the gettier problem

8/2/2019 The Gettier Problem

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The Gettier ProblemAuthor(s): Scott SturgeonReviewed work(s):Source: Analysis, Vol. 53, No. 3 (Jul., 1993), pp. 156-164Published by: Oxford University Press on behalf of The Analysis CommitteeStable URL: http://www.jstor.org/stable/3328464 .

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The GettierProblemSCOTTSTURGEONThirty years ago this journal publishedthe most influentialpaper ofmodernanalyticepistemology EdmundGettier's IsJustifiedTrueBeliefKnowledge?' (ANALYSIS3, 1963, pp. 121-23). In it Gettier refuted a clas-sic theory of propositionalknowledge by constructing hought experi-ments to test the theory.A cottage industrywas born. EachresponsetoGettierwas quicklymetbya newGettier-stylease.In turntherewouldbea response o the case, a furtherGettierscenario,and a reiterationof theprocess.The industry'soutput was staggering.Its literaturebecame socomplicated, ts thoughtexperiments o baroque, hatcommonsensewasstretchedbeyond imit. Thedeep significance f Gettier'swork drowned ntheresulting acophony.Thatsignificance an be seenby reflecting n twopoints:first,why theproblemarises;andsecond,how it is to be solved.1. WhatgeneratesTheGettierProblem?Infallibilisms the view that whatevergivesrise to epistemic ustificationguaranteesruth.According o theinfallibilist,t is impossible o justifiedlybelievesomething alse.This has the tidy result that justifications suffi-cient to convert belief into knowledge.Thus the InfallibilistView ofknowledge:

(IV) S knowsP iff (a) S believesP(b) S'sbelief n P is justified.Butsinceguaranteesof trutharehard to come by,Infallibilism eads to adilemma:either we are justified n believingfar less than commonsenseadmits,or justifications fallible.Fallibilistsopt for the latter horn of the dilemma.This has the messyresult that justificationis not sufficient to convert belief into knowl-edge. For you cannot know somethingfalse. Sinceyou can, accordingto the fallibilist, justifiedly believe something false, it follows thatknowledgeis more than justifiedbelief. The questionthen is, what hasto be added?

The view attackedby Gettieranswers this questionvery simply:addtruth.Thisis the so-called traditional iewof knowledge':(TV) S knowsP iff (a) S believesP(b) S'sbelief n P is justified(c) P is true.

ANALYSIS3.3, July 1993, pp. 156-164. @Scott Sturgeon


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THE GETTIER ROBLEM 157Heretwo ingredients re used to convertbelief ntoknowledge: allibilisticjustification ndtruth.This is the theoryrefutedby Gettier.Gettiertargetedthe right-to-leftdirectionof (TV). He presentedclearcasesin whichjustified rue beliefdoes not amountto knowledge.Hereisa typicalGettierscenario:

(S) Suppose I burgle your house, find two bottles of NewcastleBrownin the kitchen,drink and replacethem. You rememberpurchasing he ale and come to believetherewill be two bottleswaitingforyou at home.Yourbelief s justifiedandtrue,butyoudo not knowwhat'sgoingon.(TV)is thus false.Theright-hand ide does not providea sufficient ondi-tion for the left-handside. The GettierProblem s that of delineating heminimalconditionwhich,when appended o (a) to (c), generatesa suffi-cient conditionforknowledge.Inbrief,theproblem s to find theminimallink between ustification nd truthwhichprecludesGettier cenarios.2. Solvingthe GettierProblem.Thestandard olution to The GettierProblem prings rom a simple dea.Wemaysketchthis ideaas follows:(SS) S knowsP iff (a) S believesP(b) S'sbelief in P is justified(c) P is true(d) S'sjustification tandsup to the relevantset of facts.(d) is intended to capture a complex relation holding between thosefeaturesresponsible or (b) on the one hand,and a certainset of factsonthe other. To fully understand d), two things must be explained:first,which facts are relevant;and second,what it is for one'sjustification o'standup'to them.The relevant acts will varyas one thinksof the past, presentor future.To see this, supposeyou believesomethingat timet about an earlier imet*.' Whetherornot thisis knowledgewill dependon factswhichpost-datet*. Butin suchcases thepossessionof knowledgewill not dependon factspost-datingyourbelief-state.Factsof this sortcannotmakeyoursa Gettierscenario.Thus,whenyou think of thepastor presentonly factsoccurring

Forthe sake of simplicity ignoreiteratedknowledgestates,knowledgeof intentionalstates,and any othersituation whichwould force a distinctionbetween facts 'strictly'about the past (likethe fact that there was no McDonald'son the Moon in 1900) andfacts not strictlyabout the past (likethe fact that Einsteinknewthat no one would liveon the Sunin 1999).


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158 SCOTT STURGEONon or beforethe moment of thoughtwill determinewhetheryou haveknowledge.Onthe otherhand,supposeyou believe omethingat timet abouta latertime t*. Whether his is knowledgewill dependon facts whichpost-dateyourbelief-state.Not onlywill the facts at t*need to be asyou believe,butthe interim acts mustbe kosheras well. Yetwhenyou believesomethingat t about a later time t*, facts which post-date t *cannot generate a Gettierscenario.Therefore,when you think of the past or presentthe relevantfacts will obtainno later than your thought;and when you think of thefuturethe relevant actswill obtain no later thanthe time considered.Sofor any token belief at time t in a propositionabout t*, the relevant actswill be thoseoccurringupto, andincluding, he laterof the two.Let 'T' name the set of truthsdescribing hese facts in an arbitrarilychosen case. For condition (c) of (SS) to be non-redundant,we mustexcludePfromT (alongwithanytruthtrivially mplyingP).Wemaythenask: Whatis it for one'sjustificationo 'standup'to T?Letussaythat one'sjustificationorPconsists n 'evidence' orP, eavingthenatureof thisphenomenonopen.Wenotice that evidence s defeasible:{E)may be evidence or P despitethe fact that {E)u {E*)is not evidenceforP.In theeventwe saythat{E*)defeats{E),or that{E*) s a defeater or{E).Intuitively, E) is ultimatelyundefeatedrelativeto a set S iff everyelementof Swhich defeats{E) s itselfdefinitelydefeated;andsomething sdefinitelydefeated n S whensomething n S defeats t for which thereareno furtherdefeaters, r,if thereare,theyarethemselvesdefinitelydefeated.Turning hisrecursivegloss into an explicitdefinition s not hard,but weneedn'tbother.Ourpresentunderstandings enoughto explain(SS):

(M) S knowsP iff (a) S believesP(b) S'sbelief n P is justified(c) P is true(d) S'sevidence{E} s ultimatelyundefeatedrelative o T.

(M) is the standardpost-Gettiermodel of propositionalknowledge.Itsfourth conditionis intendedto capturethe minimalconnectionbetweenjustification ndtruthnecessary o excludeGettier cenarios.What does (M)teach us?

3. Internalism/Externalism.Call justification hat is ultimatelyundefeated full justification'.What-ever thiscomesto precisely, ull justifications thecrucialfeaturerespon-sible for turning belief into knowledge. One lesson to be learned from(M) is that epistemic externalism deeply characterizes the nature of full


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THE GETTIER PROBLEM 159justification.Letme explain.

Epistemology'snternalism/externalismebatespringsfrom this ques-tion:what determines pistemic ustification?nternalists ay justificationis determinedby an agent'sperspective: easonerswho are perspectivallyequivalentare justificationally quivalent;while externalists ay justifica-tion is determinedby features ndependentof an agent'sperspective.Butwhat does this difference eallycometo?Notice first that two scenariosappear the same to a person iff herperspective n eachis the same. So if we can reckon he featuresgivingriseto appearance,we will have found thosedefininganagent'sperspective.nthis regard t is customary o say thattwo scenariosappear he same to apersonwhen her relevantappearance-statesre phenomenally he same.Morecarefully, cenariosP1 and P2 appear he sameto S justin case hermental-representationsf them are, or would be, tokens of the samephenomenal ype.Epistemicnternalismhen amounts o this idea:

justifications determinedby the phenomenal eaturesof an agent'smind: reasonerswhose mental statesare phenomenallydenticalarejustificationallydentical;andepistemicexternalism mounts o this idea:

justifications determinedby features ndependentromthe phenom-enal featuresof an agent'smind.Now, we can easily see that full justification s determinedby featuresindependent roman agent'sperspective.Thus externalism s true of thecrucial ingredientneeded to convert belief into knowledge:

Lesson One- externalism s trueof full justification.Toseethis,noticethat fulljustificationmustsatisfyall externalconstraintson knowledge.For instance:

(El) one is fullyjustifiedn believingPonlyif one is reliableaboutP,(E2) one is fullyjustifiedn believinga truepropositiononly if onedoes so becauseone is reliable,(E3) one is fullyjustifiedn a perceptually-basedeliefonly if one'sperceptual tates arenon-deviantly aused.

And so forth.Thepointis:everyobjectivereal-world onnectionnecessaryforknowledgewill be necessary or fulljustification s well.Thefailureofany such connectionwill functionas a defeater or condition(b) of (M).Hence the justificationof that condition will convertto full justificationexactlywhen the externalconstraintson knowledgeare satisfied.Gettier'swork thus provides a direct route to the conclusion that epistemic exter-nalism is true of the crucial ingredient needed for knowledge.


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I60 SCOTTSTURGEON4. Infallibilism evisited.(M) asserts that knowledge is fully justified true belief. The second lessonof Gettier is this:LessonTwo- fulljustifications infallible.Whenever you are fully justifiedin believinga proposition, that propositionis true. This means that full justification is the only ingredient needed toconvert belief into knowledge. Condition (c) of (M) is redundantafter all.To see this, suppose you are fully justified in believing P. Now considerthe relationship between T and P. There are three possibilities:

(i) T logically implies P(ii) T logically implies not-P(iii) neither (i) nor (ii).Case-(i) scenarios ensure that P is true. So no beliefs in this category willbe mistaken. Case-(ii) scenarios rule out full justification. For if T logicallyimplies the falsity of your belief in P, then your justification for this beliefwill not be ultimately undefeated. There will be facts described in T whichdefeat that justification. This leaves category (iii) as the only potentialhome for fully justifiedmistakes. If there are none here, then full justifica-tion is infallible. What sort of proposition falls into category (iii)?To begin, notice that T will logically imply P if P is a nomic consequenceof the matters of fact up to the salient time. For T will contain a descriptionof the laws of nature along with those facts. Similarly, T will logicallyimply not-P if this proposition is a nomic consequence of the matters offact. So T will logically imply neither P nor its negation only if P is nomi-cally indeterminate relative to T. But for P to be logically indeterminaterelative to T, and thus belong to category (iii), it must be more than nomi-cally indeterminate relative to T. It must also fail to follow from any of thematters of fact described in T. If, for example, T describes a particularcausal relation having E as one of its relata, then T will logically predict Eeven when E is nomically indeterminate relative to T. (A case like this willbe considered shortly.)Thus, for P to be logically indeterminate relative toT it must be nomically indeterminate relative to T and logically indetermi-nate relative to that set got by subtracting the laws described in T.Three sorts of propositions have been thought to fit the bill: (a) nomicindeterminacies, (b) universalgeneralizations, and (c) laws of nature. Eachcategory gives rise to familiar epistemic problems. As we are about to see,(M) is a model of propositional knowledge which both explains and helpssolve these problems.(a) Suppose you shoot a photon toward the slit in a piece of polaroid andwonder if it will go rightor left when passing through. Suppose further that


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THE GETTIER PROBLEM 161youknow all laws of natureandall matters f factupto themoment nques-tion. In otherwords, supposeyou know everythingn T. Finally, et thisknowledge ender t indeterminate,hough ikely, hat thephotonwillgo totheright.On thebasisof thisyoucome to believe hat thephotonwillgo totheright.Andsuppose t will. Do youknowthephotonwillgo to theright?I submitthat you do not know where the photon will go. After all,there'sanotherpossibleworld exactlylike yourssave the photon goes tothe left. In it you believethe photon will go to the rightwith exactlythesame evidence namelyall theevidence butyou aremistaken.Hence theview thatyou actuallyhaveknowledge mpliesthat brute uckmakes thedifferencebetweenknowledgeand ignorance.This is unacceptable.Luckdoes not contribute o ourpossessionof knowledge.Eitherwe have located a counter-exampleo the standardpost-Gettiermodel of knowledge,or there lurks a defeatersomewhere n the photoncase. The latteroptionseemsappropriate:ndeterminacytselffunctionsasa defeater.Whenall the facts save the issue at handdo not fix the issue,thenthis is reasonto withholdjudgement.Case-(iii) cenariosof this sortareincompatiblewith fulljustification.On the otherhand,nomic indeterminacies re not unknowable.If, forexample,the photongoes to the rightand thenstrikesa screen,we mightverywell come to know the pathtaken.The lesson is: nomicindetermina-cies are knowable when they fit into mattersof fact whichforgean epis-temic route to them. In particular,nomic indeterminaciesare knownthroughtheir effects.They are known when the moment of knowledgeitself post-datesthe moment known. But T will logically imply the factknown in these cases (as suggestedfive paragraphsback).We will haveshiftedfromcategory(iii)to category(i).Thissuggests he followinglemma:

LemmaA Ifmicroscopic ndeterminacieslimb into the macroscopicdomain, then we have much less knowledge than commonsensewould admit.Indeed:f thewobblinessof thetinyreachesup into the worldof common-sense,thenI submitwe know truthsalmostexclusivelypost facto.Natu-rally,this does not meanthat our commonsensebeliefsare in any senseunreasonable r lessuseful.Theyjustdo not amountto knowledge.As faras I cantell, this differencedoes not makeanydifference.(b)Supposewe expressthe factthat all Fs are H thus:

UF (Vx)(Fx -+ Hx).Does (M) providea useful model for understandinghow we can knowfacts of this sort?


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162. SCOTTSTURGEONYes. For on the present definition of T, T will imply UF . Suppose

xl,...,xn are the Fs, and each is an H. In the event, T will not onlycapturethe fact that Hx1, and Hx2,..., and Hxn, it will also capturethefact

EF (3x)(Fx-+ (x = xl v x = x2 v ... v x = n)).Allthistogether mpliesUF. Thusknowledgeof universal act is, for (M),straightforwardase-(i)knowledge.Manywill find this a cheat.Theywill arguethat generalfactsmust beknown on the basisof non-general acts, and thus that our definitionofT should be changed.They would have us impoverishT so that it nolongerentailsfacts like UF or EF . Once trimmed n this way, T will nolongerforma set sufficientlyrobust to groundour evidence n the usualway.(M)thushelpsclarifyone particularrade-offbetweenmetaphysics ndepistemology:

LemmaBKnowledge f general act seemspossibleonlywhengeneralfact is admittedinto the backgroundontology of one's epistemictheory.Unlessyou admit ntoyour epistemic heorya background f general act,into whichreasonablebeliefmaybegrounded, uch beliefwill not amountto knowledgeof general act.But onceyou do, knowledgeof general actwill pose no special problem. It will be straightforwardcategory-(i)knowledge.(c)SupposeL statesa law of nature:

L (Vx)(Fx =- Hx).Perhapsclaimshatallmovingbjectsravel tor belowhespeed flight.Does (M)providea usefulmodel or understandingow we canknow actsof thissort?Yes.ForTwillcontain nomicruth bout very peed reaterhan hatoflight, owit,that ravellingt thatspeedsimpossible.hesewilljointlyentailL. Thus, M)renders omicknowledgen aparwithanyother ortof knowledge.Wehave t whenour evidence tandsupto thefacts,andour evidenceo standswhenthe relevant acts mply henomic actinquestion.Ontheotherhand,(M)explainswhynomicknowledges problem-aticfrom a Humeanperspective. hereare two Humeanperspectivesworthdistinguishingere:weak and strong.Accordingo the weakperspective,nomic knowledge is grounded solely in non-nomic fact.According to the strong perspective, nomic knowledge is groundedsolely in empiricalfact.


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THE GETTIER PROBLEM 163A weakHumean ersion f (M)isgot by excluding omic ruthsromT.Callsucha weakHumeanetof truthsTwH'.he ssue hen s: sLlogi-

cally ndeterminateelativeo TwH?TwHwilldescribe otonly henon-nomicactswhichareempirical,utthosewhicharemetaphysicalswell.For nstance, wHmightdescribehefactthatwatersessentially 20. Soif theempiricalactsmetaphysicallyimplyLthenthiswillbe describednTwH, ndhenceTwHwilllogicallyimplyL.The resultwillbea case-(i) cenario.On theotherhand, f theempiricalactsmetaphysicallymply henegation f L thenthiswillbedescribednTwH, nd henceTwHwilllogically mply hatnegation.Theresultwillbe a case-(ii)cenario. herefore, willbelogicallyndetermi-naterelative o TwHonlyif L does notmetaphysicallyupervenen theempiricalacts.Thus:

LemmaC Nomicknowledges possible n a weakHumean ersionof (M)only f the lawsof naturemetaphysicallyupervenenempir-icalmatters f fact.TheweakHumean ersion f (M)explainsheHumean iew hatsuper-venienceof the nomicon the non-nomics a preconditionor nomicknowledge.Accordingo thisperspective,f the laws of naturedo not

supervenen mattersffact, hen he awsof natureannotbeknown.Forwithout upervenience,omicknowledges exactlyanalogouso knowl-edge nthephoton ase.Butwe havenoknowledgenthephoton ase.Sowithout uperveniencee havenonomicknowledgeither.Finally, strongHumean ersion f (M) sgot byexcludingverythingfromT butcontingentmatters f fact.Thisnaturallyxcludes hemodalfactsusedon theweakHumeanheory o accommodateomicknowl-edge.The resultinghighly mpoverishedet of truthswill implyverylittle.Thus:LemmaD Nomicknowledges impossible n a strongHumeanversion f (M).

Hereagain M)explains trade-off etweenmetaphysicsndepistemol-ogy.Unless ouadmitntotheontology fyourepistemicheory robustbackgroundf metaphysicalact, into whichreasonable eliefmaybegrounded,uchbeliefwillnotamount o nomicknowledge. utas soonasyoudo,nomicknowledge illposenospecial roblem.t willbestraight-forwardase-(i)knowledge.Therefore, ehave ocated nepure ase-(iii)cenario:hephoton ase.And we haveclaimed hat knowledges missing n sucha case. Thisrestricts he scopeof oureverydayknowledge o theextentthatindetermi-nacy muddies our everyday world. On the other hand, general facts andlaws of nature fall into category (iii) only when substantial restrictions are


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164 ROBERT . FOGELINplaced ntheontology fourepistemicheory.Butonceenforced,he imitof ourknowledgeeemsnaturallyestricteds well.Weare eftthenwitha streamlinedost-Gettierefinition f knowledge:(PG) S knowsP iff (a)S believes(b)S'sbelief nPis fully ustified.There an be no doubtbut that Gettier uthisfinger n somethingeryimportantndeed.2 King'sCollegeLondonStrand,London WC2R2LS2 I thankthe discussiongroupto which I belongfor encouragement:Tim Crane,KeithHossack,MikeMartin,LucyO'Brien,DavidPapineau,GabrielSegal,BarrySmithandBernhardWeiss;and I thank Tom Senor,PeterSmith and an anonymousrefereeforhelpfulcomments.

Hookway on KnowledgeInferencesROBERT. FOGELINInhisbook,ScepticismLondon: outledge,990),Christopher ookwaycallsattentiono a classof knowledgeentencese labelsQ-claims:

Some knowledgeentences]ike hefollowingakean indirect ues-tioncompliment:X knowswho committedhe murderX knowswhywater xpands nfreezingX knowswhen hetrain eaves orLondonX knowswhetherhe atomicweightof sodiums 29X knowshowtheprisonerscaped.

Theirormcan beexpressed:X knowsQ. (pp.196-97)Hookwaycontrasts uchQ-claimswith sentences e call P-claims.P-claimshave he form:

X knows hatP.Hookwaypointsout, quitecorrectly,hat the analysisof knowledgesentences as to a largeextentconcentratedn P-claimso the relativeANALYSIS3.3, July 1993, pp. 164-168. @ Robert J. Fogelin

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