ÿWPCâ Æé&d‘å#„£GÝLëâ®~°Â˜eÙ­–ègòZAÙ«ìŒ>\6ü™íõÎ*>ûÄ–Rºyv*ÛÈ‚å_ð7:o‚ 8´DÛ£Ûú Ä0I9ºxv“u{®Ï«òA§dà{.½P_ ¢=#X'1¨S…Ë@jJ¬uŽ}äç7iý¡H ó+”‘3t»‹SœIÿ ® ³®±8—¿ù>ZŸÆl¢O|D3ŒEy—-ÍÓd¨ÿ,ŽÚZdM"\“ê˜3”fJé M>Ñ0ÅKø«ÍDT…RM*_Ñú Zñ ž“z¾1+£X +ó9Ę«9Ô'J‘òÀ½yˆí—Øiþv®X «°ì…UU¼ˆˆŽé†põUs4¿¯ªå.´¡Ê†Mî°UT3¥=ƒÿªS"åݱª&‡{A@¡ àŠÏô Œ ƒ9.)c©‰Ìú¯[ú$䕎ÄÞ¦u§ ¾ýoïÏQRŸ4,ñí¥1¹Ó '4±–E>à¸>Ÿ$RëñEÞ´‘à«ÙNdÑE±ªá>èzÓǨ‰ë~‘¥0õ— ш݇`,©O2]b)Ã|~¹\˜fw׬Ï$‘§i*ôBýŽV¡Ì(Ei<<àãÓ,€then€M*€is€an€òòextensionóó€of€M€just€in€case€D€is€a€subset€of€D*Ð $X" Ðand€f€is€a€subset€of€f*.€Since€there€are€no€winged€horses€in€any€€customary€model€M€forÏEnglish,€the€intersection€of€f(`winged')€and€f(`horse')€will€be€empty€in€all€the€customaryÏmodels€and€the€denotation€of€`the€winged€horse'€will€accordingly€be€undefined€in€all€theÏcustomary€models.€ÌÌHowever,€it€is€easy€to€imagine€a€model€M*€that€is€an€extension€of€M€in€which:Ïf*(`winged')€=€f(`winged')€and€f*(`horse')€=€(f(`horse')€+€1€white€seagull).€For€such€an€M*,Ïf*(`the€winged€horse')€=€that€seagull,€and€`the€winged€horse€is€white'€is€true€in€the€model.Ð h+¸&* ÐThis€model€is€ipso€facto€relevant€to€the€supervaluation€of€`the€winged€horse€is€white'.€SoÏtoo,€of€course,€is€a€model€in€which€f(`horse')€is€extended€to€include€a€black€crow€ratherÏthan€a€white€seagull€and€`the€winged€horse€is€white'€is€false.€€ÌÌSo€there€are€some€extensions€of€the€customary€model€in€which€the€value€of€`the€wingedÏhorse€is€white'€is€defined€and€the€sentence€is€true€and€there€are€some€extensions€in€whichÏits€value€is€defined€and€it€is€false.€It€follows€that€this€sentence€is€neither€supertrue€norÏsuperfalse€in€the€customary€model.€But€`the€winged€horse€is€white€or€the€winged€horse€isÏnot€white'€òòwillóó€be€supertrue€in€the€customary€model€since€it€is€true€in€every€extensionÐ  ` Ðwhere€the€value€of€`the€winged€horse€is€white'€is€defined.òò11óó€Ð ü L  ÐÌThe€reader€will,€no€doubt,€have€anticipated€our€objection:€If€all€that's€required€ofÏf*(`horse')€is€that€it€include€f(`horse')€as€a€subset,€then€extensions€won't,€in€general,€beÏmeaning€preserving.€Patently,€they€won't€be€if€f*(`horse')€includes€elements€to€which€it€isÏòòconceptually€necessaryóó€that€`horse'€does€not€apply.€Consider€an€extension€in€which€`theÐ ˜è  Ðwinged€horse€is€white'€is€true€because€f*(`horse')€contains€a€white€seagull.€There€wouldÏseem€to€be€only€two€possibilities:€either€it's€a€model€in€which€some€seagulls€are€horses,€orÏit's€a€model€in€which€€`horse'€doesn't€mean€òòhorseóó.€Since€we're€inclined€to€think€that€it'sÐ \¬ Ðsome€sort€of€necessary€truth€that€seagulls€aren't€horses;€we€think€that€the€evaluation€of€`theÏwinged€horse€is€white'€as€true€in€this€model€must€involve€an€equivocation€on€`horse'.€(If,Ïhowever,€our€modal€intuitions€strike€you€as€wrong,€the€point€can€be€adjusted€to€whateverÏones€suit€your€fancy.€Eg.€let€the€sentence€to€be€evaluated€be€`the€prime€horse€is€equal€to€2'Ïand€let€f*(`horse')=€f(`horse')€+€2.)ÌÌIf€`horse'€doesn't€mean€òòhorseóó€in€these€sorts€of€models,€then€`the€winged€horse'€doesn'tÐ Ð  Ðmean€what€it€customarily€means;€that€is,€òòit€doesn't€mean€what€it€means€in€the€models€thatÐ ¼  Ðrepresent€English.€óóIn€that€case,€it's€hard€to€see€how€a€notion€of€supertruth€that's€definedÐ ¨ø Ðrelative€to€such€models€could€be€germane€to€whether€English€sentences€of€the€form€`TheÏwinged€horse€is€F€or€the€winged€horse€is€not€F'€are€trueòò.€óóThis€is,€of€course,€the€sameÐ €Ð Ðdilemma€that€we€kept€encountering€in€the€body€of€the€text:€Where€truth€value€gaps€areÏnecessary,€the€choice€supervaluation€offers€is€to€ignore€salient€structure€or€to€equivocate.ÏNeither€alternative€strikes€us€as€awfully€attractive.ÌòòÌÓ  Óò òóóÌÓ  Óó óÐ  $X" ÐÌÓ  ÓòòNotesÐ œì ÐÓ  ÓóóÌ1.€For€simplicity,€we€assume€that€sentences€are€the€bearers€of€semantic€values,€meaningsÏand€the€like.€It's€notorious€that€there€are€more€plausible€candidates,€but€nothing€in€ourÏargument€will€turn€on€this.ÌÌ2.€It€is,€of€course,€implausible€that€òòallóó€sentences€with€vague€predicates€lack€truth€value.Ð $ t Ð`Bald'€is€paradigmatically€vague,€but€`Yul€Brenner€was€bald'€is€definitely€true.€Generally,Ïwhen€we€speak€of€vague€sentences,€we€have€in€mind€sentences€that€have€truth„value€gapsÏin€consequence€of€their€vagueness.€For€convenience,€we'll€call€such€sentences€`gapvague'.ÌÌ3.€"Thus€the€classical€valuations€do€not€admit€truth„value€gaps;€bivalance€holds€for€them.ÏThey€proceed€on€the€assumption€that€there€is€no€€possibility€of€a€failure€of€presupposition"Ï[van€Fraassen,€1969,€pp.70„71].ÌÌ4.€"[T]he€supervaluation€technique...was€motivated€in€large€part€to€reflect€the€intuitionÏthat€there€is€€difference€among€such€[i.e.,€a&a,€€av„a,€a&a]€cases:€if€a€lacks€a€truth„€value,Ïso€should€a&a,€but€a&„a€should€nevertheless€be€counted€as€definitely€false€and€av„a€asÏdefinitely€true"€[Kamp€and€Partee,€ms].ÌÌ5.€Tappenden€(1993)€suggests€that€it's€ok€if€a€penumbral€sentence€isn't€true€in€a€model,€justÏas€long€as€it€also€isn't€òòfalseóó€in€that€model.€Since€this€weak€reading€of€P€is€strong€enoughÐ øH Ðfor€our€polemical€purposes,€we€don't€propose€to€argue€the€issue.ÌÌ6.€It€has€been€suggested€to€us€that€the€conceptual€truths€that€we€want€precisification€toÏhonor€are€somehow€"metalinguistic"€or€"higher€level"€in€a€way€that€the€one's€about€`red'Ïand€`pink'€and€such€are€not.€It's€unclear€to€us€why€it€would€matter€if€this€were€so;€and,Ïanyhow,€as€far€as€we€can€see€it€isn't.€The€crucial€consideration€is€the,€as€it€were,€objectÏlevel€fact€that€òòyou€can't€make€a€man€more€(/less)€bald€without€altering€his€hair„to„head„Ð l¼ ÐññÐ l¼ Ðññratio.óó€So€if€there€is€òòanyóó€valuation€on€which€the€Al€sentence€is€true€(/false/indeterminate)Ð X ¨ Ðand€Al's€head„to„hair€ratio€is€m/n,€then€the€Al€sentence€is€true€(/false/indeterminate)€inÏòòeveryóó€valuation€in€which€Al's€head„to„hair€ratio€is€m/n.Ð 0"€  ЀÌ7.€To€be€sure,€having€a€truth€value€in€a€model€is€a€òòsufficientóó€condition€for€being€t„(or„f)„in„Ð $X" ÐññÐ $X" Ðññthat„model.€But€that's€not€enough€to€make€being€t„(or„f)„in„the„model€itself€a€semanticÏproperty.€Being€butter€is€sufficient€for€being€yellow;€it€doesn't€follow€that€yellow€is€a€dairyÏproduct.ÌÌ8.€Like€classical€evaluations€of€sentences,€classical€evaluations€of€tables€and€chairsÏpreserve€definite€truth€and€falsity.€As€it€happens,€they€do€so€vacuously.€Ìâ âÐ |*Ì%) Ð9.€Exclude€identity€statements;€and€existence€statements,€if€there€is€a€primitive€predicateÏâ âfor€existence.ÌÌ10.€Though€his€theory€has€altered€slightly€over€the€years,€we€will€restrict€our€discussion€toÏBencinvenga'a€accounts€of€(1980a,b)€and€(1991).€Bryan€Skirms€(1968,€1970)€hasÏindependently€advocated€nonholophrastic€evaulation.€We€won't€discuss€Skyrms,€but€weÏbelieve€our€criticisms€apply€to€his€proposal€too.€ÌÌ11.€This€is,€in€fact,€a€considerable€simplification€of€Bencivenga's€treatment,€but€it€conveysÏthe€underlying€intuition.€It€will€suffice€for€our€purposes€since€his€notion€of€extension€is€òòlessóóÐ ü L  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