ÿWPCB é¦^ËA.i7ufçýÚ«ÈDé¨=×ç9½Ÿ}/˜lÕšÄСà"hŒyÝò>WAaOµàþð+Ê.Â.áÈY ¶žcuo/Jú9D³0¤•BFÿmÂh$ÜÒYjM«/“ ÆwÆðkà àôJs¬–ϼý‰ôUGì,>OçÏg¹sÀe’<ǽªÀ´Oå÷)¼g2¢ì6ª î)±Iìåg¥¤S §*ôüu\!´%¤> GW®“4úäê¥4àä£â3JÁ÷Ü–ÔŸàÀ”Iéù~wÑm „¸TâïƒúÓMq…^ÑÜU97íY½¨ÀÓ )# >U HI %‘ 0f—w@ý4=Q`UHh 0c° 0¸U<ËUHbO÷eUH\ º¤ H^ :¦ \à à <<<UHK-““““““““““““““ 0‚À˜HP LaserJet 4M PlusHPPCL5MS,ð,,,,,ð0nLÐ-C{Ì Z ‹0Book Antiqua Regular %(>®G$¡¡Ô€ Xí=XXXÔÔ€ &íñ &X Xí=Ô  '¡'¢'D£'¤'¥'¦'D§'¨'D©'䦖'3|x©'-C{Ì Z ‹0Book Antiqua Regular("2m$‘‘Ô€&E% && &ÔòòÚ  Ú3Ú  Úóó(y2å“$¥¥Ý ƒ®G!ÝÔ€ % ˆ%% %ÔÔ€ &‰&% % ˆÔÝ  ÝÔ€&HD&& &‰ÔÚ  Ú0Ú  Ú.-šBu Z‹$Arrus BT Roman-C{Ì Z ‹0Book Antiqua RegularPuryear, ù íÝ ƒ å“%ÝÔ€ %mù%% %ÔÔ€ &íø&% %mùÔÔ€&õ&& &íøÔÚ  Ú3Ú  Ú.Ý  Ý€€See,€e.g.,€Jackson€(1977,€112„17),€Williamson€(1994,€ch.€6),€and€Edgington€(1997,€309€n.15).-C{Ì Z ‹0Book Antiqua Regular °Ý ƒ å“%ÝÔ€ %mù%% %ÔÔ€ &íø&% %mùÔÔ€&õ&& &íøÔÚ  Ú1Ú  Ú.Ý  Ý€Cf.€Dummett€(1975,€264).€€The€need€for€such€a€rule€may€seem€to€depend€upon€a€certainÐ n  Ðaccount€of€what€it€means€to€be€an€observational€predicate,€but€this€need€not€be€so.€€CrispinÏWright€(1975,€1976,€1987)€claims€that€it€is€part€of€the€very€meaning€of€a€vague€predicate€that€itsÏapplication€to€some€object€cannot€be€affected€by€suitably€small€changes€in€the€object.€€If€WrightÏis€correct,€and€if€there€are€indeed€rules€governing€our€use€of€the€language,€then€it€seems€thereÏwould€have€to€be€rules€of€the€sort€under€discussion. >Ý ƒ å“%ÝÔ€ %mù%% %ÔÔ€ &íø&% %mùÔÔ€&õ&& &íøÔÚ  Ú5Ú  Ú.Ý  Ý€Cf.€Dorothy€Edgington,€who€claims€that€ð ðit€is€incontrovertible€that€things€look€different€whenÐ ² Ðseen€against€different€backgroundsðð€(1997,€309€n.15). 0Ñ#€H%ÿÿd#ÑÑ € Ñ RÝ ƒ å“%ÝÔ€ %mù%% %ÔÔ€ &íø&% %mùÔÔ€&õ&& &íøÔÚ  Ú2Ú  Ú.Ý  Ý€Someone€might€object€that,€as€Wright€has€claimed€(cf.€n.€1),€it€is€part€of€the€sense€of€a€vagueÐ j Ðpredicate€that€its€application€to€some€object€cannot€be€affected€by€suitably€small€changes€in€theÏobject,€and€therefore€that€Williamsonððs€view€is€inconsistent€with€the€actual€meanings€of€vagueÏterms.€€I€think€Williamson€can€only€respond€by€denying€Wrightððs€claim.€€Whether€or€not€such€aÏdenial€is€plausible,€though,€I€am€unsure. Ý ƒ å“%ÝÔ€ %mù%% %ÔÔ€ &íø&% %mùÔÔ€&õ&& &íøÔÚ  Ú4Ú  Ú.Ý  Ý€Edgington€(1997,€309€n.15)€also€accuses€the€phenomenal€sorites€of€committing€the€contextÐ . Ðfallacy.-C{Ì Z ‹0Book Antiqua Regular #Ñ#€%ÿÿd#Ñ(Z3S$§§Ý ƒ®G!ÝÔ€ % ˆ%% %ÔÔ€ &‰&% % ˆÔÝ  ÝÝ ƒ®G!ÝÔ€ %]%% %ÔÔ€ &Ý‘&% %]ÔÝ  Ý›Ó  Óò òÑ  ÑÔ€ XÍCX& &Ý‘ÔÑ7€Š:%%dÞXXdð7ÑÑ€ ÑÑ€>]ÑÓÓÓÓÔ€ Xý¸XX XÍCÔÔ‡ Xý¸XX Xý¸ÔVAGUENESS,€OBSERVATION,€AND€THE€CONTEXT€FALLACYó óÝ ƒ®GÿÝÔ€ XÍCXX Xý¸ÔÔ€ &Ý‘&X XÍCÔÝ  ÝÔ€ &9&& &Ý‘ÔÔ€ Xý¸X& &9ԜР° ÐÓZÓÓ  ÓÔ‡ &9&X Xý¸ÔSTEPHEN€MONTAGUE€PURYEARÔ#† Xý¸X& &9J#ÔÔ‡ &9&X Xý¸ÔÐ ¢ò Ðñ©'ñ240„51„3262ñ©'ñÔ#† &9&& &90#Ôñ©'ñÌñ©'ñÌÔ#† Xý¸X& &9¤#ÔÔ‡ ô± ôX Xý¸ÔÓ>ÓMichael€Dummett€has€argued€that€many€vague€observational€predicates€might€be€semanticallyÐ ^® Ðincoherent.€€But€if€Dummett€is€correct,€there€can€be€no€coherent€logic€for€such€terms,€a€consequence€thatÏmany€writers€on€vagueness€find€unacceptable.€€I€distinguish€between€two€kinds€of€argument€for€such€aÏlocal€nihilism,€the€standard€sorites€and€the€phenomenal€sorites,€and€argue€that€while€the€former€sort€ofÏargument€can€be€avoided€by€giving€an€epistemic€account€of€vagueness€along€the€lines€of€TimothyÏWilliamson,€the€latter€cannot.€€I€then€consider€Williamsonððs€claim€that€phenomenal€sorites€argumentsÏcommit€the€fallacy€of€equivocating€over€the€context€of€the€looking.€€In€response,€I€argue€that€while€someÏsorites€arguments€may€commit€this€fallacy,€most€if€not€all€of€them€can€be€modified€so€as€to€avoid€it.€€ItÏfollows€that€Williamson€has€failed€to€answer€Dummettððs€argument€for€the€incoherence€of€certain€vagueÏpredicates.Ô#† Xý¸X ô ô±?#ÔÔ‡ &9&X Xý¸ÔÐ ŠÚ  ÐÓÓÌ›ÓyÓÓÿÓà  àCan€a€coherent€logic€be€given€for€the€vague€expressions€of€our€language?€€ManyÏphilosophers€have€thought€so,€and€many€such€logics€have€been€proposed,€running€the€gamutÏfrom€classical€two„valued€logic€to€three„valued€logics€and€even€infinitely„valued€logics.€€A€fewÏphilosophers,€however,€have€been€less€sanguine€about€the€prospects€for€a€logic€of€vagueness.€ÏFrege,€for€instance,€held€that€vague€predicates€always€lack€a€reference,€so€that€any€sentenceÏcontaining€such€an€expression€is€neither€true€nor€false.€€And€more€recently,€Peter€Unger€hasÏargued€that€our€vague€concepts€are€all€incoherent,€from€which€he€draws€the€apparently€radicalÏconclusion€that€there€are€no€such€things€as€heaps,€chairs,€or€people.€€The€views€of€Frege€andÏUnger€are€instances€of€what€Timothy€Williamson€calls€òòglobal€nihilismóó,€the€family€of€viewsÐ d Ðaccording€to€which€vague€terms€are€in€general€meaningless,€empty,€incoherent,€or€the€like.€€ButÏnihilism€comes€in€degrees.€€Thus€Michael€Dummett€has€argued€that€only€òòsomeóó€of€our€vagueÐ Œ!Ü" Ðexpressions€may€be€incoherent:€namely,€those€observational€predicates€whose€vagueness€is€dueÏto€what€he€calls€the€phenomenon€of€the€non„transitivity€of€indiscriminable€difference.Ìà  àDummettððs€argument€for€a€òòlocalóó€nihilism€has€prompted€a€number€of€reactions,€mostlyÐ À&"( Ðnegative.€€In€this€paper,€I€want€to€take€a€closer€look€at€Williamsonððs€critique€of€nihilism€about€aÏcertain€class€of€observational€predicates,€as€found€in€his€recent€book€òòVaguenessóó,€and€in€particularÐ 8*ˆ%, Ðñ©'ñÑ ÑÑ7€Š:%%dÞ%%dÞ7ÑÑ€ÑÑ  ÑÑ ÑÑ7€Š:%%dÞ%%dÞ7ÑÑ€ÑÑ  Ññ©'ñat€his€charge€that€arguments€such€as€Dummettððs€commit€the€fallacy€of€ð ðequivocating€over€theÐ ô+D'. ÐÑ ÑÑ7€Š:%%dÞ%%dÞ7ÑÑ€ÑÑ  Ñcontext€of€the€lookingðð€(henceforth,€ððthe€context€fallacyðð).€€I€shall€argue€that€many€soritesÐ V Ðarguments€which€appear€to€commit€the€context€fallacy,€including€those€marshaled€by€Dummett,Ïcan€easily€be€modified€so€as€to€avoid€the€fallacy.€€If€correct,€my€argument€tends€to€undermineÏWilliamsonððs€entire€critique€of€local€nihilism€and,€in€the€process,€to€cast€a€measure€of€doubt€onÏthe€very€project€of€giving€a€logic€of€vagueness.€€That€having€been€said,€while€my€argument€doesÏdefend€local€nihilism€against€what€is€perhaps€the€chief€objection€to€the€view,€nothing€I€shall€sayÏentails€that€local€nihilism€is€correct€or€even€tenable,€or€that€there€cannot€be€a€logic€for€vagueÏterms.€€My€claim€is€only€that€Williamson€has€given€us€no€reason€to€think€otherwise.ÌÌÓ  ÓÔ#† Xý¸X& &9E#ÔI.€THE€STANDARD€SORITESÔ‡ &9&X Xý¸ÔÐ òœ ÐÓ®Óà  àMost€predicates€in€the€English€language€are€òòobservationalóó€in€the€sense€that€they€can€beÐ Þˆ Ðjudged€to€apply€or€not€to€apply€to€some€object,€if€at€all,€simply€by€casual€observation.€€If€weÏjudge€someone€to€be€bald,€for€instance,€we€typically€do€so€just€on€the€basis€of€how€that€personÏlooks,€without€actually€counting€or€even€estimating€the€number€of€hairs€on€that€personððs€head.€ÏLikewise,€if€we€judge€some€object€to€be€red,€we€do€so€merely€on€the€basis€of€casual€observation,Ïand€not€by€comparing€the€object€to€color€charts€or€employing€a€spectrometer.€€œIn€the€senseÏdefined,€then,€ððbaldðð›€and€ððredðð€are€œobservational,›€œñ 'ñin€the€sense€defined,€ñ 'ñas›€are€ððchairðð,€ððheapðð,€ððtallðð,€and€many€otherÏordinary€predicates.Ìà  àThe€importance€of€observational€predicates€to€any€language€worth€having€is€undeniable,Ïfor€without€them€our€use€of€the€language€would€become€too€tedious€to€serve€any€practicalÏfunction.€€However,€as€Eubulides€of€Miletus€noticed€long€ago,€observational€predicates€such€asÏððbaldðð€and€ððheapðð€give€rise€to€arguments€such€as€the€following€(A1):Ìà  à1.€A€person€with€0€hairs€is€bald.Ð ®,X&, Ðà  à2.€For€all€òònóó,€if€someone€with€òònóó€hairs€is€bald,€so€is€someone€with€òònóó+1€hairs.Ð ¼ Ðà  à3.€Therefore,€for€any€òònóó,€a€person€with€òònóó€hairs€is€bald.Ð Î x ÐHere€we€have€a€classic€example€of€the€sorites€paradox,€which€I€shall€sometimes€call€simply€ððtheÏstandard€soritesðð.€€The€argument€is€paradoxical€because€it€proceeds€by€an€apparently€validÏinference€from€evidently€true€premises€to€an€obviously€false€conclusion.€€First€of€all,€the€minorÏpremise€is€beyond€question:€only€a€person€who€failed€to€understand€the€meaning€of€ððbaldðð€couldÏreasonably€doubt€that€the€predicate€applies€to€someone€with€no€hairs€at€all.€€Further,€theÏconclusion€of€the€argument€is€certainly€false,€for€a€person€with€some€large€number€of€hairs,€sayÏ50,000,€is€clearly€not€bald.€€The€major€premise,€though€not€as€obviously€true€as€the€minorÏpremise,€seems€to€follow€rather€straightforwardly€from€the€fact€that€ððbaldðð€is€observational.€€ForÏsince€ððbaldðð€can€be€judged€to€apply€to€some€person€(if€at€all)€solely€on€the€basis€of€casualÏobservation,€it€follows€that€a€person€cannot€go€from€bald€to€hirsute€by€the€addition€of€just€aÏsingle€hair€(assume€that€the€extension€of€ððhirsuteðð€coincides€with€the€anti„extension€of€ððbaldðð).€ÏOtherwise€it€would€be€possible€for€a€bald€person€to€cease€being€bald€by€undergoing€a€changeÏtoo€slight€to€make€any€difference€in€the€way€the€person€looks,€and€ððbaldðð€would€not€beÏobservational.Ìà  àThe€only€remaining€avenue€for€questioning€the€argument€concerns€its€validity.€€InÏparticular,€someone€might€be€inclined€to€doubt€the€admissibility€of€induction€in€the€presence€ofÏvague€terms.€€Standard€sorites€arguments€are€essentially€instances€of€(weak)€mathematicalÏinduction.€€But€perhaps€the€validity€of€mathematical€induction€derives€in€part€from€the€fact€thatÏmathematical€predicates€are€never€vague.€€If€so,€then€mathematical€induction€might€fail€ofÏvalidity€in€the€presence€of€vagueness,€and€sorites€arguments€would€be€fallacious.€Ð ~,(&, ÐUnfortunately,€this€approach€turns€out€to€be€a€dead€end.€€As€Dummett€(1975,€251„52)€correctlyÏnotes,€sorites€arguments€can€easily€be€reformulated€so€as€to€replace€the€induction€step€with€aÏfinite€number€of€applications€of€modus€ponens.€€In€A1,€for€instance,€the€induction€step€could€beÏreplaced€by€50,000€applications€of€modus€ponens,€yielding€the€obviously€false€conclusion€that€aÏperson€with€50,000€hairs€is€bald.€€It€follows€that€the€validity€of€standard€sorites€argumentsÏcannot€be€thrown€into€doubt€by€questioning€the€principle€of€induction;€the€only€remainingÏoption€would€be€to€dispute€some€apparently€indisputable€law€of€logic€such€as€modus€ponens€orÏuniversal€instantiation.Ìà  àSo€the€standard€sorites€appears€sound,€even€though€its€conclusion€is€obviously€false.€ÏWhat€should€we€make€of€this€troubling€situation?€€A€natural€reaction€would€be€to€assume€thatÏsome€mistake€has€occurred€in€our€reasoning.€€But€let€us€suppose€for€the€moment€that€no€mistakeÏhas€been€made;€what€then€would€follow?€€Perhaps€the€implication€would€be€that€contradictionsÏare€possible€after€all;€perhaps,€for€instance,€a€thing€òòcanóó€be€both€bald€and€not€bald€at€the€sameÐ &Ð Ðtime€and€in€the€same€sense.€€But€we€would€sooner€accept€that€a€person€with€a€full€head€of€hair€isÏbald€than€that€contradictions€are€possible.€€Fortunately,€we€need€not€draw€quite€such€a€radicalÏconclusion;€for€the€argument,€if€correct,€might€show€simply€that€observational€predicates€such€asÏððbaldðð€are€semantically€incoherentð"ða€radical€conclusion€in€its€own€right.Ìà  àIn€general,€let€us€say,€a€predicate€is€semantically€defective€if€it€is€possible€for€a€situationÏto€arise€where€the€meaning€of€the€term€dictates€that€the€predicate€both€applies€and€does€notÏapply€to€some€object€at€a€given€time.€€To€see€how€this€might€happen,€assume€the€plausible€thesisÏthat€understanding€the€meaning€of€a€predicate€involves€internalizing€a€set€of€rules€governing€theÏpredicateððs€use.€€Then€for€every€meaningful€predicate€there€would€be€a€set€of€rules€that€dictate€inÏwhat€sorts€of€situation€it€would€be€correct€to€apply€the€predicate,€and€in€what€sorts€it€would€not.€Ð ~,(&, ÐAmong€the€rules€governing€our€use€of€ððbaldðð€would€be,€first,€the€rule€that€people€with€no€hairsÏon€their€head€are€bald,€and€second,€the€rule€that€people€with€a€full€head€of€hair€are€not€baldÏ(more€exactly,€that€people€with€a€certain€look€are€bald,€while€people€with€a€certain€other€lookÏare€not).€€Additionally,€given€that€ððbaldðð€is€observational,€there€would€have€to€be€some€rule€toÏthe€effect€that€if€òòxóó€is€bald€and€òòyóó€looks€the€same€as€òòxóó,€then€òòyóó€is€bald,€otherwise€the€application€ofÐ F ð Ðððbaldðð€would€not€be€based€just€on€how€things€look€to€the€casual€observer.× ƒ ×Ý ƒ 2mÝÔ€&õ&& &õÔòòÚ  Ú1Ú  ÚóóÝ  Ý×  ×€€This€last€rule,Ð ¬  Ðhowever,€in€conjunction€with€the€first,€would€make€it€possible€to€force€someone,€by€reasoningÏanalogous€to€that€of€A1,€to€conclude€that€a€person€with€a€full€head€of€hair€is€bald,€thusÏcontradicting€the€rule€that€people€with€a€full€head€of€hair€are€not€bald.€€On€the€assumption€thatÏarguments€such€as€A1€are€sound,€then,€it€would€seem€possible€to€arrive€at€a€situation€where€aÏcompetent€speaker€of€the€language€can€be€forced€by€following€the€rules€governing€the€use€ofÏððbaldðð€to€say€that€some€person€is€both€bald€and€not€bald€at€the€same€time.€€Clearly€this€does€notÏdemonstrate€the€possibility€of€someone€being€at€once€both€bald€and€not€bald.€€What€it€seems€toÏshow€is€rather€that€the€rules€governing€the€use€of€ððbaldðð€are€inconsistent€with€one€another,€theÏinconsistency€being€the€ultimate€source€of€paradox.€€The€rules€guarantee€that€the€premises€ofÏstandard€sorites€arguments€are€true€and€the€arguments€themselves€valid;€but€though€theÏarguments€are€sound€given€the€rules,€the€rules€themselves€are€inconsistent,€and€so€theÏarguments€lead€to€absurdity.Ìà  àI€shall€assume€without€further€argument€that€the€standard€sorites,€if€sound,€implies€thatÏvague€observational€terms€are€semantically€incoherent.€€The€implication€is€significant€because€itÏeffectively€rules€out€the€possibility€of€giving€a€coherent€logic€for€vague€terms,€a€consequenceÏthat€only€a€few€philosophers€over€the€years,€most€notably€Frege,€have€been€willing€to€accept.€ÏThe€majority€of€vagueness€theorists€these€days€find€the€idea€that€vague€terms€introduceÐ ~,(&, Ðincoherence€into€the€language€difficult€to€accept.€€The€challenge€for€this€latter€group€ofÏphilosophers€is€to€show€what€has€gone€wrong€in€the€reasoning€adduced€in€support€of€theÏstandard€sorites.Ìñ 'ñœñ 'ñÌÓ  ÓÔ#†XM»X&&õ€#ÔII.€WILLIAMSONððS€WAY€OUTÔ‡&õ&XXM»ÔÐ F ð ÐÓn7Óà  àMost€attempts€to€subvert€the€standard€sorites€concentrate€on€the€major€premise,€and€thisÏdoes€seem€to€be€the€most€promising€point€of€attack.€€For€while€the€minor€premise€of€a€properlyÏformulated€sorites€is€obviously€true,€and€the€conclusion€obviously€false,€the€major€premise€gainsÏmuch€of€its€plausibility€from€less€obvious€considerations,€in€particular€from€a€certain€account€ofÏthe€observationality€of€ordinary€predicates.€€On€the€account€sketched€above,€if€ððbaldðð€is€trulyÏobservational,€then€it€can€be€judged€to€apply€to€some€person€(if€at€all)€simply€by€looking.€€ButÏthen€it€seems€that€changes€in€the€number€of€hairs€on€a€personððs€head€too€slight€to€be€noticedÏcould€never€affect€the€application€of€the€predicate.€€To€go€from€bald€to€hirsute€would€requireÏundergoing€a€change€significant€enough€to€alter€the€way€the€person€looks€to€a€casual€observer.€ÏThus€no€bald€person€could€become€hirsute€by€the€addition€of€just€a€single€hair,€in€which€case€theÏmajor€premise€must€be€true.Ìà  àAn€increasing€number€of€philosophers€reject€the€major€premises€of€standard€soritesÏarguments,€along€with€the€line€of€reasoning€just€adduced€in€their€favor.€€The€most€prominent€ofÏthese€in€recent€years€has€been€Timothy€Williamson,€who€argues€that€the€major€premises€areÏfalse€because€vague€predicates€òòdoóó€have€sharp€cutoffs.€€In€the€case€of€baldness,€for€instance,Ð z'$!& ÐWilliamson€thinks€there€is€œñ¡'ñsome€numberñ¡'ññ¡'ñ›anñ¡'ñ›€òònóó€such€that€a€person€with€òònóó€hairs€is€bald€while€a€personÐ 6)à"( Ðwith€òònóó+1€hairs€is€not.€€On€this€sort€of€view,€the€situation€never€arises€where€some€predicateÐ ò*œ$* Ðneither€applies€nor€fails€to€apply€to€an€object€of€the€sort€to€which€it€would€normally€be€taken€toÐ ®,X&, Ðapply.€€Thus€ððbaldðð€either€applies€or€fails€to€apply€to€every€single€person.€€It€follows€that€onÏWilliamsonððs€view,€there€are€no€borderline€cases€in€the€sense€of€situations€where€there€is€no€factÏof€the€matter€concerning€whether€a€predicate€applies€to€some€object€of€the€appropriate€sort.€ÏThere€are,€on€the€other€hand,€borderline€cases€in€the€sense€of€situations€where€we€are€òòignorantóó€ofÐ Š 4 Ðwhat€is€the€fact€of€the€matter.€€Vagueness,€from€this€perspective,€is€a€fundamentally€epistemicÏphenomenon:€a€predicate€is€vague€just€in€case€we€cannot€know€whether€or€not€the€predicateÏapplies€to€some€object€of€the€appropriate€kind.€€A€major€asset€of€this€sort€of€epistemic€account,Ïand€Williamsonððs€primary€motivation€for€defending€it,€is€that€it€opens€the€door€for€a€single€logicÏfor€both€vague€and€non„vague€terms€alike:€namely,€classical€two„valued€logic.Ìà  àConcerning€the€argument€for€the€major€premise€from€the€observationality€of€ordinaryÏpredicates,€it€is€not€difficult€to€anticipate€how€Williamson€might€respond.€€An€observationalÏpredicate€was€defined€above€as€any€predicate€such€that€òòifóó€it€can€be€judged€to€apply€to€someÐ j Ðobject,€it€can€be€so€judged€simply€on€the€basis€of€casual€observation.€€The€observationality€ofÏordinary€predicates€was€then€appealed€to€in€support€of€the€idea€that€the€application€of€aÏpredicate€to€some€object€cannot€be€affected€by€changes€in€that€object€too€slight€to€be€detectedÏthrough€causal€observation,€an€idea€which€in€turn€was€supposed€to€underwrite€the€majorÏpremises€of€sorites€arguments.€€From€the€perspective€of€an€epistemic€theorist,€however,€theÏconclusion€does€not€follow.€€If€vague€predicates€have€sharp€cutoffs€of€which€we€are€essentiallyÏignorant,€it€does€not€follow€from€the€above€definition€of€observational€predicate€that€theÏapplication€of€a€vague€predicate€cannot€be€affected€by€changes€too€slight€to€be€detected.€€TheÏonly€thing€that€follows€is€that€we€cannot€go€from€a€situation€where€we€òòjudgeóó€the€predicate€toÐ )°"( Ðapply,€to€one€where€we€judge€the€predicate€not€to€apply,€with€a€change€in€the€object€too€small€toÏbe€noticed.€€But€no€epistemic€theorist€would€want€to€deny€this.€€Williamson€does€not€claim€thatÐ ~,(&, Ðthere€is€some€òònóó€such€that€a€person€with€òònóó€hairs€can€be€judged€to€be€bald,€while€a€person€with€òònóó+1Ð V Ðhairs€cannot;€indeed€he€would€deny€this.€€The€claim€is€rather€that€there€is€an€òònóó€such€that€a€personÐ ¼ Ðwith€òònóó€hairs€is€bald€while€someone€with€òònóó+1€hairs€is€not,€a€claim€which€is€in€no€way€inconsistentÐ Î x Ðwith€the€account€of€observational€predicates€given€above.Ìà  àThe€observationality€of€vague€terms€would€only€support€the€major€premises€of€soritesÏarguments€on€an€account€such€as€the€following:€a€predicate€is€observational€if€and€only€if€inÏsituations€where€it€determinately€applies€or€fails€to€apply€to€some€object,€we€can€alwaysÏdiscover€which€is€the€case€simply€by€looking.€€Unlike€the€previous€account,€this€conception€ofÏwhat€it€means€to€be€an€observational€predicate€clearly€lends€support€to€the€major€premises€ofÏstandard€sorites€arguments.€€But€this€latter€account€also€begs€the€question€against€the€epistemicÏview,€while€not€offering€any€advantages€over€the€original€account€apart€from€the€fact€that€itÏsupports€the€major€premises€of€standard€sorites€arguments.€€It€therefore€seems€that€ifÏWilliamson€can€make€his€epistemic€account€of€vagueness€plausible,€he€will€have€no€difficultyÏdealing€with€standard€sorites€arguments.œ× ƒ ×Ý ƒ 2mÝÔ€&õ&&&õÔòòÚ  Ú2Ú  ÚóóÝ  Ý×  כР⌠ÐÌÓ  ÓÔ#†XM»X&&õ¸7#ÔIII.€THE€PHENOMENAL€SORITESÔ‡&õ&XXM»ÔÐ Z  ÐÓMÓà  àBut€consider€now€a€variation€on€the€standard€sorites.€€Suppose€we€are€faced€with€theÏseries€of€shapes€shown€in€Figure€1,€the€leftmost€figure€being€square€and€each€other€figure€beingÏapproximately€œone€one›„thousandth€of€an€inch€wider€than€the€figure€to€its€left.ÌÓÓÌÌÌÌÌÓQ=°‚Xr‚,ö ‚‚,þ‚‚,‚ ‚,Ð ŽX°œXQÓSòò0óó€€€€€Sòò1óó€€€€Sòò2óó€€€€Sòò3óó€€€€€Sòò4óó€€€€Sòò5óó€€€€€Sòò6óó€€€€€Sòò7óó€€€€Sòò8óó€€€€€Sòò9óó€€€€Sòò10óó€€€€Sòò11óó€€€Sòò12óó€€€€Sòò13óó€€€Sòò14óó€€€€Sòò15€€€€€€óóSòò16€€€€óó€Sòò17€€€€€€óóSòò18€€€€€óó€Sòò19€€€€€óóS€òò20óóÐ Ð+z%+ ÐÓU °œX°‚Xr‚,ö ‚‚,þ‚‚,‚ ‚,Ð ŽXUOUÓÓ  ÓÌFigure€1.Ð Œ-6'- Ðœ‡ñ¢'ñÌñ¢'ñ›œñ¢'ñÌñ¢'ñ›Ó>OÓÓQÓWe€may€now€give€our€sorites€argument€a€distinctly€phenomenal€turn€œ(A2):›Ìà  à1ð-ð.à ` àSòò0óó€looks€square.Ð ¼ ÐÓÓà  à2ð-ð.à ` àFor€any€òònóó,€if€Sòòòònóóóó€looks€square€and€Sòòòònóó+1óó€looks€the€same€with€respect€to€shape€as€Ð Î x Ðà  àà ` àSòòòònóóóó,€then€Sòòòònóó+1óó€must€also€look€square.Ð ¬ V ÐÌÓRÓà  à3ð-ð.à ` àTherefore,€Sòò20óó€looks€square.Ð h  ÐIf€we€assume€the€observer€is€viewing€the€shapes€under€normal€conditions€(in€appropriateÏlighting,€in€the€absence€of€parallax,€etc.),€then€just€as€before€the€minor€premise€is€clearly€true€andÏthe€conclusion€clearly€false.€€But€notice€that€we€cannot€deny€the€major€premise,€as€WilliamsonÏdid€before,€by€insisting€that€there€is€some€shape€Sòòòònóóóó€in€the€series€such€that€Sòòòònóóóó€looks€square€whileÐ X  ÐSòòòònóó+1óó€does€not.€€For€if€this€were€the€case,€we€would€have€to€hold€that€Sòòòònóóóó€òòlooksóó€different€with€respectÐ ¾ Ðto€shape€than€Sòòòònóó+1óó,€which€is€evidently€false.€€Consider€the€following€pairs€of€shapes,€extractedÐ Ðz Ðfrom€the€series€in€Figure€1€for€the€purpose€of€comparing€in€isolation:ÌÓÓÌÌÌÌà  àSòò0óó€€€€Sòò1óóà ` àà ¸ àà  àà h àà À àSòò4óó€€€Sòò5óóà  àà p àà È àà  àà x àSòò8óó€€€€Sòò9Ð Àj ÐóóÌÌÌÌà  àSòò12óó€€€Sòò13óóà ` àà ¸ àà  àà h àà À àSòò16€€€€óóSòò17óóà  àà p àà È àà  àà x àSòò19€€€€€óóSòò20óóÐ "À  ÐÌÓ²VÓÓ  ÓFigure€2.ÌÓ’XÓÌI€think€most€observers€would€agree€that€each€rectangle€òòlooksóó€the€same€with€respect€to€shape,€atÐ J'ô & Ðleast€to€the€naked€eye,€as€its€neighbor€to€the€side.€€(Unanimity€is€not€crucial:€those€who€disagreeÏneed€only€imagine€a€series€where€the€changes€are€more€gradual.)€€Figure€2€illustrates€what€isÏgenerally€the€case,€that€adjacent€members€of€the€series€in€Figure€1€are€indiscriminable€withÐ ~,(&, Ðrespect€to€shape€when€viewed€in€isolation€from€the€others.€€But€then€it€cannot€be€the€case€thatÏthere€is€an€Sòòòònóóóó€such€that€Sòòòònóóóó€looks€square€while€Sòòòònóó+1óó€does€not.€€Accordingly€the€phenomenal€sorites,Ð ¼ Ðunlike€the€standard€argument,€cannot€plausibly€be€called€into€question€by€denying€the€majorÏpremise.Ìà  àOne€of€the€major€strengths€of€Williamsonððs€account€was€that€it€appeared€to€do€away€withÏsorites€arguments€in€one€fell€swoop.€€As€it€turns€out,€though,€the€epistemic€view€only€has€importÏfor€a€certain€class€of€sorites€arguments:€namely,€standard€sorites€arguments€such€as€A1.€€But€asÏwe€have€seen,€there€is€a€second€class€of€sorites€arguments,€represented€by€A2,€which€theÏepistemic€account€itself€does€nothing€to€undermine.€€Hence€in€order€for€Williamson€to€achieveÏhis€broader€aim€of€giving€an€account€on€which€vague€terms€behave€according€to€the€dictates€ofÏclassical€logic,€he€needs€to€develop€some€auxilliary€strategy€for€dealing€with€the€phenomenalÏsorites.€€In€the€remainder€of€the€paper€I€want€to€consider€just€such€a€strategy:€in€particular,ÏWilliamsonððs€charge€that€phenomenal€sorites€arguments€commit€what€he€calls€the€fallacy€ofÏð ðequivocating€over€the€context€of€the€looking.ðð€€I€shall€argue€that€while€the€fallacy€may€beÏgenuine,€it€can€be€avoided€with€little€difficulty.ÌÌÓ  ÓÔ#†XM»X&&õçM#ÔIV.€THE€CONTEXT€FALLACYÔ‡&õ&XXM»ÔÐ "À  ÐÓ·_Óà  àPhenomenal€sorites€arguments€are€based€on€reasoning€of€the€following€sort.€€In€the€seriesÏdepicted€in€Figure€1,€Sòò0óó€clearly€looks€square.€€And€as€Figure€2€illustrates,€comparison€of€Sòò0óó€withÐ ¾%h$ ÐSòò1óó€in€isolation€from€the€rest€of€the€series€reveals€that€they€look€identical€with€respect€to€shape;€soÐ z'$!& ÐSòò1óó€must€look€square.€€But€then€if€we€compare€Sòò1óó€and€Sòò2óó€in€isolation,€it€is€clear€that€they€also€lookÐ 6)à"( Ðthe€same€with€respect€to€shape;€so€Sòò2óó,€like€Sòò0óó€and€Sòò1óó,€must€also€look€square.€€If€we€persist€in€thisÐ ò*œ$* Ðline€of€reasoning,€we€will€eventually€reach€the€obviously€false€conclusion€that€Sòò20óó€looks€square.€Ð ®,X&, ÐThe€œargumentñ£'ñ€thus€seems€to€commit€us€to€a€false€claim.€€Notice€that€the€argumentñ£'ñ›€could€also€be€run€in€reverse,€starting€with€the€observation€that€Sòò20óó€does€not€lookÐ V Ðsquare,€and€inferring€from€repeated€application€of€the€principle€that€if€Sòòòònóóóó€does€not€look€square,Ð ¼ Ðthen€Sòòòònóó„1óó€does€not€look€square,€that€Sòò0óó€does€not€looks€square.€€But€Sòò0óó€obviously€òòdoesóó€look€square,Ð Î x Ðand€so€once€again€we€are€forced€into€a€situation€where€the€rules€governing€our€use€of€theÏlanguage€appear€to€conflict.€€For€anyone€with€hopes€for€a€coherent€logic€of€vagueness,€suchÏarguments€cannot€go€unrefuted.€€But€what€exactly€has€gone€wrong?Ìà  àUnlike€in€the€case€of€the€standard€sorites,€denying€the€truth€of€the€major€premise€is€notÏan€option€with€the€phenomenal€œñ¤'ñsoritesñ¤'ññ¤'ñ›argumentñ¤'ñ.›€€Likewise,€it€would€be€absurd€to€deny€the€truth€of€theÏminor€premise€or€the€falsity€of€the€conclusion.€€The€only€remaining€option€would€be€somehowÏto€call€into€question€the€validity€of€the€argument.€€In€the€case€of€the€standard€sorites€we€foundÏthis€option€unacceptable,€but€with€the€phenomenal€sorites€there€is€a€new€way€of€calling€intoÏquestion€the€validity€of€the€argument€which€seems€especially€tempting.€€Several€philosophersÏhave€noted€that€the€way€a€thing€looks€can€depend€on€the€context€in€which€the€object€is€viewed,Ïthat€the€look€of€a€thing€may€change€depending€on€what€other€things€are€viewed€along€with€it.× ƒ ×Ý ƒ 2mÝÔ€&õ&&&õÔòòÚ  Ú3Ú  ÚóóÝ  Ý×  ׀Р⌠ÐTo€see€how€this€might€work,€consider€a€series€of€objects€òòaóó,€òòbóó,€and€òòcóó€such€that€òòaóó€is€notÐ žH Ðdiscriminably€different€from€òòbóó€in€isolation€from€òòcóó,€and€òòbóó€is€not€discriminably€different€from€òòcóó€inÐ Z  Ðisolation€from€òòaóó.€€It€might€seem€appropriate€to€infer€from€this€situation€that€òòaóó€and€òòcóó€are€notÐ "À  Ðdiscriminably€different€in€isolation€from€òòbóó,€but€this€does€not€œñ¥'ñautomaticalñ¥'ññ¥'ñ›necessarñ¥'ññ¦'ñiñ¦'ñly›€follow.€€In€order€forÐ Ò#|" Ðthe€conclusion€to€follow,€we€would€have€to€assume€that€òòbóó€looks€the€same€when€compared€with€òòaóóÐ Ž%8$ Ðas€it€does€when€compared€with€òòcóó.€€But€given€that€òòbóó€may€have€a€different€look€in€differentÐ J'ô & Ðcontexts,€the€assumption€seems€unwarranted.€€To€reason€thus,€in€short,€is€to€commit€the€contextÏâ âfallacy.Ð Â*l$* Ðà  àWilliamson€œ(1994,€174)›€attributes€the€same€basic€error€to€phenomenal€sorites€argumentsÏâ âsuch€as€A2.× ƒ ×Ý ƒ 2mÝÔ€&õ&&&õÔòòÚ  Ú4Ú  ÚóóÝ  Ý×  ×€€We€correctly€infer€from€the€fact€that€Sòò0óó€looks€square,€and€that€Sòò1óó€looks€the€same€asÐ ¼ ÐSòò0óó,€that€Sòò1óó€looks€square.€€We€then€attempt€to€infer€from€the€fact€that€Sòò1óó€looks€square€and€Sòò2óó€looksÐ Î x Ðthe€same€as€Sòò1óó€that€Sòò2óó€looks€square.€€But€this€inference€commits€the€context€fallacy€by€assumingÐ Š 4 Ðthat€Sòò1óó€looks€the€same€when€compared€with€Sòò0óó€as€it€does€when€compared€with€Sòò2óó.€€Given€thenÐ F ð Ðthat€a€thing€can€look€different€in€different€contexts,€it€would€be€illicit€to€infer€that€œÔ‡&õ&&&õÔSòò2óóÔ#†&õ&&&õ¶p#ÔÔ#†XM»X&&õý_#ÔÔ‡&õ&XXM»ÔÔ‡ &õ&&&õÔ›€looksÐ ¬  Ðsquare.€€By€the€same€token€it€would€be€illicit€to€infer€that€Ô#†&õ&& &õBq#ÔÔ‡&õ&&&õÔSòò3Ô#†&õ&J&õÝq#ÔÔ‡ &õ&J&õÔÔ#† XM»XJ &õ#q#ÔÔ‡ &õ&h XM»Ôóó€looks€square,€or€that€Ô#†&õ&& &õ$r#ÔÔ‡&õ&&&õÔSòò4óóÔ#†&õ&&&õÂr#ÔÔ#†XM»X&&õfr#ÔÔ‡&õ&XXM»ÔÔ‡ &õ&&&õÔ€looks€square,Ð ¾h  Ðor€òòa€fortiorióó€that€Ô#†&õ&& &õNs#ÔÔ‡&õ&&&õÔSòò20óóÔ#†&õ&&&õÌs#ÔÔ‡ &õ&&&õÔÔ#† XM»X& &õ/s#ÔÔ‡ &õ&X XM»Ô€looks€square.€€And€so€the€context€sensitivity€of€the€look€of€a€thing,€concludesÐ z$  ÐWilliamson,€seems€to€render€phenomenal€sorites€arguments€invalid.ÌÌÓ  ÓÔ#† XM»X& &õYt#ÔV.€AVOIDING€THE€CONTEXT€FALLACYÔ‡ &õ&X XM»ÔÐ ®X ÐÓ uÓà  àIf€arguments€such€as€A2€do€indeed€commit€the€context€fallacy,€they€admittedly€presentÏno€difficulty€for€Williamsonððs€account€of€vagueness.€€However,€I€think€Williamson€has€falselyÏaccused€many€phenomenal€sorites€arguments€of€being€fallacious.€€On€the€one€hand€I€do€òònotóóÐ ¼ Ðwant€to€deny€that€the€context€fallacy€is€genuine.€€For€all€I€know,€the€way€an€object€looks€mayÏvery€well€depend€on€the€context€in€which€it€is€viewed;€and€if€so,€some€sorites€arguments€at€least,Ïwill€be€guilty€of€committing€the€fallacy.× ƒ ×Ý ƒ 2mÝÔ€&õ&& &õÔòòÚ  Ú5Ú  ÚóóÝ  Ý×  ×€€But€I€do€want€to€argue€that€the€context€fallacy,€even€ifÐ F"ð  Ðgenuine,€does€not€afflict€all€phenomenal€sorites€arguments.€€First€I€shall€attempt€to€say€how€theÏcontext€fallacy€can€be€avoided,€then€I€shall€say€why€I€think€the€charge€that€phenomenal€soritesÏarguments€commit€the€context€fallacy€seems,€on€the€face€of€it,€so€persuasive.Ìà  àThe€context€fallacy€is€based€on€the€plausible€idea€that€a€thing€may€look€different€inÏdifferent€contexts.€€But€does€it€follow€that€there€cannot€be€a€change€in€the€context€without€aÏcorresponding€change€in€the€way€a€thing€looks?€€Suppose€we€have€a€sorites„susceptible€series€ofÐ ®,X&, Ðobjects€òòaóó,€òòbóó,€òòcóó,€òòdóó,€and€òòeóó€such€that€òòaóó€looks€the€same€as€òòcóó€(in€isolation),€and€òòcóó€looks€the€same€as€òòeóó€(inÐ V Ðisolation),€but€òòaóó€does€not€look€the€same€as€òòeóó.€€According€to€the€context€fallacy,€we€cannot€validlyÐ ¼ Ðinfer€from€the€fact€that€òòcóó€looks€the€same€as€òòaóó€in€one€context€and€the€same€as€òòeóó€in€another,€that€òòaóóÐ Î x Ðand€òòeóó€look€the€same€in€any€single€context,€because€òòcóó€may€look€different€in€the€two€contexts.€€ThisÐ Š 4 Ðobjection€aÔ#†&õ&&&õt#ÔÔ‡&õ&&&õÔdmittedlyÔ#†&õ&&&õJ}#ÔÔ#†XM»X&&õnu#ÔÔ‡&õ&XXM»ÔÔ‡ &õ&&&õÔ€seems€quite€persuasive.Ð F ð Ðà  àBut€now€suppose€we€bring€òòbóó€into€the€picture€and€reason€as€follows:€òòaóó€looks€the€same€as€òòbóó,Ð ¬  Ðand€òòbóó€looks€the€same€as€òòcóó;€henceòò€aóó€looks€the€same€asòò€cóó.€€Once€again€the€argument€appears€toÐ ¾h  Ðcommit€the€context€fallacy.€€But€suppose€that€òòaóó€and€òòcóó,€though€actually€different,€are€òònotóóÐ z$  Ðdiscriminably€different.€€In€this€case,€is€it€possible€that€òòbóó€looks€different€when€compared€with€òòaóóÐ 6à  Ðthan€when€compared€with€òòcóó?€€I€submit€that€it€is€not.€€In€the€first€case,€it€was€not€difficult€toÐ òœ Ðimagine€that€òòcóó€might€look€different€when€compared€with€òòaóó€than€when€compared€with€òòeóó,€becauseÐ ®X Ðòòaóó€and€òòeóó€are€discriminably€different;€the€fact€that€òòaóó€looks€different€than€òòeóó€explains€why€òòcóó€looksÐ j Ðdifferent€in€the€two€contexts.€€But€in€the€second€case,€it€is€difficult€to€see€how€òòbóó€could€lookÐ &Ð Ðdifferent€when€compared€with€òòaóó€than€when€compared€with€òòcóó,€for€unlike€òòaóó€and€òòeóó,€òòaóó€and€òòcóó€are€notР⌠Ðdiscriminably€different.€€What,€then,€could€be€the€explanation€for€òòbóóððs€looking€different€in€the€twoÐ žH Ðcontexts?€€Clearly€it€could€not€be€explained€by€some€difference€in€the€way€that€òòaóó€and€òòcóó€look,Ð Z  Ðbecause€by€hypothesis€they€look€the€same.€€I€think€we€must€conclude€that€in€such€cases€there€isÏno€threat€of€committing€the€context€fallacy;€for€while€the€two€contexts€are€indeed€different€(òòaóó€isÐ Ò#|" Ðdifferent€than€òòcóó),€they€are€not€different€in€any€way€that€is€relevant€to€the€way€òòbóó€looks€(i.e.€òòaóó€doesÐ Ž%8$ Ðnot€òòlookóó€different€than€òòcóó).€€Thus€òòbóó€could€not€look€different€in€the€two€contexts.Ð J'ô & Ðà  àIf€this€argument€is€correct,€it€would€seem€to€follow€that€the€context€fallacy€can€always€(orÏmost€always)€be€avoided€by€making€the€sorites€series€upon€which€the€argument€is€based€fine„¼grained€enough€so€that€no€member€of€the€series€is€ever€compared€with€two€members€that€lookÐ ~,(&, Ðdifferent€than€each€other.€€The€claim€that€phenomenal€sorites€arguments€commit€the€contextÏfallacy€seems€persuasive,€at€least€initially,€because€we€tend€to€pick€examples€based€on€soritesÏseries€that€are€too€coarse„grained€for€the€job;€that€is,€we€tend€to€think€of€examples€where€some€òòbóóÐ Î x Ðis€compared€with€some€òòaóó€and€òòcóó€such€that€òòaóó€and€òòc€óóare€discriminably€different.€€But€once€we€ceaseÐ Š 4 Ðto€think€in€terms€of€this€sort€of€caseð"ðonce€we€make€the€sorites€series€fine„grained€enough€soÏthat€òòaóó€and€òòcóó€are€also€indiscriminably€differentð"ð€the€context€fallacy€ceases€to€be€a€factor.Ð ¬  Ðà  àI€conclude€that€Williamson€has€provided€no€reason€to€think€phenomenal€soritesÏarguments€are€unsound.€€He€may€very€well€have€identified€a€genuine€fallacy€that€besets€someÏsorites€arguments,€but€even€so€it€appears€that€most€if€not€all€of€those€arguments€can€be€rescuedÏby€making€the€sorites€series€upon€which€they€are€based€more€fine„grained.€€Even€if€WilliamsonÏcan€successfully€defend€his€epistemic€account€of€vagueness,€then,€his€account€of€what€goesÏwrong€with€sorites€arguments€remains€incomplete.€€For€while€the€epistemic€view€may€show€usÏwhat€is€wrong€with€standard€sorites€arguments€such€as€A1,€it€doesnððt€even€begin€to€shed€lightÏon€phenomenal€sorites€arguments€like€A2.€€As€far€as€Williamsonððs€objection€is€concerned,€then,Ïthe€argument€for€nihilism€regarding€predicates€of€appearance€stands€vindicated.Ìà  àIn€closing€it€is€important€to€note€that€although€Williamsonððs€critique€of€local€nihilismÏgoes€far€beyond€just€the€context€fallacy,€his€entire€critique€is€œñ§'ñunderminñ§'ññ§'ñ›subverñ§'ññ¨'ñtñ¨'ñed›€by€my€argument.€ÏHaving€claimed€that€simple€arguments€for€local€nihilism€such€as€A2€commit€the€context€fallacy,ÏWilliamson€goes€on€to€consider€and€reject€various€other,€more€subtle€arguments€for€the€view.€€IÏhave€not€dealt€with€these€further€criticisms€because,€from€the€perspective€of€this€paper,€theÏadditional€arguments€are€unnecessary:€if€the€basic€argument€for€local€nihilism€has€not€beenÏrefuted,€there€is€no€need€to€turn€to€the€more€subtle€perturbations.€€Of€course,€the€basicÏphenomenal€sorites€argument€may€turn€out€to€be€fallacious€or€otherwise€unsound€after€all;€butÐ ~,(&, ÐÑ>]ÑÑ7€z %%dÞ%%dÞ7ÑÑ  Ññ¨'ñÑ>]ÑÑ7€z %%dÞ%%dÞ7ÑÑ  Ññ¨'ññ§'ñÑ>]ÑÑ7€z %%dÞ%%dÞ7ÑÑ  ÑÑ>]ÑÑ7€z %%dÞ%%dÞ7ÑÑ  Ññ§'ññ¦'ñÑ>]ÑÑ7€z %%dÞ%%dÞ7ÑÑ  Ññ¦'ñthen€nothing€I€have€said€here€suggests€otherwise.€€My€only€purpose€has€been€to€show€that€theÏargument€is€rather€more€resilient€than€Williamson€and€others€have€portrayed€it€to€be.ÌÌñ•'ñÑ>]ÑÑ7€*u%%dÞ%%dÞ7ÑÑ  Ññ•'ñÓ  Óò òÔ#† XM»X& &õÄ|#ÔNOTESó óÔ‡ &õ&X XM»ÔÐ Š 4 ÐÓ£ÓÓ¼ÞÓ¹Ón nÓÓÓÌÌÌÓ  Óò òÔ#† XM»X& &õÝ#ÔREFERENCESÔ‡ &õ&X XM»Ôó óÐ !*  ÐÓ[‘ÓÌDummett,€M.€1975.€ð ðWangððs€Paradox,ðð€òòSyntheseóó€30:€301„24;€reprinted€in€Dummett€(1978).Ð Ø"ú ÐÌDummett,€M.€1978.€òòTruth€and€Other€Enigmasóó.€Cambridge:€Harvard€University€Press.Ð ”$¶ ÐÌEdgington,€D.€1997.€ð ðVagueness€by€Degrees,ðð€in€Keefe€and€Smith€(1997),€294„316.ÌÌJackson,€F.€1977.€òòPerception.óó€New€York:€Cambridge€University€Press.Ð  (. ÐÌPeacocke,€C.€1981.€ð ðAre€Vague€Predicates€Incoherent?ðð€òòSyntheseóó€46:€121„41.Ð È)ê ÐÌKeefe,€R.€and€P.€Smith.€1997.€òòVagueness:€a€readeróó.€€Cambridge:€MIT€Press.Ð „+¦ ÐÌUnger,€P.€1979.€ð ðThere€Are€No€Ordinary€Things,ðð€òòSyntheseóó€41:€117„54.Ð @-b ЇWilliamson,€T.€1994.€òòVaguenessóó.€€New€York:€Routledge.Ð V ÐÌWright,€C.€1975.€ð ðOn€the€Coherence€of€Vague€Predicates,ðð€òòSyntheseóó€30:€325„65.Ð ¼ ÐÌWright,€C.€1976.€ð ðLanguage€Mastery€and€the€Sorites€Paradox,ðð€in€G.€Evans€and€J.€McDowell€Ìà  à(eds)€òòTruth€and€Meaningóó,€New€York,€Oxford€University€Press;€reprinted€in€Keefe€and€Ð ¬ V Ðà  àSmith€(1997).ÌÌWright,€C€1987.€ð ðFurther€Reflections€on€the€Sorites€Paradox,ðð€òòPhilosophical€Topicsóó€15:€227„90;€Ð F ð Ðà  àreprinted€in€Keefe€and€Smith€(1997).Ô#†&õ&& &õã|#ÔÔ#†XM»X&&õ—‘#Ô