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首页 *新书上架*【弗雷格研究】弗雷格论定义

*新书上架*【弗雷格研究】弗雷格论定义.pdf

*新书上架*【弗雷格研究】弗雷格论定义

九月虺
2009-07-16 0人阅读 举报 0 0 暂无简介

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FregeonDefinitionsThispageintentionallyleftblankFregeonDefinitionsACaseStudyofSemanticContentJohnHortyOXFORDUNIVERSITYPRESSOXPORDUNIVERSITYPRESSOxfordUniversityPress,Inc,publishesworksthatfurtherOxfordUniversity'sobjectiveofexcellenceinresearch,scholarship,andeducationOxfordNewYorkAucklandCapeTownDaresSalaamHongKongKarachiKualaLumpurMadridMelbourneMexicoCityNairobiNewDelhiShanghaiTaipeiTorontoWithofficesinArgentinaAustriaBrazilChileCzechRepublicFranceGreeceGuatemalaHungaryItalyJapanPolandPortugalSingaporeSouthKoreaSwitzerlandThailandTurkeyUkraineVietnamCopyright©byOxfordUniversityPress,IncPublishedbyOxfordUniversityPress,IncMadisonAvenue,NewYork,NewYorkwwwoupcomOxfordisaregisteredtrademarkofOxfordUniversityPressAllrightsreservedNopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeanselectronic,mechanical,photocopying,recording,orotherwise,withoutthepriorpermissionofOxfordUniversityPressLibraryofCongressCataloginginPublicationDataHorty,JohnFFregeondefinitions:acasestudyofsemanticcontentJohnHortypcmISBNFrege,Gottlob,SemanticsITitleBFHI'dcPrintedintheUnitedStatesofAmericaonacidfreepaperInmemoryofmygrandparentsRandallRosenberryandAliceWoodsRosenberryThispageintentionallyleftblankPrefaceEverybookhasahistory,andthisshortbookhasalonghistorymuchofit,infact,waswrittentwentyyearsago,aspartofadissertationonmeaninginmathematicallanguageAftercompletingthisdissertation,Iturnedatoncetoanentirelyseparatelineofresearch,centeredaroundlogicandartificialintelligence,andparticularlynonmonotoniclogicOnethingledtoanother,andasitturnsout,Ididnotthinkaboutlanguageormeaningagainfornearlytwodecades,untilachanceencounterwithsomeofthemorerecentliteratureconvincedmethattheproblemsIhadworriedabouthadnotbeenresolved,orevenaddressedinanydetail,duringtheinterveningperiodItisaninterestingexperienceworkingwithmaterialthatwasoriginallydraftedsolongago,anditisnotanexperiencethatIwouldrecommendtoafriendNevertheless,IdonotproposetousedistancefromthematerialasanysortofanexcuseAlthoughpartsofthebookareold,otherpartsarenewTheolderpartshavebeenthoroughlyrewritten,andIstandbyboththeargumentsandtheconclusionspresentedhereAsthetitlesuggests,thisbookisverymuchacasestudy,entirelyfocusedonthetreatmentofdefinedexpressionsinFrege'sownsemantictheory,althoughIhopethediscussionwillhavesomebearingonthosecontemporarytheorieswiththeirrootsinFrege'sworkAtvariouspoints,Fregeconsidersanumberofmorecontentiousstylesofdefinition,suchascontextualorimplicitdefinition,butIconcentratehereonlyonthesimplestandmostpedestrianordinarystipulativedefinitionThisformofdefinitioncanbeillustratedbytheintroductionofthenewpredicate'isprime',forexample,intoanarithmeticallanguagethroughthestipulationthatanumberxisprimejustincaseanynumberthatdividesxiseitherequaltoxorequaltoThebookisorganizedaroundtwoproblemsposedforFrege'stheory,andotherslikeit,bylanguagesthatallowfortheintroductionofdefinedexpressionslikethisFrege'ssemantictheoryisbased,firstofall,onanotionofsense,ormeaning,viiviiiPREFACEthatiscloselycorrelatedwiththepsychologicalstatesoflanguageusersbutthiscorrelationthenforcesaconflictbetweentwoofFrege'scentralthesesconcerningdefinitionsOneoftheseisthethesisofeliminability,accordingtowhichasentencecontainingdefinedexpressionsmustshareitssensewiththesentencethatresultswheneachofthesedefinedexpressionsiseliminatedinfavorofitsdefiningphrasesothattheproperintroductionofdefinedexpressionscannotactuallyincreasetheexpressiveresourcesofalanguageThisisastandardview,whichhasbeenadvocatedbyanumberofwritersaswellasFregeThesecondisthethesisoffruitfulness,accordingtowhichtheremustbethepossibility,atleast,thatgooddefinitionsmightallowustoprovethingswewouldnothavebeenabletoprovewithoutthemAlthoughtheexactinterpretationofthisthesisisamatterofdispute,itwasclearlyanimportantpartofFrege'soverallphilosophy,andithasagooddealofintuitiveappealaswellAnyonewhohasengagedinformalwork,orinformalworkofanycomplexity,isfamiliarwiththewayinwhichthejudiciousintroductionofdefinedexpressionsfacilitatesconceptualadvanceAtthispoint,wecanseethegeneralshapeoftheconflictbetweenthesetwothesesfruitfulnessandeliminabilitysimplybyasking:iftheintroductionofdefinedexpressionsdoesnotallowustoexpressanynewsenses,andifsensesreallyaresupposedtocorrelatewithpsychologicalstates,thenhowcanthesedefinedexpressionsprovideanycognitiveleverageatallHowcantheyallowustoprovethingswewouldnotbeabletoprovewithoutthemProvidingacarefuldescriptionofthisconflict,however,andsuggestingaresolution,isacomplicatedmatterthatrequiresadetaileddiscussionofFrege'sviewsthediscussionoccupiesthefirstfourchaptersofthisbookThesecondproblemIconsideriscenteredaroundFrege'sideathatthesenseofalinguisticexpressionexhibitsadeterminatestructure,andonethatisisomorphictothesyntacticstructureoftheexpressionitselfaviewalongthesegenerallinesissharedbyseveralcontemporaryadvocatesofthe"structuredmeanings"approachinsemantictheoryAgain,however,thisideaclasheswithFrege'seliminabilitythesis,accordingtowhichtheeliminationofdefinedexpressionscannotaffectsenseEliminabilitytellsus,forexample,thatthesentence'isprime'mustexpressthesamesenseasthesentence'Anynumberthatdividesiseitherequaltoorequalto',whichiswhatresultswhenthedefinedpredicated'isprime'iseliminatedinfavorofitsdefiningphraseButsincethesetwosentencesdonotthemselvessharethesamestructureoneisasimplepredication,theotheramorecomplexquantificationalconstructionhowcouldtheypossiblybeisomorphictothesamesensePREFACEixThenextfourchaptersofthebookaredevotedtoadetailedexaminationoftheissuessurroundingthisproblem,bothsyntacticandsemanticAbrieffinalchapterthencomparestheapproachestakeninthetwopartsofthebookandsuggestssomewaysinwhichtheworkpresentedheremightbedevelopedIamdeeplygratefultoNuelBelnap,whodirectedthedissertationthatledtothisbook,forhisinsightandcriticalattention,forthecountlesshourshespentwithmeatthetime,andforhisfriendshipeversinceIwouldalsoliketothanktheothermembersofmyoriginalcommitteeRobertBrandom,JohnHaugeland,DanaScott,andRichmondThomasonfortheirhelpandgenerosityIntheinterveningyears,severalpeoplehavediscussedtheseideaswithmeandencouragedmetoreturntotheprojectIthankthemall,butIoweaspecialdebttoPaulPietroski,notonlyforencouragement,butfordiscussingthematerialwithmeindetailandforreadingtheentiremanuscript,possiblymorethanonceTwoanonymousreadersforOxfordUniversityPressprovidedvaluablecomments,corrections,andadviceMyworkwassupportedbyaFellowshipforUniversityTeachersfromtheNationalEndowmentforHumanitiesThispageintentionallyleftblankContentsPrefaceviiTheintroductionofsensesFrege'sargumentExploringtheargumentPrepositionalattitudesInformationvalueSenseidentityModelsofthespeakerAyerHahnmonstersLimitedintellectsThestrictinterpretationArgumentsforthestrictinterpretationProblemswiththestrictinterpretationDefinitionsAnalyticityConceptformationFruitfulnessandeliminabilityExplicativedefinitionsStipulativedefinitionsSenseandmeaningTheconflictResolvingtheconflictIndexicalsLanguagelearningxixiiCONTENTSAsimplesemanticmodelSensesasproceduresSyntaxSemanticsReferentsSensesRemovalrulesIncompleteexpressionsTheconflictResolvingtheconflictDefinedexpressionsSyntacticandsemanticoptionsSyntacticoptionsSemanticoptionsSensesofincompleteexpressionsAdereproposalComplexincompletesensesDevelopingtheproposalExamplesandequivalenciesEvaluatingtheproposalAfterwordDevelopingtheproceduralmodelTwoapproachestodefinedexpressionsFregeonDefinitionsThispageintentionallyleftblankChapterTheintroductionofsensesGottlobFregewasthefirstpractitionerofformalsemanticsthefirsttheoristconcerned,forwhateverreason,withthesystematicassignmentofsemanticvalues,orcontents,tolinguisticexpressionsInhisearlymonograph,theBegriffsschrift,Fregereliedonanundifferentiatednotionofsemanticvalue,whichhedescribedsimplyas"conceptualcontent"(,pp,)muchofhisimmediatelysubsequentwork,particularlytheGrundlagenderArithmetik,wasdevotedtoananalysisofconceptualcontentforexpressionsbelongingtothelanguageofmathematicsSometimearound,however,FregediscoveredanargumentwhichconvincedhimthatthissimplenotionofsemanticvaluewouldnotdoThepointoftheargument,firstpresentedinhisseminal(b),wasthatsemanticvaluemustbedividedintotwocomponents,whichhethenwentontodistinguishas"referents"and"senses"Inthischapter,IreviewthisfamiliarargumentofFrege's,ashepresentsitin(b)andelsewhere,andbegintoexploresomeofitsunderlyingcomplicationsFrege'sargumentInordertounderstandtheargument,itisbesttoplaceourselvesinFrege'sshoes:weshouldimaginethinkingofsemanticcontent,atfirst,asasingle,undifferentiatednotion,andthenreasoningwiththeprinciplesthatconvincedhimitmustbeotherwisealuse'sense'and'referent'torenderFrege's'Sinn'andlBedeutungAlthoughthistranslationparticularlythechoiceof'referent'for'Bedeutung*isproblematicinvariousways,italsoallowsforcertainsimplificationsandtheproblemsshouldnotaffectourdiscussionhere,whichisentirelyfocusedonSinnenCHAPTERTHEINTRODUCTIONOFSENSESOnthemostnaturalreconstructionoftheargument,therearetwosuchprinciplesThefirstissimplytheprincipleofcompositionalitytheidea,alsoduetoFrege,thatthecontentofacompoundexpressionisentirelydeterminedbyitssyntacticformtogetherwiththecontentsofitspartsAlthoughhehadnotyetformulatedthisideaasclearlyashewouldinlateryears,orexamineditsmotivationasthoroughly,itseemsthathemeanttoabidebyitevenasearlyastheBegriffsschriftTheprincipleofcompositionalityservestoestablishacorrelationonlybetweencontentsandcontents:betweenthecontentofacompoundexpression,andthecontentsofitspartsBytheearlys,however,Fregehadapparentlydecidedthatanexpression'soverallsemanticcontentoratleastoneofitscomponentsshouldbecorrelatedalsowiththepsychologicalstatesoflanguageusersThereare,infact,anumberofwaystoachievethiskindofcorrelation,butFregeselectedamethodthatreliescruciallyonaperceiveddistinctioninwhatwemightcalltheinformationvalueofdifferentkindsofstatementsSome,hethought,couldproperlybeclassifiedasinformative,possessingrealcognitivevalueothersmustbeclassifiedasuninformative,orselfevidentExploitingthisdistinction,Fregewasthenabletoinduceacorrelationbetweensemanticcontentsandpsychologicalstatessimplybyembracing,asasecondprinciple,theideathatthesemanticcontentofasentenceshoulddetermineitsinformationvalue:iftwosentenceshavethesamesemanticcontent,theyareeitherbothinformative,possessingsomecognitivevalue,orbothuninformative,entirelyselfevidentWewillreturnshortlytothenotionofinformationvalueunderlyingFrege'sargumentbutletusseefirsthowthesetwoprinciplescompositionality,togetherwiththeprinciplethatcontentdeterminesinformationvaluecanbeusedtogeneratetheconclusionthatanexpression'soverallsemanticcontentmustbedividedintodistinctcomponentsWhattheprinciplesprovide,actually,arethematerialsfordevisingaverygeneralcriterionfordeterminingwhethertwoexpressionscanbeclassifiedasidenticalintheiroverallcontentLet'<()'representanarbitrarysententialcontext,ormoregenerally,amodeofsententialcompositionAndsupposethat'Ei'and'EVareexpressionsbelongingtoagrammaticalcategoryforwhich'<I>(Ei)'and'$(^)'aresentencesformed,asthenotationindicates,fromtheplacementofiEand'£'inthecontext'<£()',ormoregenerally,fromtheapplicationofthismodeofcompositiontothetwoexpressionsIf'Ei'Wewillreturnlater,particularlyinChaptersand,toconsiderFrege'sviewsoncompositionalityinmoredetailEXPLORINGTHEARGUMENTand'£"'areidenticalincontent,thencompositionalitytellsusthatthetwosentences'$(£")'and'$(£^)'mustlikewisesharethesamecontent,sincetheyarecomposedinthesamewayfromcontentidenticalpartsbutinthatcase,sincecontentdeterminesinformationvalue,itfollowsthatthesetwosentencesmusthavethesameinformationvalueaswellThislineofreasoningleadstowhatmightbecalledFrege'sgeneralcriterionforcontentidentity:twoexpressionscanbeclassifiedasidenticalinsemanticcontentonlyiftheirrespectiveplacementinanysententialcontextresultsinsentencesthathavethesameinformationvalueeitherbothinformative,orbothuninformativeThecriterionisuseful,ofcourse,primarilyforestablishingdifferencesincontentInordertoshowthattwoexpressionscannotcoincideintheiroverallsemanticcontent,thattheymustdifferinatleastonecomponent,itisnecessaryonlytofindsomecontextinwhichtheirrespectiveplacementyieldssentencesdistinctininformationvalueTheparticularargumentFregepresentsin(b)canbeseenasresultingfromanapplicationofthisgeneralcriteriontoaspecialkindofstatementatrueidentityoftheform'a='Sincetheidentityistrue,eventhoughitinvolvesdistinctterms,hereasonsthatthesetermsmusthavesomecomponentoftheircontentincommon:'a'and''mustpossess,ashesays,thesamereferentsButFregealsoclaimsthatthisstatementofidentityisinformative,thatitholdssomecognitivevalue,unlikethestatement'a=a',whichheviewsasselfevidentSincethetwostatements'o='and'a=a'dodifferininformationvalue,thereisthereforesomesententialcontextthecontext'a='inwhichtherespectiveplacementof'a'and''yieldsapairofsentenceswhoseinformationvalueisdistinctandsothesetwotermscannotbeentirelyidenticalinsemanticcontentTheremustbesomecomponentofcontent,atleast,inwhichthesetwotermsdifferFregecallsthesedistinctcomponentstheirsensesExploringtheargumentAlthoughthisargumentfrom(b)isfamiliar,itwillbehelpfulbeforemovingontolookabitmorecloselyattwooftheissuesitpresentsThefirstconcernstherelationoftheargumentasFregepresentsittoourmoderndiscussionofsimilartopicsthesecondconcernsanimportantassumptionunderlyingtheargumentitselfCHAPTERTHEINTRODUCTIONOFSENSESPrepositionalattitudesAswehaveseen,theneedforsenses,asanadditionalcomponentofcontentalongsidereferents,aroseultimatelyoutofFrege'sideathatsomecomponentofsemanticcontentshouldcorrelatewiththepsychologicalstatesoflanguageusersThisideahaselicitedagooddealofsympathyamongmodernsemantictheoristsHowever,incomparingFrege'sargumentwiththismodernwork,weshouldnotethattheparticularmethodFregeusedtoinduceacorrelationbetweensemanticsandpsychologybystipulatingthatsemanticcontentdeterminesinformationvalueisdifferentfromthatgenerallyemployedtodayInmoderndiscussions,thereislittledirectrelianceonFrege'snotionofinformationvalueInstead,thelinkbetweensemanticcontentsandpsychologicalstatesisusuallyderived,almostasasideeffect,fromthemoregeneralprinciplethatthesemanticcontentofasentenceshoulddetermineitstruthvalue:iftwosentencessharethesamesemanticcontent,theyareeitherbothtrueorbothfalseUsingthismoregeneralprinciple,alongwiththeoriginalprincipleofcompositionality,itiseasyenoughtoarriveatamodernversionofFrege'scriterionforcontentidentity:twoexpressionscanbeclassifiedasidenticalincontentonlyiftheirrespectiveplacementinanysententialcontextresultsinsentenceswiththesametruthvalueThelinkbetweensemanticcontentandpsychologicalstatescanthenbederivedincidentally,fromtheapplicationofthisnewcriteriontoaparticularrangeofsentences,thosedescribingtheprepositionalattitudesoflanguageusersIftheexpressions'Ei'and'£"'areidenticalincontent,itfollowsfromthismoderncriterionthatanypairofsentencesthatdiffersonlybycontainingoneoftheseexpressionsinplaceoftheothershouldcoincideintruthvalueWeshouldthereforebeabletoconcludethatasentenceoftheform'Susanbelievesthat>(Ei)',forinstance,mustshareitstruthvaluewith'Susanbelievesthat$(£)',that'KarlhopesthatH(Ei)'mustshareitstruthvaluewith'Karlhopesthat£(£)',andsoonIfweareabletofindanycounterexampletothispatternifitturnsout,say,that'Janetisafraidthatl(Ei)'istrue,while'Janetisafraidthat^(£)'isfalsethenthismethodofargumentallowsustoconcludethat'Ei'and'£'mustdifferinsomecomponentoftheiroverallsemanticcontentOurmoderninterestismoresharplyfocusedontheproblemofspecifyingtruthconditionsforsentenceslikethesedescribingourbeliefs,hopes,andThisprincipleisdescribedbyCresswell(,p)as"themostcertainthing"heknowsaboutmeaningitisofcoursenecessarytoqualifytheprinciplebyinsistingthatthetwosentencesshouldbeevaluatedinthesamecontext,asCresswellgoesontodoEXPLORINGTHEARGUMENTfearsthanonFrege'soriginalproblem,whichmayevenfeelabitantiquated,oftryingtoaccountfordifferencesininformationvalueItmightseem,therefore,thatthenotionofsensedevelopedinFrege'swritingswouldhavelittlecontemporaryrelevanceWhyshouldwebotherwithaconceptionofsemanticcontentexplicitlykeyedtoinformationvalue,ifwhatwereallywantisanotionthathelpsuscomputethetruthvalueofsentencesdescribingpsychologicalstatesTheanswer,ofcourse,isthatthesetwoconceptionsaresupposedtocoincideAlthoughhecameatitfromadiffe

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