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    False Belief in the "Theaetetus"

    Author(s): Gail FineReviewed work(s):Source: Phronesis, Vol. 24, No. 1 (1979), pp. 70-80Published by: BRILLStable URL: http://www.jstor.org/stable/4182057.

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    Falsebeliefin the TheaetetusGAIL FINE

    1. It is often supposed that Plato regardsknowledgeas some kind ofacquaintance, o thatknowingconsists n some sort of graspingorhitting,the only altemativeto which is not hitting,or missing.Knowledge s an allor nothing, hit or miss affair.It is also often assumed that this model ofknowledgeunderliesor explainsPlato'ssupposed inabilityto accommo-date false belief in dialoguesprior to the Sophist.Eitherone hits whatone is talkingabout,and so hasknowledge,not falsebelief; or elseone failsto grasp,and so has said nothing,and hence again does not have falsebelief.'A major source of evidence adduced in supportof this view is theTheaetetus' iscussionof false belief. Thatdiscussionends at an impasse,andit is often allegedthat Platofails to explain n what false beliefconsistsbecauseof an underlyingacquaintancemodel.2With thisclaim I shall notquarrel.I shall argue,however,that Platois not committed o the under-lying acquaintancemodel that occurs here. Rather,he uses it to buttressTheaetetus' uggestion,presentedust beforethe discussionof falsebelief(at 187b), hat knowledge s truebelief. When,at theend of the discussion,Socrates rejects Theaetetus' suggestion (20la-c), he also rejects theacquaintancemodel that had made Theaetetus' uggestion ook plausibleand that also precludesa satisfactoryexplanationof false belief. Thisstrategy, in addition to freeing Plato from any commitment to theacquaintancemodel here, also shows that the discussionof false belief isnot, as is usually supposed, an irrelevantdigression,awkwardlysand-wiched between Theaetetus'definition and its refutation.3Rather, thediscussion is an integralpart of Plato'sattack on that definition.I shallreturn o these generalmoralsat the closeof the paper.First,however, t isnecessary o understandSocrates'generalprocedure.Socrates presents two puzzles designed to show that false belief isimpossible, and three models that attempt, but fail, to overcome thepuzzles.I shall hereconsideronly the firstpuzzle,what I shall callK, andthe firstmodelof falsebelief,allodoxiaor otherjudging.4 arguefirstthatK rests on a strongacquaintanceview. I then arguethat allodoxia is notdefectivein any of the ways usually proposed,but that it matchesPlato'saccountof falsity n the Sophist.It failshereonlybecauseof its relianceon70

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    K. But sincePlatois notcommitted oK, this does not showthat he cannothandle the subtletiesof allodoxia.Rather,allodoxia's ailureto explaininwhat false belief consists is an indirect argument that Theaetetus'definition of knowledge as true belief is faulty, since that definitionrequiresK in its support,and K in turnprecludesa satisfactory ccountoffalsebelief.2. I turnfirst to the first puzzle (188 a-c), what I call K. Socratesarguesthat:(1) For any x, either one knowsx or one does not know x.(2) For any x such that one has a belief about x, eitherone knowsx orone does not know x.(3) It is impossible orone both toknow andnot toknowthesamething.He then arguesthat(I)-(3) ruleout false belief:(4) If one has a falsebelief thatx is y, either(a) one knowsx and y; or(b) one knowsx ory, but not both;or(c) one knowsneitherx nory.(5) None of (4) (a)-(c)is possible.(6) Therefore hereis no falsebelief.

    Two questions ariseimmediately.First,why is none of the cases desc-ribedin (4) possible? I)-(3) seemsimplyto be instancesof logical aws,(1)and (2) of the law of the excluded middle, and (3) of the principleofnoncontradiction;t is then difficultto see how they could rule out falsebelief.5Second,even if (5) follows, why does (6) follow?(5) seemsat mostto ruleout false identitybeliefs;(6) rules out all false beliefs.6Socratesdefends(5) in thisway: if one believesthatx is y, but x is not y,then one is ignorantof x and y (188b4-6).But if one is ignorantof x and y,one cannothave anybeliefs aboutthem, and hence no false beliefsaboutthem (188b6-c4). Otherwise put, whicheveroption in (2) obtains, falsebelief is impossible.If one does not know x, one cannothave any beliefsabout x; but if one doesknowx, one cannothave any falsebeliefsabout x,since knowledgeprecludeserror. f one is tohave a beliefabout x, then,onemust knowx:(2a) Forany x suchthat one hasa beliefaboutx, one knowsx.Readone way, (2a) is innocuousenough.If I have a belief aboutsome-thing, I must know it in at least the minimalsense thatI could identifyorrecognize t; I do not havebeliefs,forexample,aboutpersonsI havenevermet or heardof. (2a)then sufficesto rule out(4b)and(4c);in themI do notknow, that is, could not identifyor recognize,one of the items in a pur-

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    portedbelief. If I am totally gnorantof one of these items, t is reasonableto supposethat I cannothold the belief in question.But this still leaves (4a). SupposeI know Gerald Ford;I've heardhim,seen picturesof him,could easilyrecognizehim, and so forth.Still, I mighthave the false belief about him that he was born in Boston; (2a) is notstrongenoughto yield (5).Otherreadingsof (2) are possible,however.We mightnote, first,thatPlato's ubstitutionsor 'x' areallof persons.We mightthensupposehe hasin mindsome sort of acquaintanceprinciple:(2b) Forany x suchthat one hasa belief-aboutx, one is acquaintedwithx. However, f 'acquaintance's taken in theordinary ensein whichI can'know'a personor thing(connaitre),t is stillnot strongenough.I mayhavemet GeraldFord, and so 'know'him or be acquaintedwithhim; nonethe-less, I might still thinkhe was bornin Boston. Connatre-acquaintance illnot ruleout false belief, as Platoattempts o do.7

    Russell once held a principle like (2b), claiming that whenever arelationof judgingor supposingoccurs,the termsto which the supposingorjudgingmindis relatedby the relationof supposingorjudgingmustbetermswith whichthe mindin questionis acquainted. 8Russellexplainedfurther hat Weshallsaywehaveacquaintancewithanythingof whichweare directly aware ... no further knowledge of [such a thing] is eventheoreticallypossible. 9Acquaintance, n this sense,conferstotal knowl-edge; it is, moreover,a hit or miss, all or nothing,affair.Eitherone isacquaintedwithsomething,and so knows all thereis to knowaboutit, orelse one is not acquaintedwith it, and so has total ignorance. 2b) thenbecomes:(2c) For any x such that one has a belief about x, one either knowseverythingaboutx or is totally gnorantof x.And(2c) does yield (5). If I amignorantof x, I have no beliefsaboutx, as(2a) plausiblyclaimed;butif Iknow everything boutx, Ican havenofalsebeliefs about x. Although (2c) yields (5), (I)-(3) are now no longerinno-cuous.3.The answer o our second question,of whyPlatomovesfrom(5) to (6),emergesfroma consideration f the firstmodelof falsebelief,allodoxiaorothejudging. Socrates uggests hata false beliefoccurswhenone says nhis thoughtthat somethingof the thingsthatare is, havinginterchangedsome other thing for it. For then he always udges somethingthat is, butone thing nplaceof another,and sincehe misseswhat hewasaimingat,hecan rightlybe said to bejudgingfalsely. 189c1-4)Theaetetus uggestsasanexample whenever ne thinksuglyin placeof beautiful,orbeautiful n72

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    believe 'whatdisgusts he beholder s beauty').But aside from thislimitingcase, many instancesof the allodoxastic chema,construedas in (8), will beintelligible.For example, 'being brightly colored is beauty' is false butintelligible;and so (8) is an instanceof the allodoxastic chemathat is notunintelligible.(7) and (8) restrictthemselvesto considerationof properties.But theschema Socratesprovidescan also accommodatebeliefs concerningparti-culars:(9) Theaetetus thinks that the ugly thing (for example, Socrates) isbeautiful.

    (10) Theatetusthinks of the ugly thing (forexample, Socrates) hat it isbeautiful.In (9) and(10) 'ugly'functionsas an adjective,and some particularhingis affirmedto be beautiful.(9), like (7), is an opaquerepresentation f thebelief, and it is similarlyunintelligible.Theaetetushere explicitlyaffirmssomething ike 'ugly Socrates sbeautiful',andit is difficult o construe hisbelief so that t is intelligible. 3 (10), like (8), isa transparent epresentationof the belief, and it is a primafacie plausiblesubject-predicateentence.Theaetetus'explicit belief would be, for example,'Socrates s beautiful'.This belief is still allodoxastic, ince Theaetetushas substitutedbeautififor 'ugly';but the belief, althoughfalse, involvesno mix-upof conceptsorproperties.

    Now (8) and(10) togethershowhowallodoxiacanbe a plausiblemodelof falsebelief,andone that sperfectlygeneral.Theyshow that nstancesofthe generalschemaare neither restricted o identitybeliefs nor to beliefsinvolvingonly propertiesnorto opaque representations f beliefs; rather,the schemawill even accommodate rdinary ubject-predicateudgments.Correspondingly8) and(10)showhowPlatocan move from 5) to (6).Foralthoughthe beliefsdescribed n K may appear o be restricted o identitybeliefs, (8) and(10)showthat the restriction s unnecessaryhere,too. ForK's schemafor false belief is also 'thinking hatx is not x but somethingelse, y' (cf., e.g., 188b3-5),and (8) and (10) show that instancesof thisschema are not restricted o identitybeliefs. (8) and (10) also match theSophist'saccount of falsity,where false statementsare analyzedas caseswhere one says of somethingsomethingother than what is trueof it (cf.,e.g., 263b7-13).(8) and (10) are then prima facie plausible false beliefs;they show how allodoxiacan accommodateall false beliefs;they explainK'sseemingrestriction o identitybeliefs;and theymatchPlato'saccountof falsityin the Sophist.14But although they are possiblereadingsof theallodoxasticformulafor representing alse beliefs, this does not by itself74

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    show that they are the readingsPlato intends. All I have argued so far isthatif(8) and(10)are thereadingsPlatointends,allodoxia s moregeneraland more plausible than on any other reading;but does Plato intendallodoxia to be general andplausible9Theaetetus'openingcommentssuggestthat he does. But Socrates'con-cluding comments, n which allodoxia s rejected,rathersuggest(7) or (9).Socratesasks Theaetetusto 'try to recall whetheryou have ever said toyourselfthat assuredlywhatis uglyis beautifulor that what isunjust sjust.Or again, in general, consider whetheryou have ever tried to persuadeyourself that assuredly one thing is another thing ...' (190b2-8). Theattempt s takento be absurd;but sinceneither 8) nor(10)isabsurd, 7)or(9) should be assumedhere.Now it is usuallysupposedthatsince Socratesclearly nvokes 7)or(9) inhis rejectionof allodoxia,either they are all he considershere, or, alter-natively, that he somehow confuses them with (8) or (10).15The firstalternative s unattractive.Forif (7) or (9) areall Platoconsiders, t is, as Ihave alreadynoted, difficultto understandwhy Theaetetus nitially takesallodoxia to be a plausiblemodel of false belief, or why he needs suchlengthy persuading hatit is not. Perhaps, hen, Plato confuses the variouspossibilities, radingon theplausibilityof(8) and (10) to secureTheaetetus'agreement, but using (7) or (9) to show the absurdityof allodoxia. Anequally plausibleinterpretation hat avoids attributing onfusionto Platois to be preferred,however,and I think such an interpretations available.I shallarguethat Socratesbeginswith the plausible(8) or (10) - and henceTheaetetusacceptsallodoxiaas a plausiblemodel of false belief- but thatSocrates then argues that(8) or (10) can be reduced to (7) or (9), respec-tively; the argumenthe presents s valid, however, and does not trade onany confusion.

    The key to this interpretation ies in the interveningdiscussionbetweenTheaetetus' initial example and Socrates'criticism of it, where Socratesproposes that thinking is a sort of silent speech, 'speech the mind goesthroughwithitself aboutwhatever t is considering.' 189e6-7). In likeningbelief to speech, Socrates s saying that they are equallypropositional,orinvolvea complete sentence or theirexpression.Uttering beautiful'alone,forexample, s not the expressionof a belief, but 'Socrates s beautiful' s.Socrates then insists that in any belief 'both things'(189el-2) must beinvolved, and uses this claim to turn all cases of otherjudging ntocases of(7) or (9). Now 'boththings'clearlyrefersto 'beautiful'and 'ugly';but as(7)-(10)makeclear,thereare differentwaysin whichboth thingsmightbein the mind. For example,Socratesmightbe insisting hat when onejudges

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    of an ugly thing that it is beautiful,one'sbelief mustexplicitlycontain theterms ugly'and 'beautiful', o that even (10)involvesanexplicit mix-upofconcepts. If this is meant, t will be difficultto acquitSocratesof foul play.But anotherreadingof therequirementhat 'both things'be in the mindis possible.Socratesmightonly be insistingthat anyjudgmentaffirmingone thing to be anothermustinvolve bothitems in someway, so as to yielda completesentencein satisfactionof the logos model of belief. But theugly can be in themindwithoutbeing thereunderthedescription the ugly'if Socrates, orexample, s anugly thing andis in the mind.Both things,onthis view, might be Socrates who is the ugly thing) and beautiful.Takenthisway, Socrates'requirementdoes not illicitly require elf-contradiction(as in (7)) in every belief, but only insists,plausibly, that complete sen-tences representbeliefs: something must be affirmed to be beautiful.The requirement, hen,is consistentwith(8) and(10).Using this plausibleclaim, however, Socratescan now validly reduce(10) to (9) - given K.If 'Socrates'and 'beautiful' igurein one'sjudgment,one must, by (2c),know Socratesandbeautiful.Butif oneknowsSocrates,one knowsthatheis ugly.If one does not knowthis, he is ignorantof Socrates,andso cannothaveanybeliefsabouthim.If, though,one knowsthatSocrates sugly, yetclaimsthathe is beautiful, t is as if he saidthatuglySocrates s beautiful.And sucha belief is absurd.We can schematizePlato'sargument ike this:(I1) Theaetetus hinksthat Socrates s beautiful(10).(12) Socrates s ugly.(13) ThereforeTheaetetus hinksthatuglySocrates s beautiful.The move from(1 1)and(12) to (13)can be validatedwith the aid of K:(14) Theaetetusknows Socratesand beauty, since they figure in hisjudgment (2c).

    (15) Theaetetus, incehe knowsSocrates,knows thathe is ugly.(16) Theaetetus thinks (a) Socratesis ugly (15), and (b) Socratesisbeautiful(1 1).(17) ThereforeTheaetetus hinksthatuglySocrates s beautiful 13).Plato has not simply confused (10) and (9); he has arguedvalidly that,given K, (10)reducesto (9).4. I have arguedso far that otherudging is a plausiblemodel of falsebelief, endorsedby Plato in the Sophist; t fails herenot because of anyofits intrinsic eatures,nor because Platocannotyet handleitssubtleties,butbecause, given K, it can be reduced to absurdity.But this pushes ourproblembacka step: whyendorseK?76

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    K offersus, with (2c), a purportedlyexhaustivedichotomyof knowingall about or beingtotallyignorantof a thing,a dichotomygeneratedby aparticularmodel of acquaintance.The way to dispelK is simplyto attackthat acquaintance model, or to point out that the dichotomy is notgenuinely exhaustive. It is not the case that, for any x, either I knoweverythingabout x or am totally ignorantof it; I might be in the inter-mediateposition of havingknowledge-independent eliefs.Why does Plato not mentionthis simple refutationof (2c)?We mightthinkthe answer s that he endorsesK, thathe believesthatanygraspof athing confers total knowledgeof it, and that the only alternative s totalignorance.Knowledge sa hitormiss,allornothingaffair.There s a betterexplanationof K's presencehere,however, f we recallthe contextwithinwhich K is offered.Theaetetusproposes hatknowledge s truebelief;Socrates henturns oa discussion of false belief and, when he fails to explain it, argues thatTheaetetus'definitionis faulty; it is impossible o knowwhat[false beliefis] until one knows what knowledge is. (200d). This suggests that thediscussionof falsebelief is relative oTheaetetus'definitionandthat,sincethediscussionended in failure,the definitionthatguides it is defective.

    Now the failure to explain false belief resulted from K's strongacquaintancemodel, which precludedany distinctionbeween truebeliefandknowledge:on thatmodel,any graspof a thingamounts oknowledge,and so truebelief, since it involves a graspof a thing, is knowledge.ButofcourseTheaetetus houldwelcomethisresult, ince he suggests hatthere sno distinctionbetween knowledgeand true belief. Thus, the underlyingacquaintancemodel, although it precludesa satisfactoryexplanationoffalse belief, supportsTheaetetus'suggestion,by obliteratingany distinc-tionbetweenknowledgeandtruebelief.16K occurshere,then,notbecausePlato is vulnerable to it, but because it follows from the acquaintancemodel introduced n supportof Theaetetus' uggestion.I do not claim thatTheaetetus'definition entailsthe conundrumsof K.Rather,Iclaimthatthe acquaintancemodelthatunderliesK is a sufficientconditionof Theaetetus'definition.If the acquaintancemodelis accepted,Theaetetus generates the conundrums of K, and prevents us fromthe consequences of accepting the support used to make Theaetetus'definitionlook plausible.17But there is a problem: the acquaintance model used to supportTheaetetus generates the conumdrums of K, and prevents us fromaccommodating alse belief. The support used for Theaetetus'definitionleaves no room forfalsebelief.But sincethere s falsebelief,theremustbe

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    somethingwrongwithTheaetetus'definition;as Plato says,theirinabilityto explain false belief shows that they do not know what knowledgeis,either.If the resultof pressingTheaetetus'definition,through ts supportof acquaintance, s to precludefalse belief, then that is an indirectargu-mentthatthatdefinition s faulty.Lookedat in this way, the discussionof false belief is not an irrelevantdigression; rather, it reveals the difficulties created by acceptance ofTheaetetus'definition.Sincethesedifficultiesare intolerable,Theaetetus'definition s to be rejected.Plato thus has a two-prongedstrategyagainstTheaetetus'suggestionthat knowledgeis truebelief. At 20la-c he refutesit directly.In the dis-cussionof falsebeliefhe criticizes t indirectly,by showingthatitssupportleadsto intolerableresults.The discussionof false beliefis thenanintegralpartof the considerationof Theaetetus'definition,not a meredigression.5. If this isright, here s anotherpointworthmaking. t isoftenclaimedthat PlatoendorsesK, thathe thinksof knowledgeas a sortof grasping,oracquaintance.But if what I have said so far is right,at least this passagedoes not support hatview. For thesame two-pronged trategyPlatousedagainstTheaetetusworksas well againstK. First,K's inabilityto accom-modatefalse belief is an indirectargument hatit is faulty.Second,201a-crejectsK by a simpleapplicationof modus ollens.Plato argues herethatknowledge s not truebelief,andso Theaetetus'definition s wrong.ButifK entails Theaetetus'definition, the rejectionof Theaetetus'definitioncarrieswithit the rejectionof K.To be sure, those who ascribean acquaintancemodelof knowledgetoPlato can appealto otherpassages.Butif themodus ollensargumentustsketchedis right,they should be wary:for Platoconsistentlydenies thatknowledge s true belief (see, e.g.,Meno98a;Gorg.454d;Rep.477a).If therejection of that view here counts against acquaintance, t may do soelsewhereas well.18Cornell University

    1 For this view, cf. G. E. L. Owen, Plato on Not-being in Plato,vol 1,ed. G. Vlastos(New York, 1971),esp. 245; 262-5;J. McDowell, Plato: TheaetetusOxford, 1973);J.McDowell, IdentityMistakes:Platoand the LogicalAtomists ,PAS 70(1970) 181-196;W. G. Runciman,Plato's Later EpistemologyCambridge,1962).2 Cf. n. 1.3 For this view, see J. McDowell, Plato: Theaetetusp. 194; F. M. Cornford, Plato'sTheoryof Knowledge(New York, 1957), p. 110. McDowell does suggest two rather78

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    tenuous links, (a) that the discussionconsidersknowledge,the centraltopic of the Tht.,and (b) if there is to be true belief, there must also be false belief with which it can becontrasted. b) is also suggested by F. A. Lewis, TwoParadoxes n the Theaetetus n J.M. E. Moravcsik,ed., Patternsin Plato's Thought(Dordrecht,Holland, 1973), 123.(a)does not explainwhy false belief shouldbe consideredat thispoint in thedialogue,ratherthanelsewhere. (b) gets Plato'sargumentback to front.At 200d he claims thatthey mustknowwhatknowledge is before heycan know what false belief is. The link I suggestlaterpreservesthispriority.4 The second puzzle (188c9-189b8) is essentially the same as K. The second and thirdmodels of false belief (the wax tabletand the aviary), ike allodoxia, fail because of theirreliance on K. For furtherdefense of these claims, see my unpublished Ph. D. thesis,Platoand Acquaintance Harvard,1975).5 Lewis, op. cit., Lewis defends this view; I reject it.6 Lewis, op. cit., 124; McDowell, Plato: Theaetetuspp. 185-195;McDowell, IdentityMistakes:Plato and the LogicalAtomists ,PAS 70 (1970) 181-2;andJ. L.Ackrill, Platoon False Belief: Theaetetus187-200. Monist 50(1966)385-7agree that(5) considersonlyidentity beliefs; I argue later that this restriction s unnecessary,and that (5) does entail(6).7 McDowell, Identity Mistakes ,argues that connaitre s all that is involved. He con-siders the strongerclaim I later press,but rejects t on the groundsthat it rulesout all falsebeliefsand not merely dentity beliefs.The strongerviewdoes have thatconsequence, butI think it is a consequence Plato intends. In his book, McDowell vacillates betweenendorsing the connaltrenterpretation Acquaintance s a relationof the ordinarysort ,p. 197) and the strongerview( therewould seem to be nothingbetween blankignorance... and theunqualified orcompleteobtaining of knowledge ,p. 197);but these viewsareobviously quite distinct.8 B. Russell, Knowledge by Acquaintance and Knowledge by Description ,reprintedin Mysticismand Logic (1918),220-1. The parallelis noticed and pressedby McDowell,Theaetetus,p. 196, and IdentityMistakes , assim.9 B. Russell, The Problemsof Philosophy (New York, 1912),46-7. Cf. MysticismandLogic,202-3,and Logic andKnowledge,204.10 C. J. F. Williams, ReferentialOpacity and False Belief in the Theaetetus ThePhilosophicalQuarterly22 (1972) 289-302,also distinguishesthe opaque fromthe trans-parentreadingsof allodoxia.He argues,however,that Plato confusesthe two readings,whereasI go on to argue that he does not.11 Cf., e.g., Ackrill, op. cit., 388-389.12 Ibid.13 Althoughnot impossible.The early and middledialogues, forexample,oftenconsidercasesof the compresenceof opposites;Socratesmight be beautiful inone way and uglyinanother.But thatview does not seem to be relevant here.14 This paragraph argelyagrees with Williams, op cit., McDowell, Theaetetus,p. 203,considerstwo purported differencesbeween allodoxiaand the Sophist's later account;but if the analysis of allodoxia I offer here is correct,neither of these purported dif-ferencesis relevant.15 For a defense of the firstclaim, see Ackrill,op. cit. 388-9; for a defense of the secondclaim, see Williams, op. cit., 291 f. and McDowell,Theaetetus,pp.204 ff. Ackrill'sview iswell criticized by Williams.From now on I shall largely focus on (10); but most of myremarksapply equally well to (8).

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    16This line of reasoningshowsthattherecannot be knowledge-independent rue beliefs;but could there not be false belief?I think Plato would say thatif, for any x, I have onlyfalse beliefs about x, then I in effect have ignorance,as describedhere. If a false belief isto be about x, it cannot be all we intend to say about x; for a false belief to attach to areferent, it must be linked to other true beliefs. If all I can say of justice is that it is avegetable, this does not count as a belief about justice at all; it displays ignoranceofjustice. To count as a false belief about x, a claim must be linked to other beliefs thatmanage to refer to x. In this sense, false beliefs require there to be true beliefs,but K doesnot allow this sort of interdependence.For, by (3), one cannot both know and not knowthe same thing. Our only options, then, are all true beliefs, which here amount toknowledge, or all false beliefs, which then plausibly reduce to ignorance.Plato thusrejectsthe Kripkeanview that all my beliefs about something could be false.17 I have suggestedso far that the acquaintancemodel is usedto supportTheaetetus;butis it necessary?Plato seems to place the burden on the defender of Theaetetusto find anaccountof knowledgewhich(a) unliketheacquaintancemodel does notentailK; and(b)supportsTheaetetus'failureto distinguishknowledge and true belief.18 An earlier version of this paper was read at the meetings of the A.P.A. EasternDivision, December 1976. I wish to thank Donald Zeyl forhis helpfulcommentson thatversion.The presentversionswas acceptedfor publication by the editorof Phronesis nMay 1977.

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