that thewind scold forone of them and is not so for theother 152b). Here, to derive theProtagorean reading of theexample we need P1 to tell us that thewind scold fortheone who feels old and P3 to tellus that t snotcold for he secondperson. Foritwas not saidthat hesecondpersonfeels warmin thewind,or even that he feels the wind is not cold;given either f these as premise, o conclude that he wind s not coldforhimwe would need no more thanP IN If it seems to x thatnot-p, hen it is true forxthatnot-p.which s a simple substitutionnstance ofP1. What was said of thesecondpersonwassimply hathe does notfeelcold. On Protagoras'

9Alternatively,f x believes/judges hatp; cf. my earlier article, op. cit.,n. 2.178



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PROTAGORAS AND SELF-REFUTATIONview,then,if the wind does not appear cold to someone, that issufficient roundstoassert hat t s notcold forhim, nd thismeansthat we must include P3 (or its equivalentP2) in any completeformulation f the doctrine thatman is themeasure of all things.The doctrinemaintains hat It seems tox thatp"both mplies nd isimpliedby "It is trueforx thatp."That beingso, weneed not be surprised hat 3 should come intoplay nthearguments hat urrentlyoncernus. Considerthefirst fthetriple equence,theargument hat ftheMeasure doctrinedoesnot seem trueeither to Protagoras or to anyone else, then t is nottrue foranyoneat all. Clearly,to argue thus s to assertP3 forthespecial casewherepisthe Measure doctrine tself:f tdoes notseemto anyone thattheMeasure doctrine s true,then it is not trueforanyone. And ifP3 is partofProtagoras'theory,he argument s thatthe theory ands Protagoras n troublewhen it is applied to itself.We mayaskwhythetheory hould have to applyto itself, s it smade to do in all threeargumentsof the sequence. Plato does notconsiderthepossibilityhatProtagorasmight laimforhis doctrinea special status xempting tfrombeingcounted as one among thepropositionswith which it deals. Elsewhere,in fact, Plato insistsstronglyhat philosophical heorymustbe statablewithoutnfring-ing itself; hus n theSophist e holds itagainstmonism that everalterms enter nto the formulation f it (244bd), and he finds hatacertain ate-learners' iewofpredicationhasonlyto be statedfor ttorefute itself 252c). But even waiving twentieth-centuryualmsabout self-applicability,here s a questionthaturgently eeds tobeasked. (It is perhaps a measure of thepull exertedbytheexquisiteargumentthatno commentator, o myknowledge,has asked it.)Why s t nobjectionoProtagoras hat, n hisownshowing,fno onebelieves histheory t s not true foranybody?Protago-rasmightforvarious reasons be embarrassed to admit this,but would he berefuted? s itso surprising hat theory ccordingto which ll truthisrelative obelief houlditself e nomore thana relative ruth, rueonlyforsomeone who believes it?More important,how does thisshow that there s somethingwrongwith the theory?There can be no doubt that Socrates presents the point as anobjection;so much isguaranteedbythepositionof theargument nthesequence ofthree.Our task sto understandwhy.The solutionwanttopropose is thatPlato takes tthat, frelativism snot trueforsomeone, itdoes not hold of thatperson's udgments and beliefs.Suppose thepersoninquestion sSocrates.Applyinghisdoctrine

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M. F. BURNYEATto Socrates, Protagorasmaintainsthat for all propositions )PI s If it seems to Socrates thatp, then it is true forSocrates thatp.and P3s If it does not seem to Socrates thatp, then it isnot true forSocrates thatp.Socrates replies that he profoundlydisagrees.For a start,S1 It does not seem to Socratesthat, PIs )if itseems to Socrates thatp, then it is true forSocrates thatp.This is a plain matter f factwhichProtagoras annot credibly eny.And having asserted theconjunctionofP Is and P3s, Protagoras scommitted o agreeingthat S 1 is equivalent toS2 It is not truefor Socratesthat, P1) if it seemsto Socrates thatp, then it is true for Socratesthatp.All this s simply o say thaton Protagoras' theory, ince Socratesdoes not believeP 1, t snottrue forhim, nd a fortiorit snottrueforhim nits pplication o hisown udgmentsand beliefs P Is). Butsimpleas the deduction s, tsconclusionS2 requires nterpretation.For it nvolves hat urious ocution trueforSocrates," nd it stimeto inquiremore closely nto the meaning of the relativized diomsthatProtagorasuses to formulatehis views.One thingwe know s that"It is trueforSocratesthatp" is to beequivalent to "It seems toSocrates thatp"; ifone of these s true theother sthesame, and so too feither s falsetheyboth are. Butit s,think, mistake o suppose on thataccount thatthe two statementshave the same meaning,that the novel locution "true for Socrates"simplymeans the sameas the more familiar seemstrueto Socrates"or "is believed by Socrates."This is a mistake hathas been made inboth ancient and moderndiscussions f Protagoras nd his self-refutation.ohnPassmore,forexample, wonders (rhetorically)what it can mean to say that aproposition s truefor someone otherthanthathe thinks ttrue.10Again, there s an argument nSextuswith he form thoughnot nthiscase the name) of a peritropergument against Protagoras' op-ponents,according to which, fsomeone asserts hatman is notthe

l0Philosophical easoning London, 1961), p. 67, quoted below. The conflation sprominent lso in Lee, op. cit., p. 246-248, 253., nd important orhis account of theself-refutationrgument; see n. 23 below.180



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PROTAGORA4SAND SELF-REFUTATIONcriterion f all things,he willconfirm hatman is the criterion fallthings, incehe is a man, assertingwhat ppears tohim, nd therebyconceding that the very thinghe says is one of the thingsthatappears to him(M 7.61). This ratherfeebleargumentreceived anapprovingendorsementfromGrote,whoinsimilarvein writes s ifProtagoraswere sayingno more thanthat n discussing nyproposi-tion, heMeasure doctrine ncluded,all anyone can do isexpress hisown conviction, eliefor disbelief, nd the reasons whichseem tohim tojustifyt.1IBut Socrates says s much himself t 17 d,12nanironicalcomment on the triplerefutationhe has just concluded.Specifically, is comment s thatProtagoras mightpop up with nanswer,but nhisabsence we have to make the bestusewe canof ourownpowersofreasoningand continuetosaywhatseemstous tobethe case. Protagorasmustmean more. Otherwise why should hepress us toadopt his relativized diomand trumpet heequivalenceof "It is trueforx thatp" and "It seemstox thatp" as a substantiveand important iscovery boutour beliefs? ftheequivalenceweremeresynonymy,1 andP2 would bothreducetothebaretautology

P0 If itseems to x thatp, then it seems tox thatp.And to borrowa timely emarkthatSocratesmakesearlyon inthedialogue (152b), t snot ikely hat clever manlikeProtagoraswasmerelywaffling.Protagoras'theory s, after ll, a theoryoftruth nd a theory ftruth must link judgments to something else-the world, asphilosophersoftenput it,though fora relativist he world has to berelativized to each individual. To speak of how thingsappear tosomeone istodescribehisstateofmind,buttosaythat hings reforhimas they ppear is to point beyondhis stateof mind to thewaythings ctually re, not ndeed intheworld out ourtforProtagorasthere sno suchthing), ut nthe world as it sforhim, nhisworld.Whatthisrelativistic orldwillbe like fProtagoras'theory ftruthis takenseriously, he dialogue explains in terms f theHeracliteandoctrine of flux.13Plato uses the notion of flux to describe anontological settingwhich satisfiesProtagoras' contention that

I Op. cit.,pp. 349-350. The endorsement ftheargument nSextus s na noteonp. 352. Equally misguidedare thosewho,embarrassedbySextus' argument,wouldmake it betterby textualemendation; cf.Werner Heintz, Studienu Sextus mpiricus(Halle, 1932), pp. 88-94, for proposals byJaeger and himself.12 As Grote points out in a note, op. cit.,p. 35013 I must here simply tatewhat take to be the outcome ofTheaetetus 52a-160d,withoutdwelling on themany exegeticalquestions that arise along the way.

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M. F. BURNYEATgenuine disagreement s impossibleand no one's udgment can becorrected itherbyanotherpersonorby the udgment-makerhim-self t anothertime.The outcome of thisHeraclitean nterpretationof Protagoras s that ach of us lives n a privateworldconstituted ya successionof momentaryppearances,allof which re true nthatworldquite ndependently fwhathappens next na givenworld. na given world-say, that of Socrates-whatever appears to himisthen and there the case (P is) and nothing s the case unless itthenand there appears to him (P3s). Such is thekindof world presup-posed by Protagoras'doctrine that each man is the measure of allthings.Accordingly, 2 is not to be disarmed on the grounds that t ismerely novel way ofexpressing 1. On Protagoras'philosophy Ihas immediate nd drasticconsequences forhow things re in Soc-rates' world, and theseconsequences are whatS2 seeks to express.We mightparaphrase S2, therefore, yS3 It is not truein Socrates'worldthat, fitseemsto Socrates thatp, then it is truein Socrates'

world thatp.S3 seemstosay that nSocrates' world t s not a sufficientonditionforthetruth fa proposition hat t eem trueto Socrates.A parallelargument from Socrates' disbelief nP3s willyieldthe conclusionthat t snota necessary ondition ither.And ifthe samereasoningapplies to everyone who does not believe the Measure doctrine,which nargument 1) iseveryone, heconclusion hat he doctrine snot true for nyone s bothvalidlydeduced and highly amaging toProtagoras. No one livesin a world in which his mere beliefin aproposition seither sufficientra necessary onditionfor ts ruth(in that world). But thateveryone ives n such a world s preciselywhatthe Measure doctrine sserts.Given, herefore,heassumptionon whichargument 1) is based, thatnot even Protagorashimselfbelieves his philosophy,Protagoras' positionbecomes utterly elf-contradictory: e claims thateveryone ivesin his own relativisticworld,yetat the same time he is forcedbythatvery laim to admitthat no one does.But we can now see thatProtagoras' positionwould be equallyinconsistent f, asserting s he does that everyone ivesin his ownrelativistic orld, he could be forcedto admit that some people donot. That, in fact, seems to be the essential point of the secondargument nthesequence, (2) (a), which aysthat venifProtagorasdid believe his doctrine, t is that much less truethan it is falsein

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PROTAGORAS AND SELF-REFUTATIONproportion s thenumber ofpeople who do notbelieve t sgreaterthanthe numberofthosewhodo. Admittedly,heconclusionofthisargument s ambiguous: it is not clear whether Socrateswantstoinfer imply hatthedoctrine sfalseformorepeople than t struefor,whichon theunderstandingwe have ust reachedwould meanthat tholds of fewerpeople's beliefs han tfailsfor, rwhetherhetries ogobeyond this otheconclusionthat t smorefalsethantruein some absolute sense. If thelatter, henhe has alreadybegun torelax his grip on the relativizing ualifiersbeforehe gets to theperitropergument 2) (b).14 Supposing, however,thathe is to becensured on thisscore, his argument can still be regarded as anextension, lbeita questionableone, of the correctpointthatPro-tagorascan be forced nto nconsistencyfthere sanyonewhodoesnot believe his doctrine-indeed ifthere are people who do notbelieve tforthesimplereasonthattheyhaveneverheard of t.Foron Protagoras'own showingsuch persons do not, as Protagorasalleges we all do, live in a world in whichtheirmere belief in aproposition s a sufficientnd necessarycondition for tstruth inthatworld).All this omewhat lters hepositionwithregardtoargument 2)(b) of the sequence. The position was thatthe argument Plato ap-pears to give startsout from an unrelativizedpremise A) whichProtagorasdoes not hold, while the argumentto whichPlato isentitled,the argument under (M) whichrespectsthe role of thequalifiers,eads only to theseeminglyharmlessconclusion 0) thattheMeasure doctrine sfalseforProtagoras'opponents.Butwe nowhave reasonto askwhether0) really s as harmless s it sgenerallythought to be.15 The evidence of the earlierargumentsof the se-quence, as I have interpreted hem, s thatPlato forone would notthink tharmless. f the Measure doctrine'sbeing false fora wholelotofpeople meansthatProtagoras'Truth oes not, s itpurported

14 Eitherway,Plato evidently njoysthe ironyof measuringthe extentof truthProtagorascan claimfor histheorybycountingheads. Such a procedureshould beanathemato Protagoras, inceone greatargumentformakingtruth elative o eachman isthat therwise ruthwillbe decided by hearbitrary eight fnumbers,what scalled truth bsolutebeingnothingbut whatseemstothemajorityo be the case (forthis line of reasoning in association with Protagorean ideas, cf. Aristotle,Met.1009bl-7 and the analogous argument at Theaet.158de).

15 E.g., Sayre, p.cit.,p. 88,describes heresult hat heMeasuredoctrine strueforProtagoras nd falsefor omeoneelse as "neitherherenorthere s far s theoriginalthesis s concerned."

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M. F. BURNYEATto do, give a valid theory f truthfor their udgments and beliefs,and thisunhappy consequence (0) follows rom he assertion f theMeasure doctrine M) togetherwith heundeniablefactN) thatM)isjudged falseby ll thosepeople, then M) is ndeed self-refuting;tleast, it is self-refutingn the same sense and in the same sort ofdialectical ontext s I sketched nmy arlierpaper when discussingSextus' versionof theargumentunder A). That being so,we shouldat least consider the possibility hat theargumentunder (M) is theargument Plato intends all along. A hypothesiswhich creditsPlatowith n argument hat s both validand relevant sat least as deserv-ing of notice as hypotheseswhich accuse him ofinadvertence, on-scious overstatement, r perverse dishonesty.Let us be clearwhat thisnew hypothesis sksus to suppose. First,we are to understand true" n"Everyjudgments true" A) to mean:truefor he person whose udgmentit s.Just his, fcourse, swhatwe expecttofind fter he nitial eference oProtagoras'own view(17 la7), which A) ismeant to formulate. urthermore,f A) is notso understood,whatthe opponents disagreewithwhenthey udgethat A) is falsewill not be the view of Protagoras;that s,notonlySocrates'argumentbutProtagoras'opponentstoowillbe guilty f astriking rrelevance.Second, having once adopted theappropriatereading of "true," we must stick to it throughout the argument.Thus the conclusion (C) which follows from A), so understood,together with the empirical premise B), is that it is true fortheperson whose judgment it is-in this case, Protagoras'opponents-that the Measure doctrineis false; and the furtherconclusion D) whichfollows rom hat sthat hedoctrine s falseforthese same people. In a sense, therefore,we need onlytogive Platothe benefit f the doubt once, the first ime he omits thequalifier,where charity s easiest,and the requirementsof consistencywillcarry s through he restof the rgument. wouldclaim, tany rate,thatthis,the most charitablehypothesis, sks rather ess of one'scredulity hantherivalsuggestions f nadvertence, onscious over-statement, nd perverse dishonesty, ll of which compound theerrortheyattribute o Plato by makinghis argumentcommitthephilosophical sin of irrelevance s well.It should be emphasized thatthe hypothesis smeant to deal onlywithProtagoras' predicationsof "true" and "false,"not withhisopponents'use ofthoseterms.Theiropinion iscorrectlyepresentedbythe unrelativized ccurrenceof the predicate"false" n B) or N).The opponents are people who hold thedoctrineofMan the Mea-

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PROTAGORAS AND SELF-REFUTATIONsure to be false withoutqualification,not merely false for them-selves, for n rejectingProtagoras' philosophythey o ipso reject atthe same timehis dea that he ordinaryman'spredications f "true"and "false"stand nneed of relativizing ompletion. n this nstanceomission of the qualifier s a virtue,not a defect n Plato's exposi-tion.6Having thusdelimitedthe natureand scope of my hypothesis,should like now to plead that t has one major advantage over itsrivals, hat texplains, or explains better,why the peritropeif withSextus wemaycontinuetocall itthat)yieldsonlyan interim onclu-sion. I haveinsisted hat heperitropergument s not meantto standon itsown but is part of a more complex structure f reasoningformedby the sequence of three linked refutations.Withinthat

16 Cp. 170b8-9wherethe ordinaryman's conceptof expertise sophia) s (partially)explained nterms fthe ordinary bsoluteconceptof truth: heordinaryman thinksthat expertise s true udgment and ignoranceis false udgment, wherethis meanstrue and false simpliciter.Others who have appreciated the point are Steven S. Tigner, "The 'Exquisite'Argument at Tht. 17 a" (Mnemosyne, 971), and John McDowell, Plato Theaetetus(Oxford, 1973), p. 171, but they further uppose there is a difficultyn it forProtagoras-the difficulty,amely, hat fhe must llow his opponents tosay that heMeasure doctrine s falsewithout ualification, his commitshim to recognizingormaking ense of the ordinary,bsolute conceptof truth nd falsity. ut what xactly sthe difficulty?rotagoras'theory s a theory bout the unrelativizedpredicationsoftheform x sF," "x sG,"withwhichpeople ordinarilyxpress their iews, nd as suchit can cover unrelativizedpredicationsof "true" and "false" no less than ordinarypredicationsof "hot" and "cold," "large" and "small," etc. What the theory annotcountenance sthat uchpredications hould be true s they tand,without comple-tion specifying orwhom they re true-but that hey re so true as they tand couldhardly e established t this tage of the rgumentfrom he mere fact hatProtagoras'opponents express their opposition in ordinarynonrelativisticanguage (Tigner'scontrary iewis based on faulty easoning, exposed by Lee, op. cit.,pp. 244-245).On the other hand, the presence of one (justifiably) nrelativizedpremisemightsuggest, ywayof explanationof theotherunjustifiedne, thatPlato was confusedbythe need tohandle qualified nd unqualifiedpredications f "true"and "false" at thesame time; cf. esp. 17 b1-2 where he moves from"The opponents think hat Pro-tagoras'view smistaken" o "Protagoras oncedes thathisown view sfalse." wouldprefer hishypothesis o those of nadvertence, verstatement,nd perversedishon-esty, ut tseemsunlikely ll the same.The move at 17 b1-2,for xample, sexplicitlylicensed by Protagoras' greement thathis opponents'opinion is true,which t oncetakes us back to the question of how we are to understand A). It is perhaps sig-nificant hat Plato reservesthe verb ei68ecrOat,o be mistaken, or the opponents'unqualified views: Protagoras,theythink, s mistaken 171a8,b2),whiletheythem-selves are not (171b4). Protagoras' udgments,by contrast, se theadjectives"true"and "false" throughout17 a8-b 1.

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M. F. BURNYEATstructure t serves to complete the dilemma posed at 170e-171a.EitherProtagorasdid notbelievetheMeasure doctrine r he did. Ifhe did not,then,sinceno one else does either, he doctrine s nottrue foranybody.That was argument 1). The otherlimb of thedilemma s complicatedbythesubdivisionnto 2) (a) and (2) (b),butitseventualoutcome s meant tobe thesame: supposingProtagorasdidbelievehisdoctrine,tstill ollows hat hedoctrine snottrueforanyone. This outcome is reached-and the argument s not com-plete untilthen-when Socrates is in a positionto conclude thatsince Protagoras' Truth s disputed by everyone,Protagoras in-cluded, it is not true foranyone at all (171c5-7). (Notice thattheconclusion sexpressed nproperly elativisticerms, o lessthanonitsfirstppearance as theconclusionofargument 1].) To gettothepointwherehe can deliverthis rowningblow,Socrateshas to showthatProtagoras oins witheveryoneelse in disputinghis theoryoftruth.That is the functionof the peritrope,o demonstratethatProtagoras' own belief in his doctrine counts for naught: he iscommitted, espitehimself, o agreeingwithother people that t sfalse.False simpliciterrfalsefor hem? f(D) is takenat facevalue,assaying hatProtagoras' iew s false impliciter,ocrateswouldseemtohave completedhis refutation y 171b2,wheremyoriginalquota-tionofthe peritropeassage ended. He would haveestablishedthatthe theory in (A) -never mind that it is not Protagoras' realtheory-is false,thatProtagorasmust accept it as false,and con-sequently lso (thoughbynow it hardlymatters) hat tis falseforProtagoras. n thetext,however, ocrateshasquitea lotmoretosay.

In the firstplace, myquotation lefta dangling "for his part"(171a6: 1.v) introducingProtagoras' udgment on his opponents'opinionthathistheorysfalse.This ispickedup at 17 1b4 8Uy') anda contrast s drawn with the opponents' own judgment on thisopinionoftheirs,which s,ofcourse,that t s not mistakenbutthecorrectopinion to hold:Whereasthey, or theirpart,do not concedethatthey re mis-taken.... And he, once more,fromwhathe has written grees thatthisudgment lso is true 17 b].

This udgmentalso Protagoraswillhavetoadmit s true fhe is tobeconsistentwithwhathewrote;thefurther eference o Protagoras'written octrine, ightnthemiddleoftherefutation,harpensthedifficultyfthe nadvertence nd overstatementypotheses.On my186



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PROTAGORAS AND SELF-REFUTATIONreading, bycontrast, all we have here is a small but perfectlycorrectpoint which can be unraveled as follows: Protagoras must concedethat his opponents' judgment that their opinion that his theory isfalse (simpliciter)s not false but true (simpliciter)s itselftrue-for theopponents whose judgment it is.More important, however, than this extra turn of the screw is thatSocrates next proceeds to argue that since Protagoras joins witheveryone else in disputing his theory, it is not true for anyone,neither for him nor for anyone else.

It is disputed, then, by everyone,beginningwith Protagoras-orrather,t sagreedbyhim,when he concedes tothepersonwho says heopposite thathe judges truly-when he does that, even Protagorashimself oncedesthatneither dognor anymanyouchanceto meet sameasure concerninganything t all he has not learnt.17 s thatnotso? ... Accordingly, ince t sdisputed byeveryone, rotagoras'Truthcannotbe true foranyone: not foranyoneelse and not forProtagorashimself 171bc].My hypothesis makes intelligible the need for this last stage of theargument. If (D) is understood as stating no more than that theMeasure doctrine is false for Protagoras' opponents-that is. (D) =(0) -Socrates at 17 1b2 still has work to do to get from Protagoras'

17 After heurbane ironyof the"exquisite"paragraph,this trikinglynacoluthicsentencewith tserky yntax omes ike a suddencrescendo ofquitesavagetriumph.If thatdoes catch thetone, twouldhelp toexplainTheodorus' shockedcomment ttheend oftheargument, We are runningdown myold friend oo hard,Socrates"and Socrates'unrelenting eply, But, myfriend,t s unclear fweare also overrun-ning what is correct" (171c8-10). I would like to thinkthat while Theodorus isprepared for Protagoras to be refuted-he has, after all, undertaken to see thediscussionthroughto the pointwhereit can be decided whether t is his friend'sphilosophyor his own claims to expertisethat mustgive way (169a)-he is takenabackby thespectacularform nwhich herefutation inallyomes,withProtagorashimselfoining the ranks of the many who dispute the doctrinethat man is themeasure of all things.Certainly ocrates nhisspeech of 171c9-171d7 s as cuttinglysarcastic s anywherenthedialogue. Later,whenTheodorus has had timetoreflect,hisconsidered viewof the substanceof the argument s that t s conclusiveagainstProtagoras (179b). This verdict is not to be discounted on the grounds thatTheodorus is an old man whoprefers igressions ophilosophic rgument Sayre, p.cit.,p. 90, n. 29, alluding to 177c). Theodorus isold and a bit stiff or rgumentativecombat (162b), but we have seen enough of the great mathematician'sdramaticstaturenthispart ofthedialogue toknowthathisopinion sto be takenseriously.nanycase, the context at 179b precludesdoing otherwise.

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M. F. BURNYEATacceptanceofthis ohis final onclusionthat he doctrine sfalseforProtagorasas well as forhis opponent.How does he manage thefurther tep?Protagoras'undoing,hesays, s his admissionthat n opponentwho contradicts im udgestruly 17 1b9- 1).To admitthat s toadmitthat dog oranymanyoulike to pick is not the measure of anything t all, unless he hasacquired knowledge sc. objectiveknowledge n theordinary ense)ofthething nquestion 17 Ic 1-3).This I taketobe a reference otheclaim of the Measure doctrineto give a theory of truthfor thejudgmentsofanyand everyman, and ofhis dog too if t s insistedthatdogs are capable of udgment.18And we can understandthereference, venwhileconstruing rotagorastomean thatthe udg-mentopposed tohis assertion f theMeasuredoctrine s truefor heopponent whose udgment it is, ifwe recallwhat was said earlierabout the connectionbetweenS2 and S3. I suggest, n fact,thatSocrates is drawingthat connectionhere. He is pointingout thatwhatit means fortheMeasure doctrineto be falsefor someone isthathe is not a Protagoreanmeasure:which s to say thathismerebelief n a proposition sneither sufficient or a necessary ondi-tionforthatproposition o be true nsomerelativisticense. Thus itisfromProtagoras' dmission hat heMeasure doctrine ails ogivea generallyvalidtheory ftruth hatSocratesfinallynfers hat hedoctrine s not trueforProtagorasor for anyone else (171c5-7).This yieldsthefollowing-accountf argument 2) (b) as a whole.The peritropeetsProtagorasto accept the interim onclusionthathis theorys falsefor thers.Buttoadmit his, t s argued, s to admitthatnoteveryone s a Protagoreanmeasure.Hence itfollowsfromProtagoras' dmissionthathistheorys falseforothers hat t sfalseforhimself s well. There is a passagefrom p s falseforProtagoras'opponents" to "p is falseforProtagoras"-in the one special casewherep isthe Measure doctrine tselfM). And it sthispassage thathas still o be made after he nterim onclusionhas been reached at17 b.Such is thereadingthatmy hypothesis uggestsforthistrouble-somesectionofthe dialogue.As a hypothesis oexplainwhatPlato sup to hereit s, submit, uperiortothe rivalhypotheseswithwhich

18 A dig at Protagoras-one of several-for putting theranimalson a levelwithman as regardscognitive apacities cf.161c,171e with154a, 162e, 167b).As becomesclear at 186bc,the skirmishingn this topicdramatizesfundamentalphilosophicaldisagreement over the nature and interrelations f perception, udgment, andknowledge.188



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PROTAGORAS AND SELF-REFUTATIONI have contrasted t,but a fulltreatmentwould require an equallyclose examinationof an earlierparagraph wherethequalifiers reomitted,170c,and of thesection 170de betweenthat nd thetriplesequence which s a model ofclarityn the matter fputtingn thequalifierswhen Protagoras s speaking and leaving them outwhenotherpeople's udgmentsare reported.All this s to be weighedinthe balance and compared withother places in the dialogue wherePlato omits the qualifiers there are, in fact, a number of placeswherethishappens, though noneisso problematic s the one underdiscussion). But I do not wishtoundertakethese further xegeticalinquiries here.19 have recommended my hypothesis, nd withmore in viewthanthat tshould carryconviction s an accountofPlato's procedure. It embodies a philosophical claim which I amanxious should stand in itsown right-namely, the claimthattheargumentunder (M) is not the harmlessthingthatdefendersofProtagorashavealways aken tto be. About this have a littlemoreto say.

19Dogmatically, owever, yway of orientation: he argument t 170c s a dilemmaforcedon Protagoras by the fact that people believe, contrary o the Measure doc-trine, hatmistakes nd false udgmentsoccur. Ifthey re right o think hat here sfalse udgment, there s. But equally, fthey re wrong n thisor any otherjudgmentof theirs, hen there sfalse udgment (forhere is an instanceof t). So, whether ightor wrong, heir pinion spells troublefor Protagoras nthe form fa conclusion, heexistenceof false udgment,whichhe must deny. Accordingly, ocrates goes on toclaim thatto dodge the dilemma a Protagoreanwillhave no recourse but to deny,quite implausibly, hat people do think each other ignorant and guilty of falsejudgment (170cd).Now it s possible,but not obligatory, o understand the text s stating r implyingforthe firstimbof the dilemma not the straightforwardnferenceust given but thefollowing ariantof theperitropergument:If A) everyudgments true,and B)' it s udged that ome udgments false,thenC)' it strue hat omeudgmentsfalseand,consequently,D) (A) isfalse.

(It is not possible, because it simplydoes not square withthe text, o read back theexquisite peritrope ith B) or (N) in place of (B)', as does McDowell, op. cit.,pp.169-170.) Eitherway, he refutations so cryptichatTheodorus naturally sks for nexplanation 1 70d3). Socratesresponds by prefacinghistriple efutationwith lucidand entirely ccurate account 1 70de),firstf the key dea that ne maythink notherperson's udgment is false, and second of what Protagoras' theory ommitshim tosaying bout the situation.The effect f this ntervening aragraphisto givea modeltreatment f the qualifiers o be applied both tothe subsequent refutation-it is, nfact, he model followedby my reading of those arguments-and, so far as maybeneeded, to the preceding refutation t 170c also.189



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PROTAGORAS AND SELF-REFUTATIONAnd fromthis t is not so clear how'the argument s to proceed.Here I would liketo bring nthecurious mageSocratespresentsat 17 d ofProtagoras ticking ishead up above the groundtorebutSocrates'arguments, nd then disappearingto runaway.Platodoesnot tell us what objectionhe envisages bringingProtagorasbackfrom heunderworld,butI doubthe wouldhavewritten hisway fhe thought t a good one.2' In fact, t could notbe a good replybecause,if twere, n showing ocratesand Theodorus to be mistak-en itwould at the same time proveProtagoraswrong as well,sinceon histheoryno one ismistakenf hey aywhat eemstothem obethecase (cf. 170cand Euthydemus87e-288a). Socrates' rony t thispoint is far fromgentle. And thatmay be all there is to it: noobjectionis specifiedbecause none is possible.Even ifProtagorascannot attackSocrates,however,he might rytodefendhimself.tseemsa significantlement nthe magethatherunsaway afterdeliveringhis rejoinder;he is notpreparedto stayand defend it in discussion.22The implication s at least thatthereply,whatever t s, will notstand up todiscussion. fancy hattheirony s morepointedstill, nd thatwhattheonlyreply eft mountsto is a refusalto submitto dialecticaldiscussion.For is thisnot whatProtagoraswould be doing if he insisted hathe assertedthe Measure doctrineas true forhimself nd himselfalone?That would mean droppingthe thesis hatM) istrueof andinSocrates'world and replacing tbythe completely olipsistic laimthat t sonly nProtagoras'world thatM) is true of and inSocrates'world,where Socrates'world is now incorporatednto that of Pro-tagoras. fthis ounds incoherent, hat snot tobe wonderedat,forwhat sensecan we make of the dea thatSocratesand his world existonlyforProtagoras?Socratescannot be expectedtofind t ntelligi-ble; he cannot dentifywiththe counterpart hatbearshis name inProtagoras'world. fProtagorasdoes not speaktothehuman condi-tion,does notputforwardhis claimthat ach ofus lives nour ownrelativistic orldas somethingwe can all discussand, possibly, ometoaccept,butsimply sserts olipsisticallyhathe,forhispart, ives na world nwhichthis s so, then indeed there s no discussingwithhim. His worldand histheory o tothe gravewithhim, nd Socrates

21 As Runciman'shypothesis equires; cf. n. 5 above.22 So H. Schmidt, KritischerCommentarzu PlatosTheatet" Jahrbicherfir las-sische hilologie, Supp.-Bd. 1877-1878), pp. 492-493.

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M. F. BURNYEATis fully ntitledto leave them there and geton withhis inquiry.23Butreally ven this s toogenerous toProtagoras, o allow thathecan buy safety or histheory t the price of solipsism.The truth sthathe isstill sserting omething-namely, (Mp) tself and assert-ing it withoutqualification. This is no accident. In settingup arelativist heory ike thatofProtagorasone begins with distinctionbetween, n the one hand,the unrelativized redicationswithwhichpeople, Protagorasamong them,ordinarily xpresshowthings p-pear to them to be,whether t s that thewind is cold or that someproposition s true, nd, ontheotherhand, therelativist'sccountofthese statements,which s that they are true, and theirpredicateshold ofthe things hey re ascribed to, forand only for thepersonwhose udgment thestatement xpresses. Now consider the state-

23 I can now pickup a thread fromnn. 5-6 above and comment n Lee's interpreta-tion of the self-refutation assage, an interpretationwhich revolves around theconfessedly izarre suggestion hat he mage of Protagoras'return t 17 d presentsthe sophist as a plant rooted in the ground (Lee, op. cit., pp. 249 ff., omparingAristotle,Met. 1006a13-15). It seems an overwhelming bjectiontothis dea that, freduced to a plant, Protagorascould hardlyrun away afterdeliveringhisrejoinder(171d3: olXioto eoffrop0eXv,hich Lee, op. cit., p. 251, has to place outside theimage), and the question of the meaning of the image, though well raised, s not asnovel as Lee repeatedly vers. In fact, n behalf of the nineteenth-centurycholarswho did discuss the matter, t should be said that they came up with at least twoanswers quite as persuasive as Lee's.One interpretation akes note of the fact that the image uses a pair of verbs,'fVaKfnKVTElvnd KaTat8VVal,which oftendescribe the actionsof, respectively,iftingthe head out of and plungingdown ntowater cf., .g., Phaedo109de)and connects twiththe rather well-attested iographical detail that Protagoras died by drowning(according to the oldest source, the fourth-century.C. historianPhilochorus pudDiogenes Laertius,Lives f he hilosophers,X, 55,hisship wentdown when he was onhis way to Sicily).The explanation of the mage then s that o bringProtagorasbackfrom he dead Plato quite naturallyhas him raise his head out of the waves and sinkback again; thus August Bernhard Krische, Forschungenuf demGebiete erallenPhilosophie, (Gottingen,1840), 141; Anne Johan Vitringa,Disquisitio e Protagoraevita tphilosophiaGroningen, 1852), p. 54; Hermann Muller-Strubing,Protagorea.Zu den Vogeln des Aristophanes"NeueJahrbicherfiirPhilologiendP&dagogik1880],Erste Abteilung),pp. 96-97. Protagoras'running way sa difficultyor his nterpre-tationtoo, and a further bjection s thatthe reappearance is located "righthere"(17 Id 1:'EvTeOev) -i.e., in thepalaestraorwrestlingchoolwherethedialogue is set(cf.144cand thewrestlingmetaphor f162b,169ac). So one mayprefer n alternativeinterpretation ccording to whichProtagoras merges from he ground ust as far sthe neck because that s the way ghostsappeared in the Greek theater, oming upthroughan opening in the stage; thus Karl Steinhart n Steinhart-Mfiller,latonssdmmtliche erke,II (Leipzig, 1852), 206, n. 32; F. A. Paley, The TheaetetusfPlato(London and Cambridge, 1875), p. 59, n. 1; Schmidt, oc.cit.

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PROTAGORAS AND SELF-REFUTATIONments which formulatethe results of relativization, ropositionssuchas "The wind s cold forme"and "The Measure doctrine strueforProtagoras."More generally, uppose that, nstead ofspeakingwith he vulgar,we tailorour speechto the facts s the theorist eesthem, explicitly elativizing ur statements. hen, surely, o avoidapplying he doctrine wice ver,wemustput their ruth onditionsin absolute terms. That is, a proposition of the form"x is F" istrue (relatively)forperson a, if and only if "x is F fora" is true(absolutely).Call this he principle f translation. uch a principle sneeded, I submit, fwe are to be able to give sense to the notion ofrelativetruth nd operate with t in reasoning.There would seem, then, o be a whole series of absolute truths owhich Protagoras commits himself by propounding a relativist

Butperhapssimpler nd better hanany ofthesewould be thefollowing,uggestedby the interpretation have offeredof the philosophical point at issue. It is notProtagoras'carriage or demeanor thatmatters, or themechanics of his reappear-ance, butthe factthat, oming fromand retreating o anotherworldthanours, hedoes notreally eave theunderworldwhen, upposedly,he popsup to refute ocratesand Theodorus fortalkingnonsense (cf. 171d2-3).His "refutation" r defense, notherwordsjustis a refusal o enterfully nto common worldwithhisopponentsfordiscussion.And that, haveargued, s a fair haracterization f themove fromM) to(Me), theonly nd the obviousmoveleft oProtagorasnowthathe hasbeen refutedon the basis of theTruth s he actuallywrote t.So much for the image itself.Lee's interpretation f itis designed to supportanaccount of theperitropergument (op. cit., pp. 242 ff.)which, as I understandit,involves wo chiefclaims: a) that theeffect f the qualifiers s to make Protagoras'statements mere record of his and his opponents' subjectiveattitude,so thatProtagoras must omit them if he is to present a thesis that can significantlyediscussedor denied -although then, f course,hebecomes iableto Socrates'refuta-tion; b) that nce Protagoras tarts uttingnthequalifiers o avoid therefutation, emust nconsistency o allthe way to Me), so thathe ends up sayingnothing hat anseriouslybe discussed. On thisbasis, Lee suggeststhat Socrates' omission of thequalifiers s a deliberateirony. t showsProtagoras whatis required ifhe is to be"takenseriously,"n accordancewithhisowndemand, as one who has something osay, nd what onsequencesthenfollow, nd leaveshimtheuncomfortinglternativeof withdrawing o the reduced and, as Lee thinks,plantlikeposture of (Me).

Myquarrel withthistheory s in part thatcertain of itssupportingprops do notstandfirm nderexamination: ee n. 10aboveon theunderstanding f thequalifierspremised in (a), n. 6 on the role of irony n the passage and the importanceof themissing ualifier n A), while as for b),Protagoras sonlybound to go all the wayto(Me) ifSocrates successfullyhows, n all seriousness, hathe cannot stop at (M). Ithink, nd haveargued, thatSocratesdoes showthis, utbyhard ogicnotby ronicalinsinuation,which s all that Lee offers.Thus while I agree withLee about whereProtagoras nds up, ourinterpretations ivergefundamentally nwhat ttakesto gethimthere.193



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M. F. BURNYEATtheory f truth: hewind scold forme, thewind s not cold foryou,and so on. Equivalently,when a person a statesthatsome proposi-tionp is true, and the Measure doctrinedeclares that p is true(relatively) or , this n turn means, by theprincipleof translation,that"p is truefor " istrue absolutely). n particular,fProtagorasputs forwardhis relativism nd agrees thatthis doctrine, n con-sequence of itself nd his belief n it, s truefor him, he must stillacknowledge t tobe an absolute truth hattheMeasure doctrine strueforProtagoras Me).It may be objected here thatthe predicate"true" s a special case.In its absoluteuse it allows ndefinite eiteration f the prefix It istrue that 9.," sinceany proposition is true fand only f"It is truethatp" strue,which t s f nd only f Itis truethat t struethatp" strue, and so on indefinitely. hat being so, why should not Pro-tagoras adopt a relativisticnalogue of theprefix It is true that .. ."and say of the alleged absolute truths hattheyare not what theyappear to be -it isnot absolutely rue,but onlytrue forProtagoras,that the wind is cold for me? This is not likelyto be true forProtagoras'opponents who, iftheyknowwhat they re about, willsay that hewindmayappear cold tome butwhethert scold or notis anothermatter.And if, n the face ofProtagoras' ttempt o emptythedisputeofcontent, he opponents go further nd denythat t seven true for Protagorasthat the wind is cold for me,24cannotProtagoras come back again with It is true forProtagorasthat t strue forProtagoras that the wind is cold forme"? And so on in-definitely?

No, Protagorascannotevade the principleof translation ythismaneuver.His position ssupposed tobe thatx isF orp is true forjust in case it appears to a or a judges that x is F or p is true;and this s notan arbitraryonnection r one that an be abandonedwithout ur losing gripon the notionofrelative ruth.Protagoras,as Socrateskeepssaying,s a cleverfellow, ut he is not so clever hatthere s no limit othecomplexity fthepropositionshe can under-stand and so udge tobe true.Therefore,therelativisticrefix It istrue forProtagorasthat ...," unlike the absoluteprefix, dmitsofonly imitedreiteration.At somepoint,thoughwemaynotbe ableto say ust where, Protagorasmust topand takea stand.And oncecommitted, f only in principle,to an absolute truth,he can no

24 They ould ay his nthegroundshat othingstrue or rotagoras:ncehistheorysrejected,ts oncept f relativeruthwill ack pplication.194



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burnyeat - protagoras and self-refutation

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