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1 JONATHAN VOGEL ARB THERE TmRB COUNTEREXAMPLES TO THE Tm CU)SURE CLOSURE PRNCPLE? PRNCPLB7 Very ten, person cn't know proposition propositon without wilhout knowing vrious logicl consequences tht ht proposition. So, for fur instnce, if know ht tht r friend wering yellow tie, cn't fil to know tht lht r friend wering tie. tie, period. n th cse, he reltion logicl consequence obvious. When he reltion n't obvi- obvious, proposition know my hve logicl consequence don't know - for exmple, suitbly obscure mmticl orem. n light se considertions. considertions, it seems plusible to hold tht if person knows given proposition, tht ht person must lso know ny logicl consequence tht proposition which he or she nxognizts recognizes s such. such, Putting it differently, we might sy tht ht knowledge closed under known logicl impli- impli ction.' 1 The problem skepticm bout he externl world gives th eptemic principle (herefter, he "Closure Principle") specil interest. When skeptic rgues tht ht we hve no knowledge world cuse we don't know tht ht we ren't mssively de- deceived in some wy, he or she ppers to ssume tht ht knowledge hs closure prop- pr0perty. But if it possible 10 to find cler exmples demonstrting tht closure sometimes sometims fils, fils. crucil piece support for skeplicm skepticm will removed. The purpose th h pper to show tht even he strongest pprent counterexmples to closure don't hold up under scrutiny. To tht extent. t problem skepticm still with us. us, DRETSKES DRETSKE'S ZEBRA CASE n widely red pper, pper. Fred Dretske fered n intriguing iniguing exmple which ment to show ht tht he Closure Principle invlid. t worthwhile to 10 quote Dretske's dcussion tlenglh: length: You tke r son 10 to zoo, ux,, see severl zebrs, Wid nd when questioned quesuoncd by r son, scm, lell tell him y lhcy re zebrs. Do know kmw y re rc zebrs? Well, mos most us would hve little ble hesittion hesirdon in sying tht we did know th. We know wht zebrs look like, nd, sides, sides. th che city ZOO ux, nd nimls re in pen clerly mrked "Zebrs: "Zebrs." Yet, Y, something's ing zebr implies tht it not nol mule Wid, nd. in pniculm, prticulr, not mule muk cleverly ckverly dgued by ZOO ux, uthorities 10 to look like.zein. zebn. Do know tht se nimls re rc not mules cleverly dgued by he zoo uthorities 10 to look lmk lke O 7.ebrs? 7ebr97 f re rc empled lcmpted 10 to sy Yes" "Yes" 10 to th question, quesuon, think moment bout wht re!ons RBSDR~ hve, whl whr evidence cn produce in fvor hv thi., th clim. The evidence hd hrd (or for thinking m zebrs hs en cn effectively eltwtively DCulllil.ed, neutrliml, since it tioes clws not countlowllfd nwrd ir thlr not ing mules muler cleverly dgued 10 to look like zebrs. zebm. You hve some generl uniformities uniformiues on which rely, rdy. regulrities 10 to which yoo give expression by such rellllllb remrlcs s "Th "Thr n't very vy likely" or "Why 'Why should zoo uthorilies uthorities do tht?" Grnled, Grnted. hypos (if we my cll it thi) tht) not very plusible, plusible. given wht we know bout people pcople nd zoos. But question he'c here not wher whew th lerntive lterntive plusible, plusible. not wher it more or less plusible thwi thn tht re re rc rel zebrs zebm in lhc pen, pen. but wher know brow tht th lterntive lmdve hypos flse. don't think cto2. doz. 13

2 14 14 JONATHAN VOGEL ARE THERE COUNTEREXAMPLES TO THE CLOSURE PRNCPLE? _ 15 S According to Dretske, Zebr Cse counterexmple to closure cuse know () nimls in in pen re zebms, zebrs, but don't know cler logicl consequence (), nmely,(b) nmely.(b) nimls in in pen ren't cleverly dgued mules. find th description sitution implusible. Given wht Dretske hs sid in in lying out exmple, think it it more resonble to conclude tht if if know () know (b) s well, nd closure preserved fter ll. The reson know tht n niml in in pen not dgued mule (if do know it's zebm) zebr) tht hve true lief to tht effect bcked up by good evi evi- dedence. Tht evidence includes bckground informtion bout nture nd function zoos. You know tht zoos genemlly generlly exhibit genuine specimens, nd tht it it would gret del trouble to to dgue mule nd to to substitute it it for zebm. zebr. Only under most unlikely nd bizrre bizm circumstnces, if if t t ll, would such substitution mde, nd re no reson whtsoever to to think tht ny such circumstnces obtin. f f did feel re ws chnce tht switch hd en mde, would hve reson to doubt lht tht niml see zebt. zebr. You would nol, not, n, n. know th tht it it zebr, contmry trmy to to wht ws wr ssumed. ssctmed. con- Dretske's motivtions for denying tht know ren't seeing dgued mule re not fully cler. He himself grnts tht "hypos" tht niml relly mule "not very plusible", yet dds BUl But question here nol not wher whc~hcr lh th llcmlive llcmtive plusible, plusible. nol not whelher wher il it more or or less plusible thn thl cht lhere re re rel zebr~ zebrs in in pen, pen. bul but whelher wher /cnow know thl cht lh th llcmlive llcmlive rlse. rlsc.3 3 One might hve thought tht if if lief much more plusible thn its its denil, person would justified in in ccepting tht lief. And, And. n, brring Gettier-like complictions, complictions. tht person's lief, if if true, would knowledge. kn~wledge.~ 4 Perhps Dretske's point th: When look t t pen where niml,, hve evidence tht re zebm zebr re, re. nmely tht niml looks like zebm. zebr. Your vul evidence does not, though, give ny support to to r lief tht niml re seeing n't dgued mule. For, For. if if it it were dgued mule, mule. r vul experience pcrience would just s s it it.. As Dretske sys, sys. "The evidence hd for thinking hem m zebrs hs en effectively neutrlized, since it it does not count towrd ir not - exing mules cleverly dgued to to look like zebrs".s zebrs".5 The upshot tht do know re zebm, zebr. since hve true lief to to tht effect supported by evidence. You do not nor know tht niml n't dgued mule, since r lief in in th cse true but not supported by by vilble evidence. So, know first proposition, but don't know its its cler logicl consequence. indicted bove why think th nlys incorrect. Your bckground knowledge does give justifiction for denying tht niml mule, so so know tht it it n't one. Still, it it my pper tht possibility filure for Closure Principle res out sitution s s descrid it. it. t t seems tht usul dequte evidence for clim "t's zebr" (i.e. vul evidence) different from bckground evidence which supports "t's not cleverly dgued mule." f f so, so. could conceivbly in in position where hd vul evidence nd knew re ws bckzebr, but lcked bckground knowledge, nd hence didn't know re wsn't dgued mule. n such circumstnces, Closure Principle would fce counterexmple. To my mind, th pprl bsed on n overly tomtic conception evidence nd justifiction. Your lief tht niml t t zoo zebm zebr justified in in prt by r vul evidence, but it it lso supported by bckground informtion tht counts ginst niml's ing dgued mule. By itself, vul evidence wouldn't sufficient to give knowledge tht re zebr. To see th, consider cse where proper bckground knowledge lcking. mgine tht re driving through rnchlnd out West nd for some reson or or stop by rodside, rodside. Across wy see blck nd white striped equine creture tmnquilly trnquilly grzing gzing in in its pen. n n situ situ- counterextion th sort, it it seems to to me, it it fr from cler tht could know niml - -fore to zebm, zebr, even though it it looks just s much like zebr s s niml in in zoo does. The difference here tht hve no pplicble bckground informtion which mkes it it more likely tht zebm-like zebr-like niml relly zebr mr rr thn n oddly colored mule. So, even bck t t zoo, r justifiction tht wht see zebr depends on bckground bnckground informntion inform~~tion --just s ns justifiction j~~stifiction for r denil tht it's dgued mule would so depend."l'here h There no dcrepncy dcrepnncy here which provides grounds for thinking tht Closure Principle flse. One might object tht defense closure just given mkes unrelticlly high demnds so fr s s evidence concemed. concerned. A ng child t t zoo, zoo. seeing n niml tht resembles n illustrtion in in picture book might point nd hppily sy "Zebm''', "Zebr!". Despite fct tht child knows nothing bout how zoos work, doesn't tht child know niml zebr? The sues here re complex, but re re vrious resons not to to tke th objection s s decive. First, even if if it it grnted tht child knows in in full sense tht niml zebr, zebr. if if he or or she n't cpble dmwing drwing inference bout dgued mules, child's cse doesn't r on vlidity Closure Principle. Moreover, it's uncler tht, under circumstnces, child relly ought to descrid s s knowing tht niml zebr. Suppose tht child cn't concejr concep- infertully dtinguh tween 'looks like n n zebr' nd ' ' zebr'. Perhps child knows only tht niml it it sees looks like zebr, nd wouldn't know tht niml zebr without cquiring furr conceptul resources nd informtion.' inf~rmtion.~ CAR THEFT THET CASES hve mintined tht Dretske's Zebr Cse does not fumh furnh counterexmple to to Closure Principle. But wht hve sid so so fr fr rs lrgely on on prticulr detils cse s s Dretske sets it it up. H remrks point towrds formultion exmples which cnnot treted so so strightforwrdly. cll se "Cr Theft Cses", for resons which will come cler in in moment. t t my,. in in fct, tht Zebr Cse properly understood one se. Suppose own cr which prked few hours go on on side street smt in in mjor metropolitn re. You rememr clerly where left it. it. Do know where r cr? We re inclined to to sy tht do. Now it it true tht every dy hundreds crs re stolen in in mjor cities United Sttes. Do know tht r cr hs not en stolen? Mny people hve intuition tht would not know tht. f f th intuition combined with previous one, n it it seems tht closure principle

3 16 JONATHAN VOGEL VCGEL ARE THERE COUNTEREXAMPLES TO HE THE CLOSURE PRNCPLE? violted. Tht : You know proposition 'My cr now prked on (sy) Avenue A'. You lso know tht tht thnt proposition entils (q) (9) 'My cr hs not en stolen nd driven wy from where it ws prked'. Yet, it seems. seems, do not know q. 9, despite fct tht it for cler logicl consequence p. p, which do know. Since, in th instnce:, instnce, (pprently) fil to know cler logicl consequence proposition do know, know. Oosure Closure Principle (pprently) violted. Th exmple turns on rr unusul feture cler logicl consequence q. 9. Given r evidence. evidence, tht proposition much more probble thn not, nd it t lest s likely to true s p. To tht extent, it seems s though should s justified in lieving q s re in lieving p. Neverless, Neverless. even though r lief tht p, if true, me, my knowledge, r lief tht q, 9, if true, not. You do not know tht r cr hsn't en stolen by someone nd driven wy, despite high probbility tht r lief to tht effect true. n th respect. respect, r lief tht q resembles someone's lief tht ticket, which he holds, holds. will not win fir lonery. lottery. No mtter how high odds tht ticket will not win. it strikes us tht ticket-holder doesn't know tht h ticket will w~ll not win. n fct, fct. nlogy tween subject's lief bout holding losing lottery ticket nd one's lief tht one's cr hs not en stolen goes even furr thn th nd quite illumint illumint- ing. A numr fetures lottery sitution re especilly relevnt here. First, lthough winning lottery on pniculr prticulr ticket unlikely or improbble, it would not bnorml in some intuitive sense, for it it to tum turn out tht ticket one holds hppens to winner. Second, Second. even though weight evidence certinly ginst ny prticulr ticket's winning, re still some sttticl evidence in fvor proposition tht certin pniculr prticulr ticket will win. i. i. e. re some (smll) reson to think pr pr- prticulr ticket-holder will win.s 8 A third importnt considertion tht, with respect to its chnces winning lottery. ech ticket indtinguhble from every or one. So, ny reson hve for thinking tht r pniculr prticulr ticket will lose would n eqully good reson for lieving ny or ticket in lottery tht it. it, too. too, will lose. Under se circumstnces, circumstnces. it it would rbitrry to lieve some tickets (including r own) but not ors tht y will not win. So, So. if re constent rr thn rbitrry, nd do conclude on bs evidence vilble tht r ticket will not win, will conclude sme every or lottery ticket. Neverless, hold lief tht some ticket or or will win. On pin rbitrriness. rbitrriness, n. n, it it seems tht cn't justifibly hold both tht r ticket will lose nd tht some ticket will win. A fortiori, cn't know tht r ticket will lose nd tht some ticket will win. win? 9 Now, Now. in certin importnt wys, one's eptemic sitution with respect to lottery like one's eptemic sitution in Cr Theft Cseyl C~e.~" n effect. when prk r cr in n re with n pprecible rte uto ft, enter lottery in which crs nre re picked, essentilly t rndom, to stolen nd driven wy. Hving r cr slolen stolen unfortunte counterprt counterpn to winning lottery. And, just s one doesn'l doesn't lotknow tht one will not hve one's numr come up in lottery, it it seems one doesn't know tht one's numr won't come up. up, so to spek, for cr heft. ft. To more prticulr, lieving tht r cr won't stolen like lieving won't win lottery, in wys just cnvssed. () f prk r cr in n re with high rte cr ft, n re where it virtully certin tht some cr like rs will stolen, it would not bnorml for r cr to stolen. (2) n Cr Theft Cse, r knowledge tht re considerble mount uto ft gives some rel sttticl reson to think cr will stolen.1 11 (3) t would rbitrry rbitmy to lieve tht r cr, but nol not ll ors relevntly similr to it, won't stolen. n generl, if person fils to know proposition cuse considertions like se, will wilicll proposition not known louery lotteryproposition. The point th extended compron lottery nd Cr Theft Cse hs en to try to chrcterize fmily pprent counterexmples to Closure Principle. The essentil feture se exmples tht y re cses in which cler logicl consequence known proposition itself lottery proposition meeting criteri just dcussed. Wht mkes Zebr Cse, in my opinion, weker potentil counterexmple to Closure Principle thn Cr Theft Cse, just fct tht. ~e c1e~ cler log: log- counterexicl consequence 7.ebr &br Cse hrder to see s lottery proposllon. proposition. First, First. t it would bnorml for dgued mule to in zoo uw, enclosure mrked "Zebrs". "Zebrns". Second, s Dretske descris exmple, exnrple, it n't pprent tht hve ny reson (sttticl or orwe) to think that tht re might dgued mule in zebr pen. These two weknesses re rc relted to third: it difficult to see presence dgued mule in zebr pen s outcome ny lottery-like process. Tht, it not s though know tht dgued mule hs en plced in some zebr pen in some zoo chosen t rndom. n tht cse, ny reson hd for thinking tht ni ni- dml hppen to see n't dgued mule would pply in every or sitution. You would, n, hve to conclude tht no zoo_ zoo- hd dgued mule running round - in contrdiction with wht know to cse, viz. re dgued mule in some zoo m somewhere. However, th kind lottery element n't present in Zebr Cse s Dretske descrid it. So, it uncler why, s Dretske mintins, do not know tht striped niml fore n't dgued mule.12 ll CAR THEFT CASES AND SKEPTCSM would like to tum turn now to implictions Cr Theft Cse. Tht cse supposed to COUnt count s counterexmple to Closure Principle. For, For. in Cr Theft Cse, seem to know proposition proposition bout where r cr,. but pprently fil to know nor proposition which cler logicl consequence first one. f will mintin low tht tking Cr Theft Cse in th fshion, fshion. s counterexmple to closure, not only, only. or st wy, to understnd it. But, suppose tht Cr Theft Cse does stnd s counterexmple to closure; does tht relly help us with problem skepticm? The thought ws tht C,lr Ci~r Theft Cse would show tht closure n't vlid vr~lid in generl. Then skeptic's relince on tht principle in course rgument from deception would illegitimte, nd nrgument rgument wouldn't go through. However, wht Cr Theft Cse relly shows bout Closure Principle, if if it it shows nything t ll, ll. tht tht principle invlid when cler logicl consequence involved lottery proposition with fetures mentioned bove. The Cr Theft Cse gives us no reson to think tht closure fils to hold for cler logicl consequences which don't stfy those criteri.

4 18 JONATHAN VOGEL ARE THERE mere COUNTEREXAMPLES TO THE CLOSURE PRNCPLE? 19 The question t th point wher cler logicl consequence in skeptic's rgument lottery proposition in specified sense. The cler logicl consequence skeptic invokes something like ' m not brin in vt thoroughly deceived by sinter neurophysiologts'. And th clerly not lottery proposition stfying three criteri hving to do with bnormlity, relince on sttticl evidence. evidence, nd non-r- non-rbitrriness. Let me tke se out order. (1) f skeptic's logicl consequence were lottery proposition. proposition, would hve to n indtinguhble memr clss sub- subjects which it known tht t lest one memr brin in vt (mking it rbitrry for me to lieve tht 'm not such brin). Th hrdly cse, since 1 don't know tht re rt re ny brins in vts nywhere. The lottery-like element which ws crucil to smcture structure Cr Theft Cse refore lcking here. (2) Moreover, since re no reson to think tht some brins re put into vts s mtter course, it might well bnorml. bnonnl, in n intuitive sense, for someone to turn tum out to brin in vt. (3) Finlly, given (), re no bs for ssigning rel, positive sttticl probbility to proposition tht someone brin in vt. The force se observtions tht sitution in which skeptic invokes closure cnnot esily ssimilted to situtions like Cr Theft Cse, in which re some reson to think closure fils. Hence, Cr Theft Cse s such gives little support to clim tht Closure Principle fils when skeptic ppels to it. Th mens tht Cr Theft Cse provides no convincing bs for rejecting Deceiver Argument. t my tht, if Crtesin skepticm sue, no more needs to sid bout Zebr Cse or Cr Theft Cse. will, however, pursue question wher Cr Theft Cse genuine counterexmple to Closure Principle. Aside from whtever intrinsic inmnsic interest tht question my hve, it worth seeing tht results strengn, rr thn weken, conclusion tht se exmples do not undercut skejr skepticm. V 1V THE NTERPRETATON OF NTUTONS NTUTTONS ABOlT ABOUT me THE PROBLEM CASES The Cr Theft Cse nd its nlogues provide counterexmples to Closure Principle if we tke our intuitions bout such cses t fce-vlue. fctvlue. For, n, it seems tht in circumstnces descrid, person my know some proposition (e.g. 'My cr on Avenue A, where prked it') yet not know cler logicl consequence tht proposition (e.g. 'My cr hsn't en stolen nd driven wy from where it ws prked'). t's worth noting, though, tht some dditionl rections people hve suggest tht closure preserved in se situtions fter ll. Often, when fced with possibility tht ir crs might hve en stolen, people withdrw, t lest temporrily, ir initil clims to know where ir crs re. Such response just wht Closure Principle would require. Now, think it must dmitted tht intuitions we hve here re wek. t would difficult to find decive support for closure in tendency people hve to cllnge chnge ir minds in wy just mentioned. Still, fct tht Closure Principle seems to respected to extent tht it provides motivtion for nlyzing tht cse in wy tht doesn't presuppose filure closure. possi- The problem fcing ny such nlys to ccommodte or dcredit intu- intuitions tht produce impression closure filure in first plce. Those rt re intuitions which led us to sy, first, tht person, under certin circumstnces, would know some proposition, nd, second, tht person doesn't know cler logicl con- consequence tht proposition. One wy trying to reconcile se intuitions with closure to rgue tht some kind shift tkes plce tween se responses. The clim would n tht, for no fixed set circumstnces, do we regrd subject s knowing proposition while filing to know one its cler logicl consequences. Certin psychologicl studies provide independent resons to lieve tht shift th kind tkes plce. These studies concern people's ttitudes towrds improbble events. They re relevnt to Cr Theft Cse cuse essentil role plyed in 1 i tht cse by unlikely possibility tht r cr hs en stolen. f closure does fil 1 here, it cuse possibility ft, though highly improbble, undercuts clim! tht know tht r cr hsn't en stolen, even while tht possibility somehow leves intct r knowing tht r cr t certin spot. n studies mentioned, it hs en found tht people my mt tret improbble events eir s likelier thn y relly rc re or s hving essentilly no chnce occurring. Moreover, se ssessments rc re unstble, nd subjects cn esily influenced to grnt possibility more weight thn orwe, if tht possibility mde slient to m.13 mp Such psychologicl considertions provide n explntion for our intuitions bout Cr Theft Cse. nitilly nd generlly, in evluting knowledge clims in tht cse, we tret chnce r cr's ing stolen s essentilly zero. You cn, n, n. s sure s need to tht r cr where left it; re rt fully justified in tht lief. Thus, we re rc likely to sy without hesittion tht in sitution descrid know where r cr. Lter, however, when we dwell on rte cr ft, ft. chnce r cr's hving en stolen lent more weight. Given (now) significnt possibility tht my wrong in lieving tht r cr hsn't en stolen, we re rc no longer prepred to sy tht know it hsn't en stolen. And, viewing sitution in th light, giving weight to chnce tht cr n't where left it, we my inclined to go on to sy tht don't know where cr fter ll. Tht, re seems to motivtion to deny r initil knowledge clim in set circum circum- signiftnces where cnnot clim to know cler logicl consequence wht thought knew. n tht wy, wy. Closure Principle respected. n short, fct tht t one time we would sy tht know loction r cr, nd tht shortly refter we might sy tht don't know r cr hsn't en stolen, does not estblh invlidity Closure Principle. For, it my tht t no one time do we ffrrm ffirm tht know something yet fil to know one its cler logicl consequences. t doubtful, n, tht Cr Theft Cse, when properly understood, provides counterexmple to Closure Principle. hve suggested tht nomlous non>lous chrcter our intuitions bout Cr Theft Cse my due to some kind eptemiclly importnt shift rr thn to clo clo- unsure filure. My conjecture hs en tht shift chnge in probbility ssignment, but or mechnms my t work insted. An lterntive explntion our intuitions tht we re somehow induced to shift our sense degree ssurnce knowledge requires. Thus, our estimtion chnce subject could wrong - ssigncuse cr ft would remin constnt, but we would chnge our minds s to wher

5 20 JONATHAN VOGEL knowledge constent with tht level eptemic rk. There re still or forms shift could tke. t might even tht thnt movement in Cr Theft-type situtions tween wholly dtinct notions knowledge embodying different sets necessry nd sufficient conditions. For my purposes, detils wht ctully occurs re reltively unimponnt. unimportnt. The min point wh to mke tht re re explntions or thn closure filure for our intuitions bout Cr Theft Cses}4 Cses.14 Or, to put it differently, strightforwrd ppel to those intuitions insufficient to estblh tht Closure Principle does not hold without restriction. V TlE THE PROBLEM OF SEM-SKEPTCSM SEM-SKEmlCSM hve just rgued tht simple inspection our intuitions bout Cr Theft Cse does not conclusively refute Closure Principle. The dvocte closure cn clim tht Closure Principle only ppers to fil, s result n eptemiclly imponnt importnt switch tht tkes plce in course our thinking bout exmple. However, clim th son leves open wht subject, in fct, does nd doesn't know in Cr Theft-type situtions. The Closure Principle fces strong objection to effect tht it incomptible with ny cceptble ccount wht known in Cr Theft Cses. f closure holds, nd some uniform stndrd knowledge pplies cross bord, bord. eir don't know where r cr, or do know tht it hsn't en stolen. The ltter clim seems hrd to sustin. Th impression strengned by similrity tween Cr Theft Cse nd rel lottery sitution. Knowing tht r cr hsn't en stolen would, in wys 've mentioned, like knowing someone will lose fir lottery. And tht seems like son thing one doesn't know. So, So. given untenbility sying tht know r cr hsn't en stolen, stolen. Closure Principle will require tht, contrry to wht we might hve thought, don't know where r cr. Th result seems unwelcome, nd things worsen quickly. t turns out tht, propositions bout externl world which we tke ourselves to know, gret mny entil lottery propositions s in Cr Theft Cse. (The propositions with se con con- Princequences re, specificlly, propositions bout current stte world yond our immedite environments). To see rnge Cr Theft-type cses consider some orexmples: exmples: Bush Cse: Q. Do know who current President United Sttes? A. Yes, it's George Bush. Q. Do know tht Bush hsn't hd ftl hen ttck in lst five minutes? A. No. LuncheonetteCse: Luncheonettecse: Q. Do know where cn get good hmburger? i t ARE mere THERE COUNfEREXAMPLES COUNTEREXAMPLES TO THE CLOSURE PRNCPLE? 21 A. Yes, Yes. re's luncheonette severl blocks from here. Q. Do know tht thnt fire hsn't just broken out re? n? A. No. Meteorite Cse: Q. Do know wht stnds t mouth Sn Frncco By? A. Yes, By spnned by Golden Gte Bridge. Q. Do know tht Bridge wsn't just demolhed by flling meteorite? A. No. t's pprent tht vritions vuritions on se cses cn constructed for ny numr propositions bout people, things, or ctivities. Tht to sy, ll propositions bout such mtters, which we tke ourselves to know, entil lottery propositions which, it seems, we do not know. f closure holds, long with intuition tht we do not in fct know cler logicl consequences in question, question. result tht we hve gret del less knowledge world thn we hd supposed. n or words, Qosure Closure me- Principle leds, even without rgument from deception, to firly strong nd unpltble semi-skepticm. The cse ginst closure ppers tht much stronger. But does thret semi-skepticm relly count ginst Closure Principle? The key ide here tht re supposed to some feture which lottery proposi proposi- untions in Cr Theft Cses shre with propositions bout genuine lotteries, in virtue which we cn't correctly descrid s knowing those propositions. Wht tht feture? One nswer tht, cuse sttticl probbility tht r ticket my win in genuine lottery, re "rel" possibility error in lieving tht will lose. n or words, crucil lief in se circumstnces lcks kind certinty, nd hence cn't count s knowledge}s kno~ledge.~~ Similrly, lottery propositions which figure in Cr Theft Cses re sllch such tht "rel" possibility exts tht y re flse. Since, refore, refore. subject cn't cenin certin truth se lottery propositions, subject cn't know m. By Closure Principle, it would follow tht subject cn't hve knowledge propositions which he knows to entil those lottery propositions. Th would result, resull fes we hve seen, in pervsive semi-skepticm. The imponnt thing to relize bout th wy viewing mtters tht it doesn't relly justify concluding tht Closure Principle invlid. For, ccording to objection, jection. lesson genuine lottery exmples tht lief cn't knowledge if re "rel", "rel". nd not merely logicl, possibility tht subject wrong bout it. f th correct, n semi-skepticm follows without Closure Principle. After ll, ll. obre "rel" possibility tht, e. g. my wrong in lieving tht r cr t cenin certin spot; it possible tht r cr hs en stolen. The sme point pplies, mutt ltmutnd, to ny or Cr Theft Cse. So, perhps, re legitimte eptemo epteme mulogicl problem in thret semi-skepticm derived from certinty requirement for knowledge. However, since rejecting closure won't void tht problem, tht problem doesn't provide reson for denying Closure Principle's vlidity. On nor wy nlyzing lottery exmples, exn~ples, unknowbility in se contexts propositions like 'My ticket will lose' due to rbitrriness ccepting

6 22 JONATAN JONATHAN VOOEL VOGEL ARE THERE COUNTEREXAMPlES COUNTEREXAMPLES TO THE CLOSURE PRNCPLE? 23 ny proposition tht fonn. form. By nlogy. nlogy, in in Cr Theft Cse. Cse, wouldn't know proposition 'My cr hs not en stolen'; re reson to to think tht some cr or crs similr to to rs will stolen, nd hve no non-rbitrry non-rbiry ground for lieving tht r cr in in prticulr won't one (or one ones) stolen. Once more, it it looks s though ll dl knowledge clims bout lottery propositions in in or Cr Theft cses would undercut by similr considertions. Then, semi-skepticm will inevitble if if closure holds. Here gin, though, though. m inclined to to think tht re no rgument to to found ginst Closure Principle s s such. The nlys lottery effect now ing entertined mkes following ssumption: ll ll or things ing equl, it it unjustified to to enterccept ny memr set propositions L. L, such tht memrs L re equiprob- ble nd subject knows (or hs good reson to to lieve) tht t t lest one memr L flse.16 t t turns out tht th principle sufficient to to estblh semi-skepticm regrdless vlidity Closure Principle. To see why th might so, let's tke Cr Theft Cse s s bsic model. The present ttempt to to uch ttch burden semi-skepticm to to Closure Principle mounts to to clim tht non-rbitrriness requirement just stted defets r clim to to know lottery proposition tht r cr hsn't en stolen -- while it it leves intct r clim to to know proposition (i.e. 'My cr on Avenue A, A, where prked it') clerly entiling tht lottery proposition. But entiling proposition itself memr set equiprobble propositions which, which. hve good reson to to lieve, contins t t lest one flsehood. Tht set contins, long with 'My cr on on Avenue A, A. where prked it', propositions like 'My neighbor's cr semi-skeptiwhere he he prked it', it'. 'The postmn's cr where he he prked it', nd so so on. You my not ble to to stte ll ll memrs set explicitly. explicitly, but still hve very good reson to to think tht re such set L. L. By non-rbitrriness requirement, it it would follow tht don't know Originl originl proposition 'My cr on on Avenue A, A, where prked it'p it'.17 The sme line thought would seem to to pply to to ny cse Cr Theft-type where knowledge lottery proposition blocked by by non-rbitrriness constrint. So, if if non-rbitrriness condition strong enough to to estblh ignornce cross bord for for lottery propositions, it it lso strong smng enough to to estblh ignornce propositions which. in in Cr Theft cses, cses. entil lottery propositions. Tht to to sy, if if non-rbitrriness condition plus closure genertes semi-skepticm, so so too does non-rbitrriness condition lone. Therefore, opponent closure cnnot use tht condition s s bs for for n n rgument tht Closure Principle invlid cuse it it would led to to semi-skepticm. The preceding dcussion mkes clerer wht would required in in order to to mke cse ginst closure work. The critic Closure Principle hs to to identify some wy in in which liefs in in lottery propositions re re eptemiclly defective. defective, nd th defect must not shred by by mundne liefs whose contents, in in Cr Theft cses, re known to to entil those lottery propositions. t t n't esy to to see wht such defect would,, if if not not ones just considered.18 S n n th section, 1 hve tried to to show tht our nomlous intuitions bout Cr Theft Cses nd relted thret semi-skepticm relly hve little to to do do with closure. No NO ttempt hs en mde here to to give fully cceptble positive ccount wht relly known in se cses, nd suspect tht such n ccount my not vilble t ll. For it it my tht Cr Theft Cses toger with problem semi-skepticm reflect deep-seted, unresolved conflicts in in wy we think bout knowledge.19 V CAR THEFf THEFT CASES AND RELEVANT ALTERNATVES TVES t t tempting to to think tht omsion positive ccount wht we know could mde good by dopting version relevnt lterntives pproch to to knowledge.20 Th pproch promes ll ll dvntges, without defects, tretment just given. n n my view, view. tum turn to to relevnt lterntives pproch not dvble, but proposl interesting nd deserves considertion. According to to relevnt lternntives ltem~ives ort, ort. demnds demiincls for knowledge re restricted nd contextul. On one version ory, ory. S knows thut tht p just in in cse S possesses evidence which COunts counts ginst ll ll relevnt ltemtives ltenltives to to p; p; on on nor fonnu formu- reltion, S knows tht p just in in cse S would right bout p over some clss relevnt lterntive situtions. A mjor problem for for relevnt lterntives pproch to to explicte crucil notion relevnce it it invokes. Relevnce lterntives will vry c c- explicording to to subject's sitution; it it my lso (depending on on detils ory) detennined determined by by content subject's lief nd context ttribution thibution for for knowledge clim. f f stndrd relevnce oys certin constrints, relevnt lterntives ory my used to to explin intuitions bout Cr Theft Cses in in wy tht doesn't deny vlidity Closure Principle. How would th go? Suppose fcts re s s descrid in in Cr Theft Cse. nitilly, we we operte with stndrd relevnce ccording to to which possibility l- Cr Theft too remote to to considered. At At th point, fct tht would wrong bout loction r cr, cr, hd hd it it en stolen.21 stolen>l doesn't impir clim tht know where r cr cr.. Moreover, since possibility cr cr ft remote, tht tht possibility doesn't undercut clim tht know r cr hsn't en stolen. Closure sure mintined. Wht produces impression to to contrry? When possibility cr cr ft explicitly red, somehow new, more generous stndrd relevnce Cloinstted, ccording to to which possibility cr cr ft relevnt. By By th th stndrd, stndrd. know neir where r cr nor tht it it hsn't hilsn't en stolen. Closure still preserved. s s fore.22 There re re severl drwbcks to to nlyzing Cr Cr Theft Cses in in th th fshion. First, supposed vinue virtue nlys tht tht it it provides n n CCount ccount wht would nd wouldn't know in in circumstnces given. But in in giving such n n ccount, relevnt lterntives ort must must sy sy tht, tht, in in some sense or or from some stndpoint, ~ou would know tht r cr hsn't en stolen. Th seems plinly wrong, nd tntuition intuition tht tht it it wrong just just wht wht mkes it it so so hrd hrd to to give give n n dequte tretment Cr Cr Theft Cse Cse nd nd its its nlogues. The The relevnt lterntives pproch relly doesn't ccommodte body body our our intuitions in in n n unforced, convincing wy, wy, contrry to to wht one might hve hoped. Let Let me me tum turn to to furr point. The The relevnt lterntives ort hypolhesizes hyposizes tht, tht. in in problem cses, re shift in in stndrd eptemic relevnce. n n Cr Theft Theft Cse Cse specificlly, possibility cr cr ft ft supposed to to,, lterntively, too too remote nd nd not not too too remote to to relevnt. t t nturl to to presume tht tht "remoteness" here here

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